Metamaterial-Based Optical and Radio Frequency Sensing 9819929644, 9789819929641

Table of contents :
Preface
About This Book
Contents
About the Authors
1 Ideas of Optical Frequency-RF Signal Detection
1.1 Features of Optical, Infrared, and RF Wave Detection
1.2 Properties of the Terahertz Spectrum
1.3 Generation, Detection and Typical Application of Terahertz Waves
1.3.1 Generation of Terahertz Waves
1.3.2 Detection of Terahertz Wave
1.3.3 Typical Applications of Terahertz Technology
1.3.4 Broad-Spectrum Detection of Metamaterial Micro/Nano Structure Arrays
References
2 Fundamentals of Terahertz Detectors
2.1 Terahertz Wave Detector
2.2 Principle and Properties of Left-Handed Materials
2.2.1 Principle of Left-Handed Materials
2.2.2 Properties of Left-Handed Materials
2.2.3 Realization of Left-Handed Materials
Reference
3 Metamaterial Detection Methods
3.1 Basic Characteristics of Metamaterials
3.2 Microstructure and Electronics Configuration of Metamaterial Devices
3.3 Morphological Characteristics of Resonance Element
3.4 Metamaterial Functional Devices and Their Applications
3.4.1 Terahertz Signal Detection by Energy Absorption
3.4.2 Terahertz Signal Regulation and Sensing by Voltage Drive
3.4.3 Planar Nano-Tip Light Wave Regulation
4 Numerical Simulation of Metamaterials
4.1 Finite-Difference Time-Domain (FDTD)
4.2 Frequency Domain Finite Element Method (FD-FEM)
4.2.1 Boundary Problems in the Numerical Calculation of Electromagnetic Fields
4.2.2 Steps of Frequency Domain Finite Element Method
4.2.3 Simulation Algorithm Performance
4.3 S-Parameter Model in Electromagnetic Field Calculation
4.4 Simulation Properties of Typical SRR Element Microstructure Metamaterials
4.4.1 Terahertz Transmission Properties of Typical Microstructure Pattern Metamaterials
4.4.2 Influence of Opening Size on Resonance Characteristics
4.4.3 Influence of Line Width on Resonance Frequency
4.5 Summary
5 Design and Fabrication of Metamaterial Devices
5.1 Semiconductor Based Metamaterials
5.2 Key Fabrication Process of Metamaterials
5.2.1 Cleaning and Film-Formation
5.2.2 Photoresist Coating
5.2.3 Soft Baking
5.2.4 Alignment and Exposure
5.2.5 Post Exposure Bake (PEB)
5.2.6 Development
5.2.7 Hardening
5.2.8 Etching
5.2.9 Photolithography Inspection
5.2.10 Wafer Cutting
5.2.11 Pressure Welding
5.3 Layout Characteristics of Planar Metamaterial Detectors Based on Micro/Nano Semiconductor Processes
5.4 Typical Process Flow of Schottky Metamaterials
5.5 Evaluation and Analysis on Electronic Properties of Schottky Metamaterials
5.6 Summary
6 Modeling of Infrared Long-Wave Detection for Metamaterials
6.1 Modeling of Metamaterial Detection Architecture
6.1.1 Electromagnetic Properties Simulation of Terahertz Metamaterials
6.1.2 Electronic Characteristics Simulation of Long Wave Infrared Metamaterials
6.2 Photoelectric Response Testing Scheme
6.3 Photoelectric Response Test Electrode
6.4 Summary
7 Metamaterial Signal Sensing Based on Continuous Terahertz Waves
7.1 Preface
7.2 Generation and Measurement of Continuous Wave Terahertz (CW-THz) Lasers
7.3 Design and Fabrication of Terahertz Band Metamaterial Devices
7.3.1 Metamaterial Device Model
7.3.2 Metamaterial Device Fabrication Process
7.4 Transmission Characteristics of Metamaterial Devices in Terahertz Bands
7.4.1 Experimental Principle and Apparatus
7.4.2 Experimental Analysis on Transmission Properties of Metamaterials Based on Multi-Band Continuous Terahertz Waves
7.4.3 Simulation of Transmission S-Parameter of Metamaterials Under Terahertz Frequency Bands
7.5 Summary
References
8 Signal Sensing of Electrically Controlled Metamaterials Based on Terahertz Time-Domain Spectra (THz-TDS)
8.1 Preface
8.2 Structural Design and Fabrication of Electrically Controlled Metamaterial Devices
8.3 Transmission Properties of Dipole Model Metamaterials in Reflective THz-TDS
8.3.1 Reflective Time-Domain Pulsed Terahertz Wave
8.3.2 Terahertz Transmission Properties of Metamaterials
8.4 Transmission Behavior of Metamaterials in Photoconductive THz-TDS Based on Fabry-Pérot Model
8.4.1 Photoconductive Antenna THz-TDS System
8.4.2 Theoretical Analysis on Terahertz Waves Generated by Photoconductive Antennas
8.4.3 Terahertz Transmission Properties of Electrically Controlled Metamaterials
8.5 Summary
References
9 Induction and Detection of Optical Frequency Infrared Signals by Metamaterials
9.1 Preface
9.2 Induction and Detection of Near Infrared Laser by Metamaterials
9.2.1 Near Infrared Semiconductor Laser
9.2.2 Principle Analysis on Near Infrared Semiconductor Laser
9.2.3 Scheme and Architecture
9.2.4 Near Infrared Laser Sensing of Metamaterials
9.3 Induction and Detection of Blackbody Infrared Wave by Metamaterials
9.3.1 Sensing Properties of Metamaterials to Blackbody Radiation
9.4 Summary
References
10 Induction and Detection of RF Millimeter Wave Signals by Metamaterials
10.1 RF Millimeter Wave Characteristics
10.2 Millimeter Wave Sensing of Metamaterials
10.2.1 Scheme and Apparatus
10.2.2 Sensing Properties and Analysis of Metamaterials to Millimeter Waves
10.3 Summary
References
11 Subwavelength Stealth Technology of Metamaterials
11.1 Metamateria-Based Antireflection Technology
11.1.1 Nano-Tip-Structure Based Electromagnetic Antireflection Technology
11.1.2 Inner-Ring-Tip Antireflection Film
11.2 Vertical-Tip Metamaterials
11.2.1 Fabrication of Vertical-Tip Metamaterials
11.2.2 Optical Near-Field Properties of Vertical-Tip Metamaterials
11.2.3 Reflection Characteristics of Vertical-Tip Metamaterials
11.3 Electrically Controlled Infrared Transmittance Metamaterials
11.3.1 Electrically Controlled Infrared Transmittance Metamaterial
11.3.2 Electrically Controlled Transmission Characteristics of Electrically Controlled Infrared Transmittance Metamaterials
11.3.3 Current–Voltage Characteristics of Electrically Controlled Infrared Reflectivity Metamaterials
11.3.4 Controlling Principle of Electronically Controlled Infrared Transmission Metamaterials
11.4 Electrically Controlled Infrared Reflective Liquid Crystal (LC) Metamaterial Devices
11.4.1 Electrically Controlled Infrared Reflective LC Metamaterials
11.4.2 Electrical Control Characteristics of LC Metamaterial Devices
References
12 Optical Frequency-RF Integrated Detection Architecture Based on Metamaterials
12.1 Optical Frequency-RF Detection Architecture
12.2 Detected Microstructure Characteristics
12.3 Summary

Citation preview

Advances in Optics and Optoelectronics

Jun Luo · Dong Wei · Xinyu Zhang

Metamaterial-Based Optical and Radio Frequency Sensing

Advances in Optics and Optoelectronics Series Editor Perry Ping Shum, Southern University of Science and Technology, Shenzhen, China

The Advances in Optics and Optoelectronics series focuses on the exciting new developments in the fast emerging fields of optics and optoelectronics. The volumes cover key theories, basic implementation methods, and practical applications in but not limited to the following subject areas: AI Photonics Laser Science and Technology Quantum Optics and Information Optoelectronic Devices and Applications Fiber-Based Technologies and Applications Near-infrared, Mid-infrared and Far-infrared Technologies and Applications Biophotonics and Medical Optics Optical Materials, Characterization Methods and Techniques Spectroscopy Science and Applications Microscopy and Adaptive Optics Microwave Photonics and Wireless Convergence Optical Communications and Networks Within the scopes of the series are monographs, edited volumes and conference proceedings. We expect that scientists, engineers, and graduate students will find the books in this series useful in their research and development, teaching and studies.

Jun Luo · Dong Wei · Xinyu Zhang

Metamaterial-Based Optical and Radio Frequency Sensing

Jun Luo Huazhong Agricultural University Wuhan, China

Dong Wei Huazhong University of Science and Technology Wuhan, China

Xinyu Zhang Huazhong University of Science and Technology Wuhan, China

ISSN 2731-6009 ISSN 2731-6017 (electronic) Advances in Optics and Optoelectronics ISBN 978-981-99-2964-1 ISBN 978-981-99-2965-8 (eBook) https://doi.org/10.1007/978-981-99-2965-8 Jointly published with National Defense Industry Press The print edition is not for sale in China (Mainland). Customers from China (Mainland) please order the print book from: National Defense Industry Press. Translation from the Chinese Simplified language edition: “Chao Cai Liao Guang Xue She Pin Yuan Li Yu Fang Fa” by Jun Luo et al., © National Defense Industry Press 2021. Published by National Defense Industry Press. All Rights Reserved. © National Defense Industry Press 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Currently, a hot spot of research in the international field of high-performance ultrabroadband spectrum detection is how to explore a way to fuse optical and RF frequency detection technologies together. The key to realizing integrated optical and RF detection is to find a physical structure that is suitable for both types of electromagnetic wave fields, so as to ensure the miniaturization and high image quality of optical frequencies as well as the long-range detection and strong penetration effects of RF bands. For fast-developing metamaterial devices, a metamaterial of artificial pattern structure shows a strong induction effect on efficiently coupling electromagnetic wave fields with both optical and RF electromagnetic spectrum properties to a micro-/nano-characteristic scale-patterned photosensitive structure and sensing this physical property of electromagnetic radiation through a micro-/ nano-metal structure, in terms of Terahertz (THz) resonant induction. As for the electromagnetic resonant induction behavior of the metamaterial, this book elaborates on the metamaterial sensing characteristics of THz signals. By solving the basic problems related to basic theories, basic methods and key processes, the metamaterial is further extended to the inductive detection of electromagnetic signals in the ultra-broadband optical and RF spectrum range. The principles and methods for metamaterial-based optical frequency and RF detection proposed in this book, which are designed from a unique perspective, have important enlightening and demonstration significance for the development of new detectors with regard to ultra-broadband optical RF spectrum. This book gives a comprehensive explanation to the basic principles, design theory, computational simulation and instrumentation method of broad-spectrum metamaterial devices, including the electromagnetic mechanism, calculation and analysis of metamaterial design; dwells on the detection methods for metamaterialenhanced infrared signals, THz signals and RF millimeter-wave signals and other contents such as drive and control electronic configuration. In addition, this book offers a comprehensive introduction to the design of a metamaterial-based integrated optical and RF detection architecture. This book is innovative in advanced imaging detection technology, especially in the development of new detectors for optical and RF bands. The manufacturing v

vi

Preface

technology of the Schottky metamaterial detection devices described in this book is a disruptive engineering technique. The metamaterial detection technology developed in this book has important development prospects and application value for the new principles and processes required by modern weapons and equipment. At present, there are few studies in China on the principles and methods of metamaterial-based optical frequency and RF detection. It should be pointed out that the research on new detectors covering infrared and RF millimeter-wave spectra is of great importance for the development of modern defense science and technology. The book consists of 12 chapters, of which Chaps. 1–3 were written by Xinyu Zhang, a professor at the Huazhong University of Science and Technology, Chaps. 4– 10 were written by Jun Luo, and Chap. 11 was written by Dong Wei. During the process of writing, the authors read a large number of books and references in Chinese and English. They also wrote the book based on their experience in metamaterial production and signal detection. The authors would like to thank the postgraduate students who offered assistance during the writing of this book, including Ji Hongwu, Bie Yehua, Ke Diqun, Li Weijun and Zhu Yaping, for their contribution to everything from theoretical research to experimentation. This book is designed for the technical and engineering personnel engaged in the research and/or development of semiconductor devices, applied optics and infrared RF signal detection. It can also be used a teaching reference book for relevant undergraduate and postgraduate students at colleges, universities and research institutes. With their limited scope of knowledge, the authors might inevitably make errors in the book. It would be much appreciated if you could provide any constructive criticism and/or feedback. Wuhan, China September 2019

Jun Luo Dong Wei Xinyu Zhang

About This Book

This book elaborates on metamaterial devices, their signal sensing behaviors and basic methods for electromagnetic signal detection. Based on engineering practice, a detailed introduction is given to the metamaterial structure, drive and control circuit system, IC layout design and fabrication methods and experimental results. This book is of important enlightening and demonstration significance for the development of new detectors with regard to ultra-broadband optical and radio frequency (RF) spectrum. This book is designed for the technical and engineering personnel engaged in the research and/or development of semiconductor devices, applied optics and infrared RF signal detection. It can also be used as a teaching reference book for relevant undergraduate and postgraduate students at colleges, universities and research institutes.

vii

Contents

1

Ideas of Optical Frequency-RF Signal Detection . . . . . . . . . . . . . . . . . 1.1 Features of Optical, Infrared, and RF Wave Detection . . . . . . . . . 1.2 Properties of the Terahertz Spectrum . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Generation, Detection and Typical Application of Terahertz Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Generation of Terahertz Waves . . . . . . . . . . . . . . . . . . . . . 1.3.2 Detection of Terahertz Wave . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Typical Applications of Terahertz Technology . . . . . . . . 1.3.4 Broad-Spectrum Detection of Metamaterial Micro/Nano Structure Arrays . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 3

8 10

2

Fundamentals of Terahertz Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Terahertz Wave Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Principle and Properties of Left-Handed Materials . . . . . . . . . . . . 2.2.1 Principle of Left-Handed Materials . . . . . . . . . . . . . . . . . . 2.2.2 Properties of Left-Handed Materials . . . . . . . . . . . . . . . . . 2.2.3 Realization of Left-Handed Materials . . . . . . . . . . . . . . . . Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13 13 14 14 15 17 18

3

Metamaterial Detection Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Basic Characteristics of Metamaterials . . . . . . . . . . . . . . . . . . . . . . 3.2 Microstructure and Electronics Configuration of Metamaterial Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Morphological Characteristics of Resonance Element . . . . . . . . . . 3.4 Metamaterial Functional Devices and Their Applications . . . . . . . 3.4.1 Terahertz Signal Detection by Energy Absorption . . . . . 3.4.2 Terahertz Signal Regulation and Sensing by Voltage Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Planar Nano-Tip Light Wave Regulation . . . . . . . . . . . . .

19 19

4 4 5 6

20 20 21 22 22 23

ix

x

4

5

6

Contents

Numerical Simulation of Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Finite-Difference Time-Domain (FDTD) . . . . . . . . . . . . . . . . . . . . 4.2 Frequency Domain Finite Element Method (FD-FEM) . . . . . . . . . 4.2.1 Boundary Problems in the Numerical Calculation of Electromagnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Steps of Frequency Domain Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Simulation Algorithm Performance . . . . . . . . . . . . . . . . . . 4.3 S-Parameter Model in Electromagnetic Field Calculation . . . . . . 4.4 Simulation Properties of Typical SRR Element Microstructure Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Terahertz Transmission Properties of Typical Microstructure Pattern Metamaterials . . . . . . . . . . . . . . . . 4.4.2 Influence of Opening Size on Resonance Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Influence of Line Width on Resonance Frequency . . . . . 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47 48 49

Design and Fabrication of Metamaterial Devices . . . . . . . . . . . . . . . . . 5.1 Semiconductor Based Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Key Fabrication Process of Metamaterials . . . . . . . . . . . . . . . . . . . 5.2.1 Cleaning and Film-Formation . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Photoresist Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Soft Baking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Alignment and Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.5 Post Exposure Bake (PEB) . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.6 Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.7 Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.8 Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.9 Photolithography Inspection . . . . . . . . . . . . . . . . . . . . . . . . 5.2.10 Wafer Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.11 Pressure Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Layout Characteristics of Planar Metamaterial Detectors Based on Micro/Nano Semiconductor Processes . . . . . . . . . . . . . . 5.4 Typical Process Flow of Schottky Metamaterials . . . . . . . . . . . . . . 5.5 Evaluation and Analysis on Electronic Properties of Schottky Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77 77 82 84 85 86 87 88 89 89 90 90 91 91

50 51 52 52 54 54 70 73 75

91 93 97 97

Modeling of Infrared Long-Wave Detection for Metamaterials . . . . 99 6.1 Modeling of Metamaterial Detection Architecture . . . . . . . . . . . . . 99 6.1.1 Electromagnetic Properties Simulation of Terahertz Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.1.2 Electronic Characteristics Simulation of Long Wave Infrared Metamaterials . . . . . . . . . . . . . . . . . . . . . . . 107 6.2 Photoelectric Response Testing Scheme . . . . . . . . . . . . . . . . . . . . . 110

Contents

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6.3 6.4

Photoelectric Response Test Electrode . . . . . . . . . . . . . . . . . . . . . . . 116 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

7

8

Metamaterial Signal Sensing Based on Continuous Terahertz Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Generation and Measurement of Continuous Wave Terahertz (CW-THz) Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Design and Fabrication of Terahertz Band Metamaterial Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Metamaterial Device Model . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Metamaterial Device Fabrication Process . . . . . . . . . . . . . 7.4 Transmission Characteristics of Metamaterial Devices in Terahertz Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Experimental Principle and Apparatus . . . . . . . . . . . . . . . 7.4.2 Experimental Analysis on Transmission Properties of Metamaterials Based on Multi-Band Continuous Terahertz Waves . . . . . . . . . . . . . . . . . . . . . . . 7.4.3 Simulation of Transmission S-Parameter of Metamaterials Under Terahertz Frequency Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signal Sensing of Electrically Controlled Metamaterials Based on Terahertz Time-Domain Spectra (THz-TDS) . . . . . . . . . . . . 8.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Structural Design and Fabrication of Electrically Controlled Metamaterial Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Transmission Properties of Dipole Model Metamaterials in Reflective THz-TDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Reflective Time-Domain Pulsed Terahertz Wave . . . . . . . 8.3.2 Terahertz Transmission Properties of Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Transmission Behavior of Metamaterials in Photoconductive THz-TDS Based on Fabry-Pérot Model . . . . 8.4.1 Photoconductive Antenna THz-TDS System . . . . . . . . . . 8.4.2 Theoretical Analysis on Terahertz Waves Generated by Photoconductive Antennas . . . . . . . . . . . . . 8.4.3 Terahertz Transmission Properties of Electrically Controlled Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

121 121 122 124 125 126 128 128

128

133 134 135 137 137 137 138 140 140 144 144 145 148 162 162

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9

Contents

Induction and Detection of Optical Frequency Infrared Signals by Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Induction and Detection of Near Infrared Laser by Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Near Infrared Semiconductor Laser . . . . . . . . . . . . . . . . . . 9.2.2 Principle Analysis on Near Infrared Semiconductor Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.3 Scheme and Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.4 Near Infrared Laser Sensing of Metamaterials . . . . . . . . . 9.3 Induction and Detection of Blackbody Infrared Wave by Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Sensing Properties of Metamaterials to Blackbody Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Induction and Detection of RF Millimeter Wave Signals by Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 RF Millimeter Wave Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Millimeter Wave Sensing of Metamaterials . . . . . . . . . . . . . . . . . . . 10.2.1 Scheme and Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2 Sensing Properties and Analysis of Metamaterials to Millimeter Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Subwavelength Stealth Technology of Metamaterials . . . . . . . . . . . . . 11.1 Metamateria-Based Antireflection Technology . . . . . . . . . . . . . . . . 11.1.1 Nano-Tip-Structure Based Electromagnetic Antireflection Technology . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Inner-Ring-Tip Antireflection Film . . . . . . . . . . . . . . . . . . 11.2 Vertical-Tip Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1 Fabrication of Vertical-Tip Metamaterials . . . . . . . . . . . . 11.2.2 Optical Near-Field Properties of Vertical-Tip Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.3 Reflection Characteristics of Vertical-Tip Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Electrically Controlled Infrared Transmittance Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.1 Electrically Controlled Infrared Transmittance Metamaterial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.2 Electrically Controlled Transmission Characteristics of Electrically Controlled Infrared Transmittance Metamaterials . . . . . . . . . . . . . . . . . . . . . . .

165 165 166 166 167 169 169 181 185 186 187 189 189 191 191 192 203 203 205 205 206 209 211 211 213 215 216 216

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11.3.3 Current–Voltage Characteristics of Electrically Controlled Infrared Reflectivity Metamaterials . . . . . . . . 11.3.4 Controlling Principle of Electronically Controlled Infrared Transmission Metamaterials . . . . . . . . . . . . . . . . 11.4 Electrically Controlled Infrared Reflective Liquid Crystal (LC) Metamaterial Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.1 Electrically Controlled Infrared Reflective LC Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.2 Electrical Control Characteristics of LC Metamaterial Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Optical Frequency-RF Integrated Detection Architecture Based on Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Optical Frequency-RF Detection Architecture . . . . . . . . . . . . . . . . 12.2 Detected Microstructure Characteristics . . . . . . . . . . . . . . . . . . . . . 12.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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About the Authors

Jun Luo, an associate professor at Huazhong Agricultural University and a post-doctoral of Huazhong University of Science and Technology. His research is in the area of ultra-wide spectrum signal detection, imaging system and image processing. He has published more than 30 academic papers and 20 invention patents.

Dong Wei received Ph.D. degree in control science and engineering from Huazhong University of Science and Technology. His research interests include optical imaging system and detector. He has published more than 10 papers in international journals and academic conferences.

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About the Authors

Xinyu Zhang, a professor at Huazhong University of Technology. His research interests include micro-/nanooptics and photoelectric technology, imaging detection technology, optical and RF detection and optical image processing. He has published more than 50 academic papers in international journals in recent years.

Chapter 1

Ideas of Optical Frequency-RF Signal Detection

1.1 Features of Optical, Infrared, and RF Wave Detection Optical frequency imaging technology is characterized by higher imaging resolution, range resolution and sensitivity, smaller equipment size, lower mass and power consumption, and better structure and system compatibility than RF imaging technology. This is because the wavelength is far shorter than the RF electromagnetic radiation range [1]. However, it is subject to short observation distance, weak target penetration (perspective), and influence of atmospheric window effect, climate, weather, solar radiation and other interference. At present, it is widely used in missile (terminal) guidance, medium/short range imaging observation, battlefield imaging detection, etc. RF imaging technology adopted by synthetic aperture radars (SAR) etc. is characterized by its strong imaging detection, long observation distance, allweather 24 h operation, better target penetration and camouflage recognition when compared to optical frequency detection, as well as its good environmental adaptability. It has been widely used in remote measurement, ocean surveillance, moving target indication, moving/static target interception, identification, camouflage recognition and detection, high orbit imaging satellite and deep space exploration, etc. However, the imaging definition is still far lower than that of optical frequency electromagnetic mediums, the equipment’s overall size, mass and power consumption are higher, and the system structures are complex, so antennas with far higher receiving and transmitting capabilities than the objective lens of optical frequency systems are required. This makes current optical frequency and RF imaging detection technologies hard to integrate. Exploring the methods and technical measures used to integrate the advantages of optical frequency and RF imaging technologies has become a topic of great global importance, particularly regarding further development of high-performance broadspectrum imaging detection methods. So far, the typical practice is to integrate or combine the imaging detection devices or equipment of optical frequency and RF systems respectively, namely to adopt special designs or architectures, and to © National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_1

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adopt special methods in image information fusion. However, the inherent defects of combining the two systems are still fundamentally unavoidable, and therefore their respective advantages are difficult to truly integrate and receive improve results. The difference in physical behavior between optical and RF electromagnetic waves is in their distinct wavelengths. Optical signals have wavelengths measured in the micrometer/submicron range while RF signals are measured in the millimeter/ centimeter or even higher ranges. Because of this, both have the physical capability to convert from spatial electromagnetic field data to image information, and stateof-the-art technology can help realize efficient image detection in optical and RF frequencies. Therefore, a key step to achieve the real optical frequency-RF integrated imaging detection is to find the theoretical system and physical sensitive architecture being available for both optical frequency and RF electromagnetic wave fields at the same time for the sake of miniaturized, handy and high-definition imaging being similar to or even better than the optical frequency system, as well as strong remote detection capability under the RF system. Fortunately, such physical architecture has been proposed in recent years in several rapidly developed typical photoelectric conversion methods based on the terahertz electromagnetic wave field imaging detection technology. Terahertz waves are electromagnetic waves of 1012 Hz. Their special position in the electromagnetic spectrum is included in the transitional area between optical frequencies and RF, namely in the electromagnetic frequency range of 0.1 ~ 10 THz (electromagnetic wave band of 30 ~ 3000 µm), and thus display properties of both the optical frequency and RF spectrums. Terahertz imaging detection is a new highperformance imaging detection technology that has appeared in recent years, which is characterized by deep penetration, long range coverage, high imaging resolution, good imaging contrast and uniformity [2–4]. It is useful in effectively identifying camouflaged, stealthy and deceptive targets that are hard identify through conventional methods; it can be adopted to identify hidden objects, buried objects and underground bunkers made of metal and inorganic non-metallic materials, etc., and it can be used to detect and locate occluded targets. Terahertz detection technology has shown a broad development potential and application prospects in anti-terrorism, counterfeit currency identification, postal system security, metal and plastic mine detection, nondestructive testing of composite materials for aerospace vehicles, space-based imaging detection, guidance and communication, etc. The rapid development of the terahertz imaging detection technology shows that optical frequency and RF imaging detection methods can coexist in one physical architecture, providing a theoretical and methodological basis for the development of optical frequency-RF integrated electromagnetic wave field detection models and technology. At present, a variety of optoelectronic materials and structures have displayed strong responses to terahertz frequencies, such as high-temperature superconducting materials, quantum dot/line structures, nanotube devices and several photonic crystals [5–7]. Diffractive optical elements with various functions, flexible manipulation, small sizes, light weight and relatively low prices have been used for optical systems matched with imaging detectors, reducing the overall sizes and masses of the imaging systems, improving the system performance indexes and expanding the system

1.2 Properties of the Terahertz Spectrum

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functions. At present, in-depth research on terahertz imaging detection modules throughout the world has been done with the intention to further enhance detection efficiency, achieve adaptive multispectral imaging detection, reduce costs, optimize structures, increase the size of photosensitive device arrays and adopt new photoelectric materials and structures, etc. For example, typical high-sensitivity ferroelectric thin films, porous Si or VO2 Bolometer type broad-spectrum detection modules, etc. have been used. Generally, photonic modules can only work in a relatively narrow spectral domain, and the photoelectric sensitivity of spectral thermal devices based on energy conversion is greatly limited due to their own thermal inertia. It should be pointed out that the above progress is based on property of longer optical frequencies in the electromagnetic wave field to extend into the RF domain. This progress is as of yet incomplete in regards to the physical nature of the electromagnetic wave field, and therefore the detection efficiency of such is expected to see further improvements. In summary, there is an extreme lack of detectors with large-scale area arrays, high sensitivity, fast gain and arrayed response in the integration of optical frequency and RF electromagnetic mediums based on the intrinsic physical properties of the electromagnetic field. The goal of optical frequency-RF integrated detection is to obtain arrayed micro-structure detectors (sensitive to broad-spectrum electromagnetic radiation) with extremely high sensitivity and gain coefficient, integrated optical frequency and RF spectrum attributes, small size, light mass, flexible manipulation, fast response to picosecond and even femtosecond pulse signals and easy integration with other functional structures. In recent years, electromagnetic wave field detection technology based on resonance induction is a potential model that can solve the above problems. In terms of terahertz resonant induction detection based on artificial micro/ nano metamaterial patterns, this technology has shown efficient functionality in effectively coupling the electromagnetic wave field with optical frequency and RF electromagnetic spectrum attributes to photosensitive structures with patterned micro/ nano characteristic scales. Considering the potential high induction efficiency, strong wave field regulation capability, signal gain capability and optical frequency-RF integrated induction capability, it has attracted extensive attention since its appearance, showing immense potential.

1.2 Properties of the Terahertz Spectrum Terahertz waves refer to the electromagnetic wave range of 0.1 ~ 10 THz. The wavelength of 1 THz corresponds to 300 µm. The wave number radiation energy is equivalent to 33.3 cm−1 and 4.14 meV, respectively. This wavelength range is between the far-infrared and millimeter wave, namely “submillimeter wave”. It can be seen that the terahertz wave takes a very special and important position in the electromagnetic spectrum. However, compared with a large number of successful applications in visible light, microwave and other frequency bands, many fundamental and application problems in the terahertz band have not been resolved well. Therefore, we call the terahertz band as “terahertz gap” as shown in Fig. 1.1. The problem of the

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1 Ideas of Optical Frequency-RF Signal Detection Electronics Microwave, RF, millimeter wave

Terahertz

Photonics

Infrared light, visible light

X-ray

γ-ray

Unit: Hz

RF communication and radar application

Optical applications

Medical and space applications

Fig. 1.1 Distribution of electromagnetic wave spectrum and terahertz frequency band

terahertz gap has two main causes: (a) A lack of broadband high-power terahertz radiation sources and supporting high-sensitivity and high-speed detectors at this stage; (b) A lack of high-sensitivity and multi-characteristic controllable terahertz optical devices, such as filters with terahertz broadband, multi-frequency and high gain, lenses with adjustable terahertz optical characteristic parameters, modulators with adjustable high terahertz gain, broadband, amplitude and phase, and terahertz-band high gain optical antenna made with new materials. Much research has been conducted on solving the first problem of “terahertz gap” suppression, based on which the CO2 pumped continuous wave terahertz laser (CW-THz) and pulsed terahertz time-domain spectroscopy systems (THz-TDS) were designed and manufactured [8, 9]. The successful development of these devices provides valuable terahertz sources for related research. At present, research on terahertz light sources has become the focus in the field of terahertz study, and constant breakthrough progress in relation to its design and manufacture technology has been made [10]. Since the terahertz wave is between the optical frequency and RF, its common optical frequency and RF characteristics are more obvious than those of electromagnetic waves in other bands. Although researchers have developed some terahertz detectors, research on ultra-wideband detectors that cover the optical frequency and RF is still in its infancy. Therefore, this book will give an exploratory introduction to ultra-wideband large area array detectors with integrated optical frequency and RF, and provide readers with a methodology for reference.

1.3 Generation, Detection and Typical Application of Terahertz Waves 1.3.1 Generation of Terahertz Waves Terahertz waves have a high frequency, and the corresponding spatial resolution is high, and at the same time the terahertz pulse is very short with a high temporal resolution. Such high temporal and spatial resolutions lay a good foundation for the successful application of terahertz technology [9, 10]. At present, the long-term

1.3 Generation, Detection and Typical Application of Terahertz Waves

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efforts of researchers at home and abroad have resulted in the discovery of reliable pulsed terahertz sources, and continuous wave terahertz laser sources have been successfully developed. These terahertz sources are widely used in material structure detection, security inspection imaging and medical applications, etc. The pulsed terahertz (THz) wave is a periodically repeated picosecond ultrafast pulse signal that does not continue over time. At present, the most commonly used THz radiation light source is the picosecond pulse radiation wave generated by a photoconductive dipole antenna on a semiconductor substrate irradiated by a femtosecond laser, or the terahertz pulse radiation generated by a nonlinear crystal excited by an ultrafast laser through nonlinear effects such as optical rectification and optical frequency difference. This pulsed terahertz wave is generally a broadband terahertz wave within a spectrum range of 0.01 ~ 3.0 THz, which is suitable for spectral measurement of different components. A very typical application of this pulsed terahertz wave is that it can be used as an incident light source of the terahertz time-domain spectral system. The continuous terahertz wave (or terahertz laser) is an electromagnetic wave that continues over time and only has a single output frequency. Its output laser spot has the typical characteristics of Gaussian spots. At present, continuous terahertz waves can be generated through different means, for example, continuous terahertz wave radiation can be generated through free electron lasers, CO2 gas lasers, cold plasmas, quantum cascade lasers (QCLs) and backward wave oscillators (BWO), etc. Depending on the equipment, the minimum diameter of the continuous terahertz wave laser at its beam waist is generally 1 ~ 3 mm, and the output effective laser power is generally 10 mW ~ 1 W.

1.3.2 Detection of Terahertz Wave Pulsed terahertz wave detection systems mainly include photoconductive dipole antennas, electro-optic crystals and Schottky semiconductor detectors, and among which electro-optic crystals represented by ZnTe and photoconductive dipole antennas represented by GaAs are the most common laboratory detection devices [11]. The direct results obtained by detecting terahertz pulse signals are mainly time-domain spectra, and the corresponding frequency spectra and other information can be obtained through Fourier analysis. The terahertz detectors of the continuous terahertz wave systems mainly include Bolometer thermal radiation detectors and pyroelectric detectors. The results obtained by this detection method rely on thermal effects, and mainly power or voltage data. Therefore, the detection methods of pulsed terahertz wave and continuous terahertz wave are quite different, which leads to their different application methods and results. In application, it is necessary to fully consider the characteristics of the two different systems for targeted measurement and analysis. The basic principle of pulsed terahertz source detection is to utilizes the terahertz wave of a known frequency range as the incident light source to collect the transmitted

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or reflected time-domain signal of a sample [12]. By analyzing the intensity, phase or related time–frequency characteristics of the time-domain signal, characteristic information such as complex dielectric constant, refractive index, optical length and characteristic absorption peak of the sample can be obtained. The basic principle of continuous wave terahertz source for detection or imaging is to use the terahertz wave of a known frequency or a wavelength as the incident light source, define the 2D spatial distribution of a sample as (X, Y ), and then collect the intensity or power signal Z of the transmitted or reflected terahertz wave of the sample to form a 3D space (X, Y, Z) that is equivalent to the intensity distribution diagram of the transmitted signal and can be converted into a transmission image after proper digital processing. A remarkable feature of terahertz wave imaging technology is that it has a large amount of information, each image source corresponds to a terahertz time-domain spectrum, and through Fourier transform of the time-domain spectrum, the terahertz frequency response spectrum of each point can be obtained.

1.3.3 Typical Applications of Terahertz Technology Terahertz time-domain spectrum detection and continuous terahertz wave detection are the two most widely used and mature terahertz detection technologies. Compared with X-rays, terahertz waves have an exclusive advantage in nondestructive testing of materials thanks to their extremely low photon energy. This is because the electromagnetic radiation of 1 THz is only about 4 meV, which will not cause photoionization damage to the tested materials; The vibration and rotation frequencies of biological macromolecules are usually included in the terahertz frequency band, and terahertz detection technology is often used in material composition and molecular research; Since there are still a lot of gaps in the research of terahertz applications in the agriculture and food processing industries, terahertz technology will be of great significance in grain seed selection, strain selection, etc.; as terahertz waves have very weak water penetrability, they can be used to detect the moisture content in materials to control the corresponding product quality. For example, they usually can be used to determine the freshness of food by measuring the moisture content; terahertz radiation can penetrate tissue, plastic, clothing and foam, making it quite suitable for mail packaging, drug identification and nondestructive metal surface testing; terahertz waves are between the optical frequency and RF, making it of great significance in radar applications and communication, especially in space communication. The prospective optical frequency-RF integrated detection is very achievable through in-depth research on new detection technologies and physical models in relation to the terahertz band between the optical frequency and RF. The radiation energy of continuous terahertz waves is low, with a working wavelength at the submillimeter level. The wavelength can penetrate paper, plastic, thin clothes and skin surfaces, allowing perception through the whole human body with a low electromagnetic wave energy without causing photoionization of biological tissues. Therefore, terahertz wave detection technology can be used for security

1.3 Generation, Detection and Typical Application of Terahertz Waves

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checks in public places such as airports and railway stations. Non-destructive and non-contact terahertz wave imaging is of great value to studying objects such as precious artworks and paleontological fossils. For example, visualizing the interior through the surface of an artwork and identifying the contents of books without touching or damaging fragile papers. At present, the CW-THz detection imaging systems have shown great prospective applications in human safety detection, packaging materials, hidden target recognition and biomedicine, etc. Generally, a continuous terahertz wave imaging detection system is mainly composed of the following parts: femtosecond laser, delay device, terahertz ray emission source, optical imaging system composed of focusing lens, etc., sample to be tested, detector and scanner, etc. The ultra-fast laser pulse from this imaging system is divided into two beams by a beam splitter, where the strong one is used as the pump light to irradiate on the terahertz wave transmitter to generate terahertz rays. The terahertz rays, after being focused and collimated twice through two pairs of off-axis parabolic mirrors, focus on the sample first and then on the detector. The weak one used as the detection light irradiates the detector after a scanning delay, detecting the terahertz radiation field and measuring the instantaneous electric field strength. The measured signal is sent to the computer for image restoration after being processed by the current preamplifier and digital signal processor. The working principle of data acquisition and processing of the continuous terahertz wave imaging detection systems is to first define the relative position of a target on the X–Y axis of the view field, use the terahertz laser to scan the target, collect the voltage or power Z of each point (X, Y ) after the transmission or reflection of the target, and form a (X, Y, Z) data set. The data set can be converted into a gray-scale image or a pseudo color image to reflect the transmission or reflection properties of the target under terahertz wave irradiation. The gray-scale or pseudo color of the image is manually defined. Different color areas represent the transmission or reflection properties of the terahertz wave at the corresponding part of the target. For example, the color depth can be defined to represent the ratio of transmission power to total power. The lighter the color is, the higher the transmission power will become. Imaging systems composed of a continuous terahertz wave laser source and a corresponding focal plane array detector can obtain images of the target’s features through 2D transmission scanning imaging [13, 14]. This type of experiment assumes that the power of the transmission signal is consistent with Poisson’s Equation (1.1), and that during image conversion, the Absorption Coefficient Equation (1.2) is used for normalization, allowing the target position and shape to be clearly obtained. The power distribution of the transmitted signal is defined according to Eq. (1.1). P = P0 e−αχ

(1.1)

Then the absorption coefficient will be: α=−

  P 1 ln χ P0

(1.2)

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1 Ideas of Optical Frequency-RF Signal Detection

where P0 is the reference laser power without any sample; P is the transmitted laser power with samples; and X is the sample thickness. The continuous terahertz wave imaging detection system is popular both at home and abroad, and is mainly used to detect the transmission power of samples [15]. Because the small amount of information obtained and the resolution of the converted image is mainly determined by the frequency of the incident terahertz source, the detected results will consistently be lacking target depth and phase data. Continuous terahertz wave imaging detection technology can be used in industry, agriculture and security monitoring, etc., however it should be noted that the image resolution obtained through terahertz detection is much lower than that of visible light, and the penetration capability is also inferior to that of millimeter waves. Therefore, in order to give full play to the optical frequency-RF integrated detection capability, this book intends to make preparations for achieving frequency-RF integrated detectors relying on the development of terahertz band detection devices [16].

1.3.4 Broad-Spectrum Detection of Metamaterial Micro/ Nano Structure Arrays Generally, a special metal structure with electromagnetic waves detected through induction can generate an oscillating voltage closely related to the incident electromagnetic radiation. The relevant research shows that electromagnetic waves covered in several frequency bands can make certain metal pattern structures with micro/ nano characteristics generate a large number of electrons. These electrons can induce secondary electromagnetic oscillations or plasma in micro/nano pattern structures through collective oscillation, completing the physical process of sensing the incident electromagnetic wave field through special micro/nano metal structures. The short and quick signal response in the nanosecond or even sub-nanosecond time domain, as well as the strength of the induced signal, can be thousands or even millions of times higher than that of the conventional optical frequency or RF signals, namely, the output response signal should be more than three orders of magnitude higher than conventional modes, and can be quantized and regulated through electric or magnetic controls. In other words, a closely arranged special metal pattern structure array with micro/nano characteristic scales is characterized by its high sensitivity induction and high-gain-amplification of the electromagnetic wave field, which is a kind of optical frequency-RF integrated detection mode and structure that efficiently couples and responds to electromagnetic waves through induction. In the metamaterial device architecture, metamaterials with artificial pattern are an artificial composite material or structure with extraordinary physical properties that natural materials do not have. A patterned micro/nano structure specially designed according to the requirements can make the dielectric constant or permeability reach a required value, or even a negative value, to obtain special physical properties. This

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9

is also called a left-handed material or structure, as the dielectric constants or permeabilities of natural electromagnetic materials are both positive. The characteristic scale of its basic structural elements is generally one order of magnitude lower than that of processed electromagnetic radiation wavelengths. At present, a typical metamaterial structure is usually formed by coupling a split-ring resonator with a metal line array. Split-ring micrometer resonators induce ring currents through resonance, and have negative permeability under the excitation of electromagnetic radiation, as they should resist the change or influence of the incident electromagnetic radiation in the electromagnetic state, while their coupled line arrays provide a plasma-shaped dielectric coefficient. When the electromagnetic radiation frequency is lower than the resonance frequency, a negative dielectric coefficient will be created. The relevant research shows that several kinds of artificial metamaterial structures of differing structures and patterns have a strong inductive reception or electromagnetic antishielding effect on electromagnetic radiation. In recent years, the development of wave field regulation and conversion technology based on the induction of broadband electromagnetic waves by artificial metamaterial structures has become a global research hotspot, and new related breakthroughs are expected to occur. In-depth research on the relevant applications of the terahertz band has recently been conducted, such as terahertz filters, terahertz short-range communications, terahertz antennas and terahertz detectors, etc. There is still a lot of work do on terahertz detection and induction research in these fields. Finding a quick and highly sensitive detection method in the terahertz band, and the key device process of this, can provide a methodological basis for new forms of broad-spectrum signal detection. This book describes the optical frequency-RF integrated detection method of metamaterials in the metamaterial architecture according to developments trend at home and abroad. The metamaterial mentioned in this book is composed of a cyclical split resonant ring (SRR) micro structure array and a semiconductor substrate material. The cyclical SRR array has a resonant electromagnetic response in a specific spectral range, which can be utilized to design energy absorbing or sensing devices, see Fig. 1.2. Ideally, a terahertz sensor array can convert continuous terahertz waves into an array electrical signal by suitable means. The accurate measurement of this electrical signal is related to the terahertz power actually absorbed. The existing research shows that self-excited magnetic resonance of electrons is caused when the incident terahertz wave passes vertically through an SRR array of a specific shape. The capability of the metamaterial in absorbing terahertz waves in the resonance process is related to the SRR microstructure and its pattern configuration. The basic modes and characteristics of flexible and sensitive optical frequency-RF electromagnetic wave field integrated induction detection technology can be obtained by solving the basic scientific problems involving basic theories, basic methods and key processes, etc. Examples include the complete characterization of resonance induction and electronic response between an electrically controlled micro/nano artificial metamaterial structure and a broad-spectrum electromagnetic wave field, the influence of the pattern shape, parameter characteristics and electronic configuration of the metamaterial structure on the induction detection efficiency, as well as reducing the

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Fig. 1.2 Schematic diagram of broad-spectrum detection of artificial metamaterial micro/nano structure array based on different patterns and structural parameters

illumination of the electromagnetic wave field and changing its spectrum, polarization and incident direction and based on improving the key factors such as induction and detection efficiency of the micro/nano material as well as their interrelationships.

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References

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12. Holloway CL, Dienstfrey A, Kuester EF, et al. A discussion on the interpretation and characterization of metafilms/metasurfaces: the two-dimensional equivalent of metamaterials. Metamaterials. 2009;3(2):100–12. 13. Lu T, Lee H, Chen T, et al. High-sensitivity nanoparticle detection using optical microcavities. Proc Natl Acad Sci USA. 2011;108(15):5976–9. 14. van Exter M, Grischkowsky D. Characterization of an optoelectronic terahertz beam system. IEEE Trans Microw Theory Tech. 1990;38(11):1684–91. 15. Li M, Cho GC, Lu T, et al. Time-domain dielectric constant measurement of thin film in GHz–THz frequency range near the Brewster angle. Appl Phys Lett. 1999;74(15):2113–5. 16. Yen TJ, Padilla WJ, Fang N, et al. Terahertz magnetic response from artificial materials. Science. 2004;303(5663):1494–6.

Chapter 2

Fundamentals of Terahertz Detectors

2.1 Terahertz Wave Detector Terahertz wave detection is one of the most popular research fields. Detecting terahertz wave requires a highly sensitive detection technology, because the transmission power of the terahertz wave is relatively low and the terahertz wave is liable to be coupled with the thermal background, thus affecting the accurate detection of terahertz frequencies. Chapter 1 describes the main characteristics of typical terahertz detectors, and the following shows the performance comparison of various detectors, see Table 2.1. Table 2.1 compares the performances of commonly used terahertz detectors. Photoconductive antennas and electro-optic crystal detectors are mainly used in pulsed terahertz technology. By eliminating environmental noise, these two detectors have high signal to noise ratios, and can simultaneously be used to obtain the amplitude and phase information of terahertz signals; however, their working range is narrow; thermal radiometers and Golay cells are direct detectors which are based on the mechanism of radiant heat measurement. They can be used for detecting different terahertz radiation conditions; however they have low detection sensitivities and are liable to be affected by the ambient electromagnetic radiation. Detectors based on electronic mixers have a high sensitivity, but their structures are complex and the measurement results can be affected by mixers and local oscillators. These are heterodyne detectors. It can be seen from the above that existing terahertz detectors are subject to narrow response range, low sensitivity, complex structure or environmental influences, etc. The development of new terahertz detectors has become a new scientific research direction in order to sensitively, quickly and reliably detect terahertz frequencies.

© National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_2

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2 Fundamentals of Terahertz Detectors

Table 2.1 Comparison of terahertz wave detectors Detector

Working NEP freq. range (W Hz−1/2 ) (THz)

Photoconductive antenna

0.1 ~ 20

Electro-optic crystal

Coherence

Response Working speed temp.

10−15

Coherent

~ 100 fs

Normal temp.

0.1 ~ 100

10−15

Coherent

~ 10 fs

Normal temp.

Thermal radiometer

0.1 ~ 100

10−15 ∼ 10−12

Noncoherent ~ ms

Liquid nitrogen

Golay cell

0.1 ~ 1000 10−10

Noncoherent ~ 100 ms

Normal temp.

Schottky diode (direct)

< 1.8

10−13 ∼ 10−10

Coherent

~ ps

Normal temp.

Heterodyne Schottky diode

Depends on local oscillator

10−19

Coherent

~ ps

Normal temp.

Superconducting Depends insulator-superconducting on local mixer oscillator

10−21

Coherent

~ ps

Liquid nitrogen

Thermionic bolometer

10−21

Coherent

ps ~ ns

Liquid nitrogen

Depends on local oscillator

2.2 Principle and Properties of Left-Handed Materials 2.2.1 Principle of Left-Handed Materials In physics, dielectric constants and permeabilities are usually used to describe the electromagnetic properties of materials, which are relatively common physical quantities. According to common sense, the dielectric constants and permeabilities of materials in nature are always higher than zero. However, theoretically, materials with these two parameters less than zero (such as plasma) can also exist. In 1968, the scientist V. G. Veselago, proposed that when the dielectric constant and permeability of a certain medium are negative at the same time, the materials will have many electromagnetic properties that conventional materials do not have. He studied the transmission properties of electromagnetic waves in this imaginary medium in detail, and found that, according to the Maxwell equation, the phase transmission direction of the electromagnetic waves in this medium are not the same as that of energy transmission, but rather the opposite. In ordinary materials, Electric Field E, Magnetic Field H and Wave Vector k are subject to the right-handed rule; However, when the dielectric constant and permeability are negative, the direction of the wave vector will be opposite to that of the Poynting vector. At this time, the electric field,

2.2 Principle and Properties of Left-Handed Materials

15

magnetic field and wave vector are subject to the left-handed (LH) rule, so Veselago named this material “left-handed material”. The appearance of left-handed materials expands the connotation of dielectric constant and permeability and changes our understanding of these two physical quantities. In dielectric materials with negative dielectric constants and permeabilities, the electromagnetic waves can also be transmitted, showing a backward wave effect [1]. In addition, such mediums also have many other special electromagnetic properties, such as negative refraction, perfect lens effect and inverse Doppler effect, etc. These special properties of left-handed materials can help in achieving slab focusing and make directional antennas through gathered antenna beams. At present, left-handed materials have been widely used in multiple frequency bands of the electromagnetic spectrum, and also play an extremely important role in military applications and daily life.

2.2.2 Properties of Left-Handed Materials The transmission of electromagnetic waves in left-handed materials is quite different from that of conventional materials, displaying many special properties. The transmission properties of electromagnetic waves in left-handed materials were deeply analyzed during the period Veselago proposed the concept of left-handed materials. Based on the theory, a variety of special electromagnetic properties of lefthanded materials have been summarized, including: inverse Doppler effect, inverse Cherenkov radiation and slab focusing, etc. In 2000, Pendry put forward the “perfect lens” concept. When both the dielectric constant and permeability of a medium are − 1, once an electromagnetic wave passes through the left-handed material, all highorder Fourier components of the light source will be restored at the image points, perfectly realizing the reproduction of the light source. The perfect lens concept has promoted understanding of the imaging resolution limit and further research on left-handed materials. 1. Negative refraction effect According to Snell’s law, the refractive index can be shown by the expression of the Dielectric Constant E and Permeability μ: n2 = Eμ. Refraction will occur at the interface of two kinds of mediums when a plane monochromatic wave beam irradiates it. The refraction is consistent with Snell’s law: n 1 sin θ1 = n 2 sin θ2

(2.1)

√ √ where n 1 = εr 1 μr 1 is the refractive index of Medium 1; n 2 = εr 2 μr 2 is the refractive index of Medium 2; θ 1 and θ 2 are the incident angle and refraction angle, respectively.

16

2 Fundamentals of Terahertz Detectors

For conventional materials (E > 0, μ > 0), the refractive index is positive, namely, √ the refractive index of conventional materials is n = εμ. If Medium 1 is a righthanded material (E > 0, μ > 0) and Medium 2 is a left-handed material (E < 0, μ < 0), when the light irradiates the interface between the two mediums, the refracted light and incident light will appear on the same side of the interface. 2. Anomalous Doppler effect The Doppler effect was first discovered by an Austrian physicist named Doppler in acoustic wave transmissions. In a left-handed material, the phase velocity direction of the electromagnetic wave is opposite to the group velocity direction, so when the phase velocity and group velocity are opposite one another, the phase velocity vector will be far away from the observer, and the observer will observe a reduced frequency; Similarly, when the phase velocity and group velocity move in opposite directions, the phase velocity vector will be close to the observer, and the observer will observe an increased frequency; This is the anomalous Doppler effect of lefthanded materials. If the reflecting interface is far away from the wave source, the frequency of the reflected wave in an ordinary material will be reduced, while in the left-handed material, the frequency of the reflected wave will be increased. The anomalous Doppler effect can be easily found in left-handed materials, which will help promote the revolutionary application of the anomalous Doppler effect. 3. Anomalous Cherenkov radiation In 1934, Cherenkov, a physicist, found in his experiment that charged particles would not radiate electromagnetic waves when moving at a uniform speed in a vacuum. This phenomenon is called Cherenkov radiation. When moving at a uniform speed in a medium, charged particles will radiate electromagnetic waves around them, causing induced currents. These induced currents can generate a variety of secondary waves radiating outwards on the path of the electric particles. The angle between the directions of energy radiation and particle motion is expressed by θ, which can be determined by Eq. (2.2). cos θ =

c nv

(2.2)

In a medium with a negative refractive index, the direction of energy transmission is opposite to that of the phase velocity, so the radiation direction will be the same as the motion direction of the particles in the opposite direction, and the radiation direction will form a forward cone angle in relation to the direction of motion. 4. Perfect lens effect Considering that the evanescent wave component carrying the object information is lost, the resolution of ordinary optical lenses, as well as the ratio to the wavelength λ, will always be limited. However, lenses made of left-handed materials can preserve this information. A lens made of left-handed material can keep all the energy while completely replicating the image points, perfectly reproducing the source. When

2.2 Principle and Properties of Left-Handed Materials

17

both the dielectric constant and permeability values are negative, the energy flow and wave vector will go in opposite directions. A field originally attenuated in a conventional material will be enhanced after entering the left-handed material, while a field originally enhanced in the conventional material will gradually attenuate after entering a left-handed material lens. An evanescent field with exponential decay can become an enhanced field with an exponential increase in lenses composed of lefthanded materials. In this way, an evanescent wave that would have been attenuated in the conventional material can be enhanced in the left-handed material slab, and the magnified evanescent wave signal will participate in the imaging, keeping the more microscopic details of the object to the new image points and increasing the imaging resolution greatly. For an ordinary lens, an optical axis is always provided, while no fixed optical axis is provided for lenses made of left-handed material, as they are flat. Thus, the paraxial condition for an ordinary lens is not valid for a left-handed material lens. The left-handed material lens can form an upright, faithful image of the light source of equal size, which contains both the transmitting wave and evanescent wave components of the light field, so that all components of the light field can participate in the imaging, breaking the diffraction limit. Therefore, left-handed material lenses are called “perfect lenses” thanks to this remarkable feature. 5. Anti-light pressure effect When irradiating an object, light waves will generate pressure on the surface. The pressure exerted by the light wave on the object per unit area is called the light pressure, or radiation pressure intensity. When photons collide with the surface of an object, they will transfer their momentum to the reflecting object, generating light pressure. Light has a wave particle duality, so the incident beam can be considered as a particle stream containing multiple photons. When the light beam irradiates an object, the particle flow will collide with the surface of the object. These particles will transfer their momentum to the object, generating a certain pressure intensity on its surface. The momentum and wave vector travel in the same direction. In an ordinary medium space, the momentum direction of the photons emitted by a light source is the same as that of the photon flow. Photons can be reflected after irradiating on the surface of an object. The increased momentum from the irradiated object is equal to the change of the photon momentum, but their directions are opposite to each other. However, in a left-handed medium space, the momentum direction of the photon flow emitted by a light source is opposite to that of its motion, so the role of the photons received by the irradiated object becomes different, which can be considered as an attractive force.

2.2.3 Realization of Left-Handed Materials So far, there have been many methods proposed to design left-handed materials, such as metal split-rings, metal line arrays, magnetic composite structures and nano

18

2 Fundamentals of Terahertz Detectors

array structures, etc. The frequency response range of left-handed materials has been gradually expanded to the microwave, terahertz and visible light frequency bands.

Reference 1. Yen TJ, Padilla WJ, Fang N, et al. Terahertz magnetic response from artificial materials. Science. 2004;303(5663):1494–6.

Chapter 3

Metamaterial Detection Methods

3.1 Basic Characteristics of Metamaterials Metamaterial is a new academic term in the field of physics over the past decade, which means “beyond”. There is not a uniform definition for the term metamaterial currently. Generally, metamaterials are “artificial composite materials or structures with extraordinary physical properties that natural materials do not have” and provided with three important characteristics. (1) Metamaterials are usually composites with novel artificial structures; (2) Metamaterials often have extraordinary physical properties that natural materials do not have; (3) The properties of metamaterials are usually determined by artificial structures. Subwavelength metal structures are those whose cyclical sizes are shorter than the incident wavelength. When a metal structure interacts with the electromagnetic wave, since its cyclical size is shorter than or far shorter than the wavelength, the details of the metal structure will not be “perceived” by the electromagnetic wave. Therefore, this composite material containing the subwavelength metal structure can show electromagnetic properties similar to those of homogeneous mediums on the whole. If these electromagnetic properties, such as negative permeability and negative refractive index, etc., are those that “natural” materials do not have, this artificial composite material can be called a metamaterial. It is generally believed that this definition was first proposed by Rodger M. Walser in 1999, while the concept and special properties of metamaterials were boldly conceived and systematically studied by Veselago as early as 1968. However, the strange material envisaged by Veselago was not found in the nature until Pendry, a British scientist, theoretically proved that negative dielectric constant materials and negative permeability materials could be constructed manually in 1996 and 1999, respectively and achieved experimental success in the microwave band in 2000. At present, the design models, fabrication

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3 Metamaterial Detection Methods

processes, electronic configuration and properties of metamaterials in the visible to microwave band have been widely studied by researchers at home and abroad.

3.2 Microstructure and Electronics Configuration of Metamaterial Devices In recent years, more and more materials have been used for fabricating metamaterial devices. The selected substrate materials have been expanded from Si, GaAs, GaN, etc. to various semiconductor mediums and graphene. Most of these manufacturing methods are subject to the photolithography. With the continuous development of the related processes, flexible device technology can also be used to make metamaterials. However, metal arrays for constituting metamaterials are mainly composed of SRR elements of cyclically patterned micro/nano structures. Therefore, the traditional photolithography is still the most widely accepted technology for fabricating metamaterials. Generally, two methods are selected for metamaterial fabrication and processing. The first is to use a semiconductor, such as semi-insulating gallium arsenide (SI GaAs), as the substrate to grow N-type gallium arsenide (n-GaAs) film through intermingling by utilizing metal–organic chemical vapor deposition (MOCVD) technology, finally fabricating a Schottky array of the ohmic electrode and cyclical SRR microstructure on the n-GaAs layer based on the photolithography to form a Schottky diode structure. This structure can be controlled by an external DC or AC voltage and the devices can be regulated through a variety of flexible and controllable ways, see Fig. 3.1a. The second is to first select an appropriate insulating medium layer, such as sapphire and glass (SiO2 ), etc., make a cyclical SRR microstructure array on the top surface of the medium layer based on the photolithography, and then make metal electrode lines or panel on the bottom surface of the medium layer according to the metal evaporation process. Metamaterial devices made in this way are composed of a cyclical SRR microstructure layer, insulating medium layer and metal panel layer from top to bottom, see Fig. 3.1b. Both of two metamaterial fabrication methods shown in Fig. 3.1 are a three-layer structures, which aims to regulate the metamaterial device function through external devices (such as DC power supply) and also provide interfaces for the subsequent function expansion of the device.

3.3 Morphological Characteristics of Resonance Element A typical SRR structure is shown in Fig. 3.2. The line width of this structure is 10 μm and the sizes of the four openings are all 6 μm. The line width of the narrowest side in the middle is 3 μm and the length is 30 μm.

3.4 Metamaterial Functional Devices and Their Applications

Ohmic electrode

21

Schottky electrode

Metal

Intermediate medium n-GaAs SI-GaAs Metal

(a)

(b)

Fig. 3.1 Two fabrication methods and device structure diagram of metamaterials. a Device structure 1; b device structure 2 Fig. 3.2 Schematic of a typical SRR

The SRR structure is taken as an element for periodization and expansion into an SRR array. Each SRR element in each row of the array is connected by metal. The rows can be connected in series or in parallel. See Fig. 3.3 for a microscopic image of the SRR array after being magnified 200 times.

3.4 Metamaterial Functional Devices and Their Applications When the metal SRR array is coupled with an incident electromagnetic wave, the generated resonance often occurs at two places. One is at the current loop and splitring of the SRR element, where the split-ring provides Inductance L, and the openings of the SRR element provide Capacitance C, making this model equivalent to an LC resonance; The other occurs at the boundary of the SRR element, where high-frequency dipole resonance is easily generated. Therefore, the induction of incident electromagnetic waves by means of metamaterial resonance has gradually been developed into a direction for designing metamaterial functional devices.

22

3 Metamaterial Detection Methods

Fig. 3.3 Typical micromagnified SRR array

3.4.1 Terahertz Signal Detection by Energy Absorption Metamaterial devices constructed from SRR microstructures usually have absorption or induction properties at a single frequency point. The relevant researches shows that when a metamaterial contains two SRR structures, it can be considered as being equivalent to two LC resonant circuits, making this structure have two characteristic response frequencies at the same time. This provides a new detection method for the absorption or response of multiple independent narrowband terahertz waves. This design is an effective extension of the previous single frequency point absorption metamaterial, and provides a reference for the signal detection of multiple characteristic frequency points.

3.4.2 Terahertz Signal Regulation and Sensing by Voltage Drive Generally, for a SRR based metamaterial device, the cyclical metal SRR array can be fabricated into a Schottky device based on the standard ultraviolet photolithography by taking silicon (Si) or SI GaAs as the substrate. Voltage signals can be applied at both ends of such device. By changing the voltage, the metamaterial device can be used to regulate the amplitude and phase of the incident THz wave. The actual result of this is that with the increase of the voltage, the depletion layer of the Schottky device becomes wider, leading to changes of the intensity and position of the electromagnetic resonance and a monotonous redshift or blueshift of the phase of the THz wave. This phase shift can promote the modulation of the bandwidth, realizing the THz wave sensing function at room temperature.

3.4 Metamaterial Functional Devices and Their Applications

23

3.4.3 Planar Nano-Tip Light Wave Regulation Surface plasmon polariton (SPP), an objective vibration mode composed of surface electron density waves and the excited electromagnetic field, can be significantly excited, effectively transported, and functionally arranged on metamaterials. Research indicates that a metamaterial with sub-wavelength characteristics can efficiently constrain incident light energy to medium interfaces, such as a typical metal– dielectric interface, thus realizing effective reflection and transmission of incident light waves. There exist high-density surface states in tip structures, such as the typical Nano-tip surface, making it possible to significantly increase the distribution density of tip charges by gathering large amounts of charges such as tip electrons. Surface waves can be transported and even gathered through tip boundaries to enhance local light wave amplitude, i.e., light intensity. High-density charge distribution and largeamplitude electromagnetic fields are achievable through Nano-tips, which implies that light waves can go beyond the diffraction limit and get further gathered through the tips. 1. Surface wave regulation The Feynman model can be used to describe the light-caused forced vibration of free electrons on metal-dielectric surfaces, and electron motion satisfies the vibrational equation. See Eq. (3.1):   qe x¨ + 2γ x˙ + ω2P + ω02 x = − ∗ E(ω, t) me

(3.1)

where −qe E(ω, t) represents the photogenic driving force for the vibration of surface electrons; γ represents the damping action on the lattice scattering of free electrons at the metal–dielectric interface; ω0 represents the restoring force for the vibration of free electrons at the metal–dielectric interface, which is bound by the weak lattice electric field; ω P represents the restoring force for the vibration of the free electron cluster and localized positive lattice cluster generated by excitation at the metal– dielectric interface. The eigenmode of the forced damped vibration can be expressed by Eq. (3.2): qe /m ∗e  x= 2 E(ω, t) 2 ω − ω P − ω02 + 2iγ ω

(3.2)

When light hits the localized surface, exciting vibration of the free electron gas, the density of free electron gas is shown in Eq. (3.3): N =

  N x s = N 1− x + s x

(3.3)

In this area, the net charge is the combined effect of the free electron gas microcluster and positive lattice micro-cluster at the surface. The net charge density is given in Eq. (3.4):

24

3 Metamaterial Detection Methods

  s ρ = −qe N  − N = qe N x According to Maxwell’s equation ∇ · E P = surface electric field is shown in Eq. (3.5):

ρ , ε0

(3.4)

the restoring force from the

qe N ∂s ∂ EP = ∂x ε0 ∂ x qe N s+C EP = ε0

(3.5)

where C is a constant. Under the irradiation of pulsed light, the surface localized free electron gas is subject to undamped vibration, i.e., when C = 0, its restoring force field is shown in Eq. (3.6): EP =

m∗ qe N x = e ω2p x ε0 qe

(3.6)

The vibration of the localized free electron gas is shown in Eq. (3.7). N m ∗e

d2 x N 2 qe2 = −N q E = − x e p dt 2 ε0

(3.7)

For the harmonic vibration equation x¨ + ω2p x = 0, the vibration mode is offered in Eq. (3.8): x=

qe Ep m ∗e ω2p

(3.8)

 2 Nq where ω p = ε0 me∗ represents the vibration frequency of the surface free electron e gas. The surface wave propagating at the metal–dielectric interface satisfies the wave equation: ∇ 2 E + k02 ε E = 0. It is assumed that the z = 0 plane is a metal–dielectric interface, i.e., the transmission wavefront of surface wave, the electric field distribution can be defined as Eq. (3.9): E(x, y, z) = E(z)eikx

(3.9)

where k is the propagation constant of the surface wave and a wave vector component in the direction of propagation. Substituting it into the wave equation, we get Eq. (3.10):  ∂ E(z)  2 + k0 ε − k 2 E = 0 2 ∂z

(3.10)

3.4 Metamaterial Functional Devices and Their Applications

25

According to the time-harmonic variable ( ∂t∂ = −iω), and considering that there is ∂∂x = ik for the wave propagating along the x-axis and that the partial derivative of the wave propagating along the y-axis concerning y is zero, the components of electric field E and magnetic field H in each direction can be written as Eq. (3.11): ∂ Ey = −iωμ0 H x ∂z ∂ Ex − ik E z = iωμ0 H y ∂z ik E y = iωμ0 H z ∂ Hy = iωε0 ε E x ∂z ∂ Hx − ik H z = −iωε0 ε E y ∂z ik H y = −iωε0 ε E z

(3.11)

There are two independent solutions to the equations concerning waves transmitted in different polarization modes: The group is transverse magnetic (TM or p-wave), i.e., the magnetic-field component is zero in the direction of propagation, i.e., there are only components E x , E z , and H y ; the second group is the transverse electric mode (TE or s), i.e., the electric-field component is zero in the direction of propagation, i.e., there are only components H x , H z , and E. For TM, the equation can be simplified to Eq. (3.12).  ∂2 H y  2 + k0 ε − k 2 H y = 0 2 ∂z

(3.12)

The electromagnetic field in the area where z > 0, i.e., in the dielectric region, is shown in Eq. (3.13): H y (z) = A2 eikx e−k2 z 1 E x (z) = iA2 k2 eikx e−k2 z ωε0 εd k E z (z) = −A2 eikx e−k2 z ωε0 εd

(3.13)

The electromagnetic field in the area where z < 0, i.e., in the metal region, is shown in Eq. (3.14): H y (z) = A1 eikx eik1 z 1 k1 eikx ek1 z E x (z) = −iA1 ωε0 εm

26

3 Metamaterial Detection Methods

E z (z) = −A1

k eikx ek1 z ωε0 εm

(3.14)

where k i = k z, j , (j = 1, 2) is the wave vector component in the direction perpendicular to the metal–dielectric interface. According to the boundary relation presented in Maxwell’s equations, we get Eq. (3.15), en × (E 2 − E 1 ) = 0 en × (H 2 − H 1 ) = α en · ( D2 − D1 ) = σ en · (B 2 − B 1 ) = 0

(3.15)

where σ and α represent the surface density of free charges and the linear density of the free current, respectively. Since there is no free charge or free current at the interface, E x , H y , Dz and Bz are continuous. So, A1 = A2 . Moreover, we get Eq. (3.16) k1 k2 + =0 ε1 ε2

(3.16)

The above equation is also known as Asymptotic Impedance Match (AIM). To constrain a transmitted wave mode near the interface, it is required that the wave vector components perpendicular to the interface should move in opposite directions in the metal and dielectric, i.e., Re[k 1 ] > 0 and Re[k 2 ] < 0. AIM shows that surface wave exists only at the interface of two materials with a dielectric constant opposite in the real part of the symbol. Substituting component H y of the magnetic field into the wave equation, we get Eq. (3.17): k12 = k 2 − k02 ε1 k22 = k 2 − k02 ε2

(3.17)

We can reveal the dispersion relation between surface plasmon polaritons based on AIM. See Eq. (3.18):  k = k0

ε1 ε2 ε1 + ε2

(3.18)

For TE, the equation can be simplified to Eq. (3.19).  ∂2 Ey  2 + k0 ε − k 2 E y = 0 2 ∂z

(3.19)

The electromagnetic field in the area where z > 0, i.e., in the dielectric region, is shown in Eq. (3.20):

3.4 Metamaterial Functional Devices and Their Applications

27

E y (z) = A2 eikx e−ik2 z 1 k2 eikx e−k2 z H x (z) = −iA2 ωμ0 k ikx −k2 z H z (z) = A2 e e ωμ0

(3.20)

The electromagnetic field in the area where z < 0, i.e., in the metal region, is shown in Eq. (3.21): E y (z) = A1 eikx ek1 z 1 H x (z) = iA1 k1 eikx ek1 z ωμ0 k ikx k1 z e e H z (z) = A1 ωμ0

(3.21)

Considering that E y and H x are continuous, A1 (k 1 + k 2 ) = 0. Since Re[k 1 ] > 0 and Re[k 2 ] > 0, A1 = 0. Similarly, A2 = 0. Therefore, no surface wave exists in TE mode, while only surface waves exist in TM mode. The dispersion relation for the SPP (surface plasmon polariton) transmitted along the metal–dielectric interface is given by Eq. (3.22): 

εm εd   = kspp + ikspp εm + εd       ε εm εd 3/2 εm εm d + ik0  = k0   2 εm + εd εm + εd 2 ε

kspp = k0

(3.22)

m

  where εm and εd represent dielectric constants of metal and dielectric; εm = εm +iεm ,   where εm represents the real part of the dielectric constant of metal; εm represents  represents the real part of the imaginary part of the dielectric constant of metal; kspp  SPP wave vector; kspp represents the imaginary part of SPP wave vector. The wavelength of SPP is given by Eq. (3.23):

 λspp =

 2π/kspp

= λ0

 +ε εm d  ε εm d

(3.23)

The propagation constant of SPP depends on the imaginary part of the SPP wave  . The transmission range is defined as a range in which traveling SPP wave vector kspp energy is attenuated to 1/e in the direction of propagation. Traveling wave energy is

2  attenuated exponentially as per e−|kspp ||x| , so propagation length can be obtained, as shown in Eq. (3.24):

28

3 Metamaterial Detection Methods

δspp

  2    2      εm εm εm εm + εd 3/2 + εd 3/2 1 =  = = λ 0   ε   ε 2kspp k0 εm εm 2πεm εm d d

(3.24)

The component k z of the SPP wave vector perpendicular to the interface is Eq. (3.25):  In metal: kz = kspp − εm k0 = k0



2 −εm εm + εd   −εd2 In dielectric: kz = kspp − εd k0 = k0 εm + εd

(3.25)

Since the SPP wave attenuates exponentially e−|kz ||z| in a direction perpendicular to the interface, the location where the field strength decays to 1/e is defined as penetration depth. See Eq. (3.26): 

 +ε εm d 2 εm   +ε 1 εm d In dielectric: δd = k0 εd2

1 In metal: δm = k0

(3.26)

The wavelength, propagation length, and penetration depth of SPP are all related to the material’s dielectric constant. For the selection of materials for devices of various sub-wavelengths, it is important to study the property of SPP existing at the different material interfaces. For example, if a sub-wavelength device needs to be designed and used to transmit surface waves in the infrared band, a material with a long propagation length of SPP at the metal/semiconductor interface must be selected. For a particle with a radius much smaller than its wavelength, it scatters light, generating localized SPP, as shown in Fig. 3.4. For the interaction between a spherical particle with a small radius and an electromagnetic field, a quasi-static approximation (QSA) analysis can be conducted. In this approximation, the phase of the spatial electromagnetic field remains unchanged, and only the spatial intensity distribution of the electromagnetic field is analyzed. Then, an electrostatic field model can be used to calculate the electric-field distribution of metal particles placed in an external electric field. First, an isotropic metallic particle with a radius of a and a dielectric constant of εm is placed in an absorption-free, uniform dielectric with a dielectric constant of εd . Under the irradiation of a uniform plane wave with a uniform plane wave electric field component E = E 0 Z , the electrostatic field can be calculated according to electrodynamic force.

3.4 Metamaterial Functional Devices and Their Applications

29

Fig. 3.4 Localized SPP analysis model

According to Laplace’s equation ∇ 2 ϕ = 0, electric fields E = −∇ϕ. ϕ 1 and ϕ 2 represent the potential of the outer and inner spherical regions. The general solution for the two regions is given by Eq. (3.27)   bn an R n + n+1 Pn (cos θ ) R n   dn n ϕ2 = cn R + n+1 Pn (cos θ ) R n ϕ1 =

(3.27)

Pn (cos θ ) is the Legendre function, where an , bn , cn , and d n are the undefined constant. These undefined constants can be calculated under boundary conditions. The boundary conditions are as follows: (1) E → E 0 at infinity; (2) ϕ 2 has a finite value at R = 0; 1 1 = εm ∂ϕ . (3) At R = a, on the dielectric sphere, ϕ1 = ϕ2 , εd ∂ϕ ∂R ∂R The solution for the equation is given by Eq. (3.28): ϕ1 = −E 0 R cos θ + ϕ2 = −

εm − εd E 0 a 3 cos θ εm + 2εd R2

3εd E 0 R cos θ εm + 2εd

(3.28)

In the inner spherical region, the electric field is always smaller than the original external electric field E 0 . This is because polarization charges are generated on the dielectric sphere. The electric field generated by the polarization charges is in the reverse direction to the original electric field, weakening the total electric field. See Eq. (3.29) for the intensity of polarization:

30

3 Metamaterial Detection Methods

P = χe εd E = (εm − εd )E =

εm − εd 3εd E 0 εm + 2εd

(3.29)

The total polar moment is given by Eq. (3.30): p=

4π 3 εm − εd a P= 4πεd a 3 E 0 = εd α E 0 3 εm + 2εd

(3.30)

−εd where α = εεmm+2ε 4πa 3 represents polarizability. d The potential generated by this dipole moment is shown in Eq. (3.31):

1 p· R εm − εd a 3 E 0 = cos θ 3 4πε0 R εm + 2εd R 2

(3.31)

It is the right term for the potential in the outer spherical region. In other words, the potential in the outer spherical region is the sum of the external electric field potential and the potential generated by the dipole induced by the metal sphere. The electric field distribution inside and outside the metal sphere can be obtained according to the electric field. See Eq. (3.32): E1 = E0 + E2 =

3(en · p) − p 4πεm R 3

3εd E0 εm + 2εd

(3.32)

where en is the unit vector at point p. QSA can find the electric field strength. The electric field of the incident electromagnetic wave is time-varying E(r, t) = E 0 e−iωt , and the electric dipole induced by it also oscillates with time p(t) = εd α E 0 e−iωt . In the outer spherical region, electromagnetic waves’ electric and magnetic field components oscillate with time and can be written as E(t) = Ee−iωt and H (t) = H e−iωt . See Eq. (3.33) for their expressions:

    1 eik R  ik 1 2 ik R k (en × p) × en + 3en (en · p) − p − 2 e E= 4πεd R R3 R   2 ik R 1 ck e 1− (3.33) H= (en × p) 4π R ik R where k = 2π/λ en is the directional unit vector at point P. When k R  1, i.e., in the near-field region of the metal sphere, the strength of the electric and magnetic fields can be calculated by Eq. (3.34): E=

3en (en · p) − p 4πεd R 3

3.4 Metamaterial Functional Devices and Their Applications

H=

ick 1 (en × p) 2 4π R

31

(3.34)

In the near-field region, the magnitude of the magnetic field component to that √ of the electric-field component is rough H/E ≈ ε0 μ0 (k R). Because k R  1, the magnetic-field component is a much smaller quantity than the electric-field component, i.e., the magnetic-field component approaches 0 at k R → 0. When k R 1, i.e., in the far-field region, the strength of the electric and magnetic fields can be calculated by Eq. (3.35): ck 2 eik R (en × p) 4π R eik R 1 2 k (en × p) × en E= 4πεd R

H=

(3.35)

Its absorption cross-section and scattering cross-section can be found by calculation. See Eq. (3.36): Csca Cabs

  k4 2 8π 4 6  εm − εd 2 |α| = k a  = 6π 3 εm + 2εd    εm − εd 3 = k Im[α] = 4πka Im εm + 2εd

(3.36)

The scattering cross-section is directly proportional to the 6th power of the particle radius, while the absorption cross-section is directly proportional to the 3rd power of the particle radius. Therefore, their scattering power is very low for Nanoparticles with a small radius, making it difficult to distinguish from background scattering. However, the absorption cross-section is directly proportional to the 3rd power of the radius. Therefore, the absorption cross-section can be detected according to the photothermal effect, thereby detecting particles with a less than 40 nm radius. When Re[εm ] = −2εd , i.e., at the dipole resonance frequency point, the polarizability α, dipole moment p, near-field photoelectric field component E, absorption cross-section Csca , and scattering cross-section Cabs are greatly enhanced. The energy of incident light is partly radiated to the far field and partly localized in the near field. In the near-field region, the electric-field component is greatly enhanced, but considering that the magnetic-field component is a small quantity, the energy of near-field light divided by the energy of incident light is not greater than 1. 2. Nano-tip near-field light enhancement Due to the tip effect, many surface states filled with free electrons are generated at the Nano-tip so that free electrons have high surface distribution density at the Nano-tip. This chapter establishes a theoretical model for calculating free electron distribution based on Nano-tip surface energy states. Also, when the excited surface wave propagates to the Nano-tip, the tip boundary guides the surface wave in gathering to the Nano-tip, finally achieving Nano-focusing of incident electromagnetic radiation.

32

3 Metamaterial Detection Methods

The free surface of the lattice causes its periodic field to be interrupted at the surface and generate an additional energy level in the forbidden band. A model can be established by starting with the energy band structure and used in combination with the wedge-shaped tip structure to calculate electron distribution at the tips. This section studies the charge distribution at different tip angles and positions, as shown in Fig. 3.5. In a 3D crystal, the atomic bond ruptures into an acceptor level at the interface. The acceptor energy level of each surface atom at the interface corresponds to a surface energy level in the forbidden band. These dense surface energy levels make up a surface energy band. If each surface energy level is considered an acceptor energy level, the concentration of acceptor energy levels is as follows: N A = a 2SV , where a represents the lattice constant; aS2 represents the number of surface atoms. The higher the density of acceptor energy levels is, the stronger the ability to hold electrons is, indicating a higher concentration of free electrons at this location. For the metal sector shown in Fig. 3.5b, the surface area V and volume S can be calculated

(a)

(b) θ r

metal

∆r

h

substrate bulk semiconductor

quantum dot

nano-tip structure

Energy

(c)

density of states

density of states

density of states

Fig. 3.5 The model used for charge density calculation. a Physical structure of device; b device parameters; c schematic diagram of energy band

3.4 Metamaterial Functional Devices and Their Applications

33

by Eqs. (3.37) and (3.38): S = r [θr + θ (r + r )] + 2r · h V =

(3.37)

1 r [θr + θ (r + r )] 2

(3.38)

Therefore, when r → 0, h ∼ 0, we get Eq. (3.39) NA =

S a2 V

=

2 2 + 2 2 a h a θr

(3.39)

Let the ground-state degeneracy (GSD) of an acceptor energy level be g A . Equation (3.40) shows the probability that the hole occupies the acceptor energy level: f A (E) =

1 1+

1 e gA

(3.40)

E F −E A k0 T

The hole concentration PA of the acceptor energy level is given by Eq. (3.41).  PA = N A f A (E) =

2 2 + 2 2 a h a θr



1 1+

1 e gA

E F −E A k0 T

(3.41)

When E − E F k0 T , we get Eq. (3.42)  PA = If f (θ, r ) =

2 a2 h

+

2 , a 2 θr

 E −E 2 2 − F A + g A e k0 T 2 2 a h a θr

(3.42)

then the above equation can be simplified to Eq. (3.43): PA = f (θ, r )g A e

−

E F −E A k0 T

(3.43)

The hole density on the acceptor energy level PA equals the density of volume charges and is directly proportional to the function f (θ, r ). The chemical potential of free electrons on the Nano-tip surface can be adjusted according to its distribution density. Its value should be smaller than the chemical potential inside the tip. SPP is an electromagnetic mode constrained in the vertical direction of the metal– dielectric interface, including the oscillating waves of free electrons on the metal surface and the electromagnetic waves coupled together. The equivalent refractive index of SPP is jointly determined by the dielectric and metal, which make up the interface, so we get Eq. (3.44)

34

3 Metamaterial Detection Methods

 ne f f =

εm εd εm + εd

(3.44)

where εm and εd are the relative permittivity of the metal and dielectric, respectively. The propagation constant of SPP is given by Eq. (3.45)  kspp = k

εm εd = kn e f f εm + εd

(3.45)

where k represents the wavenumber (WN) in a vacuum, k = 2π/λ. At the Nanotips, the input SPP converges continuously to the tip after continuous refraction and reflection under the constraint of the tip boundary, generating strong Nano-focusing. As shown in Fig. 3.6, the SPP mode has effectively reflected the tip or transmitted it into the air at the tip boundary. The component of the SPP mode in the direction of the tip, kτ , continues to propagate towards the tip and converges at the tips. As shown in Fig. 3.6, the SPP wave vector can be decomposed in the tangential and vertical directions of the metal boundary. The tangential component kτ propagates continuously along the boundary, which can be revealed by calculation according to the equation kτ = kspp cos θ2 . The vertical components generate wave vectors that propagate in the air. The tangential components moving along the metal–dielectric interface or each Nano-tip wall meet and superimpose at the Nano-tips. Owing to the symmetry of the triangular Nano-tips, the two SPP tangential components converging to the tips are the same in phase, so wave vector superposition is enhanced when these two wave vector components meet at the tips. Thus, surface wave amplitude increases, leading to a significant increase in the vibrational energy of electrons at the tips. In addition, many hot free electrons converge at the tips, greatly enhancing the electron energy at the tips. In this section, FDTD is used to simulate the propagation of surface waves at the tips. In FDTD, the physical space is gridded using the finite-difference time-domain (FDTD) method, and for each grid, the electromagnetic field problem is solved using Fig. 3.6 Schematic diagram of SPP convergence at the tips

θ

k1

kτ1

kτ2

surface wave

k2

3.4 Metamaterial Functional Devices and Their Applications

35

(a)

(b) 200nm z 400nm θ y

φ

x

Fig. 3.7 Au-based twin-tip structure and its parameters. a Diagram of Au-based twin-tip structure; b parameters of Au-based twin-tip structure

3D Maxwell’s equations. In terms of time, an iterative calculation is made to obtain frequency-domain results from time-domain signals. There is an Au-based double twin-tip structure, as shown in Fig. 3.7a, and four tips are on the structure. The two opposite Nano-holes and Nano-tips are 400 and 200 nm, respectively. The Au-based double twin-tip structure is periodic, and its period is set to 900 nm. A laser irradiates the Au-based double twin-tip structure with the same wavelength as that used for near-field optical testing, with a spherical coordinate system established to describe the incident direction of the laser. Both θ and ϕ are set to 45°, and the incident laser is p-polarized. Laser incidence is marked with a red arrow, while polarization is marked with a blue arrow. This section analyzes SPP’s propagation behavior on the Au-based double twin-tip structure under the condition that the laser comes in along the long and short axis directions of the Au-based double twin-tip structure, exciting SPP in the long and short axis directions of the Au-based double twin-tip structure. SPP wave vector decomposition is shown in Fig. 3.8a, c. FDTD simulates the near-field electric field distribution. The results are shown in Fig. 3.8b, d. When an incident laser drives the free electrons on the metal surface, they can oscillate along the incident polarization direction. When the wave of free electron oscillation on the surface reaches the boundary or interface, it is decomposed in two directions. The vertical component propagates in the air or is reflected in the metal; the tangential component continues propagating from the interface. According to this principle, the vector decomposition of surface waves excited by different incident lights on the structure can be plotted to analyze the convergence of the tangential component continuing to propagate forward. Figure 3.8 shows the results of wave vector decomposition on the Au-based double twin-tip structure. The red, blue, and black arrows indicate the original wave vector e, tangential and vertical components, respectively. Figure 3.8a shows the wave vector decomposition that occurs at the boundary when the polarization direction of the laser is parallel to the twin-tip direction of the double twin-tip structure. At this point, there are two tips in the polarization direction. The tangential component continues to propagate along the boundary, finally converging at apex-1 and apex-2 at the

36

3 Metamaterial Detection Methods

Fig. 3.8 Plasmon wave vector decomposition and near-field distribution on the Au-based double twin-tip structure. When the laser comes in along the twin-tip direction, on the Au-based double twin-tip structure: a plasmon wave vector decomposition; b near-field distribution. When the laser comes in along the twin-hole direction, on the Au-based double twin-tip structure: c plasmon wave vector decomposition; d near-field distribution

upper left and lower right points. Figure 3.8c shows the wave vector decomposition that occurs at the boundary when the polarization direction of the laser is parallel to the twin-hole direction of the double twin-tip structure. At this point, none of the tip directions align with the polarization direction. According to the results of wave vector decomposition, the tangential component cannot converge or scatter at the edge of the structure. Taking the upper boundary as an example, the tangential component of the surface wave vector is the first to be transmitted from left to right along the upper boundary. When it reaches the upper tip, it turns and continues to propagate forward, finally converging at corner-1 with the tangential component of the right boundary. A primary convergent point (corner-1) and a secondary convergent

3.4 Metamaterial Functional Devices and Their Applications

37

point (upper tip) are formed at the upper boundary. Owing to the excessive spacing between every two tips on the Au-based double twin-tip structure (148 nm or 200 nm), the focus points formed by different Nano-tips cannot couple with each other, so the coupling effect between the convergent points is not taken into consideration here. The simulation diagrams of near-field optical distribution on the surface of the Au-based double twin-tip structure are shown in Fig. 3.8b, d, depicting surface wave transmission and convergence at the tips and concave corners. When the polarization direction of the laser is parallel to the twin-tip direction of the double twin-tip structure, there is a light spot at the upper left corner of apex-1. When the polarization direction of the laser is parallel to the twin-hole direction of the double twin-tip structure, there are two focus points at the tips and left end. As mentioned earlier, the electric field intensity distribution of near-field light on the metal surface is influenced by the distribution density of free electrons on the surface and the amplitude of electron density waves. The focus point formed at each Nano-tip can also be approximated as a near-field light focus spot. In Fig. 3.8b, the focus spot is located at the apex of the gold module and shows high a distribution density of oscillating free electrons. It is also the convergent point for the tangential component of SPP. As shown in Fig. 3.8d, the convergent points are mainly distributed at the upper tip and the left tips. Here, the near-field electric field components at the upper and left tips are relatively large due to the sub-convergent point of the tangential component of the surface wave vector and the high-density distribution point of free charges. 3. Surface wave sensing based on an infrared differential system In this section, the near-field optical properties of the sample are observed under laser irradiation using a scattering scanning near-field optical microscope. The scanning near-field optical microscope is a type of optical microscope has high spatial resolution developed in the 1980s and 1990s. It is a kind of scanning probe microscope. It has many advantages, as follows: It can be used to conduct experiments in a general atmospheric environment without the need for a low-pressure or vacuum environment; visible or infrared light is used as the detection signal, causing hardly any damage to the sample. The near-field optical information on the surface of microNanostructures can be observed under the scanning near-field optical microscope, which is of great significance for studying the plasmon principle. Also, the scanning near-field optical microscope can be used to detect the near-field spectrum, which is great help for studying the sample’s chemical composition and structural information. The scanning near-field optical microscope shown in Fig. 3.9 is a type of holeless scanning near-field optical microscope. Its principle is as follows: Due to the local SPP effect, when a particle is irradiated by incident light, an enhanced optical field is formed in the near field on its surface. The enhanced near-field optical field is changed by the micro/Nano-sample in its vicinity so that the scattered light received in the far field of the detection area carries the local photoelectric field information of the sample. In the test, a general atomic force microscope (AFM) probe is used as the scattering source and also used to focus near-field light and far-field scatter light.

38

3 Metamaterial Detection Methods

Fig. 3.9 Scanning near-field optical microscope. a Schematic diagram; b real object

Its spatial resolution is determined by the radius of curvature of the AFM probe, about 10 ~ 30 nm. During the probing process, the AFM probe vibrates along the vertical component. It scans horizontally to collect information about near-field optical distribution from the sample’s surface. The AFM probe vibrates in the vertical direction, revealing the relationship between the photoelectric field component and the vertical distance. The photoelectric field component detected contains both a background signal and a near-field signal. Still, the background signal is linearly correlated with the vertical distance since its photoelectric field is only attenuated owing to transmission loss. The near-field photoelectric field signal attenuates exponentially with the vertical distance. The photoelectric field signal collected can be differentiated about the vertical distance to separate the near-field optical signal from the background signal.

3.4 Metamaterial Functional Devices and Their Applications

39

For the surface wave signal, its near-field photoelectric field intensity is: E 1 (z) = −Ae−k2 z , which is exponentially correlated with Z. For the background signal propagating in the Z direction, its photoelectric field intensity is: E 2 (z) = B − C Z , where A and B are both constants. In SNOM measurements, a probe detects the near-field photoelectric field signal. The obtained near-field photoelectric field is the sum of the near-field optical signal and background signal, i.e., the obtained electric field signal is: E(z) = E 1 (z) + E 2 (z) = −Ae−k2 z + B − C Z . We take the first derivative of the electric field signal, obtaining a second-order signal. After taking the derivative, the signal strength is: E(z) = Ak2 e−k2 z − C. As can be seen, the second-order signal contains a near-field signal and a constant term only, while the near-field signal has been separated from the background signal. We take the derivative again, obtaining a third-order signal. The third-order signal strength is: E(z) = −Ak22 e−k2 z . As can be seen, the third-order signal is already a pure near-field optical signal. After taking the derivative again, the fourth-order signal strength is: By differentiation, the near-field signal can be separated from the background signal, making it possible to realize surface wave sensing. 4. Near-field light focusing of Au-based nano-tip array metamaterial In the test, the scattering scanning near-field optical microscope detects the near-field optical distribution of the Au-based planar Nano-tip array metamaterial. Figure 3.10 shows the schematic diagram of laser incidence. First, the metamaterial is irradiated by a 633-nm red light to study the near-field optical properties of the Au-based double twin-tip structure under red light irradiation. Meanwhile, the free electrons on the surface of the micro-Nano gold are observed to reveal their properties shown under red light irradiation. Because the strength of near-field light on the Nano-tip metamaterial is stronger and easier to detect under red light irradiation, a silicon AFM probe is used here to detect the electrical signal of near-field light. As shown in Fig. 3.10a, b, it can be seen from the near-field optical properties that a clear, bright spot is visible on the metamaterial with an Au-based double twin-tip structure, indicating that the metamaterial with an Au-based double twin-tip structure can effectively achieve Nanofocusing of light in visible wavelengths. This is in good agreement with the simulation results. By measuring the electric field strength along the red line shown in Fig. 3.10a, we see that the maximum and minimum electric field strengths are 2.12 μV and 0.2 μV, respectively. By measuring the full width at half maximum (FWHM) of the light spot, we see that the focusing spot is 37 nm in size. Considering that the excitation wavelength is 633 nm, the current spot size is in order of magnitude lower than the incident light wavelength, greatly breaking through the diffraction limit of near-field light. Since the sample tilted somewhat during a SNOM measurement, there was a slight drift in the near-field optical micrograph, causing a slight difference between the measured and simulation results. Some faint interference fringes are observed around the Nanopore. Its strength is much lower than that of the focusing spot, and this is due to the periodic structure of the Au-based double twin-tip array. As shown in Fig. 3.10b, there exists an elliptical focusing spot on the surface of the Au-based double twin-tip structure. The measurement of its

3 Metamaterial Detection Methods

Intensity

Intensity

40

Fig. 3.10 Near-field optical properties of the Au-based double twin-tip structure. a Near-field optical properties of Au-based double twin-tip structure-1; b near-field optical properties of Aubased double twin-tip structure-2

FWHM shows that its width is about 38 nm. Finally, the experimental results well validate the simulation results, verifying the theory’s accuracy. The infrared reflectance spectrum of the double twin-tip structure on the gold film was measured using the Fourier transform infrared spectrometer (FT-IR). All the data collected were compared with the reflectivity of a gold-plated plane mirror with high reflectivity in the IR region. For the reflection spectrum shown in Fig. 3.11, there is an external reflection valley at 9.5 μm. Figure 3.11a, b show the reflection spectrum of different double twin-tip array structures. Although the two structures are the same in element pattern, but since there is a difference in pattern direction and array pattern between them, they differ in the reflection spectrum. The simulation results are the same as the measured results in reflected wave valley wavelength, proving the correctness of the simulation results. Besides, different micro-Nano tip array structures are designed in this chapter. Their near-field optical response was measured under 633 nm red light irradiation. Figures 3.12 and 3.13 show the near-field optical properties of several typical tip structures. As can be seen, there are similar near-field electric field distributions at the interface of different tip array structures. There is obvious near-field focusing spots at the Nano-tips, which can be applied to optical lithography beyond the diffraction limit.

3.4 Metamaterial Functional Devices and Their Applications

41

Fig. 3.11 Infrared reflection characteristics of double twin-tip structure. a Double twin-tip structure-1; b double twin-tip structure-2

Figures 3.12 and 3.13 show the near-field optical distributions of several typical tip structures. The left side shows the geometric structure; the middle shows the nearfield optical distribution; the right side shows a 3D near-field optical distribution obtained by processing in Matlab. The tip array structure with curved boundaries, analogous to the tip array structure with square boundaries, also focuses 633 nm red light and forms a focusing spot beyond the diffraction limit in the near field of the device. Notably, near-field focusing spots can be as small as 30–40 nm through different structural profiles. Some spots are distributed at the tips, some at the structure boundaries, and others at some ten nanometers from the tips. Different structures mainly provide different boundary conditions for the electron density waves excited by light to modulate the propagation of electron density waves, thus forming different near-field optical patterns in the device’s near field.

42

(a)

3 Metamaterial Detection Methods 0.0 μm

0.4

0.8

0.0

1.75μV 1.2

0.4 0.8 0.4

0.8

0 0.0 μm

(b)

0.0

0.4

0.8 1.23μV 1

0.4

0.8 0.6 0.4

0.8 0

Fig. 3.12 Near-field optical properties of several tip structures with curved boundaries. a Circular four-tip array structure; b circular-tip array structure

Localized SPP is a broad-spectrum effect, and a near-field Nano-focus with a relatively broad-spectrum band can be created in an Au-based Nano-tip array metamaterial. The infrared near-field optical distribution properties of the Nano-tip array metamaterial were investigated by applying 10.274-μm excitation to Nano-tip samples of different shapes. Since the near-field optical signal excited by infrared light is relatively weak, a platinum probe with high detection performance should be chosen for near-field optical measurements. Figure 3.14a shows an enlarged near-field optical micrograph of the square-tip array structure. Near-field optical line distribution properties were measured along the red line. Since the red line crosses the linear spot of the square-tip array structure, spot information, such as strength and FWHM, can be obtained. Therefore, several pieces of key data can be collected, such as maximum strength of 71.4 μV, minimum strength of 22.5 μV, and FWHM of 44 nm in the x-direction. Figure 3.14b shows an enlarged view of the white dashed box presented in Fig. 3.14a. Since the bright linear spot tilts at about 30° to the x-direction, the actual width of the linear spot should be 20 nm, and the width is three orders of magnitude lower than that excited at 10.274 μm.

3.4 Metamaterial Functional Devices and Their Applications

(a)

0.0 μm

0.4

43

0.8

0.0

2.12μV 1.6

0.4

1.2 0.8

0.8

0.4 0 0.0 μm

(b)

0.4

0.8

0.0

5.99μV 5 4

0.4

3 2 0.8 0

(c)

0.0 μm

0.4

0.8

0.0

2.7μV 2

0.4

1.5 1

0.8

0.5 0

(d)

0.0 μm 0.0

0.4

0.8 2.31μV 2 1.6

0.4 1.2 0.8 0.8

0.4 0

Fig. 3.13 Near-field optical distribution of several typical tip structures. a Two-tip array structure-1; b twin-tip array structure-2; c square-tip array structure; d square twin-tip array structure

Interestingly, the total length of the bright linear spot exceeds 400 nm. There are linear focusing spots similar to the square-tip structure. The IR near-field optical photographs of other tip structures, and they also have a sub-wavelength size.

44

3 Metamaterial Detection Methods

(a) 0.0 μm

0.4

0.8

0.0

89 μV 80 70 60

0.4

(b)

50 40 30

0.8

20

y x

0

(c)

80 70

Intensity(μV)

60 50 40 30

44nm

20 10 0

0

0.1

0.2

0.3

0.4

0.5 0.6 X (μm)

0.7

0.8

0.9

1

Fig. 3.14 Near-field optical properties of the square-tip array structure in the infrared band. a Nearfield optical micrograph; b enlarged view of near-field focused spot; c near-field optical distribution at the red line

Figures 3.15 and 3.16 show the near-field optical characteristics of several typical tip structures. As shown in the figures, different Nano-tips of varying sharpness can be arranged at different positions relative to each other to create different micro-Nano array structures to generate different types of coupling. Arranged above are multiNano-tip structures, including both blunt and acute Nano-tips, arched and square tip structures. Surface waves converge, forming a very fine linear sport, thereby greatly enhancing near-field light strength. A very fine linear spot can be observed along the boundary of each Nano-tip, which differs from the one discovered in the visible wavelength band. Considering that the basic structural size of Nano-tips ranges from 300 to 700 nm, the incident infrared light is of the sub-wavelength structure compared to 10.274 μm. As can be seen, every Nano-tip structure significantly focuses on the incident infrared light of 10.274 μm.

3.4 Metamaterial Functional Devices and Their Applications

45

0.0 μm

(a)

0.2

0.4

0.0

66μV 50 40

0.2

30 20 0.4

10 2 0.0 μm

(b)

0.4

0.8

0.0

86μV

0.4

70 60 50 40 30 20 0

0.8 0.0 μm

(c)

0.4

0.8 89μV 80

0.0

60 0.4 40 20

0.8

0 0.0μm

(d)

0.0

0.2

0.4 84μV 70 60

0.2

0.4

50 40 30 20 6

Fig. 3.15 Near-field optical properties of the square boundary-tip micro-nano array structure under 10.274-μm laser irradiation. a Two-tip array structure-1; b square two-tip array structure; c squaretip array structure; d two-tip array structure-2

46

3 Metamaterial Detection Methods 0.0 μm

(a)

0.4

0.8

0.0

137μV 120 100 80

0.4

60 40 1

0.8 0.0 μm

(b)

0.0

0.2

0.8 129μV 100 80

0.4

60 40

0.8

2

Fig. 3.16 Near-field optical properties of the curved-tip micro-nano array structure under 10.274μm laser irradiation. a Circular two-tip array structure; b circular-tip array structure

Chapter 4

Numerical Simulation of Metamaterials

With the popularization and development of computer technology, numerical simulation has been widely adopted in various basic theories and engineering practices. In the past, model designs based on prediction and qualitative analysis have rapidly developed into quantitative designs relying on computer simulation and optimization to ensure correctness and reliability for basic and applicative research. Therefore, numerical simulation calculations play a more and more important role in various fields of natural science research, actively promoting the development of modern applied mathematics and its related disciplines. Generally, when using a mathematical method to solve problems of various electromagnetic field applications, it is necessary to first establish a suitable mathematical model, and then conduct theoretical analysis and scientific research on that basis. Matching mathematical models to objective items will always result in some errors, which may be related to many factors; for example, the difference between the incident electromagnetic wave waveform and the actual one, the multi-layer structure of a device making the relevant physical quantities may fail to be accurately expressed, etc. Such problems are common in simulation and actual measurement. Therefore, an actual mathematical model is always a mathematical description given after an idealized assumption of the actual problem, and is as close to the actual problem as possible. Maxwell put forward the basic equations of electromagnetic fields in 1865, and predicted the existence of electromagnetic waves. The rapid development of electromagnetic waves, electromagnetic fields and many other engineering applications over the past 100 years have proved that Maxwell’s equations are universally applicable mathematical models for macro electromagnetic fields, which have become the basis of the classical electromagnetic theory. By constructing appropriate mathematical models to solve Maxwell’s equations, we can achieve results that match actual problems. Usually, mathematical models can be divided into differential equations, integral equations and optimization models, etc. By setting the boundary conditions and initial conditions in an actual electromagnetic wave transmission © National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_4

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process and combining the corresponding mathematical model, namely, a numerical calculation method, the results of various electromagnetic wave transmissions and electromagnetic field distributions consistent with the expected target can be obtained. In the optical frequency—RF millimeter wave frequency band, when the electromagnetic wave irradiates the metamaterial surface of an artificial structure, the corresponding electric field and magnetic field components will be coupled at the top interface of the metamaterial according to Maxwell equations. If the size of each SRR element in the metal microstructure array on the top layer of the metamaterial is much longer than the incident electromagnetic wavelength, this coupling effect can be essentially ignored. However, when the SRR element size of the metal microstructure is much shorter than the incident electromagnetic wavelength, LC electromagnetic resonance, dipole resonance and surface plasmon resonance will most likely be caused according to the equivalent transmission line circuit model. Therefore, it is necessary to find the best numerical method to analyze the SRR of the artificial microstructure pattern in the electromagnetic field as well as the electronic configuration of the metamaterial as well.

4.1 Finite-Difference Time-Domain (FDTD) The Finite integration technique (FIT) is a numerical calculation method derived by Weiland in 1977 according to the integral form of Maxwell equations, and has been successfully applied to the numerical simulation of electromagnetic fields. Of the numerical algorithms of electromagnetic fields, only FIT can be adopted to and be suitable for obtaining all the solutions to analyze the Maxwell equations. The Maxwell integral equations are defined by Eq. (4.1): ⎧ ⎪ ⎪ ⎪ δA ⎪ ⎪ ⎪ ⎪ ⎨ δA ⎪ ⎪ ⎪ ⎪ δV ⎪  ⎪ ⎪ ⎩ δV

Eds = − Hds = −

˜ A ˜

Dd A = Q

A

Bd A ( D + J )d A (4.1)

Bd A = 0

For FDTD, only a step-by-step iterative calculation rather than a matrix inversion operation, is needed. The currently popular 64-bit computer can be used to simulate the electrical size of up to hundreds of wavelengths.

4.2 Frequency Domain Finite Element Method (FD-FEM)

49

4.2 Frequency Domain Finite Element Method (FD-FEM) The basic idea of FD-FEM is to “break up the whole into parts”, namely adopting it to decompose a complex continuous region into several small regions with specific regular shapes. This method for solving problems via deconstruction is suitable for simplifying a complex problem into sub-problems of finite elemental nodes. The traditional finite element method is based on the variational principle. First, the differential equation to be solved can be converted into the corresponding variational equation, namely the functional extremum problem; then, the interpolation function can be used to convert the variational problem into an extremum solution problem of a multivariate function, which is equivalent to a multivariate algebraic equation set. As such, the finite element method is adopted to simplify a problem into an extremum problem of solving the algebraic equation set by “breaking the whole into parts”. According to the above analysis, a key step of the finite element method is to divide a large continuous region into finite sub-regions by interpolation, and the segmentation method of this region set needs to set appropriate boundary conditions. Therefore, when adopting the finite element method, the boundary conditions are always taken as the preconditions for numerical simulation calculation. The basic idea of the finite element method was first proposed by Courant in 1943 for solving the St. Venant problem by the continuous function defined on the triangular piecewise and the principle of minimum potential energy, making it the original form of the finite element method. In the 1950s, the finite element design method was first applied in analysis of aviation structures, but the name and complete definition of the finite element method were first proposed by Clough in 1960. In 1965, Winslow applied the finite element method to electrical engineering problems. In 1969, Silvester applied the finite element method to the solution of electromagnetic field problems. With the wide application of computer discrete mathematics and numerical simulation calculations, the finite element method was gradually used to solve various engineering and scientific problems. Feng Kang, et al., Chinese mathematicians, proved the convergence of the finite element method and created a systematic finite element algorithm. At present, the finite element method is widely used in research fields such as mechanics, acoustics, electromagnetic fields, metamaterial and plasma, and has become the main numerical simulation calculation method for the quantitative analysis and optimization design of various electromagnetic field and electromagnetic wave engineering problems. The main characteristics of the finite element method are as follows. (1) Provided with a good adaptability. Compared with other numerical calculation methods, the finite element method is highly adaptable to the numerical calculation of irregular boundaries and complex regions, thanks to its high numerical simulation calculation accuracy. (2) Provided with a large number of modular subprogram sets that can be used for generic purposes. This makes it convenient to write general computer programs and expand numerical calculation functions, with the purpose of generating high-performance program libraries suitable for different applications.

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(3) As an important branch of applied mathematics, finite elements help to promote the development of functional analysis and calculation methods. The finite element method has been developed into one of the most widely used numerical calculation methods in various engineering and basic research fields. FD-FEM calculation includes three steps: first, establish an elemental model, then use an appropriate finite element analysis program, and finally evaluate and check the finite element calculation results. In these three steps, it is easy to find that the main difficulty for finite element analysis is the generation of discrete meshes when big regions are segmented into finite sub-regions, namely the finite element mesh model corresponding to the first step of the finite element method. The quality of mesh generation directly affects the accuracy of the results obtained in the subsequent analysis process. For complex geometrical bodies, mesh generation is usually not easy, since too few meshes will lead to big calculation errors, while too many meshes are time-consuming for operation and prone to errors.

4.2.1 Boundary Problems in the Numerical Calculation of Electromagnetic Fields When the finite element method is used to solve an electromagnetic wave transmission problem, the control equation should be determined first. Equation (4.2) can be used for the definition: FΦ = q

(4.2)

where F is a differential or integral operator; p is the excited electromagnetic wave signal; F is the unknown electromagnetic wave field function (such as electric field value, magnetic field value, electric potential energy or magnetic potential energy, etc.) to be solved. The boundary conditions can be Newman boundary conditions or Dirichlet boundary conditions, etc. In the process of electromagnetic field analysis, the wave properties of timeharmonic electromagnetic fields are always considered, which can be described by the Helmholtz electric field wave equation or Helmholtz magnetic field wave equation and defined by Eqs. (4.3) and (4.4), respectively.   ∇ × μr−1 ∇ × E(r ) − k0 εr E(r ) = − jk0 Z 0 J

(4.3)

  ∇ × μr−1 ∇ × H(r ) − k0 μr H(r ) = ∇ × εr−1 J

(4.4)

For passive devices, in Eqs. (4.3) and (4.4), J = 0. Therefore, the Helmholtz electric field wave equation or Helmholtz magnetic field wave equation is equivalent to the control equation of two high-frequency electromagnetic field problems, and the finite element method can be used for modeling and numerical simulation calculation.

4.2 Frequency Domain Finite Element Method (FD-FEM)

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At present, the most widely used boundary conditions are the perfect electric condition (PEC) and perfect magnetic condition (PMC). For a perfect electric wall, the boundary condition can be expressed as: nˆ × E(r ) = 0

(4.5)

For a perfect magnetic wall, the boundary condition can be expressed as: nˆ × ∇ × E(r ) = 0

(4.6)

After the boundary condition is set, the next operation is to solve the unknown electric field, magnetic field or other potential energy functions through the finite element method and numerical calculation. If the overall region of the device is complex, the entire problem region should be discretized and meshed, and then an approximate solution for each sub-domain mesh should be conducted according to Ritz variational method.

4.2.2 Steps of Frequency Domain Finite Element Method When the finite element method is used to solve the electromagnetic field boundary value problem, the steps shall be generally as follows: Step 1: Establish appropriate differential control equations and boundary conditions; Step 2: Discretize and mesh the target; Step 3: Select the basis function and weighting function and discretize the control equation into a linear equation set according to the Galerkin weighted residual method or Ritz variational method; Step 4: Eliminate unknown quantity on the boundary and solve the matrix equation to obtain the field distribution in the analyzed area; Step 5: Conduct post-processing to calculate the required parameters. Once the control equation and calculation solution region are determined, the simulation region of the device should be meshed and discretized. The method selected for this region discretization is very important. The mesh element quantity obtained varies greatly depending on the different mesh discretization methods. Too many meshes can lead to a large demand for computer memory, a long CPU computing time and an accuracy decline of numerical results, etc. For different types of devices, the finite element method can be used to select tetrahedrons, quadrangular pyramids, triangular prisms and hexahedrons, etc. to segment the meshes. The segmentation characteristics of various discrete meshes make the finite element method quite suitable for simulating arbitrary shape boundary problems. In CST microwave studios, the most used finite element discretization and segmentation method involves tetrahedron meshes, see Fig. 4.1.

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Fig. 4.1 Schematic diagram of finite element tetrahedron structure

After mesh segmentation, the interpolation function should be selected for establishing the finite element equation.

4.2.3 Simulation Algorithm Performance The time complexity of frequency domain simulation algorithms is proportional to the square of mesh points. When the electrical size of a structure is relatively big or complex, the quantity of mesh points will gradually increase. For 32-bit computers, the demand for memory will become large.

4.3 S-Parameter Model in Electromagnetic Field Calculation The metamaterial structure is composed of a cyclical metal SRR structure that is far shorter than the THz wavelength. The SRR openings provide most of the capacitance C. In addition, a small amount of capacitance is provided by the remaining space of the SRR. The Inductance L is provided between every two SRRs and the entire SRR planar array is equivalent to an LC oscillation circuit. The oscillation frequency of this equivalent LC circuit is: w0 =

1 √ 2π LC

(4.7)

When the electromagnetic wave passes through the planar cyclical structure and the frequency of the electromagnetic wave just meets the resonance frequency, this structure will resonate and the energy will be consumed in the structure, so the energy passing through the structure will become very low.

4.3 S-Parameter Model in Electromagnetic Field Calculation Fig. 4.2 S-parameter model of metamaterial transmission signal

Incident signal

Metamaterial device

53 Transmi tted signal

S21

In order to make a metamaterial adjustable to different THz frequencies, a semiconductor should be used as the substrate. When the THz wave irradiates the surface of the metamaterial, the carrier concentration in the semiconductor will change at the SRR openings, changing the Capacitance C, while the Inductance L is basically unchanged, meaning the Resonance Frequency w0 strongly depends on the Capacitance C. When the THz optical power increases, the carrier concentration and C will increase and w0 will decrease, performing a monotonic shift to a lower frequency. In order to make the frequency detection of the SRR planar array more sensitive and have broadband properties, the metal SRR can be made on GaAs and other semiconductor materials that are lossless or have a less loss within the THz band. When no any voltage is applied between the metal and semiconductor, the resonance frequency intensity of the SRR planar array will not be high. The depletion layer between the metal and semiconductor can be used to regulate the Capacitance C. When the metal planar array generates a reverse voltage with respect to the semiconductor, the depletion layer will thicken, enhancing the resonance amplitude, and modulating the bandwidth simultaneously through phase shifts. When designing an SRR structure, the Resonance Frequency w0 should be obtained, which can be calculated via the S-parameter model. When processing a high-frequency network, the S-parameter can be considered as a network parameter based on the relationship between the incident wave and reflected wave. The circuit network is described by the reflected signal of the device port and the signal transmitted from this port to another. S 21 is the most commonly used measurement parameter, see Fig. 4.2. Since the S-parameter is a complex number, the amplitude and phase can be obtained respectively. The key is solving S 21 (ω) defined in Eq. (4.8). |S21 (ω)| = |E t (ω)/E i (ω)|

(4.8)

where E t (ω) and E i (ω) are the transmission electric field and incident electric field, respectively. After the S 21 parameter is calculated, the transmission amplitude and phase of the corresponding electromagnetic wave field can be obtained, and then the entire forward electromagnetic wave transmission network can be characterized.

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4.4 Simulation Properties of Typical SRR Element Microstructure Metamaterials The metamaterial model has a three-layer structure. See Fig. 3.1a for the structural schematic diagram. In order to realize the Schottky contact between the metal SRR planar array and n-GaAs, the relevant material parameters are set below during simulation. The SRR element fabrication material of the top metamaterial is set as aurum (Au). According to the fabrication process, the thickness of this aurum layer is set as 200 nm, and its conductivity σ, 4.09 × 107 S/m. The thickness of n-GaAs in the intermediate layer is set as 1 μm according to the requirements of semiconductor fabrication process and metamaterials. The dielectric constant ε = 12.9, carrier concentration n = 1.9 × 1016 cm−3 .

4.4.1 Terahertz Transmission Properties of Typical Microstructure Pattern Metamaterials 1. Terahertz transmission properties of single-opening metamaterial structures The line width, opening and overall dimensions of the SRR microstructure shown in Fig. 4.3 are 4 μm, 3 μm and 36 μm, respectively. The single openings of SSRs are located in the center, which is equivalent to the butt-joint of two loops. According to the basic principle of equivalent circuit of transmission lines, the openings of this microstructure mainly provide Capacitance C, and the loop mainly provides Inductance L. Therefore, when the incident terahertz wave is coupled with this LC circuit, electromagnetic resonance will occur, which can greatly absorb, or sense, the incident terahertz signal. According to parameters such as line width, cyclical size, metal layer characteristic parameters, GaAs substrate of the SRR element structures shown in Fig. 4.3, the frequency domain finite element method is adopted to conduct a full wave electromagnetic field simulation within 0 ~ 2 THz and obtain the transmission properties of the metamaterial within the terahertz frequency band, as shown in Figs. 4.4 and 4.5. The single-opening SRR microstructure shown in Fig. 4.4 can sense incident electromagnetic waves of 1.28 THz. At this frequency point, the resonant electric field inside the SRR metal structure at the opening is quite obvious, and the current intensity along the inner edge of the loop is the highest. It can be seen from Fig. 4.5 that this single-opening SRR microstructure can sense the incident electromagnetic wave of 1.01 THz. At this frequency point, the resonant electric field inside the SRR metal structure at the opening is quite obvious, and the current intensity along the inner edge of the loop is the highest. The above results

4.4 Simulation Properties of Typical SRR Element Microstructure …

55

Fig. 4.3 Microstructure and size parameters of two square single-opening SRR elements. a Singleopening structure 1; b single-opening structure 2

indicate that the artificial metamaterial SRR microstructure can be used to sense terahertz waves. 2. Terahertz transmission properties of double-opening metamaterial structures Figure 4.6 shows five types of double-opening metamaterial structures. It can be seen from Fig. 4.6 that the opening distribution of the double-opening SRR microstructures is not uniform, some are in the middles, and some are at the edges. The equivalent Capacitance C and Inductance L of these SRR microstructures are similar to those of single-opening ones. Therefore, when the incident terahertz wave is coupled with the LC circuit, electromagnetic resonance will occur, which can greatly absorb or sense the incident terahertz signal. The finite element method is used for modeling and transmission property simulation. See Figs. 4.7, 4.8, 4.9, 4.10 and 4.11 respectively for the obtained results. It can be seen from Fig. 4.7 that the double-opening SRR microstructure can sense the incident electromagnetic wave of 1.828 THz. At this frequency point, the electric field, under the influence of the electric field polarization direction of the SRR structure at the vertical opening, is only obvious at the vertical opening, and the current intensity along the inner edge of the loop is the highest. It can be seen from Fig. 4.8 that the double-opening SRR microstructure can sense the incident electromagnetic wave of 0.694 THz. At this frequency point, the electric field of the SRR structure at the openings is quite obvious, and the current intensity along the inner edge of the loop is the highest. It can be seen from Fig. 4.9 that this double-opening SRR microstructure can sense the incident electromagnetic wave of 0.71 THz. At this frequency point, the electric field of the SRR structure at the openings is quite obvious and at its highest, and the current intensity along the inner edge of the loop is at its highest.

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(b)

Transmission intensity/dB

Transmission phase/degree

(a)

Freq./THz

Freq./THz

(c)

(e)

(d)

(f)

Fig. 4.4 Electromagnetic field simulation properties of single-opening structure 1 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 7513 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 1.28 THz frequency point; f current distribution of metal SRR surface at 1.28 THz frequency point

4.4 Simulation Properties of Typical SRR Element Microstructure …

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

57

Freq./THz

Freq./THz

(c)

(e)

(d)

(f)

Fig. 4.5 Electromagnetic field simulation properties of single-opening structure 2 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 7678 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 1.01 THz frequency point; f current distribution of metal SRR surface at 1.01 THz frequency point

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(a)

(b)

(c)

(d)

(e) Fig. 4.6 Microstructure and size parameters of five double-opening SRR elements with different shapes. a Double-opening structure 1; b double-opening structure 2; c double-opening structure 3; d double-opening structure 4; e double-opening structure 5

4.4 Simulation Properties of Typical SRR Element Microstructure …

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

59

Freq./THz

Freq./THz

(c)

(e)

(d)

(f)

Fig. 4.7 Electromagnetic field simulation properties of double-opening structure 1 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 8867 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 1.828 THz frequency point; f current distribution of metal SRR surface at the 1.828 THz frequency point

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(b)

Transmission intensity/dB

Transmission phase/degree

(a)

Freq./THz

(c)

(e)

Freq./THz

(d)

(f)

Fig. 4.8 Electromagnetic field simulation properties of double-opening structure 2 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 15,530 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 0.694 THz frequency point; f current distribution of metal SRR surface at 0.694 THz frequency point

4.4 Simulation Properties of Typical SRR Element Microstructure …

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

61

Freq./THz

Freq./THz

(c)

(e)

(d)

(f)

Fig. 4.9 Electromagnetic field simulation properties of double-opening structure 3 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 7397 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 0.71 THz frequency point; f current distribution of metal SRR surface at 0.71 THz frequency point

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4 Numerical Simulation of Metamaterials

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

Freq./THz

Freq./THz

(c)

(e)

(d)

(f)

Fig. 4.10 Electromagnetic field simulation properties of double-opening structure 4 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 1.836 THz frequency point; f current distribution of metal SRR surface at 1.836 THz frequency point

4.4 Simulation Properties of Typical SRR Element Microstructure …

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

63

Freq./THz

Freq./THz

(c)

(e)

(d)

(f)

Fig. 4.11 Electromagnetic field simulation properties of double-opening structure 5 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 10,583 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 1.766 THz frequency point; f current distribution of metal SRR surface at 1.766 THz frequency point

It can be seen from Fig. 4.10 that this double-opening SRR microstructure can sense the incident electromagnetic wave of 1.836 THz. At this frequency point, the electric field of the SRR structure near the openings is quite obvious and at its highest, and the current intensity along the inner edge of the loop is at its highest.

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It can be seen from Fig. 4.11 that this double-opening SRR microstructure can sense the incident electromagnetic wave of 1.766 THz. At this frequency point, the electric field of the SRR structure near the openings is quite obvious and at its highest, and the current intensity along the inner edge of the loop is at its highest. 3. Terahertz transmission properties of quadruple-opening metamaterial structures Figure 4.12 shows the quadruple-opening metamaterial structures.

Fig. 4.12 Microstructure and size parameters of four quadruple-opening SRR elements with different shapes. a Quadruple-opening structure 1; b quadruple-opening structure 2; c quadrupleopening structure 3; d quadruple-opening structure 4

4.4 Simulation Properties of Typical SRR Element Microstructure …

65

It can be seen from Fig. 4.12 that the opening distribution of the quadruple-opening SRR microstructures is not uniform, some are in the middles, and some are at the edges. The equivalent Capacitance C and Inductance L of these SRR microstructures are similar to those of single/double-opening ones. Therefore, when the incident terahertz wave is coupled with the LC circuit, electromagnetic resonance will occur, which can greatly absorb or sense the incident terahertz signal. The finite element method is used for modeling and transmission property simulation. See Figs. 4.13, 4.14, 4.15 and 4.16 respectively for the obtained results. It can be seen from Fig. 4.13 that the quadruple-opening SRR microstructure can sense the incident electromagnetic wave of 1.254 THz. At this frequency point, the resonant electric field of the SRR structure, influenced by the polarization direction, is quite obvious and at its highest at the horizontal openings, and the current intensity along the inner edge of the loop is at its highest. It can be seen from Fig. 4.14 that this quadruple-opening SRR microstructure can sense the incident electromagnetic wave of 1.028 THz. At this frequency point, the resonant electric field of the SRR structure near the four openings is quite obvious and at its highest, and the current intensity along the inner edge of the loop is at its highest. It can be seen from Fig. 4.15 that this quadruple-opening SRR microstructure can sense the incident electromagnetic wave of 1.306 THz. At this frequency point, the resonant electric field of the SRR structure near the four openings is quite obvious and at its highest, and the current intensity along the inner edge of the loop is at its highest. It can be seen from Fig. 4.16 that this quadruple-opening SRR microstructure can sense the incident electromagnetic wave of 1.362 THz. At this frequency point, the resonant electric field of the SRR structure near the four openings is quite obvious and at its highest, and the current intensity along the inner edge of the loop is at its highest. 4. Terahertz transmission properties of cascaded metamaterial structures Figure 4.17 shows two types of cascaded SRR metamaterial structures. It can be seen from Fig. 4.17 that the opening distribution of the cascaded SRR microstructures is not uniform, some are in the middles, and some are at the edges. The equivalent Capacitance C and Inductance L of these SRR microstructures are similar to those of single/double-opening ones. Therefore, when the incident terahertz wave is coupled with the LC circuit, electromagnetic resonance will occur, which can greatly absorb or sense the incident terahertz signal. The finite element method is used for modeling and transmission property simulation. See Figs. 4.18 and 4.19 respectively for the obtained results. It can be seen from Fig. 4.18 that this SRR microstructure can sense the incident electromagnetic wave of 0.474 THz. At this frequency point, the resonant electric field of the SRR structure near the openings is quite obvious and at its highest, and the current intensity along the inner edge of the loop is at its highest. It can be seen from Fig. 4.19 that this SRR microstructure can sense the incident electromagnetic wave of 2.205 THz. At this frequency point, the resonant electric

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4 Numerical Simulation of Metamaterials

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

Freq./THz

Freq./THz

(c)

(e)

(d)

(f)

Fig. 4.13 Electromagnetic field simulation properties of quadruple-opening structure 1 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 5795 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 1.254 THz frequency point; f current distribution of metal SRR surface at 1.254 THz frequency point

4.4 Simulation Properties of Typical SRR Element Microstructure …

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

67

Freq./THz

Freq./THz

(c)

(e)

(d)

(f)

Fig. 4.14 Electromagnetic field simulation properties of quadruple-opening structure 2 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 4304 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 1.028 THz frequency point; f current distribution of metal SRR surface at the 1.028 THz frequency point

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4 Numerical Simulation of Metamaterials

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

Freq./THz

Freq./THz

(c)

(e)

(d)

(f)

Fig. 4.15 Electromagnetic field simulation properties of quadruple-opening structure 3 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 10,542 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 1.306 THz frequency point; f current distribution of metal SRR surface at the 1.306 THz frequency point

4.4 Simulation Properties of Typical SRR Element Microstructure …

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

69

Freq./THz

Freq./THz

(a)

(e)

(d)

(f)

Fig. 4.16 Electromagnetic field simulation properties of quadruple-opening structure 4 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 6100 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 1.362 THz frequency point; f current distribution of metal SRR surface at the 1.362 THz frequency point

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(a)

(b) Fig. 4.17 Microstructure and size parameters of two cascaded SRR elements with different shapes. a Cascaded structure 1; b cascaded structure 2

field of the SRR structure near the openings is quite obvious and at its highest, and the current intensity along the inner edge of the loop is at its highest.

4.4.2 Influence of Opening Size on Resonance Characteristics Figure 4.20 shows a typical single-opening microstructure. 3 and 4 in Fig. 4.21 mean that the size of the middle opening shown in Fig. 4.20 is set to 3 μm and 4 μm, respectively. It can be seen that when the line width of the SRR element structure is fixed, the capacitance provided at the opening decreases as the opening of the gap increases, and the equivalent LC resonance frequency

4.4 Simulation Properties of Typical SRR Element Microstructure …

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

71

Freq./THz

Freq./THz

(c)

(e)

(d)

(f)

Fig. 4.18 Electromagnetic field simulation properties of cascaded structure 1 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 8633 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 0.474 THz frequency point; f current distribution of metal SRR surface at 0.474 THz frequency point

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4 Numerical Simulation of Metamaterials

(b)

Transmission intensity/dB

Transmission phase/degree

(a)

Freq./THz

(c)

(e)

Freq./THz

(d)

(f)

Fig. 4.19 Electromagnetic field simulation properties of cascaded structure 2 within 0 ~ 2 THz. a Metamaterial 3D device model; b finite element mesh generation model with 12,284 tetrahedrons; c terahertz transmission intensity simulation; d terahertz transmission phase simulation; e resonant electric field distribution at 2.205 THz frequency point; f current distribution of metal SRR surface at the 2.205 THz frequency point

increases. Therefore, its resonant induction frequency to the incident THz wave gradually increases gradually.

4.4 Simulation Properties of Typical SRR Element Microstructure …

73

Fig. 4.20 Single-opening (3 μm) microstructure diagram

Fig. 4.21 Terahertz transmission properties under a line width of 4 μm and openings of 3 and 4 μm

4.4.3 Influence of Line Width on Resonance Frequency Figure 4.22 shows a typical double-opening microstructure. 4 and 6 in Figs. 4.23 and 4.24 mean that the SRR line width in Fig. 4.22 is set to 4 μm and 6 μm, respectively. It can be seen from Figs. 4.23 and 4.24 that when the opening size of the SRR element structure is fixed, with the increase of the line width, the split-ring region inside the SRR structure will become smaller, the inductance provided by the loop becomes lower, and the equivalent LC resonance frequency increases accordingly. Therefore, its resonant induction frequency to the incident THz wave gradually increases gradually.

74 Fig. 4.22 Double-opening SRR microstructure with a line width of 4 μm

Fig. 4.23 Terahertz transmission simulation under a double-opening of 3 μm and line width of 4 and 6 μm for SRR microstructure

Fig. 4.24 Terahertz transmission simulation under a double-opening of 4 μm and line width of 4 and 6 μm for SRR microstructure

4 Numerical Simulation of Metamaterials

4.5 Summary

75

4.5 Summary The resonant induction capability of an artificial metamaterial constructed with SRR microstructure pattern to the electromagnetic wave field is restricted by factors such as the properties and coupling behavior of the electrode and substrate materials, the shape, structure size and arrangement of induction gaps, the concentration, energy state, migration behavior and mode of carriers of the substrate material controlled by bias voltage, the influence of the electromagnetic form of an incident wave on the refractive index, dielectric coefficient and permeability of the substrate material, the high frequency inductance and capacitance effect between dipole structures, the sensed controlled signal and incident wave field seriously affecting the interelectrode and surface barrier, especially the Schottky barrier, as well as the gain mode and degree of the induction signal. The expected electrically controlled resonance induction efficiency and high gain induction signal, etc. are influenced and restricted by the electromagnetic properties of materials, devices and wave fields, the electronic configuration, the driving mode and behavior of devices and the environmental factors, etc. By synthesizing ➀ the shape, arrangement, line width, number of openings, size and period related to SRR microstructure elements, ➁ the dielectric constant, thickness and conductivity related to metal materials, ➂ the electronic concentration, dielectric constant and Drude model parameters related to semiconductor substrate GaAs materials, ➃ the boundary conditions and polarization conditions of the incident wave fields as the simulation model parameters of metamaterial devices and conducing numerical simulation calculations for the above parameters based on the frequency domain finite element method, it is found that the metamaterial device constructed by metal SRR array can be used to sense the incident terahertz wave, and at the resonance frequency point, the maximum value of the resonant electric field appears at the opening gap of the SRR element structure, indicating that the SRR array absorbs the power radiated by the incident terahertz wave, which is converted into electromagnetic resonance. This conversion effect can be expressed by the S-parameter intensity and phase curves.

Chapter 5

Design and Fabrication of Metamaterial Devices

Metal SRR microstructures can sense the incident electromagnetic wave fields through resonance. In order to control the SRR arrays as comprehensively as possible, it is necessary to make SRR structures into artificial metamaterial devices in a scientific and reasonable way. The resonance induction capability of electrically controlled artificial metamaterial micro/nano pattern structures to the electromagnetic wave fields is restricted by many factors. The expected electrically controlled resonance induction efficiency and high gain induction signal, etc. are influenced and restricted by the material, device and electronic configuration, etc. Therefore, exploring an optimal semiconductor fabrication process is prerequisite to ensuring the performance of metamaterial devices. According to the photolithography of the microelectronic integrated semiconductor manufacturing technology, micrometer-level SRR structures can be transferred to semiconductor substrate materials to make metal electrodes. After repeated experiments and tests, the researchers involved in this book proposed a micro/nano process and key technology for Schottky metamaterials for layout design and device fabrication of metamaterials. This chapter will focus on the design and fabrication methods of artificial metamaterials, discuss the materials required for preparation and their working principles, and finally detail the device fabrication scheme that meets the expected requirements.

5.1 Semiconductor Based Metamaterials In recent years, in-depth research on terahertz band applications, such as terahertz filters, terahertz short-range communications, terahertz antennas, terahertz detectors, etc. have been made. A lot of work has been done in terahertz detection and induction research, but more progress is still needed, such as developing quick and highly sensitive detectors suitable for the terahertz band, so as to provide a method for new signal detection. © National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_5

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A metamaterial is usually composed of a cyclical metal SRR array and a semiconductor material. The cyclical SRR array has a certain resonant electromagnetic response, which can be utilized to design energy absorbing or sensing devices. Ideally, a terahertz sensor array can help to convert the continuous terahertz wave into an array electrical signal by appropriate means. The accurate measurement of this electrical signal is related to the terahertz power actually absorbed. The existing research shows that an incident terahertz wave passing vertically through an SRR array of a specific shape causes a self-excited magnetic resonance in electrons. The capability of the metamaterial in absorbing terahertz wave in the resonance process is related to the SRR microstructure and its pattern configuration. Semiconductors such as Si, GaAs, etc. are used as substrate materials in the fabrication method and process of metamaterials. Electrodes with metal patterns are made on the corresponding substrates to allow metal–semiconductor contact. The related principles of metal–semiconductor contact are discussed first below. 1. Semiconductor substrate The most commonly used semiconductors are single crystals of diamond lattices (Ge and Si) and zinc blende lattices (GaAs). Both the lattices can be regarded as being constructed of two nesting face-centric cubic sublattices. One sublattice can move along the diagonal of the cube by 1/4 of the length to replace the other. All atoms in the diamond lattice are the same, and each atom is bordered by four adjacent atoms belonging to other face centered sublattices, forming a tetrahedron, and shares four external electrons of the adjacent atoms, forming a covalent bond. Compared with other materials, semiconductors have some excellent properties which make them suitable for high-frequency electromagnetic wave detection. Si, as a very important material for transistors and microelectronic circuits, is popular in the design and manufacture of detectors. Detector-electronic-circuit integration is the basic idea for signal detection. Ge, Si and GaAs are currently popular semiconductor materials. Ge and Si are indirect semiconductors. Ge, with its shorter radiation length, has a band gap twice as that of Si. Ge is suitable for X-ray and near-infrared detection, however, considering the possibility of band-to-band excitation at room temperature and the high pulldown current, special refrigeration equipment is required for detectors made of Ge. Si is widely used in the electronic industry thanks to its mature semiconductor manufacturing technology. GaAs is a kind of direct semiconductor with a high electron mobility. It is popular in ultrahigh-speed electronic circuit devices and suitable for infrared, far infrared, terahertz and even millimeter wave detection. The high-speed and high mobility of GaAs allow it to be used in making optical frequency—RF integrated detectors. 2. Semiconductor doping Semiconductor doping means adding a small amount of foreign atoms. This doping can be conducted through crystal growth processing. These doped atoms, as interstitial ones, are squeezed among normal lattices, causing distortion of the local lattices and their chemical structures. Doping in the crystal means replacing a small amount

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of the original crystal atoms with doped atoms, which can only result in a light lattice distortion, not a change of the chemical binding form of the lattice. Doped atoms are embedded in the normal lattice position by heating the crystal after ion implantation, which is called “activation”. In Group IV semiconductors (Ge and Si), doping with Group III elements can produce shallow acceptors, while doping with Group V elements can produce shallow donors. In Group III–V compound semiconductors, shallow donors and shallow acceptors can be produced by doping Group IV elements. For Si and Ge, a standard doping acceptor is B, and the doping donor is P and As; For GaAs, elements Se, Si and S are used for N-type doping, while elements Zn, Cd, Be and Mg, for P-type doping. 3. Schottky contact Generally, the Schottky barrier resulting from metal–semiconductor contact has typical rectification characteristics. In the past, the fabrication method was to press a metal line on the surface of a semiconductor. After the innovation of microelectronics technology, the current metal–semiconductor contact is realized by the planar process. The function of metal–semiconductor contact can be explained by an energy band model. Metal conductors are different from semiconductors with partially filled conduction bands. 50% of the Fermi level in a metal can enter the conduction band, so there are many effective carriers in the metal, and at this time, the internal electric field of the metal under static conditions can be considered as zero. Assume that the work function qΦ is the energy required to move the electrons from the Fermi level to a vacuum. Φ m is the work function of a metal, and Φ s is the work function of a semiconductor. The value of Φ m is dependent on the type of the metal, and the value of Φ s is dependent on its doping concentration. The Electron Affinity qx is the difference between the conduction band edge and the vacuum energy level. When Φ m > Φ s , the contact between metal and the N-type semiconductor will have rectification properties. When the metal contacts the semiconductor, an electric potential difference will be formed on the contact surface, which can be defined by Eq. (5.1): Vbi = Φm − Φs

(5.1)

This potential difference makes the energy band near the contact interface bend. The carrier redistribution in the semiconductor makes all points meet the thermal equilibrium conditions, and the surface charge of the metal is positively charged by the space charge in the semiconductor boundary region. The height of the Schottky barrier being equal to the threshold value of the work function required for an electron with an average energy in the metal to reach the semiconductor region is defined by Eq. (5.2): qΦBn = q(Φm − χ )

(5.2)

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Schottky diodes are made based on the principle of metal–semiconductor junctions formed by metal–semiconductor contact, which are also called metal–semiconductor (contact) diodes or surface barrier diodes, and have advantages such as low power consumption, high current and ultra-high speed. For a Schottky diode, the reverse recovery time is very short (can be as short as a few nanoseconds), the forward conduction voltage drop is only about 0.4 V, while the rectified current can reach thousands of amperes. The Schottky diode usually uses noble metals (such as gold, silver and platinum, etc.) as Schottky electrodes and N or N+ type semiconductors as ohmic electrodes. Since the electronic concentration of the semiconductor layer after N-type doping is high, and the distribution of free electrons in the metal is very low, electrons will diffuse from the semiconductor layer with high concentration to the metal layer with low concentration within the region where the metal contacts the semiconductor. Physically, there are not any holes in metals, so there is no diffusion of holes from the semiconductor layer. With the continuous diffusion of electrons from the semiconductor to the metal, the surface electrical neutrality will be destroyed, so a potential barrier will be formed with the electric field direction of the semiconductor pointing to the metal. However, under this electric field, the electrons in the metal will also drift from the metal to the semiconductor, weakening the electric field formed by diffusion. When a spatially charged region with a certain width is established, the electron drift motion caused by the electric field and the electron diffusion motion caused by different concentrations will reach a relative balance, forming a Schottky barrier. When a positive bias voltage is applied at both ends of the Schottky barrier, the Schottky barrier will be narrow and its internal resistance will be low; On the contrary, when a reverse bias is applied at both ends of the Schottky barrier, the Schottky barrier will be wide and its internal resistance will be high. Metal conductors have a lot of conductive electrons. When a metal contacts a semiconductor (the distance between them is only the magnitude order of an atomic size), the Fermi level of the metal will be lower than that of the semiconductor. For the subenergy-level inside the metal corresponding to the semiconductor conduction band, the electron density is lower than that of the semiconductor conduction band. Therefore, after they contact one another, electrons will diffuse from the semiconductor to the metal, making the metal negatively charged and the semiconductor positively charged. Since metal is an ideal conductor, the negative charge is only distributed in a thin layer with an atomic surface area. For an N-type semiconductor, the donor impurity atoms that lose electrons become positive ions, which are distributed in a thicker range. The diffusion of electrons from the semiconductor to the metal leads to the formation of a space charge region, a built-in electric field and a potential barrier, and the depletion layer is only on the side of the N-type semiconductor (the entire potential barrier region is on the side of the semiconductor). The direction of the built-in electric field in the barrier region points from the N-type region to the metal. With the enhancement of the built-in field after thermionic emission, the drift current opposite to the direction of the diffusion current increases, and finally reaches a dynamic equilibrium, forming a contact barrier between the metal and the semiconductor, namely the Schottky barrier.

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Fig. 5.1 Charge distribution

Metal

— — —

+ + +

N-type semicondu ctor

W0 When the applied voltage is zero, the diffusion current of the electrons will be equal to the reverse drift current, reaching a dynamic equilibrium. When a positive bias voltage is applied (namely a positive voltage is applied to the metal, and a negative voltage is applied to the semiconductor), the built-in field will be weakened, and the potential barrier on the side of the semiconductor will lowered, forming a positive current from the metal to the semiconductor. When a reverse bias is applied, the built-in field will be enhanced and the barrier height will be higher, forming a low reverse current from the semiconductor to the metal. Therefore, SBD, like a PN junction diode, is a nonlinear device with unidirectional conductivity. For an N-type semiconductor (such as the N-type doped GaAs), the charge distribution is shown in Fig. 5.1. The spatially charged region generates the Built-In Electric Field E, which is directed from the N-type semiconductor to the metal. This electric field can be expressed by the following 1D Poisson equation: ε

dE = eND dx

(5.3)

where E is the dielectric constant of the semiconductor; e is the electric quantity of electrons; N D is the doping concentration of the N-type semiconductor. The electric field distribution of the metal–semiconductor junction is: E i (x) =

eND (x − W0 ) ε

(5.4)

where W 0 is the width of the depletion layer, and the potential is expressed by the following equation: x ϕ(x) = −

E i (x)dx

(5.5)

0

Then the potential distribution is expressed by the following equation: ϕ(x) =

eND (x − W0 )2 2ε

(5.6)

When x = 0, the potential will become the contact potential difference or the builtin potential difference of the metal–semiconductor junction. A Schottky barrier can

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be generated when the metal contacts N-type or P-type semiconductors. Regarding the actual fabrication, considering that the mobility of electrons is much higher than that of holes, it is easier to achieve good device performance. Therefore, the N-type semiconductor is generally used as the wafer substrate material to make detection devices. 4. Ohmic contact Ohmic contact refers to a metal–semiconductor contact that is negligible compared with a semiconductor resistance or series resistance. Generally, the current generated by metal–semiconductor contact mainly comes from thermionic emission. When the doping concentration of the semiconductor reaches 1018 cm−3 or above 1019 cm−3 , the barrier width of the contact surface will become very narrow, at this time the tunneling effect will become very important and the characteristic resistance of the metal–semiconductor contact will be very low, leading to ohmic contact. Once ohmic contact occurs, the contact surface will not have a rectification effect, and its current and voltage will be provided with linear characteristics.

5.2 Key Fabrication Process of Metamaterials Among the various semiconductor-microelectronics integrated fabrication technologies, photolithography can help to etch the pattern configuration of micro/nano structures onto the substrate material by optical exposure according to the optical replication method, thus providing a basis for making complex circuits. The substrate materials used in the photolithography can be semiconductors, insulating mediums and metals, etc. Since its inception in 1959, this technology has been widely used in the production processes of integrated circuit chip processing and semiconductor pattern configuration, etc. Photolithography-based patterns and electronic configuration have become key indicators in determining the performance of semiconductor integrated circuits. So far, most of the micro/nano fabricating processes of integrated circuits are subject to photolithography, therefore, photolithography has become the most important and critical technology in microelectronic integrated processing technology. At present, metamaterial pattern element arrays are generally made through projection photolithography. The composition of this photolithography system is shown in Fig. 5.2. In Fig. 5.2, the light source is generally a UV light source with short wavelength, which is suitable for the photolithography of microstructure array elements. The exposure mode shown in the figure is a repeated distribution projection, namely a group of cyclical patterns that can be repeated hundreds of times on the substrate of a semiconductor. The indexes for evaluating photolithographed pattern quality include resolution, line width alignment accuracy and yield rate, etc. In order to obtain high-quality

5.2 Key Fabrication Process of Metamaterials

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Substrate

Spin-coating

Substrate

Substrate Development

Electron beam lithography

photolithography Substrate ICP Etching

Plasma

Pattern transfer

Metal

Metal evaporation

Substrate Substrate Photoresist stripping and SEM observation Fig. 5.2 Components of projection photolithography system

pattern arrays through photolithography, it is necessary to carry out a preliminary design on the exposure system, exposure mode, photolithographic mask, photoresistancy and etching method to determine the best scheme. During the application of photolithography, the photoresist is coated on the substrate surface, and then the photoresist area is irradiated by a light source with a specific wavelength. Two types of photoresist, namely photonic/anti-etching photoresist—the so-called positive photoresist and negative photoresist—are often used. In the positive photoresist process, after the light source irradiates positive photoresist through the mask, the exposed area will be dissolved in the developer, leaving an unexposed photoresist layer. In the negative photoresist process, the exposed area will not be dissolved in the developer, on the contrary, the unexposed area will be dissolved. After developer processing, the pre-designed photolithographed pattern and its configuration can be retained. The photolithography process is complicated and has many steps, so each step must be conducted carefully and with caution for the sake of the final product. The photolithography process for semiconductor processing mainly includes the following steps.

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5.2.1 Cleaning and Film-Formation Before photolithography, preparations such as cleaning, dehydration and surface film-formation of the substrate are required in order to enhance the adhesion between the substrate material and the subsequently coated photoresist. The substrate surface after SiO2 growth is an insulator, which is liable to the accumulation of electrostatic charges and adsorption of fine dust in the air. These fine interfering particles will affect the adhesion and airtightness of the subsequent photoresist. Once the interfering particles attach to the SiO2 surface, the photoresist layer will thicken, causing errors in the photolithographic exposure, resulting in insufficient exposure and residual photoresist material after development. In addition, the effective stripping of patterned electrodes in the subsequent etching process will be affected. Therefore, a successful cleaning is the basic requirement of the entire photolithography process. See Fig. 5.3 for a full automatic ultrasonic cleaner. The substrate cleaning method can be divided into two types: dry cleaning and wet cleaning. The dry cleaning process converts the oxygen in a space into ozone through ultraviolet or far ultraviolet radiation, and then generates active oxygen radicals to remove the organic impurities on the surface of the substrate. The wet cleaning process includes brushing, ultrasonic cleaning, high-pressure flushing and chemical solution cleaning, etc. The brushing method uses a cylinder brush dipped with a certain amount of cleaning agent, which is rubbedback and forth on the hard substrate surface to remove the fine ash layer and particles. The brushing method generally does not allow direct contact with the metal pattern array. The most feasible way to accomplish this is to place the cylinder brush near or above the substrate and rotate it to generate water flow for cleaning. The high pressure flushing method is to spray or flush the substrate surface with high pressure water flow to remove particles with low adhesion. However, considering the high strength and speed of the water flow, metal arrays with a nanometer-level thickness may be damaged, for example by breaking the connecting line and shedding in metallic areas. Therefore, in order to prevent the metal pattern electrode of the photolithographed microstructure from being damaged, Fig. 5.3 Full automatic ultrasonic cleaner

5.2 Key Fabrication Process of Metamaterials

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Fig. 5.4 Cleaning operation platform

organic solvent such as deionized water is always used in combination with ultrasonic cleaning during the wet cleaning process. The deionized water can be used to remove ions of electrically active salts through specially made ion exchange resin. This process transforms the water from a conductive medium to a resistive medium with a resistivity of 18 M/cm at room temperature, which, to the greatest extent, can help to remove dirty objects such as organic substances attached to the substrate surface. The industrial standard Si wafer wet cleaning process refers to the RCA process: SC1 solution NH4 OH:H2 O2 :5H2 O and SC2 solution HCl:H2 O2 :6H2 O. When using the ultrasonic cleaning method, the sound energy of the ultrasonic waves is utilized to subject the cleaning solution to a low-frequency vibration, removing the small particles scattered on the surface of the substrate with weak adhesion. After cleaning, it is necessary to dehydrate and dry the substrate in a closed oven to ensure that the surface is clean and dry without stains and traces. After the substrate is dried, HMDS is used for surface film-forming treatment as required to enhance the adhesion of the surface. Figure 5.4 shows a common operation platform.

5.2.2 Photoresist Coating After the surface film-formation treatment, the substrate surface should be evenly coated with liquid photoresist. Figure 5.5 shows a programmable desktop homogenizer. Photoresist is generally composed of aldehyde resin, photosensitive material, viscosity solvents and additives, etc. There are two ways to apply photoresist: rotary coating and slit coating. Because the substrate used in experiments is a 2 or 4 GaAs wafer with a circular structure and a thickness of less than 1 mm, rotary coating is the most reliable method. When applying photoresist, place the GaAs substrate on the suction cup of the rotary platform, which is a horizontally placed metal or PTFE tray with a large number of vacuum pores distributed on its surface for adsorbing devices on the

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Fig. 5.5 Programmable desktop homogenizer

substrate; Then use a pipette to absorb a certain amount of liquid photoresist and gently drop it on the substrate surface. Coat the photoresist evenly on the substrate surface according to the set rotating speed (e.g. 1000 rpm for 60 s) of the suction cup. This photoresist coating method is quite easy, but the film may be damaged due to the high-speed rotation. Therefore, this method is more suitable for smaller GaAs or other similar substrates. Different photoresists shall be used for coating according to the function and process requirements of the fabricated devices. The model of the photoresist should be determined prior to photoresist coating. According to the exposure requirements and developer properties, the photoresist includes positive photoresist and negative photoresist. The exposed area of the positive photoresist can be dissolved by the corresponding developer, and the unexposed area of the negative photoresist can be dissolved by the corresponding developer. During application of the photoresist, since the thickness and uniformity of the photoresist can affect light scattering and diffuse reflections generated by the device surface during exposure, the amount of photoresist coated, the coating time and the coating speed, etc. should be calculated in advance for the sake of a higher electrode pattern accuracy after photolithography. After rotary coating, a microscope shall be used to check for defects such as uneven coating, particle adhesion and pinhole gaps, so as to ensure a good photoresist coating. If problems exist, correction work can be done or the surface recoated with photoresist until it meets the requirements of subsequent photolithography.

5.2.3 Soft Baking The substrate surface after rotary coating should be subject to soft baking, primarily to remove the chemical solvent components of the photoresist. The adhesion of the substrate can be further enhanced after soft baking, and the uniformity of the photoresist on the substrate can also be improved, which can help to facilitate the subsequent precision control of line width. A common soft baking operation is to

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87

keep the temperature at 100 °C for 5 min in an electric heating oven, and then slowly cool off from the heating oven. The quality of the coated photoresist substrate after soft baking is uniform.

5.2.4 Alignment and Exposure Before the optical exposure of multi-layer photomask nesting, the corresponding photomask of each layer should be aligned with that of the previous layer or those of the previous layers. The accuracy of the alignment mark determines the accuracy of the metal electrode pattern after nesting exposure. Figure 5.6 shows a photolithography layout alignment mark designed by the author. If there is a micrometer-level difference during alignment, the electrode pattern after nesting may deviate from the original position, resulting in defects such as fractures or gaps in the electrode pattern. After the multi-layer photomask is aligned, the microstructure array pattern on the mask will be transferred to the photoresist-coated device substrate through the exposure operation of the mask aligner. Figure 5.7 shows a typical UV mask aligner and its control system. Ultraviolet Light (UV-L) forms parallel light rays when irradiating a plane reflector, then irradiates vertically on the photomask. When the positive photoresist is selected, because the device surface coated with the positive photoresist is close to the array pattern on the photomask, the ultraviolet light will penetrate the patternless mask area of the photolithography layout, as shown in Fig. 5.8. The corresponding positive photoresist area will have a chemical reaction under ultraviolet radiation, which will be dissolved by the developer during development, retaining the corresponding pattern electrode array on the photomask. During exposure, appropriate environmental conditions shall be considered, for example, the mask aligner should be preheated before use; White light sources should not be used during operation, appropriate exposure time should be used to prevent the edge of the photolithography electrode pattern from being blurred or deformed by overexposure or underexposure. Fig. 5.6 Alignment mark of photomask

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5 Design and Fabrication of Metamaterial Devices

Fig. 5.7 Control system of a typical UV mask aligner Light source

photomask

Miniature lens

Wafer to be exposed

Fig. 5.8 Schematic of UV-L photolithography

5.2.5 Post Exposure Bake (PEB) Once the photoresist is exposed, it is sometimes necessary to bake it in a closed oven. Since this is a baking operation done immediately after exposure, this step is also called “post exposure baking (PEB)”. The PEB temperature is generally about 100 °C, which aims to reduce the standing wave effect of micro/nano structure patterns during the optical exposure process. At the same time, high temperature

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89

baking stimulates and enhances the acid substance produced by the photo acid generator (PAG) component of the photoresist. This acid substance will have a chemical reaction with the protective groups of the photoresist, dissolving these protective groups in the developer.

5.2.6 Development Developing is the key step of pattern configuration after photoresist exposure. The chemical composition of the developer dissolves the soluble part of the photoresist, leaving the undissolved area as the required electrode pattern. Common development operations are spray and immersion modes. The immersion development is adopted for making metamaterials. When development is required, a pair of tweezers is used to clamp one end of the device with GaAs substrate, immerse it in the developer, and slowly rotate the solution at a small angle. In experiments, the proportion concentration and development time in relation to the developer should be strictly controlled. After development, the device shall be washed with deionized water until the surface is free of impurities and dried with high-speed nitrogen. The developer and photoresist are acquired together, so the control of development time is crucial. If the development operation is improper or takes too long, the edge of the unexposed part will be dissolved and damaged from the outside to the inside, resulting in unclear pattern edges or even gaps caused by the broken edge. If the development time is too short, the exposed area will not be completely dissolved and the photoresist will be left unprocessed, affecting the accuracy of subsequent etching and stripping, etc.

5.2.7 Hardening In order to further volatilize and remove the small amount of photoresist solvent remaining on the device surface and enhance the adhesion of photoresist on the device surface, the device should be immediately placed in a closed oven after development to dry and stabilize the photoresist. A common hardening operation is to place the device in a closed oven. The hardening temperature is higher than that of soft baking. If the soft baking temperature is 100 °C, the hardening temperature should be set to at least 110 °C, and the baking time should be longer. During hardening, the pattern configuration of the device surface should be carefully protected. Device hardening is the basic requirement for subsequent operations such as corrosion, electron beam evaporation and ion implantation.

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5 Design and Fabrication of Metamaterial Devices

5.2.8 Etching Etching, also known as corrosion, is done to dissolve the area without photoresist and leave the required pattern as the electrode. In this step, a certain concentration of acid or alkaline solution is usually used to etch the device. Etching includes dry and wet methods. Dry etching is a method that makes ionic groups or active groups in plasma chemically react with materials to etch the corresponding areas. This method is not suitable for experiments; therefore, wet etching is adopted in the preparation of metamaterials. Wet etching can also be divided into spray and immersion methods. The spray method aims to spray the etching solvent, continuously etching the device surface through rapid flow of the liquid. This method is not time-consuming, but the accuracy is hard to control, and is sometimes liable to damaging the surface pattern of the device due to flushing. The immersion method aims to clamp one end of the device with tweezers and gently immerse it into the etching solution; once the set etching time is complete, the device is then removed. Too short an etching time will cause the area to be removed undissolved. If the etching takes too long, then the pattern will be damaged. Therefore, the etching time for experiments should depend on the thickness of the surface SiO2 or metal film.

5.2.9 Photolithography Inspection This inspection generally focuses on the difficulties encountered during the aforementioned process in order to further determine the quality of the electrode pattern after photoresist development, and describes the performance of the photolithography process, such as whether the line width, edge and spacing, etc. have reached the expected goals. This inspection method can be automatically implemented for highly integrated automation systems. The correct implementation of the photolithography process is to ensure that the product is free of defects after exposure. During the inspection, if any defect of the device is found, the photoresist can also be removed according to the related method to restore the device to the state it was in before photolithography. At this time, the device can be reworked. If no inspection is carried out or the inspection is not carried out carefully, defects such as impurities or edge fractures may be created in the photoresist, and the fabricated device may be an irreversibly defective one after beginning the next phase of the process, which is not conducive to the development of subsequent experiments. Therefore, timely discovering problems and making immediate corrections can help in the adoption of the most appropriate device photolithography method, while also improving the quality of devices.

5.3 Layout Characteristics of Planar Metamaterial Detectors Based …

91

Fig. 5.9 Grinding wheel wafer cutter

5.2.10 Wafer Cutting Figure 5.9 shows a typical grinding wheel cutting system that can cut wafers up to 4 in. into multiple devices of different shapes and sizes.

5.2.11 Pressure Welding A pressure welder is usually used for electrode welding. An Au line with a diameter of 25 µm can be selected as the welding wire, and the area of welding spot is usually 100 µm2 .

5.3 Layout Characteristics of Planar Metamaterial Detectors Based on Micro/Nano Semiconductor Processes Many processes and methods can be used to make metamaterials, among them, metamaterials with Schottky diode structures are provided with more control functions for incident electromagnetic waves. Through the repeated implementation of the

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Schottky diode fabrication process, the existing research has established theoretical and process models of artificial micro/nano metamaterial structures, including key pattern shapes, structural parameters and electronic configurations; By optimizing the layout design of micro/nano structures, a complete set of layout design methods and models, covering far-infrared to millimeter waves, can be realized. Based on this technical scheme, artificial metamaterials for sensing far-infrared to millimeter waves can be integrated into a chip. Figure 5.10 shows an overall design layout after planning and layout on a 4 substrate. The metamaterial device is implemented through a 4-layer nesting layout. Figure 5.11 shows the layout design of a single device, and the meaning of each layer is as below. The first, second, third and fourth layers are used to make round ohmic electrode openings, round ohmic electrodes, SRR array openings and Schottky electrodes, respectively. The fourth layer, from left to right, is an SRR array, parallel line and square metal electrode.

Fig. 5.10 Total layout of metamaterial device

5.4 Typical Process Flow of Schottky Metamaterials

93

Ohmic electrode

Ohmic electrode opening

SRR array

Metal electrode

Fig. 5.11 Layout of a single device

5.4 Typical Process Flow of Schottky Metamaterials In order to completely describe the metamaterial process flow for making GaAs substrate Schottky diodes, the detailed steps of each stage according to the process sequence in combination with the actual situation is shown below. Step 1: Design the layout first, which is a four-layer photomask. Step 2: Clean the n-GaAs epitaxial wafer and ensure that the surface is free of stains and water traces through microscope observation. Step 3: Grow a 300 nm thick SiO2 layer on the epitaxial wafer based on the PECVD method to ensure a uniform surface. This layer is mainly used for insulating. Step 4: The first photolithography: Adopt the positive photoresist process to photolithograph ohmic electrode contact openings. Adhesive baking: 140 °C, 20 min; Coating: Photoresist model: 6130, Coating thickness: 1.8 µm, Rotational speed of homogenizer: 3000 rpm; Soft baking: 105 °C for 5 min; Exposure: UV mode for 15 s; Development: Developer proportion: 1:4; Hardening: 115 °C for 20 min; Bottom film removal: O2 flow: 300 L/m for 1 min; power: 200 W. Step 5: Wet etching of SiO2 : BOE is used as the etchant for etching at room temperature for 50 s, respectively. Step 6: Perform an organic cleaning for the substrate after the first photolithography and ensure that the surface is free of stains and water traces through microscope observation. Step 7: The second photolithography: Adopt the negative photoresist process to photolithograph the ohmic electrode.

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Coating: Photoresist model: 4620, Coating thickness: 2.5 µm, Rotational speed of homogenizer: 4000 rpm; Soft baking: 90 °C for 5 min; Exposure: UV mode for 18 s; Development: Developer ratio: 1:4; Hardening: 115 °C for 20 min; Bottom film removal: O2 flow: 300 L/m for 50 s; power: 200 W. Step 8: E-beam evaporation metal Ni/Ge/Au, thickness: 25 nm/250 nm/25 nm respectively. Step 9: Stripping of photoresist. Step 10: Perform an organic cleaning of the substrate after the second photolithography and ensure that the surface is free of stains and water traces through microscope observation. Step 11: Anneal the alloy. The temperature, time to be used and N2 flow are 400 °C, 60 s, and 2 L/min, respectively. Step 12: The third photolithography: Adopt the positive photoresist process to photolithograph Schottky array contact openings. Coating: Photoresist model: 6130, Coating thickness: 1.8 µm, set rotational speed of homogenizer: 2000 rpm; Soft baking: 100 °C for 5 min; Exposure: UV mode for 15 s; Development: Developer ratio: 1:4 for 40 s; Hardening: 110 °C for 320 min; Bottom film removal: O2 flow: 300 L/m for 45 s; power: 200 W. Step 13: Wet etching of SiO2 : BOE is used as the etchant for etching at the room temperature for 50 s, respectively. Step 14: Perform an organic cleaning for the substrate after the third photolithography, and ensure that the surface is free of stains and water traces through microscope observation. Step 15: The fourth photolithography: Adopt the negative photoresist process to photolithograph the Schottky array contact electrode. Coating: Photoresist model: 4620, coating thickness: 2.5 µm, set rotational speed of homogenizer: 2000 rpm; Soft baking: 105 °C for 10 min; Exposure: UV mode for 20 s; Development: Developer proportion: 1:4 for 40 s; Hardening: 110 °C for 320 min; Bottom film removal: O2 flow: 300 L/m for 60 s; power: 200 W. Step 16: E-beam evaporation metal Ti/Au, thickness: 20/200 nm, respectively; Evaporation rate: 1.5 Å/s. Step 17: Stripping of photoresist. Step 18: Wafer cutting. Use a wafer cutter to cut out each device in turn. Step 19: Substrate pasting. Paste the cut substrate onto the corresponding PCB. Figure 5.12 shows the PCB after fabrication.

5.4 Typical Process Flow of Schottky Metamaterials

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Fig. 5.12 Electrode PCB. a Front view; b back view

Step 20: Use a press welder based on the 25 µm Au line process to pressure weld the electrode of the device with the PCB electrode. The basic structure of the metamaterial device fabricated according to the process flow meets the functional characteristics requirement of Schottky diodes, see Fig. 5.13 for the corresponding process flow. It should be noted that when the metal SRR element structure is subject to the following, it will be hard to conduct the conventional single positive or negative photoresist stripping process: (1) The metal line width is narrow (≤ 3 µm); (2) Irregular line width distribution: the metal line widths at different positions are inconsistent; (3) Dense gaps inside the structure (≥ 1000/mm2 ); (4) Narrow pores in the structure (≤ 3 µm); (5) Various and irregularly arranged gaps such as triangular, polygonal and other holes distributed in different positions. When the above mentioned occur, it can be implemented through the positive/ negative photoresist alternate photolithography, which can help to ensure that the SRR metal electrodes made by photolithography be subject to good shape and uniform distribution. The positive photoresist ensures the normal stripping of the big size structure, while the negative photoresist makes the stripping of the smaller size structure consistent. Therefore, the process flow shown in Fig. 5.13 is applicable to the photolithography operation with a dense cyclical SRR element structure pattern array. GaAs substrates are very brittle. According to the current wafer cutting process, it is only necessary to set the horizontal or vertical spacing between adjacent devices to be higher than or equal to 100 µm, so this spacing parameter can be taken into account in layout design to ensure the yield of cut devices.

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5 Design and Fabrication of Metamaterial Devices SiO2 deposition

Positive photoresist photolithography 1

SiO2 etching

Photoresist removal and cleaning

Negative photoresist photolithography 2

Ohmic electrode evaporation

Stripping and cleaning

Alloy annealing

Positive photoresist photolithography 3

Photoresist removal and cleaning

Negative photoresist photolithography 4

Schottky electrode evaporation

Stripping and cleaning

Substrate

SiO2

Wafer cutting

Electrode pressure welding

Fig. 5.13 Process flow for fabricating GaAs substrate metamaterials

Ohmic electrode

Schottky electrode

5.6 Summary

97

5.5 Evaluation and Analysis on Electronic Properties of Schottky Metamaterials After a GaAs substrate Schottky diode metamaterial is fabricated, the device quality should be evaluated. There are two evaluation methods. In the first, the experimenter observes the quality of the magnified electrode pattern on the device surface with a microscope. This method mainly aims to observe the device surface visually, including checking the line width, the connecting line straightness, the photolithography quality of the right angle or inclination of the connection line, the pattern spacing and checking for defects such as damages, fractures and surface impurities, etc. The other method tests the forward current conduction and reverse current cutoff performance of Schottky diodes with special electrical testing instruments. The test results can help to form the voltage-current forward/reverse performance curves of diodes. The forward/reverse voltage-current performance between a Schottky electrode and an ohmic electrode should be tested immediately after the fabrication of the metamaterial device.

5.6 Summary The resonance induction capability of electrically controlled artificial metamaterial micro/nano pattern structures to electromagnetic wave fields is restricted by many factors. The expected electrically controlled resonance induction efficiency and high gain induction signal, etc. are influenced and restricted by the material, device and electronic configuration, etc. Therefore, exploring an optimal semiconductor fabrication process is the basic premise to ensuring the performance of metamaterial devices. After repeated experiments and tests, the micro/nano process flow and the related technologies of Schottky metamaterials have been proved to be applicable to metamaterial layout design and device fabrication.

Chapter 6

Modeling of Infrared Long-Wave Detection for Metamaterials

6.1 Modeling of Metamaterial Detection Architecture A typical metamaterial structure is a sub-wavelength split-ring resonator, in which every structural element is just like every atom of a natural material. The current in the split-ring resonator can be affected by the electromagnetic wave’s electric or magnetic field or both, and then generate a strong resonance response, just like the response of the LC circuit in an electrical architecture to the time-varying voltage. The resonance frequency of the split-ring resonator is mainly determined by the equivalent inductance and capacitance of the metamaterial structure element. Its equivalent inductance and capacitance can be changed by simply adjusting the shape or size of the structural element. Therefore, artificial metamaterials can be designed with functions of induction detection relying on their responses to most electromagnetic waves including terahertz waves. Some symmetric split-ring resonators are provided with strong electrical response characteristics. Figure 6.1 shows a typical terahertz metamaterial structural element with electrical response characteristics. The line width of this structural element is 10 µm. The opening gap width, overall dimension and cyclical size are 6 µm, 66 µm and 74 µm, respectively. The metamaterial microstructure can be fabricated on an N-GaAs substrate. The square array composed of several elements is connected by metal lines. The microstructure SRR array and semiconductor substrate form a Schottky structure. The functional induction of the incident electromagnetic wave can be realized through changing the depletion layer carrier concentration by applying an external voltage as well as adjusting the local dielectric coefficient at the SRR split-ring. The metamaterial microstructure element has a strong resonance response to the electric field. A symmetrical design can help to reduce or weaken the magnetic field response. When the metamaterial microstructure element resonates, the surface currents of the left and right parts are in opposite directions, making the induced magnetic fields cancel each other out, see Fig. 6.2. © National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_6

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6 Modeling of Infrared Long-Wave Detection for Metamaterials

Fig. 6.1 Metamaterial structural element with electrical response characteristics

Capacitor plate Charging current Dielectric plate

Extremely weak current

Extremely weak current

Dielectric plate

Capacitor plate

Fig. 6.2 Surface current distribution during resonance

In an electromagnetic radiation environment, the upper/lower parts of the metamaterial structure element can be regarded as the positive/negative plates of the capacitor. When the incident electromagnetic wave field E directs from bottom to top, it is considered to be a charging process, with the upper and lower ends of the capacitor being the positive and negative plate, respectively. During this process, the positive charge flows upward along the middle metal part to the positive plate, and the left and right LC circuits share a common path. The metal part inserted between the capacitor plates, the positive charge flows downward along the electric field of the capacitor respectively under the action of the electric field of the positive and negative plates and form a complete LC charging circuit with the current in the inductor. However, the direction of the exciting electric field is vertical, so it is opposite to that of the electric field between the capacitor plates. Under an external electric field, part of the positive charge flows in a vertical direction in the metal dielectric. This effect will cancel out the total current in the metal dielectric. According to the above mentioned, it can be considered that the current in the metal dielectric is extremely

6.1 Modeling of Metamaterial Detection Architecture

101

weak, while that in the middle metal path is very strong. When charging is finished, the electric field formed by the upper and lower charge of the metal dielectric will be the same size as the external electric field, but in the opposite direction. At this time, a large amount of charge has accumulated at the gaps of each split ring, stimulating a large electric field at the gaps. Contrarily, the discharge process is similar to the charging process, except that the direction of the electric field and capacitor plates are the opposite. Therefore, during the charging and discharging process of the metamaterial microstructure, there will be a strong current flowing through the middle metal part and a weak current flowing through the metal parts used as dielectrics on both sides. This resonance element structure can be equivalent to two ring LC oscillation circuits. The split-ring is a capacitor, and the part where the middle current flows is an inductor. The leftmost and rightmost metal parts can be considered as metal mediums inserted between the capacitor plates. When the frequency of the external electric field changes quickly, the current direction of the middle metal part will also change with the direction of the external electric field, generating a continuous high-frequency current, making the middle metal part generate a lot of heat and increasing the resistor resistance of the metal part while the LC oscillation circuits become LCR oscillation circuits. The method of measuring the voltage at both ends of the resistor can be adopted to detect terahertz signals. The values of L and C in the equivalent circuits can be changed by changing the shape and size of the metamaterial structure element to change the resonant frequency of the metamaterial structure element. The metal resistance R can be defined by Eq. (6.1): R=ρ

l s

(6.1)

where ρ is the resistivity; l is the length; and S is the cross-sectional area. The resistance can be appropriately increased by changing the cross-sectional area of the metal. The resistance of the middle metal part can be adjusted by changing the typical metamaterial microstructure element appropriately. Long wave infrared and terahertz waves can be covered in overlapped bands; for example, an electromagnetic band with a wavelength within 30 ~ 100 µm. For this band, the metamaterial microstructure and its electronic characteristics under infrared wave excitation are shown in Fig. 6.3. The element structure shown in Fig. 6.3 can be equivalent to two ring-shaped LC oscillating circuits, with a capacitor at the split ring and an inductor at the middle, through which current flows, wherein the leftmost and rightmost metal can be regarded as a metal-dielectric inserted between the capacitor plates, as shown in Fig. 6.4a. When the frequency of the external electric field changes fast, the sense of current in the middle metal also changes with the external electric field, i.e., there is persistent high-frequency current flowing through the middle metal. It is therefore concluded

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6 Modeling of Infrared Long-Wave Detection for Metamaterials

Fig. 6.3 A typical metamaterial microstructure and surface current excited by incident infrared wave. a Metamaterial element structure; b surface current distribution

Fig. 6.4 Oscillating circuit. a LC oscillating circuit; b LCR oscillating circuit

that the middle metal is extremely apt to heat up, thus further leading to a change in its resistance. After a certain period, the magnitude of its resistance cannot be ignored. Eventually, the LC oscillating circuit is turned into an LCR oscillating circuit. Thus, terahertz detection can be performed using a method by which the voltage across this resistor is measured. By changing the shape and size of the metamaterial structure elements, we can change the magnitude of L and C in the equivalent circuit to change the resonant frequency of the metamaterial structure elements (ω0 ∼ √ 1LC ). According to the

calculation formula of metal resistance, R = ρ sl , where ρ is the resistivity, l is the length, and s is the cross-sectional area, a change in the cross-sectional area of metal leads to a proper increase in its resistance. Hence, it is also possible to properly change typical structure elements to increase the resistance of the middle metal. By designing the microstructure pattern of the artificial metal metamaterial, the transmissivity of long wave infrared bands at 30 ~ 100 µm can be controlled to absorb the energy of the incident electromagnetic wave by resonance, which provides an energy source for obtaining the induced signal of the metamaterial structural element, realizing the induction and detection of the signal within the long wave infrared band.

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103

6.1.1 Electromagnetic Properties Simulation of Terahertz Metamaterials As shown in Fig. 6.5, four representative metamaterial structure elements are selected as simulation objects in this chapter. For the convenience of description, these four structures are numbered A, B, C, and D, respectively. The size of every structure is marked in the figure, while the electromagnetic field directions are also indicated. Figure 6.6 shows surface current distribution concerning these four structures at resonance. There is a heavy current on the metal surface on the left and right sides of the structure A. According to the opening position of structure A, the metal on the left and right sides can be equivalent to L in the LC circuit. The current on the surface of

Fig. 6.5 Four typical metamaterial structure elements. a Structure A; b structure B; c structure C; d structure D

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6 Modeling of Infrared Long-Wave Detection for Metamaterials

Fig. 6.6 Surface current distribution. a Structure A; b structure B; c structure C; d structure D

structures B, C, and D, it is heavier on the metal surface in the middle of the element structure, especially at the edges and corners where the metal is thinner. This is because charges always accumulate at the tip of metal. The surface current does not remain unchanged during the simulation; instead, it varies with the periodicity of the electric field. The simulation data are consistent with the above theoretical analysis of current distribution in such an element structure at resonance and also provide good support for designing a terahertz induction element model based on this structure. Figure 6.7 shows the four resonance structures’ electric field distribution simulation results. As can be seen from the figure, the electric field is strong at the gaps of the split ring and weak at other sites. Judging from the equivalent circuit, the opening can be equivalent to a capacitor, and large amounts of charges are accumulated between the capacitor plates, exciting a very strong electric field. Figure 6.8 shows electric field energy density distribution in element structures at resonance. As shown in Fig. 6.8, the electric field energy density is very high at the gaps of the split ring, whereas it is very low at other parts of the structure. The opening can be equivalent to a capacitor, and large amounts of charges are accumulated on the

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105

Fig. 6.7 Electric field distribution. a Structure A; b structure B; c structure C; d structure D

equivalent capacitor plates, thus exciting a very strong electric field. The capacitor is used as an energy storage device. Figure 6.9 shows energy loss density distribution. Similarly, the loss density is higher at the openings and lower at other parts. As shown from the detailed parameters shown in Fig. 6.5, the SRR element structures selected for experimentation all have an opening size of 6 µm, a basic line width of 10 µm, and a structural period of 74 µm. A simulation was performed using the transmission matrix algorithm to investigate the resonance characteristics of several sample structures. The analysis results show that the transmissivity of metamaterial samples B, C, and D all reach a minimum at the frequency of 2.56 THz. In comparison, the transmissivity of the sample A reaches its minimum at 2.6 THz.

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6 Modeling of Infrared Long-Wave Detection for Metamaterials

Fig. 6.8 Electric field energy density. a Structure A; b structure B; c structure C; d structure D

Moreover, the minimum transmissivity of all these four samples is extremely low. Thus, the inference results achieved in the previous chapter are confirmed. This shows that at these two frequency points, the metamaterial element structures resonate with terahertz waves so that these element structures absorb almost all the energy of the incident waves. As shown by the simulation results of the above four structure elements, all the above four structures have the following characteristics at the resonance point: a heavy current on the middle metal path. Under the excitation of the external electric field, the element structures fall into resonances, with the gaps of the split ring serving as a capacitor C, and the metal on both sides or middle metal serving as an inductor L, both making up an LC oscillating circuit, which acts as an energy storage device during resonances to absorb and accumulate a large quantity of energy. Considering the heavy current with high oscillation frequency on the metal path. In contrast, the cross-sectional area and length of the metal are small, and the metal is apt to heat up, so that its resistance value increases. As a result, the LC oscillating circuit is turned into an LCR oscillating circuit, which eventually stabilizes in a certain resonance state under the continuous excitation of the external electric field. The increased metal resistance makes it possible to extract the metamaterial induction signal and

6.1 Modeling of Metamaterial Detection Architecture

107

Fig. 6.9 Energy loss density. a Structure A; b structure B; c structure C; d structure D

sense the voltage across the resistor R to reveal the strength of metamaterial resonance to realize terahertz induction and detection.

6.1.2 Electronic Characteristics Simulation of Long Wave Infrared Metamaterials In addition to simulating metamaterial structure elements in the terahertz band, the metamaterial element structures in the overlapping area between long-wave infrared and terahertz, i.e., the area with wavelengths from 30 to 100 µm, was simulated, too. The size of metamaterial element structures for this band tends to vary accordingly, but the basic principles are similar. Figures 6.10, 6.11, 6.12, 6.13, 6.14, 6.15, 6.16, 6.17, 6.18 and 6.19 show the element structures with different shapes and their simulation results, respectively.

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6 Modeling of Infrared Long-Wave Detection for Metamaterials

Fig. 6.10 Induction effect and long-wave infrared simulation of square-hole micro-nano structure (wavelength range: 30 ~ 100 µm). a Metamaterial element structure; b electric field distribution; c surface current distribution

The observation of the simulation results shows that the metamaterial element structures of this size generally have extremely low transmissivity in the long-wave infrared band (30 ~ 100 µm). This indicates that almost all the energy of incident electromagnetic waves is absorbed by such structural elements. Also, extracting inductive signals from the metamaterial structure elements is convenient, making it possible to conduct induction and detection in the long-wave infrared band (30 ~ 100 µm).

6.1 Modeling of Metamaterial Detection Architecture

109

Fig. 6.11 Induction effect and long-wave infrared simulation of two-sided wedge-shaped squarehole micro-nano structure (wavelength range: 30 ~ 100 µm). a Metamaterial element structure; b electric field distribution; c surface current distribution

Despite differences in the shape or size of all the above structures, their principles are the same. Their simulation results support for the theoretical analysis conducted in the previous section, and their design ideas are also consistent with the idea of terahertz detection. An IC layout has been designed for the device to reveal the actual transmission characteristics of metamaterial structure elements, and a real object has been made for actual testing. The relevant content is presented in the next chapter.

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6 Modeling of Infrared Long-Wave Detection for Metamaterials

Fig. 6.12 Induction effect and long-wave infrared simulation of four-sided wedge-shaped squarehole micro-nano structure (wavelength range: 30 ~ 100 µm). a Metamaterial element structure; b electric field distribution; c surface current distribution

6.2 Photoelectric Response Testing Scheme The circuit test can be performed in the ultra-clean chamber, with the following equipment required: a signal generator, DC power, an oscilloscope, a THz source, etc. The framework diagram of the test circuit is shown in Fig. 6.20.

6.2 Photoelectric Response Testing Scheme

111

Fig. 6.13 Induction effect and long-wave infrared simulation of regular triangle-hole micro-nano structure (wavelength range: 30 ~ 100 µm). a Metamaterial element structure; b electric field distribution; c surface current distribution

Figure 6.21 shows the physical diagram of the connection between the probe array and the electrodes. The three electrodes are connected to the probe array through a wire, the THz source is used for excitation. The output signal can be measured by observing the oscilloscope.

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6 Modeling of Infrared Long-Wave Detection for Metamaterials

Fig. 6.14 Induction effect and long-wave infrared simulation of regular pentagon-hole micro-nano structure (wavelength range: 30 ~ 100 µm). a Metamaterial element structure; b electric field distribution; c surface current distribution

In Figs. 6.20 and 6.21, there are three electrodes on the detector, two of which are Schottky electrodes, a and b, while one is an ohmic electrode, c. Bias voltage needs to be applied to circuit testing. The ohmic electrode c is the common ground terminal; the Schottky electrode a is connected to the AC signal, while the electrode b is connected to the DC bias voltage. The output signal is obtained from the electrode a. The electrode a is also connected to the input AC signal, with a signal fed back when the induction array resonates under terahertz wave excitation. The resonant signal strength of the detection array can be measured by measuring this signal. The physical diagram of the test circuit connection is shown below.

6.2 Photoelectric Response Testing Scheme

113

Fig. 6.15 Induction effect and long-wave infrared simulation of regular hexagon-hole micro-nano structure (wavelength range: 30 ~ 100 µm). a Metamaterial element structure; b electric field distribution; c surface current distribution

The parameters to be tested are signal strength, signal-to-noise ratio (SNR), bandwidth, and detection sensitivity of the detector. Signal strength refers to the amplitude of the signal output from the detector under a certain bias voltage and excitation signal. It is the most intuitive data output from the detector. Given certain input power, the signal strength of the detector characterizes its ability to respond to a signal. The detector’s bandwidth refers to the range of frequencies detectable for the detector. The detector responds most intensely at the resonance point and thus the strongest signal strength there. When the frequency of the THz source is increased or decreased, the signal√output from the detector becomes weaker. When the strength of the output signal is 2/2 lower than that of the signal output at the resonance point, i.e., output signal’s power drops to 1/2 of the output signal’s power at resonance, the

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6 Modeling of Infrared Long-Wave Detection for Metamaterials

Fig. 6.16 Induction effect and long-wave infrared simulation of round-hole micro-nano structure (wavelength range: 30 ~ 100 µm). a Metamaterial element structure; b electric field distribution; c surface current distribution

detector is considered not in normal operation. Therefore, if there are frequencies f min and f max , f min < f < f max , where f represents resonant frequency, so that the power of signal output from the detector P fmin = P fmax =

1 Pf 2

(6.2)

The bandwidth of the detector is B = f max − f min

(6.3)

6.2 Photoelectric Response Testing Scheme

115

Fig. 6.17 Induction effect and long-wave infrared simulation of two-sided wedge-shaped roundhole micro-nano structure (wavelength range: 30 ~ 100 µm). a Metamaterial element structure; b electric field distribution; c surface current distribution

The detector’s sensitivity is an important indicator, which refers to the amount of change in the strength of signal output from the detector that takes place with a tiny increase in the signal tested. The expression of sensitivity is S=

Sout put Sinput

(6.4)

Sensitivity is one of the important parameters of the detector. It has two physical meanings. One refers to the photoelectric conversion capability of the device, while the other refers to the lowest radiant power that the device can sense. Detector

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6 Modeling of Infrared Long-Wave Detection for Metamaterials

Fig. 6.18 Induction effect and long-wave infrared simulation of four-sided wedge-shaped roundhole micro-nano structure (wavelength range: 30 ~ 100 µm). a Metamaterial element structure; b electric field distribution; c surface current distribution

sensitivity should be kept within a certain range because excessively high sensitivity makes the device vulnerable to the environment. In contrast, excessively low sensitivity undermines the response speed of the device so that it cannot be used for real-time detection.

6.3 Photoelectric Response Test Electrode A metamaterial device consists of three electrodes, namely the Ohmic Electrode 1, Schottky Electrode 2 and Schottky Electrode 3 as shown in Fig. 6.22. The Ohmic Electrode 1 is a common ground terminal, the Schottky Electrode 2 is connected to the

6.3 Photoelectric Response Test Electrode

117

Fig. 6.19 Induction effect and long-wave infrared simulation of orthogonal cross-hole round-hole micro-nano structure (wavelength range: 30 ~ 100 µm). a Metamaterial element structure; b electric field distribution; c surface current distribution

AC signal, and the Schottky Electrode 3 is connected to the DC bias voltage. When the metamaterial array resonates under terahertz wave excitation, the resonance signal strength relationship can be obtained by measuring the feedback signal between electrodes. The data to be tested includes the signal strength, signal-to-noise ratio (SNR), bandwidth and detection sensitivity of a detector. The signal strength is the amplitude of a detector output signal under a certain bias voltage and excitation signal, which is the most intuitive data output by the detector. Under a certain input power, the signal strength of the detector indicates its capability to respond to signals.

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6 Modeling of Infrared Long-Wave Detection for Metamaterials

THz wave

signal generator

oscilloscope Fig. 6.20 Framework diagram of the test circuit

Fig. 6.21 Physical connection between the probe array between the electrodes

DC power

6.4

Summary

119

Fig. 6.22 Electrode distribution of metamaterial device 2 1

6.4

3

Summary

This chapter mainly introduces the detection methods of terahertz and long wave infrared detectors of metamaterials, establishes the relationship between the electromagnetic characteristics of long wave infrared and the electronic characteristics of long wave infrared metamaterials and shows the detection scheme.

Chapter 7

Metamaterial Signal Sensing Based on Continuous Terahertz Waves

7.1 Preface In recent years, progress has been made in in-depth research on metamaterials in relation to terahertz band applications, such as terahertz filters, terahertz short-range communications, terahertz antennas and terahertz detectors, etc. The measurement of terahertz data is mostly limited in laboratories or obtained relying on the terahertz time-domain spectroscopy, and it precedes the real-time measurement [1–5]. Therefore, it is necessary to find a suitable method to design terahertz detectors with high sensitivity and efficiency. Ideally, a terahertz sensor array can help to convert the continuous terahertz wave into an array electrical signal by appropriate means. The accurate measurement of this electrical signal is related to the actually transmitted terahertz power. Therefore, the actual transmission power of the incident terahertz wave can be used as a reference to measure the induction efficiency. The existing research shows that when the incident terahertz wave passes vertically through a metamaterial plane with a specific shape, self-excited magnetic resonance of electrons will be caused. The capability of the metamaterial in transmitting terahertz wave in the resonance process is related to the SRR microstructure and its pattern configuration. By designing metamaterials with various pattern configurations and measuring their power transmission properties within 1.04–4.25THz, it is found that these metamaterials have global transmission peaks and several local transmission peaks, these transmission peaks and their transmission efficiency are related to the SRR array microstructure. For these experiments, the summary of the design method and the SRR configuration parameters of these devices can help to provide a basis for the subsequent research in order to gradually fabricate terahertz induction devices. A metamaterial structure consists of a cyclical SRR element array and a GaAs substrate. For the SRR element, according to the transmission line theory, the SRR openings can provide most of Capacitance C. In addition, a small amount of capacitance can be provided at the remaining space of the SRR. Inductance L can be provided between every two rings and the SRR. The entire SRR array is equivalent © National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_7

121

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7 Metamaterial Signal Sensing Based on Continuous Terahertz Waves

to an LC oscillation circuit. When the terahertz wave passes through this cyclical SRR array, if the frequency of the electromagnetic wave exactly matches the resonant frequency of the LC circuit, the structure will resonate, and the energy will be consumed in the SRR array structure, which is equivalent to an absorber of the terahertz wave energy.

7.2 Generation and Measurement of Continuous Wave Terahertz (CW-THz) Lasers The common CW THz laser is the CO2 pumped terahertz laser (model: SIFIR-50) of Coherent. Its output frequency spectra are listed in Table 7.1. The diameter of the output beam is about 3–5 mm. If the structure size of a single SRR element is a micron-level one, the terahertz laser beam can cover about 1000–2000 SRR elements. 1. Working principle of CW-THz laser To date, over one thousand usable terahertz spectral lines within 40–1200 μm have been found through optical pumping, which are widely used in optical measurement, nondestructive testing and material analysis, etc. It can be seen from Fig. 7.1 that the methanol molecule is an asymmetric rotor structure. During optical pumping, the C–O bond is subject to tensile vibration, external rotation vibration and internal rotation vibration. Since the energy for the vibration and rotation energy levels differs greatly, most of the energy from the pumped laser is converted into heat or other energy, or is Table 7.1 Theoretical power of terahertz wave generated by CO2 pumped laser exciting different gas molecules

Wavelengh (μm)

Freq. (THz)

Far infrared laser gas

42.16

7.09

CH3 OH

70.51

4.25

CH3 OH

96.52

3.11

CH3 OH

109.30

2.74

CH2 F2

117.73

2.55

CH2 F2

118.83

2.52

CH3 OH

134

2.24

CH3 OH

158.51

1.89

CH2 F2

184.31

1.63

CH2 F2

214.58

1.40

CH2 F2

236.59

1.27

CH2 F2

287.67

1.04

CH2 F2

334

0.90

CH3 Cl

349.3

0.86

CH3 Cl

7.2 Generation and Measurement of Continuous Wave Terahertz (CW-THz) …

123

Fig. 7.1 Methanol molecule structure

otherwise lost during terahertz wave generation. This means that the efficiency of the terahertz laser generated by CO2 pumping is usually low. The above energy conversion can be solved according to Manley Rowe Eq. (7.1). η=

f THz 2 f IR

(7.1)

where ï is the conversion efficiency of CO2 pumped laser to THz laser; f THz is the frequency of the emergent terahertz laser; f IR is the frequency of CO2 pumped laser. Ideally, the corresponding conversion efficiency of a laser that generates 2.52 THz by methanol gas molecules through CO2 pumping is 4%, while in actual experiments, the incident CO2 pumped laser power is 50 W, and by adjusting the laser wavelength line and the corresponding cavity length, the actual output power of 2.52 THz laser is about 100 mW, so the conversion efficiency is about 0.2%. Under a laboratory environment, the corresponding conversion efficiency of THz laser generated by a SIFIR-50 laser is generally kept within 0.001–0.2%. If the generation efficiency of a CO2 pumped laser is about 10–15%, it can be seen that the conversion efficiency of the whole CO2 pumped THz laser is very low. This is one of the reasons why it is difficult for researchers at home and abroad to obtain terahertz radiation sources with a high output power and conversion efficiency, which, to some extent, also restricts the application of terahertz radiation sources. 2. Measurement method of CW-THz laser Two main methods can be adopted for measuring CW THz laser, which are the pyroelectric detection method and image acquisition method. (1) Pyroelectric detection method Pyroelectric detectors are provided with a very wide frequency response range, which are mainly made from pyroelectric effect produced by some crystal materials with the change of temperature. When a crystal is irradiated, the spontaneous polarization intensity will change due to the change of temperature, so an induced charge will appear between the two outer surfaces of the crystal perpendicular to the direction of spontaneous polarization. The energy of light radiation can be measured based on the change of the induced charge. Since the electrical signal of a pyroelectric detector is

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7 Metamaterial Signal Sensing Based on Continuous Terahertz Waves

Terahertz laser

Pyroelectric detector

Fig. 7.2 Experimental scheme for CW-THz laser power measurement

proportional to the change rate of the detector temperature with the time, the thermal balance process is not required, so the response time is relatively short. When the absorption frequency of the pyroelectric crystal is the electromagnetic wave of ω and the temperature changes with ω, the surface charge density of the crystal will also change with ω. If the external electrodes on both sides of the crystal are connected with the load resistor, there will be a current on the load resistor. For specific experiments, the common measurement scheme is shown in Fig. 7.2. (2) Image acquisition method When collecting terahertz images, a Spiricon Pyrocam III-CA solid-state pyroelectric camera can be used. This camera is a laser beam analysis imager with ultra-wide spectral detection capabilities. Its spectral detection is set within 13–355 nm and 1.06 μm–3 mm, covering the deep UV wave band and the near-infrared to millimeter wave band. The sensitivity of the detector is 2.2 mW/cm2 , and the planar array of the chip is 12.7 mm × 12.7 mm. The camera’s image acquisition interface is subject to the IEEE 1394a protocol for the sake of quick response. The maximum linear dynamic range can reach 1000:1, which shows a good performance in the detection of high/low laser power.

7.3 Design and Fabrication of Terahertz Band Metamaterial Devices The resonance induction capability of electrically controlled artificial metamaterial micro/nano pattern structures to electromagnetic wave fields is restricted by many factors, such as the properties of electrode and substrate materials, the structure size and layout, the carrier concentration of substrate materials and the electromagnetic form of incident waves, etc. Therefore, the expected electrically controlled resonance induction efficiency and high gain induction signal, etc. are influenced and restricted by the material, device, wave-field electromagnetic properties, electronic configuration, device control mode and behavior and environmental factors, etc.

7.3 Design and Fabrication of Terahertz Band Metamaterial Devices

125

7.3.1 Metamaterial Device Model 1. Overall structure of metamaterial devices The metamaterial device layers are shown in Fig. 7.3, primarily including the following three parts: The top layer metal array is planar, formed from the cyclical expansion of patterned SRR elements. Each SRR element can be connected with metal lines, forming the entire metal SRR array. According to this design, parameters such as SRR element structure, characteristic scale, pattern shape and fabrication material at the top layer will become the key factors for inducing incident Terahertz waves. Designed SRR elements with different characteristic patterns and shapes will provide different control and induction functions with regard to transmission signals. The intermediate layer is N-type doped GaAs, which changes the electronic concentration of the intrinsic GaAs by doping Si or Ge atoms to achieve Schottky and ohmic contact with the metal and constructing a Schottky diode device. Therefore, the electronic concentration formed by doping will become a key factor in making Schottky contact regions. The bottom layer is SI-GaAs. The intrinsic GaAs absorb very little terahertz wave, so the terahertz wave loss in this layer is very low. However, it must be noted that normal transmission/reflection effects will also occur when the terahertz wave is transmitted in this layer. When the thickness of this layer changes, multiple reflections may result in the Fabry–Perot interference effect of the terahertz wave. Therefore, the thickness of the SI-GaAs layer will become an important factor affecting the performance of the entire metamaterial device. 2. SRR element structure SRR elements can be designed into round and square structures, see Fig. 7.4a, b. Since current will be generated under resonance, each SRR element can be connected with lines to form an array, see Fig. 7.4c, d. Other common metamaterial structures are shown in Fig. 7.5, and their size parameters are the same as the SRR shown in Fig. 7.4. Fig. 7.3 Layers of Schottky metamaterial device

Alloy N-GaAs

SI-GaAs

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7 Metamaterial Signal Sensing Based on Continuous Terahertz Waves

Fig. 7.4 SRR elements and array structures. a Round SRR element; b square SRR element, d = 5 μm, r = 33 μm, t = 10 μm, l = 66 μm. Element cyclical constant p = 75 μm; c round SRR array; d square SRR array

Fig. 7.5 Structural diagram of Metamaterial Element N1-N17

7.3.2 Metamaterial Device Fabrication Process 1. Selection of fabrication materials In order to achieve Schottky contact between the metal SRR planar array and n-GaAs, the relevant material parameters are set as follows. The top layer SRR element is Au or an alloy with a thickness of 200 nm and a typical Conductivity σ of 4.09 × 107 S/m. The thickness of n-GaAs in the middle

7.3 Design and Fabrication of Terahertz Band Metamaterial Devices

127

layer is 1 μm. The dielectric constant and typical carrier concentration are 12.9 and 1.9 × 1016 cm−3 , respectively. The thickness parameters commonly used for the bottom layer SI GaAs is 350 μm or 700 μm, etc. 2. Layout design According to the process standard of Schottky devices, Schottky metamaterial devices can generally be fabricated with a 4-layer nesting layout. The typical photolithography layout is shown in Fig. 7.6. As shown in Fig. 7.6, the left round one is an ohmic electrode, and the middle SRR array and the rightmost one are Schottky electrodes. Each SRR element inside the array can be connected in series or in parallel by using metal lines. The fabricated metamaterial devices after cutting are shown in Fig. 7.7.

Fig. 7.6 Single metamaterial device layout Fig. 7.7 Picture of typical metamaterial devices

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7 Metamaterial Signal Sensing Based on Continuous Terahertz Waves

Fig. 7.8 Measurement platform of terahertz wave transmission experiment

7.4 Transmission Characteristics of Metamaterial Devices in Terahertz Bands 7.4.1 Experimental Principle and Apparatus At present, the sensitivity and response speed of terahertz detectors are not ideal. Since SRR metamaterials are resonant devices, their induction rate is very quick, and the induction characteristics have a close relationship with the SRR element microstructure and pattern configuration. The platform apparatus for terahertz wave transmission experiments using metamaterial devices is shown in Fig. 7.8. The corresponding supporting apparatuses, such as circulating water cooler, vacuum pump, oscilloscope and laser control system are required in order to make the terahertz laser work normally.

7.4.2 Experimental Analysis on Transmission Properties of Metamaterials Based on Multi-Band Continuous Terahertz Waves For SRR microstructures, since the split ring is subject to a certain directivity, the magnetic field or electric field of the incident terahertz wave may have a certain angle with the SRR structure. Generally, the loss or change of actual incident power

7.4 Transmission Characteristics of Metamaterial Devices in Terahertz Bands Terahertz laser

Metamaterial device

129

Pyroelectric detector

Fig. 7.9 Transmission principle of metamaterial irradiated by continuous terahertz waves

caused by this angle is low, and a change in this angle is inevitable. Therefore, for the moment, the power characteristics under an average sense should be discussed, rather than the influence of this angle. According to the transmission direction of the terahertz wave, the incident continuous terahertz wave is perpendicular to the SRR plane. The transmission signal can be captured by a pyroelectric detector and converted into the actual power signal for display. See Fig. 7.9 for the schematic diagram of the entire experiment. 1. Transmission characteristics of typical metamaterial devices under incident terahertz waves at different frequencies According to the continuous terahertz wave power output by the terahertz laser listed in Table 7.1, terahertz lasers with high reliability and stable power are selected for the experimental research. The commonly used terahertz frequencies are 4.25, 2.52, 1.89 and 1.40 THz, respectively. The selected Metamaterial Devices N1-N17 are shown in Fig. 7.5, as well as their tested terahertz wave transmission characteristics, respectively. The experimental results are shown in Figs. 7.10, 7.11, 7.12, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18 and 7.19. 2. Inductive performance analysis Since fabricated metamaterial devices are of three-layer structures, the distribution density of the top metal SRR array area is fixed, the reflection performance of each device under the same frequency incident terahertz wave is basically the same. The Fig. 7.10 Normalized transmission power of Metamaterial N1–N17 under laser irradiation of 4.25 THz

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7 Metamaterial Signal Sensing Based on Continuous Terahertz Waves

Fig. 7.11 Normalized transmitted power of metamaterials N1–N17 under laser irradiation of 2.74 THz

Fig. 7.12 Normalized transmission power of Metamaterial N1–N17 under laser irradiation of 2.55 THz

1

Transmission intensity

Fig. 7.13 Normalized transmission power of Metamaterial N1–N17 under laser irradiation of 2.52 THz

0.8 0.6 0.4 0.2 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17

Metamaterial No.

difference is that the internal response losses of the devices to the incident THz wave can directly affect the transmitted terahertz signal strength after transmission. Therefore, if the transmission signal strength of a metamaterial device is low, when the reflectivity does not change, it can be considered that this device powerfully

7.4 Transmission Characteristics of Metamaterial Devices in Terahertz Bands 1

Transmission intensity

Fig. 7.14 Normalized transmission power of Metamaterial N1–N17 under laser irradiation of 2.45 THz

131

0.8 0.6 0.4 0.2 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17

Metamaterial No.

1

Transmission intensity

Fig. 7.15 Normalized transmission power of Metamaterial N1–N17 under laser irradiation of 2.24 THz

0.8 0.6 0.4 0.2 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17

Metamaterial No.

Fig. 7.16 Normalized transmission power of Metamaterial N1–N17 under laser irradiation of 1.89 THz

absorbs or consumes terahertz waves through induction, and the sensing performance of the device is good. An in-depth analysis of the THz transmission signals obtained in Figs. 7.10, 7.11, 7.12, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18 and 7.19 shows that the metamaterial numbered

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7 Metamaterial Signal Sensing Based on Continuous Terahertz Waves

Fig. 7.17 Normalized transmission power of Metamaterial N1–N17 under laser irradiation of 1.63 THz

Fig. 7.18 Normalized transmission power of Metamaterial N1–N17 under laser irradiation of 1.40 THz

1

Transmission intensity

Fig. 7.19 Normalized transmission power of Metamaterial N1–N17 under laser irradiation of 1.04 THz

0.8 0.6 0.4 0.2 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17

Metamaterial No.

N5 responds better to 4.25-THz waves than the other materials. The metamaterials numbered N8, N10 and N13 responds better to 2.74-THz waves than the other materials. The metamaterial numbered N1 response better response to 2.55-THz waves than the other materials. The metamaterial numbered N11 responds better to 2.52THz waves than the other materials. The transmission characteristics revealed under

7.4 Transmission Characteristics of Metamaterial Devices in Terahertz Bands

133

2.24-THz laser irradiation are shown in the figure. As can be seen, there is little difference in this group. The metamaterial numbered N5 responds better to 1.89THz waves than the other materials. The metamaterial numbered N5 responds better to 1.63-THz waves than the other materials. The metamaterial numbered N8 responds better to 1.40-THz waves than the other materials. The metamaterial numbered N1 responds better to 1.04-THz waves than the other materials.

7.4.3 Simulation of Transmission S-Parameter of Metamaterials Under Terahertz Frequency Bands In order to further study the transmission characteristics and efficiency of different SRR pattern structures under the terahertz frequency bands, four metamaterial devices, namely Sample A, B, C and D are selected for an analysis, as shown in Fig. 7.20. The opening size of the four metamaterial SRR element structures is 5 μm, and the line width is 10 μm. The relevant material parameters are consistent with the above. See Fig. 7.21 for the simulation results. Metamaterial Device B, C and D have a global transmission peak at about 2.52 THz, and Sample A has a transmission peak at about 2.6 THz, which can be explained as the electromagnetic effect caused by the equivalent LC resonance. It should be noted here that the resonance properties of SRR arrays are equivalent to the configuration of basic interfaces such as split-ring pattern and metal linewidth. Therefore, the pattern interface layout and corresponding electronic configuration of these metamaterial samples are referable to some extent, and can be adopted to design new terahertz sensing devices. Fig. 7.20 Four metamaterial devices. a Single SRR element of Sample A; b single SRR element of Sample B; c single SRR element of Sample C; d single SRR element of Sample D

(a)

(b)

(c)

(d)

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7 Metamaterial Signal Sensing Based on Continuous Terahertz Waves 0.9 Sample Sample AA Sample Sample BB Sample Sample CC Sample D

Transmission intensity

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

1

1.5

2

2.5

3

3.5

4

Freq./THz Fig. 7.21 Transmission performance curves of Sample A (solid line), B (dotted line), C (short dotted line) and D (dashed/dotted line)

7.5 Summary The established metamaterial wave field induction models in the existing literature are mainly based on the LC oscillation model, and their induction mechanism adopted to describe the artificial metamaterial micro/nano structures is still rough and unable to fully describe, characterize, reproduce and predict the complex resonance induction properties, characteristics and details used for wide spectrum wave field detection. At the same time, the existing device simulation design algorithm based on the dipole inductance model does not introduce the parameters such as frequency spectrum, polarization, intensity and incident direction of wave fields and their interactions into the shape and structure parameter configuration constructed micro/nano metamaterials. When sensing a simple mode wave field through an SRR metal electrode, the introduced errors are acceptable; however, it is obviously not applicable to the resonant induction detection of wave fields involving the above complex factors. For the purpose of continuous terahertz wave transmission based on metamaterials, relying on cyclical subwavelength SRR microstructure elements and pattern configurations, we designed and fabricated 17 metamaterials devices for sensing continuous terahertz waves. The difference in the terahertz wave induction efficiency of each device is mainly related to the interface layout of pattern electrodes and the corresponding electronic configuration. The element microstructure and electronic configuration are references for the architecture design of terahertz detectors.

References

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References 1. Sprik R, Duling IN, Chi C-C, et al. Far infrared spectroscopy with subpicosecond electrical pulses on transmission lines. Appl Phys Lett. 1987;51(7):548–50. 2. Laman N, Harsha SS, Grischkowsky D, et al. High-resolution waveguide THz spectroscopy of biological molecules. Biophys J. 2008;94(3):1010–20. 3. Gallot G, Jamison SP, Mcgowan RW, et al. Terahertz waveguides. J Opt Soc Am B. 2000;17(5):851–63. 4. Theuer M, Harsha SS, Grischkowsky D. Flare coupled metal parallel-plate waveguides for high-resolution terahertz time-domain spectroscopy. J Appl Phys. 2010;108(11): 113105. 5. Laman N, Harsha SS, Grischkowsky D. Narrow-line waveguide terahertz time-domain spectroscopy of aspirin and aspirin precursors. Appl Spectrosc. 2008;62(3):319–26.

Chapter 8

Signal Sensing of Electrically Controlled Metamaterials Based on Terahertz Time-Domain Spectra (THz-TDS)

8.1 Preface The THz-TDS system has a high sensitivity and can effectively be used to detect the transmission and reflection characteristic spectra of materials. THz-TDS is usually composed of components like a femtosecond laser, optical retarder, emitter, optical system for collimating and focusing beam, sample, detector, phase-locked amplifier [1–4]. This system is not only helpful for spectral research but also for imaging research. Generally, the metal SRR microstructure array is a key component in sensing incident electromagnetic wave signals. The Schottky structure formed by this metal array contacting with GaAs represents the semiconductor substrate, and can help to effectively control the amplitudes and phases of terahertz waves. The sensing capability of a metamaterial to a terahertz wave can be enhanced by applying an external voltage at both ends of the Schottky metamaterial electrode and changing the current in the metal SRR layer and the electronic configuration of the metamaterial.

8.2 Structural Design and Fabrication of Electrically Controlled Metamaterial Devices 1. Principle and structure of electrically controlled metamaterial devices A 350 μm thick SI-GaAs wafer (dia. 2 ) was selected as the substrate of an entire metamaterial device. Si atoms were doped using the MCVD technology to grow a layer of 1 μm thick N-type GaAs film (free electron concentration: n = 4.7 × 1017 cm−3 ).

© National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_8

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138 Fig. 8.1 Structural schematic diagram of electrically controlled metamaterial device

8 Signal Sensing of Electrically Controlled Metamaterials Based …

Ohmic electrode

Schottky electrode

For fabrication, the Schottky diode process was adopted, and cyclical metal SRR arrays were used as the Schottky electrodes. Figure 8.1 shows the overall structure of an electrically controlled metamaterial device. 2. Electrically controlled metamaterial device structure In order to explore the characteristics of electrically controlled metamaterials in sensing terahertz waves, the edge of a standard SRR is narrowed to the metal line of the SRR. The narrow angle can be set as 30°, 45° and 60°, etc. By taking the narrowed-edge metamaterial pattern structure as the basic element for extension, more microstructural elements with different shapes can be designed, see Fig. 8.2. Figure 8.3 shows the physical picture of the Schottky metamaterial devices made by standard UV photolithography. The device performance can be adjusted under an external power supply.

8.3 Transmission Properties of Dipole Model Metamaterials in Reflective THz-TDS Cyclical SRR metamaterial planar arrays can give relatively strong electromagnetic resonances in certain frequency ranges [5], which has been explained by researchers through equivalent LC oscillator circuits and dipole models [6]. In recent years, many studies have proven that metamaterial structures can show obvious electromagnetic wave absorption properties under an equivalent LC resonance given by a transmission line model. However, few studies have been conducted on the dipole resonance properties in SRR elements. This section analyzes the correlation properties between terahertz wave transmission and dipoles of a metamaterial device within 0.1–3.0 THz. The THz-TDS experimental system is usually installed in a dry and closed environment filled with nitrogen, and the ambient temperature is 21–24 °C.

8.3 Transmission Properties of Dipole Model Metamaterials in Reflective …

Fig. 8.2 Optical micrograph of metamaterials with various shapes

Fig. 8.3 Schottky metamaterial devices

139

140

8 Signal Sensing of Electrically Controlled Metamaterials Based …

8.3.1 Reflective Time-Domain Pulsed Terahertz Wave An InAs crystal with the lattice orientation of < 100 > is a common terahertz radiation element. This crystal is a narrow band semiconductor. When it is irradiated by femtosecond pulse laser, the photogenerated carriers in the crystal can give terahertz electromagnetic radiation under the Dember electric field, and the THz pulse (2.6 THz or higher) emitted has a wide bandwidth. Therefore, InAs crystals have become one of the most commonly used semiconductor materials to generate THz radiation sources [7–9]. A common sensing element of the THz detection system is ZnTe crystal with the lattice orientation of < 110 > , the THz signal detected through which has the characteristics of high sensitivity, low noise and broadband spectral response, etc. The spatial resolution of the THz-TDS system is dependent on the diameter of the spot emitted by the terahertz beam focused on a sample. Generally, the terahertz wave is approximate to the Gaussian wave, and its spot size is defined as: √ 4 2λ f · R= π d

(8.1)

where d is the beam diameter of the terahertz wave after the first parabolic mirror is collimated; f is the focal length of the second off-axis parabolic mirror; λ Is the wavelength corresponding to the spectral peak of the terahertz signal. The Beam Waist Diameter R of a common THz spot is 1.1 mm.

8.3.2 Terahertz Transmission Properties of Metamaterials 1. Device structure Metamaterial elements can be a variety of microstructure forms, such as single gap SRR (SG-SRR), four-gap SRR (FG-SRR), etc. Metamaterial devices made of SGSRR structure arrays are expressed by M-SG-SRRs. Figure 8.4 shows a typical square SG-SRR element. The top and bottom of each SG-SRR element is narrowed, the width of which can be set to a micrometer scale value, e.g. 1–10 μm. By changing the shape of the boundary line, the narrow edge resistance becomes higher, changing the current flow direction and value of the SRR element. The adjacent SG-SRR elements are connected with lines to control the current in Schottky devices. 2. Test analysis The substrate of a Schottky device is a 350 μm thick SI GaAs that is doped with Si based on MOCVD technology, and a layer of 1 μm thick n-GaAs film is grown with a free electron concentration of 4.7 × 1017 cm−3 .

8.3 Transmission Properties of Dipole Model Metamaterials in Reflective …

141

Fig. 8.4 Structure of a single-gap SRR. a Optical micrograph of SG-SRR element, d = 6 μm, h = 3 μm, t = 10 μm, l = 130 μm; b 3 × 3 array cyclically formed by SG-SRR elements, cycle p = 140 μm

Figure 8.5 shows the polarization direction of a terahertz electric field irradiating a metamaterial device. Several experimental measurement signals are shown in the figure, including original terahertz pulse signals (TP), terahertz time-domain transmission signals of the M-SG SRRs metamaterial device and terahertz wave signals penetrating the n-GaAs film and SI GaAs substrate (i.e. the GaAs substrate transmission signal) for reference. The measured time-domain signal data acquisition is kept within 0–14 ps. It can be clearly seen from Fig. 8.5 that the time interval characteristics of the terahertz time-domain transmission signals of the M-SG-SRRs metamaterial device are obvious. The whole terahertz time-domain transmission signals can be divided into ordinary terahertz transmission signal, intrinsic signal and characteristic signal areas. The ordinary terahertz transmission signals are kept within 0–4 ps, and their deadline position is shown at A in Fig. 8.5; The terahertz transmission intrinsic signals generated by the excitation of the M-SG-SRRs device vertically irradiated 0.002

TP substrate GaAs transmission signal × M-SG-SRRs

Original THz signal

Transmission intensity

Fig. 8.5 Terahertz time-domain transmission signal collected during metamaterial device experiment

0.001

15 GaAs Substrate × 2

SG metamaterial device signal

A

B

0.000

-0.002 0.0

P1

E

-0.001

H 2.0

4.0

6.0

8.0

Time delay/ps

10.0

12.0

14.0

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8 Signal Sensing of Electrically Controlled Metamaterials Based …

Fig. 8.6 Terahertz spectrum signals during metamaterial device experiment

GaAs substrate transmission signal

Transmission intensity

Original THz signal

SG metamaterial device signal

Freq./THz

through TP are kept within 4–10.5 ps as shown in the Interval A–B in Fig. 8.5; The characteristic signals closely related to the M-SG-SRRs metamaterial device that appear after terahertz transmission intrinsic signals are shown in Dotted Box P1 in Fig. 8.5, which last about 3.5 ps. Figure 8.6 shows the terahertz transmission spectrum corresponding to Fig. 8.5, including the original terahertz spectrum, the terahertz transmission spectrum of the GaAs substrate and the terahertz transmission spectrum of the M-SG-SRRs metamaterial device. Several slight absorption peaks appear near 1.1, 1.7 and 2.4 THz in the original terahertz spectrum, the terahertz transmission spectrum of the GaAs substrate and the terahertz transmission spectrum of the M-SG-SRRs metamaterial device, respectively shown in Fig. 8.6 at dotted lines P2, P3 and P4. The positions and absorption intensities of these absorption peaks are independent of the materials and tested devices during the experiment, which are caused by water vapor absorption. It can be clearly seen from Dotted Box K in Fig. 8.6 that the terahertz transmission spectrum of the M-SG-SRRs metamaterial device has obvious intensive oscillation properties within 0.1–1 THz, which are closely related to the metal SG-SRR array. By comparing the significant difference between the transmission spectrum of the M-SG-SRRs metamaterial device and that of the GaAs substrate, it can be considered that this vibration effect is an unusual transmission. According to the analysis, the metal SG-SRR structure in the top single gap form in the M-SG-SRRs metamaterial device is a split-ring resonant element in the form of a dipole, which gives a dipole resonance effect during the transmission process of terahertz waves. FFT is used to calculate the corresponding areas of the ordinary terahertz transmission signals, intrinsic signals and characteristic signals, respectively, to obtain the original transmission spectrum, intrinsic transmission spectrum and characteristic transmission spectrum as shown in Fig. 8.7.

8.3 Transmission Properties of Dipole Model Metamaterials in Reflective …

Original transmission spectrum

Transmission intensity

Fig. 8.7 Terahertz transmission spectra of each area in metamaterial device experiment

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Intrinsic transmission spectrum

Characteristic transmission spectrum

Freq./THz

The intrinsic transmission spectrum shown in Fig. 8.7 is consistent with the transmission spectrum of the GaAs substrate. It must be noted that the original transmission spectrum of the M-SG SRRs metamaterial device is subject to intensive oscillation within 0.1–1 THz. In Fig. 8.7, the local maxima of the transmission spectrum within 0.1–1 THz are 0.2, 0.345, 0.505, 0.665 and 0.825 THz, respectively, and the local minima of the spectrum within this range are 0.15, 0.28, 0.44, 0.59, 0.74 and 0.9 THz, respectively. The transmission peaks corresponding to these local extreme values have a wave effect with a uniform interval of f = 0.15 THz. The results in Fig. 8.7 indicate that the spectrum vibration characteristics within 0.1–1 THz are obvious, while the transmission spectrum within 1–3 THz is consistent with the terahertz transmission signal spectrum of the GaAs substrate. The vibration only occurs within the frequency band of 0.1–1 THz; and for other areas, it is consistent with the transmission spectrum of the substrate, so the Fabry–Perot interference effect can be ruled out. Only the dipole resonance from the cyclical structure SG-SRR element can make the terahertz transmission spectrum of the M-SG-SRRs metamaterial device be subject to a significant intensive oscillation in a certain frequency band. As shown in Fig. 8.7, this dipole oscillation is consistent with the characteristic transmission spectrum range of the M-SG-SRRs metamaterial device. 3. Resonance property analysis According to the equivalent LC circuit model of transmission lines, the electromagnetic resonance frequency of SRR is generally defined as: f s ∝ 1/(LC)1/2

(8.2)

where L and C are the inductance and capacitance of the transmission line circuit being equivalent to the metamaterial device within a terahertz frequency band, respectively. The dipole resonance frequency of the SRR microstructure element is:

144

8 Signal Sensing of Electrically Controlled Metamaterials Based …

nc 

fD = 2l

εr +1 2

, n = 1, 2, 3 . . . . . .

(8.3)

where l is the effective length of the dipole antenna; c is the light velocity in the free space; E is the relative dielectric constant of the metamaterial substrate. According to the parameters shown in Fig. 8.4, the values of n, l and Er are 1, 110 μm and 13, respectively. According to the equation calculation, the center frequency of the dipole resonance from the SG-SRR microstructure element is f D = 0.515 THz, which is consistent with the tested frequency response. The center frequency of the principal component of the characteristic transmission spectrum obtained according to Fig. 8.7 is 0.51 THz. Therefore, the center frequency of the measured characteristic terahertz transmission spectrum is consistent with that calculated based on the dipole resonance frequency equation.

8.4 Transmission Behavior of Metamaterials in Photoconductive THz-TDS Based on Fabry-Pérot Model Photoconductive antennas are currently prevalent terahertz pulse signal transmitters and detectors. Their basic principle for generating terahertz waves is to irradiate a semiconductor with a femtosecond laser to generate photogenerated carriers, which can generate quickly changing photoconductive current under an external electric field and give terahertz wave radiation through antennas [10–14].

8.4.1 Photoconductive Antenna THz-TDS System Figure 8.8 shows a typical photoconductive antenna. The substrate materials used for photoconductive antennas are generally semiconductor materials with high dielectric constants, such as low temperature grown gallium arsenide (LT-GaAs), Si, GaAs and InGaAs, etc. Among them, LT-GaAs is characterized by short carrier life (about 0.25 ps) and high breakdown electric field value (> 5 × 105 V/cm) and high mobility (> 200 cm2 /Vs), etc., becoming the most commonly used substrate material for photoconductive antenna devices. An external voltage is required at both ends of the photoconductive antenna to generate terahertz waves. No bias electric field is required for receiving terahertz signals. Figure 8.9 shows the structure diagram of a typical photoconductive antenna, which is composed of a LT-GaAs substrate, a pair of dipoles and a DC bias power supply. When a femtosecond laser pulse irradiates between the dipole electrode gaps of the photoconductive antenna, and the value of the photon energy is higher than that of the semiconductor energy band, the electrons in LT-GaAs will transit

8.4 Transmission Behavior of Metamaterials in Photoconductive THz-TDS … Fig. 8.8 Photoconductive antenna

145

Metal electrode

Femtosecond laser

Electron Hole

Semiconductor

Fig. 8.9 Operating principle of photoconductive antenna

Incident light

accel erate

THz pulse

accel erate

from the valence band to the conduction band, resulting in free carrier electron hole pairs. At this time, the dipole electrodes are equivalent to a capacitor. Under an external bias electric field, these photogenerated carriers accelerate to form a transient photocurrent, generating a terahertz radiation.

8.4.2 Theoretical Analysis on Terahertz Waves Generated by Photoconductive Antennas When femtosecond laser pulses excite photogenerated carriers, the carrier concentration will change with the lasted laser irradiation, which is defined as (1 − R) ∂ Iopt (x, t) n(x, t) ∂n(x, t) =− · − ∂t hv ∂t τr

(8.4)

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where n(x, t) is the carrier concentration of a photoconductive substrate material; I opt (x, t) is the intensity of a laser pulse; R is the emission coefficient of the photoconductive surface; x is the distance from the semiconductor surface; τ r is the recombination time of the carriers in the photoconductivity; hv is the photon energy of the excited terahertz pulse. The photoconductive carrier concentration is defined as: ∞ n(t) =

n(x, t)dt

(8.5)

0

If the photoconductive antenna absorbs the incident femtosecond laser, the change rate of the carrier concentration of the epitaxial layer for the photoconductive antenna with time is:  ∂n epl (x, t) 1 − R = Iopt (0, t) − Iopt (l, t) ∂t hv  n epl (t)  n epl (t) 1− R Iopt (0, t) 1 − e−αl − − = τr,epl hv τr,epl

(8.6)

Similarly, the change rate of the carrier concentration of the substrate layer for the photoconductive antenna with time is:  n sub (t) 1 − R ∂n sub (x, t) = Iopt (0, t) − Iopt (l, t) − ∂t hv τr,sub   n 1− R sub (t) Iopt (0, t) 1 − e−αl − = hv τr,sub

(8.7)

Under an external bias voltage, the carriers (electrons and holes) accelerate towards the electrode, with the corresponding acceleration being:  dv

e

dt dvh dt

= − τvr eel +

= − τvrhel +

qe E m e f f,e qh E m e f f,h

(8.8)

where ve and vh are the drift velocities of electrons and holes, respectively; qe and qh are the electric quantities of electrons and holes, respectively; τ rel is the carrier relaxation time; E is the local electric field. The local electric field has a value much lower than the external bias electric field, which can be defined as: E = Eb −

P 3εr

(8.9)

where Er is the dielectric constant; P is the polarization intensity obtained after the separation of electrons and holes; Its change rate with the time is defined as:

8.4 Transmission Behavior of Metamaterials in Photoconductive THz-TDS …

P dP =− +J dt τr ec

147

(8.10)

where τ rec is the recombination time of electrons and holes; The Carrier Density J can be expressed as: J = envh − enve

(8.11)

where e is the mass of an electron. Therefore, the electric field in relation to the distant field radiation of terahertz waves generated by the photoconductive antenna is:

n 2 le ∂v ∂n n 2 le ∂ J (t) = + en g g ev E f ar (t) = 4πεr c2 ∂t 4πεr c2 ∂t ∂t

(8.12)

where l e is the effective length of the dipole antenna electrode gap. It can be seen from Eq. (8.12) that the terahertz far-field radiation intensity is related to the carrier concentration change rate and the carrier acceleration factor under a bias electric field. The change rate of the carrier concentration with the time contributes much more to the terahertz wave radiated by the photoconductive antenna than carrier acceleration. The terahertz pulse width radiated by the photoconductive antenna increases with the increase of the femtosecond laser pulse width, and the terahertz far-field radiation is proportional to the derivative of the effective mass of the carriers. For GaAs materials, the effective mass of holes is five times that of electrons, so the holes contribute very little to the terahertz radiation field. Figure 8.10 shows the terahertz picosecond pulse signal generated by the photoconductive antenna. Fig. 8.10 Terahertz pulse signals generated by a typical photoconductive antenna

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Fig. 8.11 Structure of a typical four-gap FG-SRR. a Optical micrograph of FG-SRR element, d = 6 μm, h = 3 μm, t = 10 μm, l = 66 μm, cycle p = 75 μm; b 3 × 3 array cyclically formed by FG-SRR elements

8.4.3 Terahertz Transmission Properties of Electrically Controlled Metamaterials 1. Device structure Figure 8.11 shows a typical square FG-SRR element. The internal design of the FG-SRR element is narrowed, and the width can be set to a micrometer level value, such as 1–10 μm. By changing the shape, the narrow edge resistance becomes higher, changing the current flow direction and value of the SRR element. The adjacent FG-SRR elements are connected with lines to control the current in Schottky device. 2. Experimental analysis In order to fully study the terahertz transmission properties of a M-FG-SRRs metamaterial device, a DC voltage source is set at both ends of the ohmic electrode and the Schottky electrode. The ohmic electrode is connected to the positive pole of the DC power supply, and the Schottky electrode is connected to the negative pole of the DC electrode, thus the width of the depletion layer and the relative dielectric constant of the device can be controlled through the reverse bias of the Schottky diode. Furthermore, the terahertz wave penetrating the metamaterial device can also be further regulated. During the experiment, the transmission direction of the incident terahertz wave is set to be perpendicular to the surface of the metal SRR array on the top layer of the metamaterial, see the polarization direction of the electric field shown in Fig. 8.12. The figure also shows several typical signals, including the time-domain terahertz transmission signals when the applied DC reverse bias is 0 V (black line), 4 V (blue line) and 8 V (red line). The time-interval for signal acquisition is 0–40 ps. It can be clearly seen that in the whole signal acquisition interval, each time-domain terahertz transmission signal contains the primary transmission component, the second transmission component, the third transmission component and the fourth transmission

8.4 Transmission Behavior of Metamaterials in Photoconductive THz-TDS … 0.8

0.8 0.7

0.6

0V 4V 8V

0.6

Transmission intensity

Fig. 8.12 Terahertz time-domain transmission signals under external reverse bias voltage of 0 V (solid line), 4 V (dotted line) and 8 V (dotted line) respectively

149

0.4

0.5

5.6

5.8

6.0

0.2 0.0 -0.2 -0.4

t1

-0.6 0

5

10

t2 15

20

t3 25

30

35

40

Time delay/ps

component in order, and their terahertz wave transmission signal strength gradually attenuates successively. The obvious multi-transmission effect and the gradual attenuation of the signals are mainly caused by the multi-reflection of the terahertz wave when transmitted in the metamaterial device and the corresponding energy loss during each transmission. In Fig. 8.12, the terahertz wave time-domain transmission signal of the M-FGSRRs metamaterial device under the external DC reverse bias of 4 V is almost the same as that under the reverse bias voltage of 0 V. The lasted time intervals between transmission peaks of adjacent time-domain transmission signals, from left to right, are t1 = ~ 9 ps, t2 = ~ 9.1 ps and t3 = ~ 9.2 ps, respectively. However, when the DC reverse voltage between the ohmic electrode and Schottky electrode of the metamaterial device increases to 8 V, the lasted time intervals of transmission peaks between adjacent time-domain transmission signals will be t1 = ~ 9 ps, t2 = ~ 9.3 ps and t3 = ~ 9.6 ps. Therefore, it can be considered that the increase of the time intervals is caused by the increase of the external reverse bias to 8 V. Compared with when the reverse bias is 4 V, the increase of voltage increases the transmission time of the third and fourth terahertz waves to some extent, causing a delay of the third and fourth transmission components. Since the overall structure of the M-FG SRRs metamaterial device is a Schottky diode, when the external DC reverse bias is connected between the ohmic electrode and the Schottky electrode of this diode, the width of the depletion layer in the Schottky region formed by the contact between the top metal SRR array and the middle n-GaAs layer will increase, and with the increase of the voltage, the width of the depletion layer will also expand quickly, so the increase of the depletion layer width leads to the delay of the time-domain transmission signals. It can be clearly seen from the figure that transmission signals with multiple uniform intervals and the gradual attenuation of intensity can be explained by the FP resonance principle.

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According to Fig. 8.12, the electric field components of the first, second, third and fourth transmission time-domain signals change periodically, and the phases of their adjacent transmission terahertz waves change to π. Generally, according to the reflection principle of electromagnetic waves at the interface, when transmitting in the isotropic medium, the corresponding electromagnetic wave phase will change by π after each reflection. Therefore, according to the classical electromagnetic wave reflection principle, the changed phases of the terahertz waves obtained by the second, third and fourth transmission should be 2π. Then, from the waveform of the timedomain terahertz transmission signals shown in the figure, it can be found that the adjacent time-domain transmission signals are generated by two reflections, and the phases changed after the transmission are π. It can be concluded that in the fabricated metamaterial device, the phases of the terahertz wave reflections are changed to π/2 each time. Since the M-FG-SRRs metamaterial device is a three-layer structure, the top layer is a cyclical FG-SRR metal planar array, the middle layer is n-GaAs, and the bottom layer is an SI-GaAs substrate, the metamaterial device fabricated by this composite multilayer structure makes the reflection phase change by π/2. Figure 8.13 shows the terahertz transmission spectrum of the M-FG-SRRs metamaterial device under the external reverse bias DC voltage. The polarization direction of its incident terahertz electric field has been clearly marked in the figure. The following is the discussion about the properties of the transmission spectrum obtained by calculating the time-domain transmission signals through FFT according to intervals. The peak frequency points of their transmission spectrum within 0.1–1.25 THz are respectively at 0.025, 0.07, 0.115, 0.145, 0.175, 0.21, 0.28, 0.32, 0.4, 0.52, 0.63, 0.74…, 1.21 THz. From the change of these peak frequency points, it can be clearly seen that the transmission spectrum of the M-FG-SRRs metamaterial device has an obvious intensive fluctuation effect within 0.01–0.21 THz in Region K1 as shown in Fig. 8.13. In addition, a very special transmission peak appears at the frequency point at 0.32 THz marked by S1 in Fig. 8.13. Near this transmission peak, when the external reverse bias reaches 8 V, a transmission peak with a slight amplitude also appears at the frequency point at 0.52 THz marked by S2, while when the voltage is 4 V, the corresponding transmission peak at this frequency point is not obvious. The peak frequency points of the above transmission spectrum within 0.025– 1.25 THz should be further analyzed. Among them, uniform spectral fluctuation or vibration of transmission peaks at the frequency points of 0.025, 0.145, 0.28, 0.4, 0.52, 0.63, 0.74…, 1.21 THz happens, and the spectral interval is f = 0.12 THz. The spectral interval of this uniform fluctuation or vibration is generally considered as an FP resonance effect, and this FP resonance happens when the terahertz wave transmits M-FG-SRRs metamaterial devices. The spectral interval of FP resonance is defined by Eq. (8.14).  f = c/2d

(8.14)

where c is the light velocity in vacuum; d is the optical length from top to bottom of the M-FG-SRRs metamaterial device. The calculated optical length is 1.25 mm.

8.4 Transmission Behavior of Metamaterials in Photoconductive THz-TDS … 10.0

0V 4V 8V

f

8.0

Transmission intensity

Fig. 8.13 Terahertz transmission spectrum of M-FG-SRRs metamaterial device under external reverse DC voltage of 0 V (black line), 4 V (blue line) and 8 V (red line)

151

6.0

P1 4.0

S1

S2

P2 S3

K3 K2

2.0

K1

0.0 0.0

0.3

0.6

0.9

1.2

Freq./THz

In the above frequency range of 0.025–1.25 THz, several scattered frequency points have unusual transmission peaks. These frequency points are found at 0.07, 0.115, 0.175, 0.21, 0.32 and 0.52 THz, respectively. Since having obvious transmission enhancement or suppression effects, these transmission peaks can be considered as having different micro-optics properties from the FP effect. Figure 8.14 describes the schematic diagram of an optical microcavity based on the FP resonance properties of the Schottky diode metamaterial structure. From the previous discussion, it is known that the thickness of the M-FG-SRRs metamaterial device is s = 0.381 mm. In addition, the relative refractive index of the GaAs substrate within 0.1–1.5 THz can be approximately 3.3, so the corresponding actual optical length can be 1.257 mm. This length is consistent with the results calculated according to the equation given above, indicating that the designed M-FG-SRRs metamaterial device is an FP resonant functional device in the terahertz band.

Fig. 8.14 Structural schematic diagram of Fabry-Pérot resonant optical microcavity based on metamaterials relating to terahertz transmission

Incident terahertz wave Metal SRR layer n-GaAs

s

SI-GaAs

Transmitted terahertz wave

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According to the actual measurement during the experiment, when the external reverse bias is 0 V, the electric field energy of the terahertz wave transmitted through the M-FG-SRRs metamaterial device will be ~ 1% that of the original incident terahertz wave. The Au film on the top-layer of the metamaterial device can reflect most of the incident terahertz wave, and at the same time the absorption capability of the GaAs substrate is weak within the far infrared to terahertz band, which can be considered that it absorbs a small part of the terahertz wave. Therefore, the reflectivity of the metal layer on the top-layer of the metamaterial device to the terahertz wave can be considered as ~ 90%. This high reflective film just facilitates the FP resonance of the metamaterial device, so under the optical length mentioned above, the fluctuation or vibration within the terahertz transmission spectrum of the M-FG-SRRs metamaterial device are caused by the FP resonance effect. In the transmission spectrum of the metamaterial device in Region K2 shown in Fig. 8.13, a transmission peak with a small amplitude at ~ 0.32 THz marked by S1 appears, which shows a transmission enhancement effect when the external reverse bias is 4 and 8 V. The enhancement amplitude when the voltage is 8 V is only a little bit higher than that when the voltage is 4 V. These transmission peaks are essentially different from other FP transmission peaks shown in the spectrum, because a transmission enhancement effect of the terahertz waves through M-FG-SRRs metamaterial devices appears. At present, related researchers have found through a large number of studies that the transmission enhancement of terahertz waves is mainly caused by FP resonance and surface plasmon polariton (SPP) resonance, etc. The above figure shows that the transmission enhancement peak at ~ 0.32 THz is different from that of the transmission peaks formed by control of other FP, therefore, it can be considered that it is related to the SPP effect of the top metal FG SRRs array of the metamaterial device. The fabricated metamaterial device M-FG-SRRs is composed of a typical subwavelength-level metal array, and the basic SPP mode of this metal SRR element can be defined as: f P S P = c(i 2 + j 2 )1/2 /Pn e f f

(8.15)

where c is the light velocity in the free space; i and j are integers, respectively; P is the cycle of the metal SRR element; neff is the effective dielectric constant of the dielectric. In the experiment, parameters i, j, P and nef are 1, 0 and 75 μm and ~ 12.5, respectively. Therefore, according to Eq. (8.15), the SPP resonance center frequency of the metal FG-SRR microstructure is 0.32 THz. According to the obtained transmission spectrum, the SPP effect center frequency of the M-FGSRRs metamaterial device is ~ 0.32 THz, which is consistent with the result of f PSP obtained based on Eq. (8.15). At the frequency point of 0.32 THz as shown in Fig. 8.13, when the external reverse bias is 4 V, the transmission intensity will be enhanced by ~ 16.7% compared with that when the voltage is 0 V. When the voltage is increased to 8 V, the transmission intensity will be enhanced by ~ 33.3% compared with that when the voltage is 0 V. It can be seen that when the voltage is doubled, the transmission intensity will also be

8.4 Transmission Behavior of Metamaterials in Photoconductive THz-TDS …

153

doubled because twice the electronic energy can be transmitted under the external voltage of 8 V compared with that under 4 V. The SPP effect of the metal layer of the metamaterial device within 0.01–0.52 THz is continuously excited by the incident terahertz wave. According to the unusual transmission in the terahertz spectrum regions marked by K1, K2 and K3 in the figure, these spectrum regions have obvious enhanced transmission properties. In the frequency spectrum part covered by Region K3, when the external reverse bias is increased to 8 V, compared with the transmission spectrum when the external reverse bias values are 0 and 4 V, the transmission spectrum at the frequency point of 0.52 THz has an obvious SPP effect and a transmission enhancement peak. This is mainly because the external power supply helps to transmit part of the electronic energy, making the amplitude of the SPP effect be higher. As shown in Fig. 8.13, for the frequency spectrum characteristics of Region K1, the corresponding frequency spectrum interval of FP resonance is ~ 0.12 THz. The starting frequency point of FP resonance is at 0.025 THz, which is indicated by Dotted Line P1. However, it is difficult to find the second FP resonance transmission peak that should have appeared at 0.145 THz in the spectrum results of the figure. Since the SPP component excited by the metamaterial device and the transmission peak generated by FP resonance have aliased in the low terahertz region (see Fig. 8.13 for the aliased region marked by S3), and the strength of the SPP component is not weak compared with FP, the SPP component is likely to affect the strength of the FP transmission peak within the aliased region. Therefore, the SPP effect slightly enhances the outgoing intensity of the first FP transmission peak, which is marked by P1, and at the same time, it greatly weakens the second FP transmission peak that should have appeared at frequency point P2, making the intensity of the transmission peak at this frequency point abnormal and obviously lower than the actual value. As shown in Fig. 8.13, when the external reverse DC bias is increased to 8 V, the FP transmission peak of the transmission spectrum of the M-FG-SRRs metamaterial device shifts monotonously to the low frequency direction, which is equivalent to the redshift of the spectrum. This is related to the change of the equivalent capacitance in the LC resonance circuit. According to the fabrication process of the metamaterial device described above, the top metal FG-SRR array film has a Schottky contact with the intermediate n-GaAs layer, and the depletion layer generated between the two layers can be controlled by the external reverse DC bias, making the charge accumulation in the depletion layer as a capacitor change correspondingly during LC resonance. Compared with the case when the reverse bias values are 0 and 4 V, the capacitance C in the depletion layer will become higher when the reverse bias is increased to 8 V within 0.28–1.25 THz, then the terahertz transmission spectrum of the metamaterial device will shift to the low frequency direction.

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The transmission spectrum of the M-FG-SRRs metamaterial device within 0.4– 0.72 THz is analyzed below. When the reverse DC bias is 4 V, the transmission intensity, compared with that when the voltage is 0 V, will be increased by 9%. When the voltage is increased to 8 V, the transmission intensity will be increased by 21% compared with that when the voltage is 0 V. The increase of this transmission intensity is closely related to the external DC voltage, indicating that it is caused by the change of current in the metal SRR layer. The Lorentz resonance property of this metal SRR unit can be expressed by the complex dielectric constant defined by Eq. (8.16). ε(ω) = ε1 (ω) − j σ/ω = ε1 (ω) + j ε2 (ω)

(8.16)

where E1 (ω) and E2 (ω) are the real part and imaginary part of the effective complex dielectric constant, respectively; σ is the conductivity of the metal SRR array on the top-layer of the M-FG-SRRs metamaterial device. The reflectivity of the metamaterial device can be defined by Eq. (8.17).      2 R(ω) =  (ε1 (ω) + j ε2 (ω))1/2 − 1 / (ε1 (ω) + j ε2 (ω))1/2 + 1 

(8.17)

When the external reverse DC bias increases from 4 to 8 V, the current in the metal film on the top-layer of the M-FG-SRRs metamaterial device will increase from 50 to 200 mA. As the current in the metal circuit increases, the surface temperature of the metal SRR layer rises obviously, increasing the resistance of the metal layer, which will lead to the reduction of Conductivity σ and Imaginary Part E2 (ω) for the dielectric constant of the metal layer. Therefore, after the external reverse DC bias is increased from 4 to 8 V, the terahertz reflection of the metal film will be reduced, and the reduction of the reflection capacity will be equivalent to the enhancement of the transmission signal through the metamaterial device. So it can be concluded that in the whole FP transmission process, the external reverse DC bias also plays a significant role in regulating the transmission performance. 3. Transmission characteristics in different SRR structures and THz electric field polarization directions In this section, metamaterial devices of different micro-SPP structures are tested and the electric field polarization direction of incident terahertz waves is changed in order to verify the FP resonance found in the experiments. (1) Transmission characteristics of the four-opening SRR structure with a narrowed middle line Figure 8.15 shows the structure of the four-opening SRR device with a narrowed middle line. In the following, we further study a metamaterial device of an SRR structure with a narrowed middle line. Since the transmission signal described above is related to a type of incident THz wave with an electric field in the vertical polarization direction, it is changed into the horizontal polarization direction below. Figure 8.16

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155

Fig. 8.15 Four-opening SRR structure with a narrowed middle line

Fig. 8.16 Time-domain THz transmission signals of narrowed middle line Four-opening SRR structure with an external reverse bias voltage of 0 V (black line), 4 V (blue line), and 8 V (red line), respectively

shows the transmission signals collected using the measurement method applied to the photoconduction experiment conducted above. The time-domain signal presented in Fig. 8.16 can be converted into a frequencydomain signal by FFT to obtain a THz transmission spectrum, as shown in Fig. 8.17. (2) Transmission characteristics of a four-opening SRR structure with a nonnarrowed middle line Figure 8.18 shows the structure of the four-opening SRR device with a non-narrowed middle line. The signals, which are time-domain THz transmission signals, are acquired twice for the metamaterial device of a four-opening SRR structure with a non-narrowed middle line. First, time-domain THz transmission signals are acquired from the THz wave with an electric field in the vertical polarization direction. Second, time-domain

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Fig. 8.17 THz transmission spectrum of narrowed middle line M-FG-SRRs metamaterial device with external DC reverse voltage of 0 V (black line), 4 V (blue line) and 8 V (red line)

Fig. 8.18 Structure of the four-opening SRR device with a non-narrowed middle line

THz transmission signals are acquired from the THz wave with an electric field in the horizontal polarization direction. Figure 8.19 shows the time-domain THz transmission signals acquired from the incident THz wave with an electric field in the vertical polarization direction using the measurement method applied to the photoconduction experiment conducted above. The time-domain signal presented in Fig. 8.19 can be converted into a frequencydomain signal by FFT to obtain a THz transmission spectrum, as shown in Fig. 8.20. Figure 8.21 shows a transmission signal acquired with the direction of the electric field of the incident THz wave changed into the horizontal polarization direction. The time-domain signal presented in Fig. 8.21 can be converted into a frequencydomain signal by FFT to obtain a THz transmission spectrum, as shown in Fig. 8.22. (3) Transmission characteristics of the SRR structure with a single central opening and a narrowed edge line Figure 8.23 shows the structure of the device with a single central opening and a narrowed edge line.

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Fig. 8.19 Time-domain THz transmission signals of non-narrowed middle line Four-opening SRR structure with an external reverse bias voltage of 0 V (black line), 4 V (blue line) and 8 V (red line), respectively

Fig. 8.20 THz transmission spectrum of non-narrowed middle line M-FG-SRRs metamaterial device with external DC reverse voltage of 0 V (black line), 4 V (blue line), and 8 V (red line)

Time-domain THz transmission signals are still acquired twice for the metamaterial device of an SRR structure with a single central opening and a narrowed edge line. First, time-domain THz transmission signals are acquired from the THz wave with an electric field in the vertical polarization direction. Second, time-domain THz transmission signals are acquired from the THz wave with an electric field in the horizontal polarization direction. Figure 8.24 shows the time-domain THz transmission signals acquired from the incident THz wave with an electric field in the vertical polarization direction using the measurement method applied to the photoconduction experiment conducted above. The time-domain signal presented Fig. 8.24 can be converted into a frequencydomain signal by FFT to obtain a THz transmission spectrum, as shown in Fig. 8.25. Figure 8.26 shows the time-domain transmission signals required by changing the polarization direction of the electric field of THz waves to vertical.

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Fig. 8.21 Horizontal polarization electric field Time-domain THz transmission signals of non-narrowed middle line Four-opening SRR structure with an external reverse bias voltage of 0 V (black line), 4 V (blue line) and 8 V (red line), respectively

Fig. 8.22 Horizontal polarization electric field THz transmission spectrum of non-narrowed middle line M-FG-SRRs metamaterial device with external DC reverse voltage of 0 V (black line), 4 V (blue line), and 8 V (red line)

Fig. 8.23 SRR structure with a single central opening and a narrowed edge line

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159

Fig. 8.24 Time-domain THz transmission signals of a single central opening and a narrowed edge line with an external reverse bias voltage of 0 V (black line), 4 V (blue line), and 8 V (red line), respectively

Fig. 8.25 THz transmission spectrum of a single central opening and a narrowed edge line M-SG-SRRs metamaterial device with external DC reverse voltage of 0 V (black line), 4 V (blue line), and 8 V (red line)

The time-domain signal presented Fig. 8.26 can be converted into a frequencydomain signal by FFT to obtain a THz transmission spectrum, as shown in Fig. 8.27. (4) Analysis of the transmission characteristics of different SRR structures under different electric field polarizations of incident THz wave During the abovementioned experiments on different SRR structures under different electric field polarizations of incident THz wave, the propagation direction of the incident THz wave must be perpendicular to the surface of the metallic SRR array on the top layer of the metamaterial. Three types of typical signals are presented in each of these figures, including time-domain THz transmission signals with an external DC reverse bias voltage of 0 V (black line), 4 V (blue line), and 8 V (red line), all collected in the time interval of 0–40 ps. In the entire time interval of signal acquisition, each time-domain THz transmission signal contains the primary, second,

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Fig. 8.26 Horizontal polarization electric field Time-domain THz transmission signals of a single central opening and a narrowed edge line with an external reverse bias voltage of 0 V (black line), 4 V (blue line) and 8 V (red line), respectively

Fig. 8.27 Horizontal polarization electric field THz transmission spectrum of a single central opening and a narrowed edge line M-SG-SRRs metamaterial device with external DC reverse voltage of 0 V (black line), 4 V (blue line) and 8 V (red line)

third, and fourth transmission components in order. Moreover, their THz transmission signal strength decreases in order. Such an apparent multiple transmission effect and the successive attenuation of signals are mainly attributed to the various reflections of the THz wave that occur when it is transmitted inside the metamaterial device and to the corresponding energy loss caused in each transmission process. The THz wave time-domain transmission signal of the metamaterial device under the external DC reverse bias of 4 V is almost the same as that under the reverse bias voltage of 0 V. In contrast, the time intervals between transmission peaks of adjacent time-domain transmission signals, from left to right, are 9 ps or so. However, when the DC reverse voltage between the ohmic electrode and Schottky electrode of the metamaterial device increases to 8 V, the lasting time intervals of transmission peaks

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161

between adjacent time-domain transmission signals will change more sharply. It can be considered that the rise of the external reverse bias to 8 V causes an increase in the time intervals. Compared with when the reverse bias is 4 V, the rise in voltage increases the transmission time of the third and fourth terahertz waves to some extent, causing a delay of the third and fourth transmission components. The overall structure of the metamaterial device is a Schottky diode. Therefore, when the external DC reverse bias is connected between the ohmic electrode and the Schottky electrode of this diode, the width of the depletion layer in the Schottky region formed by the contact between the top metal SRR array and the middle n-GaAs layer will increase. With the increase of the voltage, the width of the depletion layer will also expand quickly, so the rise of the depletion layer width leads to the delay of the time-domain transmission signals. As shown in the figure, transmission signals with multiple uniform intervals and the gradual attenuation of intensity can be explained by the FP resonance principle. For the THz transmission spectrum of the metamaterial device under the control of the external reverse bias DC voltage shown in Figs. 8.17, 8.20, 8.22, 8.25, and 8.27, there is a significant intensive fluctuation effect in the range of 0.01–0.21 THz. Besides, a very particular transmission peak appears at the frequency point at 0.32 THz. Near this transmission peak, when the external reverse bias reaches 8 V, a transmission peak with a small amplitude also appears at the frequency point at 0.52 THz, while when the voltage is 4 V, the corresponding transmission peak at this frequency point is not apparent. The peak frequency points of the above transmission spectrum within 0.025– 1.25 THz should be further analyzed. Among them, uniform spectral fluctuation or vibration of transmission peaks at the frequency points of 0.025, 0.145, 0.28, 0.4, 0.52, 0.63, 0.74…, 1.21 THz happens, and the spectral interval is f = ~ 0.12 THz. The spectral interval of this uniform fluctuation or vibration is generally considered an FP resonance effect, and this FP resonance happens when the terahertz wave transmits the metamaterial devices. In the transmission spectrum of the metamaterial device shown in Figs. 8.17, 8.20, 8.22, 8.25 and 8.27, there is an enhanced transmission effect at the 0.32-THz transmission peak when the external reverse bias is 4 and 8 V. Moreover, the enhancement amplitude at the voltage of 8 V is a bit greater than that at the voltage of 4 V. This transmission peak is essentially different from other FP transmission peaks shown in the spectrum because a transmission enhancement effect of the terahertz waves through the metamaterial devices appears. At present, related researchers have found through many conducted studies that the transmission enhancement of terahertz waves is mainly caused by FP resonance and SPP) resonance, etc. The above figure shows that the transmission enhancement peak at 0.32 THz differs from that of the transmission peaks formed by control of other FP. Therefore, it can be considered that it is related to the SPP effect of the top metal FSRRs array of the metamaterial device.

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8.5 Summary Metal SRR micro structure array is a key part for inducing incident THz waves. This chapter discusses the resonance mechanism of electrically controlled Schottky metamaterial devices sensing incident THz waves. (1) Based on the SRR element model with a narrowed middle part or edge, the metamaterial device and its wide opening of electronically controlled pins are fabricated; (2) For the reflective THz-TDS system, the transmission experiment is carried out by using a single-opening and a four-opening SRR element structure metamaterial devices. The single-opening metamaterial is subject to intensive oscillation within 0.1–1 THz, which is consistent with the frequency range of the characteristic transmission spectrum of metamaterials devices. The center frequency of the characteristic terahertz transmission spectrum measured during the experiment is consistent with the dipole resonance frequency of about 0.51 THz. The original transmission spectrum of the four-opening metamaterial device has an obvious fluctuation effect within 0.6–1.23 THz and 1.52–2.4 THz, which is consistent with frequencies of 0.51, 1.02, 1.53, 2.04 and 2.55 THz calculated based on the center frequency of the dipole resonance in the microstructure. (3) For the photoconductive THz TDS system, all the different SRR structure metamaterial devices have a FP effect. When the reverse DC voltage of a metamaterial device is increased to 8 V, the time-delay of the time-domain transmission signal becomes higher due to the increase of the depletion layer width, and uniform spectral fluctuation or vibration in the frequency spectrum can happen with an interval of f = ~ 0.12 THz. In addition, the micro-optics properties at different frequencies correspond to the SPP effect, which is consistent with the result of 0.32 THz obtained based on the SPP equation. When the external reverse DC bias increases from 4 to 8 V, the current in the metamaterial device will increase, resulting in a decrease of the conductivity of the metal layer and the imaginary part of the dielectric constant, which will weaken the terahertz reflected by the metal film and enhance the transmission intensity. Therefore, during the whole FP transmission process, the external reverse DC bias also plays a significant role in regulating the transmission performance.

References 1. Krishnamurthy S, Reiten MT, Harmon SA, et al. Characterization of thin polymer films using terahertz time-domain interferometry. Appl Phys Lett. 2001;79(6):875–7. 2. Lee KS, Lu TM, Zhang XC. The measurement of the dielectric and optical properties of nano thin films by THz differential time-domain spectroscopy. Microelectron J. 2003;34:63–9. 3. Brucherseifer M, Bolivar PH, Kurz H. Combined optical and spatial modulation THzspectroscopy for the analysis of thin-layered systems. Appl Phys Lett.2002;81(10):1791–93.

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4. Hashimshony D, Geltner I, Cohen G, et al. Characterization of the electrical properties and thickness of thin epitaxial semiconductor layers by THz reflection spectroscopy. J Appl Phys. 2001;90(11):5778–81. 5. Dai J, Xie X, Zhang XC. Detection of broadband terahertz waves with a laserinduced plasma in gases. Phys Rev Lett. 2006;97(10): 103903. 6. Xie X, Dai J, Zhang XC. Coherent control of THz wave generation in ambient air. Phys Rev Lett. 2006;96(7): 075007. 7. Kim KY, Taylor AJ, Glownia JH, et al. Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions. Nat Photonics. 2008;2(10):605–9. 8. Laman N, Harsha SS, Grischkowsky D et al. 7 GHz resolution waveguide THz spectroscopy of explosives related solids showing new features. Opt Express. 2008;16(6):4094–05. 9. Harsha SS, Grischkowsky D. Terahertz (far-infrared) characterization of tris(hydroxymethyl)aminomethane using high-resolution waveguide THz–TDS. J Phys Chem A. 2010;14(10):3489–94. 10. Cunningham J, Byrne M, Wood CD, et al. On-chip terahertz systems for spectroscopy and imaging. Electron Lett. 2010;46(26):S34–7. 11. Pendry JB, Holden AJ, Robbins DJ, et al. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans Microw Theory Tech. 1999;47(11):2075–84. 12. Driscoll T, Andreev GO, Basov DN, et al. Tuned permeability in terahertz split-ring resonators for devices and sensors. Appl Phys Lett. 2007;91(6): 062511. 13. Sun Y, Xia X, Feng H, et al. Modulated terahertz responses of split ring resonators by nanometer thick liquid layers. Appl Phys Lett. 2008;92(22): 221101. 14. Bingham CM, Tao H, Liu X, et al. Planar wallpaper group metamaterials for novel terahertz applications. Opt Express. 2008;16(23):18565–75.

Chapter 9

Induction and Detection of Optical Frequency Infrared Signals by Metamaterials

9.1 Preface Optical frequency infrared detection technology is widely used in airport security inspection system, material detection, spatial signal detection, aerospace, industrial and agricultural production, etc. Common optical frequency infrared detectors mainly include temperature detectors, high-temperature superconducting detectors, and semiconductor detectors made of Si or GaAs. The principles of these detectors are mature and have been widely used. However, for high-speed and high-sensitivity signal detection, existing infrared detectors have the following problems: the spectral imaging device of detectors still needs to be equipped with complex and precise servo, driving or scanning mechanisms, so they are always big and heavy; The response speed of detectors is slow; The spectral detection wavelength range of detectors is fixed and cannot be adjusted or changed. In recent years, a lot of studies on metamaterials have proved that electromagnetic waves within several frequency bands can make some special metal patterns with micro/nano characteristic dimensions generate a large number of electrons. These electrons induce secondary electromagnetic oscillations or plasmas in micro/ nano patterns through collective oscillation, thus completing the physical process for sensing incident electromagnetic wave fields through special micro/nano metal structures. The short and quick signal response is kept within a nanosecond or even sub-nanosecond time-domain, and can be quantitatively adjusted by means of electric or magnetic control. The special micro/nano metal pattern arrays of metamaterials can help to sense incident electromagnetic wave field at a high speed and sensitivity. This efficient coupling of and response to electromagnetic waves through resonance induction is a new detection mode and structure for sensing optical frequency infrared signals [1–4].

© National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_9

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Under the excitation of electromagnetic radiation within an optical frequency infrared band, the split-ring resonator of artificial metamaterials needs to resist the change or influence of incident electromagnetic radiation on their electromagnetic state. It can sense the ring current by the physical form of resonance, and has a negative permeability. The line array coupled with it provides the plasma dielectric coefficient. When the electromagnetic radiation frequency is lower than the resonance frequency, a negative dielectric coefficient will appear. This chapter will discuss the basic method for sensing optical frequency infrared signals of artificial metamaterials made of micro structures. For this method, a CCD sensor is used to acquire its transmission images, and converts the detection of infrared signals into the detection of visible light signals, which can be considered as a new optical frequency signal sensing mode. This research has a positive effect on the development of new optical frequency infrared detectors in the future, and therefore new breakthroughs are expected.

9.2 Induction and Detection of Near Infrared Laser by Metamaterials 9.2.1 Near Infrared Semiconductor Laser In 1961, Basov first proposed the possibility of current injection of free carriers into semiconductor PN junctions to realize population inversion. This semiconductor material based lasers, like crystal diodes in structure, are also based on the PN junction properties of materials, so semiconductor lasers are often called diode lasers. Common semiconductor lasers include edge emission and surface emission semiconductor lasers, homojunction semiconductor lasers, heterojunction semiconductor lasers, visible light semiconductor lasers, distributed feedback semiconductor lasers and quantum-well lasers [5–7]. Semiconductor lasers are devices that taking some semiconductor materials as working materials to allow stimulated emission. Their operating principle is to realize the population inversion of non-equilibrium carriers between the energy band (conduction band and valence band) of a semiconductor material or between the energy band of the semiconductor material and the impurity (acceptor or donor) energy level through a certain excitation mode. When a large number of electrons in the population inversion state are combined with holes, the stimulated emission will occur. Semiconductor lasers are mainly provided with three excitation modes, namely current injection, optical pumping and high-energy electron beam excitation modes. Current injection semiconductor lasers are generally semiconductor junction diodes made of CaAs, InP, and ZnS, etc., which can be excited by injecting current along the forward bias to allow stimulated emission at junction plane areas. Generally, optically pumped semiconductor lasers take N-type or P-type semiconductor single-crystals as the working materials, and laser emitted by other lasers as the optically pumped excitation. High-energy electron beam excited semiconductor lasers

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take N-type or P-type semiconductor single-crystals as working materials and are excited by external injection of high-energy electron beams. For semiconductor laser devices, current injection GaAs diode lasers with doubleheterostructure and excellent performance are widely used at present. They are also called semiconductor junction diode injection lasers because they can inject carriers into the positive biased PN junctions of semiconductors to generate light radiation [8–10]. Generally, gallium arsenide is used as the semiconductor material. The wavelength of 84 nm is covered in the near infrared region.

9.2.2 Principle Analysis on Near Infrared Semiconductor Laser 1. Shape and core structure of GaAs lasers The casing of a typical GaAs laser has a small window for laser output. The electrodes of the laser are used for external power supply. Inside the casing is the laser tube core that can be rectangular, mesa shaped and strip shaped. Its core part is a PN junction. The two end faces of the PN junction of the semiconductor laser are cut according to the natural crystal plane of a crystal, which is called cleavage plane. These two surfaces are extremely smooth and can be directly used as parallel mirrors to form a laser resonant cavity. Laser can be output from one side or both sides of the cleavage surface. 2. Beam characteristics of semiconductor lasers If the half power beamwidth of laser in the direction of the junction plane is θ // , and the beamwidth perpendicular to the direction of the junction plane is θ ⊥ , the beamwidth of the fundamental mode will be: θ// = λ/ω

(9.1)

where ω is the horizontal dimension of junction area; λ Is the laser wavelength. The beamwidth perpendicular to the junction plane is: θ⊥ = 2λ/d

(9.2)

where d is the thickness of the active area, which is usually higher than l µm and can be calculated approximately according to the width of the narrow single-gap diffraction angle. In fact, θ ⊥ is in line with the actual situation, while θ // is quite different from the actual situation, so it cannot be calculated according to the calculation method of source field divergence angle.

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Due to the short resonant cavity of the semiconductor laser and the poor laser directivity, the divergence angle in the vertical plane of the junction can reach up to 20°–30°. In the horizontal plane of the junction, the divergence angle is about several degrees. The operating wavelength of semiconductor lasers varies with the structure. For example, for double-heterostructure lasers, lasers with different wavelength ranges can be generated by changing the Al content of AlGaAs materials. Currently, the laser wavelength of 0.85 m is popular. Due to the development of optical fiber manufacturing technology, the transmission loss of optical fibers within 1.0–1.8 m, especially within 1.3–1.55 m, is extremely low. Therefore, with the promotion of optical fiber communication, researches on long wave lasers such as Inx Gal−x As lasers (0.87– 1.7 µm), GaAsl−x Sbx lasers (0.4–1.4 µm), Inx Gal−x Asl−y Py lasers (0.92–1.7 µm) are under progress. 3. Conversion efficiency The current injection semiconductor laser is a device that directly converts electric power to luminous power with high conversion efficiency. The conversion efficiency is usually determined by quantum efficiency and power efficiency. (1) Quantum efficiency The quantum efficiency is defined as: ηD =

(P − Pth )/ hν (i − i th )/e

(9.3)

where P is the output power; Pth is the emitted light power threshold; hv is the emitted photon energy; i is the forward current; ith is the forward threshold current; e is the electronic charge. Since P  Pth , Eq. (10.3) can be changed to: ηD =

P P/ hν = (i − i th )/e (i − i th )V

(9.4)

where V is the forward bias. It can be seen from this equation that ïD actually corresponds to the slope in the linear range above the threshold in the relationship curve between the output power and forward current. (2) Power efficiency Power Efficiency ïP is defined as the ratio of the laser output power to the input electric power. ηP =

P i V + i 2 RS

(9.5)

where V is the voltage drop of the PN junction; RS is the series resistance of the laser (including material resistance and contact resistance). The working current of

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Fig. 9.1 Optical detection scheme of metamaterial for near-infrared laser

the laser and resistance power consumption are high, so the power efficiency under room temperature is only a few percent.

9.2.3 Scheme and Architecture Under near infrared radiation excitation, since it is necessary to resist the change or influence of incident electromagnetic radiation on the electromagnetic state of the metamaterial device, the metal SRR array on the top-layer of the metamaterial device and the Schottky contact region will produce some induction characteristics, which are very likely to be observed in images in the optical CCD after the signals are amplified by the microscopic objective. Therefore, the detection scheme of a typical metamaterial sensed near infrared laser is shown in Fig. 9.1. In order to clearly show the relative position of the metamaterial in the optical path, the detection part of the metamaterial device in Fig. 9.1 is magnified to obtain the working area of the metamaterial device as shown in Fig. 9.2. The microscopic objective is kept very close to the top-layer metal SRR array area of the metamaterial device, and this distance can be adjusted from 0.1 to 10 mm. The microscopic objective can be used to magnify the optical changes of the metal array surface on the top-layer of the metamaterial device for observation.

9.2.4 Near Infrared Laser Sensing of Metamaterials Metamaterial devices made of metal microstructure element patterns can be used for sensing near infrared laser. 1. Light spot of near infrared semiconductor laser source At the beginning of the experiment, use a laser beam profiler first to acquire the laser spot image output by a near infrared laser for the subsequent comparison of experimental data. Then according to the optical path operating principle of experimental optical detection, place an objective with a 20 × magnification next to the front end

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Metamaterial device

Fig. 9.2 Working area of metamaterial device

of the laser beam profiler to amplify the acquired near infrared laser spot images. The spot diameter acquired in the experiment is about 2 mm, see its 2D image and 3D distribution view shown in Fig. 9.3. 2. Focusing experiment of near-infrared laser optical transmission For designed and fabricated metamaterial devices, since their overall thickness, metal film thickness and GaAs substrate thickness are the same, the imaging positions of each metamaterial device in the entire optical path should be uniform. First, a focusing experiment should be carried out for the fabricated metamaterial device for obtaining the optimal imaging positions in the optical path. The microstructure metamaterial device as shown in Fig. 10.4 should be selected for the focusing experiment. The horizontal distance between the near infrared laser source in the optical path and the circuit board of the metamaterial device is 40 cm. The laser beam profiler and 20 × objective are used to acquire the near infrared transmission image when the horizontal distances to the metal array surfaces of the two metamaterial devices are 0.4 mm, 0.5 mm and 0.6 mm, respectively, see Fig. 10.5a–c (Fig. 9.4). It can be seen from Fig. 9.5 that the definition of the transmission images acquired is the highest when the horizontal distance to the metal array surfaces of the metamaterial devices is 0.5 mm. In the subsequent experiment, this value will be determined as the focusing distance of the metamaterial devices in the optical path. Fig. 9.3 Near infrared laser Gaussian spot. a 2D image; b 3D perspective view

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Fig. 9.4 Two metamaterial element structures used in focusing experiment

Fig. 9.5 Near infrared transmission images of metamaterials acquired by laser beam profiler and 20 × objective. a Distance between metamaterial and objective: 0.4 mm; b distance between metamaterial and objective: 0.5 mm; c distance between metamaterial and objective: 0.6 mm

3. Optical transmission images of metamaterial sensed near infrared laser at different exposure time settings In order to explore the sensing effect of metamaterials on near-infrared signals as comprehensively as possible, the metamaterial structure shown in Fig. 9.6 is selected. The horizontal distance between the near infrared laser source in the optical path and the circuit board of the metamaterial device is 40 cm. The near infrared transmission image reflecting a horizontal distance of 0.5 mm to the metal array surface of the metamaterial device is acquired with a laser beam profiler and a 20 × objective. The exposure time settings are 0.04 ms, 0.4 ms, 0.6 ms, 0.8 ms 1.0 ms and 1.5 ms, respectively, see Fig. 9.7. It can be seen in Fig. 9.7 that in the near infrared transmission images acquired by the CCD detector of the laser beam profiler under different exposure time settings, a large number of dense and scattered bright spots appear on the top metal-free area of the metamaterial device. The near infrared transmission image acquired at the exposure time of 1.0 ms is partially magnified for the sake of easy observation, see Fig. 9.8.

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Fig. 9.6 Optical micrograph of metamaterial microstructure under d = 6 µm, h = 3 µm, t = 10 µm, l = 66 µm

Fig. 9.7 Optical images of metamaterial sensed near infrared laser at different exposure time settings. a exposure time: 0.04 ms; b exposure time: 0.4 ms; c exposure time: 0.6 ms; d exposure time: 0.8 ms; e exposure time: 1.0 ms; f exposure time: 1.5 ms

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Fig. 9.8 Partial magnification of near infrared transmission image at exposure time of 1 ms

As shown in Fig. 9.8, it can be concluded that the image has the following characteristics according to the carefully observed bright spots: (1) Very short diameter. Because the minimum line width of the SRR pattern is 3 µm, according to the comparison, the bright spot size is about 1 µm. Considering that the spot diameter of the output near infrared laser is 2 mm, it is concluded that the metamaterial can be used to sense near infrared light to some extent, and generate a large number of transmission bright spots. (2) Different strength distribution. The intensity of brightness at different positions varies, which, on the one hand, may be related to the lights with different wavelengths in the near infrared laser and on the other hand, to the characteristics of the SRR array. The visible image of the metamaterial irradiated by the near infrared laser has special micro-optics characteristics. Since the GaAs substrate is a material with strong transmissivity in the infrared band, GaAs will not stop too much energy of the incident near infrared light. The material characteristics of the metal SRR array area made of Ti/Au make the metal covered part stop the transmission of most near infrared light, so the metal area in the transmission image is black, i.e. there is no any detected light energy or the detected light energy is low. After magnification, bright spots with maximum strength and minimum area are generated at the internal gap of the metal SRR and that between adjacent SRRs. According to the relationship between the scale and bright spot sizes, it can be calculated that the diameter of the smallest bright spot in Fig. 9.8 is about 1 µm. These characteristics of light detailing and partial extremely bright light spot generating after transmission are novel. 4. Transmission images of different areas in the SRR array of the same metal under near-infrared irradiation The metamaterial device corresponding to the SRR cell shown in Fig. 9.9 is selected further to investigate the sensing effect of metamaterials on near-infrared signals.

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Fig. 9.9 Four-opening SRR element

The horizontal distance between the near-infrared laser source in the optical path and the circuit board of the metamaterial device is 40 cm. The time of exposure is set to 0.2 ms. The near-infrared transmission image reflecting a horizontal distance of 0.5 mm to the metal array surface of the metamaterial device is acquired twice with a laser beam profiler and a 20 × objective. Images are obtained from the metamaterial device’s lower left and middle regions at the first time and second time, as shown in Figs. 9.10 and 9.11. As shown in Figs. 9.10 and 9.11, the visible image of the metamaterial irradiated by the near-infrared laser has unique micro-optic characteristics. Since the GaAs substrate is a material with strong transmissivity in the infrared band, GaAs will not stop too much energy from the incident near-infrared light. The material characteristics of the metal SRR array area made of Ti/Au make the metal-covered part prevent the transmission of most near-infrared light. So the metal area in the transmission image is black, i.e., there is no any detected light energy or the detected light energy is low. An in-depth analysis of (e) and (f) in Figs. 9.10 and 9.11 shows that after magnification, bright spots with maximum strength and minimum area are generated at the internal gap of the metal SRR and that between adjacent SRRs. According to the relationship between the scale and bright spot sizes, it can be calculated that the diameter of the minor bright spot in (e) and (f) is about 1 µm. 5. Transmission images are captured when there are positional relations between the near-infrared laser source and the metamaterial device Two metamaterial devices corresponding to SRR elements, as shown in Fig. 9.12, are selected to investigate further the sensing effect of metamaterials on near-infrared signals at different spatial distances. The laser beam profiler and 20 × objective lens in the optical path at a horizontal distance of 0.5 mm from the surface of the metallic array of the metamaterial devices, and the time of exposure is 0.2 ms. The horizontal distance between the near-infrared laser source in the optical path and the circuit board of the metamaterial devices is set to 20 cm, 35 cm, and 50 cm for acquiring near-infrared transmission images at corresponding distances, respectively. First, the metamaterial device built from the SRR element shown in Fig. 9.12a is investigated. Experiments are conducted in three cases. According to the principle of optical circuit design, the horizontal distance between the near-infrared laser source and the circuit board of the metamaterial device is set to 20 cm, 35 cm, and 50 cm,

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Fig. 9.10 The experiment at the first time, transmission intensity images of metamaterial device’s lower left regions under near-infrared irradiation. a Transmission image of the metal array and local enlargement effect of the metamaterial under near-infrared laser irradiation; b 3D intensity distribution of transmission image; c intensity distribution of transmission image in the horizontal direction; d intensity distribution of transmission image in the vertical direction; e enlarged view of area 1 in transmission image; f enlarged view of area 2 in the transmission image

respectively for acquisition of metamaterial transmission images at corresponding distances. Figure 9.13 shows the near-infrared transmission images of the metamaterial collected with the CCD camera in the laser beam profiler when the near-infrared laser source is set at a horizontal distance of 20 cm from the circuit board of the metamaterial device.

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Fig. 9.11 The experiment at the second time, transmission intensity images of metamaterial device’s middle regions under near-infrared irradiation. a Transmission image of the metal array and local enlargement effect of the metamaterial under near-infrared laser irradiation; b 3D intensity distribution of transmission image; c intensity distribution of transmission image in the horizontal direction; d intensity distribution of transmission image in the vertical direction; e enlarged view of area 1 in transmission image; f enlarged view of area 2 in the transmission image

Figure 9.14 shows the near-infrared transmission images of the metamaterial collected with the CCD camera in the laser beam profiler when the near-infrared laser source is at a horizontal distance of 35 cm from the circuit board of the metamaterial device. Figure 9.15 shows the near-infrared transmission images of the metamaterial collected with the CCD camera in the laser beam profiler when the near-infrared laser

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Fig. 9.12 SRR element structures for experiments conducted at different distances from the laser source. a Square four-opening SRR; b circle four-opening SRR

Fig. 9.13 Metamaterial transmission images are acquired when the near-infrared laser source is at a horizontal distance of 20 cm from the circuit board of the metamaterial device. a Transmission image of the metal array and local enlargement effect of the metamaterial under near-infrared laser irradiation; b 3D intensity distribution of transmission image; c intensity distribution of transmission image in the horizontal direction; d intensity distribution of transmission image in the vertical direction

source is at a horizontal distance of 50 cm from the circuit board of the metamaterial device. For the convenience of observation, areas 1 and 2 in Fig. 9.15a are enlarged to obtain the locally enlarged image shown in Fig. 9.16. Then, the metamaterial devices built out of the SRR elements shown in Fig. 9.12a are investigated. Experiments are conducted in three cases. According to the principle of optical circuit design, the horizontal distance between the near-infrared laser

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Fig. 9.14 Metamaterial transmission images are acquired when the near-infrared laser source is at a horizontal distance of 35 cm from the circuit board of the metamaterial device. a Transmission image of the metal array and local enlargement effect of the metamaterial under near-infrared laser irradiation; b 3D intensity distribution of transmission image; c intensity distribution of transmission image in the horizontal direction; d intensity distribution of transmission image in the vertical direction

source and the circuit board of the metamaterial device is set to 20 cm, 35 cm, and 50 cm, respectively for acquisition of metamaterial transmission images at corresponding distances. Figure 9.17 shows the near-infrared transmission images of the metamaterial collected with the CCD camera in the laser beam profiler when the near-infrared laser source is at a horizontal distance of 20 cm from the circuit board of the metamaterial device. Figure 9.18 shows the near-infrared transmission images of the metamaterial collected with the CCD camera in the laser beam profiler when the near-infrared laser source is at a horizontal distance of 35 cm from the circuit board of the metamaterial device. Figure 9.19 shows the near-infrared transmission images of the metamaterial collected with the CCD camera in the laser beam profiler when the near-infrared laser source is at a horizontal distance of 50 cm from the circuit board of the metamaterial device. For the convenience of observation, areas 1 and 2 in Fig. 9.19a are enlarged to obtain the locally enlarged image shown in Fig. 9.20.

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Fig. 9.15 Near-infrared transmission images of the metamaterial captured when the laser source is at a horizontal distance of 50 cm from the circuit board of the metamaterial device. a Transmission image of the metal array and local enlargement effect of the metamaterial under near-infrared laser irradiation; b 3D intensity distribution of transmission image; c intensity distribution of transmission image in the horizontal direction; d intensity distribution of transmission image in the vertical direction

Fig. 9.16 Enlarged view of transmission image. a Enlarged view of area 1 in the transmission image at the distance of 50 cm; b Enlarged view of area 2 in the transmission image at the distance of 50 cm

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Fig. 9.17 Near-infrared transmission images of the metamaterial devices. a Near-infrared transmission image of the metamaterial acquired when the near-infrared laser source is 20 cm away from the metamaterial; b 3D intensity distribution of transmission image; c intensity distribution of transmission image in the horizontal direction; vertical intensity distribution of transmission image

Figure 9.21 shows the near-infrared transmission images of the metamaterial collected with the CCD camera in the laser beam profiler when the near-infrared laser source is at a horizontal distance of 65 cm from the circuit board of the metamaterial device. For the convenience of observation, areas 1 and 2 in Fig. 9.21a are enlarged to obtain the locally enlarged image shown in Fig. 9.22. As can be seen from the locally enlarged images in Figs. 9.20 and 9.22, the visible image of the metamaterial irradiated by the near-infrared laser has unique micro-optic characteristics. Since the GaAs substrate is a material with strong transmissivity in the infrared band, GaAs will not prevent too much energy from the incident nearinfrared light. The material characteristics of the metal SRR array area made of Ti/ Au make the metal-covered part prevent the transmission of most near infrared light. So the metal area in the transmission image is black, i.e. there is no any detected light energy or the detected light energy is low. An in-depth analysis of (a) and (b) in Figs. 9.20 and 9.22 shows that after magnification, bright spots with maximum strength and minimum area are generated at the internal gap of the metal SRR and that between adjacent SRRs. According to the relationship between the scale and bright spot sizes, it can be calculated that the diameter of the minor bright spot in the figures is about 1 µm. These characteristics of light detailing and partial extremely bright light spot generating after transmission are novel.

9.3 Induction and Detection of Blackbody Infrared Wave by Metamaterials

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Fig. 9.18 Near-infrared transmission images of the metamaterial devices. a Near-infrared transmission image of the metamaterial acquired when the near-infrared laser source is 35 cm away from the metamaterial; b 3D intensity distribution of transmission image; c intensity distribution of transmission image in the horizontal direction; vertical intensity distribution of transmission image

9.3 Induction and Detection of Blackbody Infrared Wave by Metamaterials Blackbodies are idealized objects for absorbing all external electromagnetic radiation without any reflection and transmission. The absorption and transmission coefficients of blackbodies for electromagnetic wave of any wavelength are 1 and 0, respectively. However, a blackbody is not necessarily black. Even if it can not reflect any electromagnetic wave, it can also emit electromagnetic waves. The wavelength and energy of these electromagnetic waves depend on the temperature of the blackbody and will not be changed by other factors. Of course, a blackbody looks black when it is below 700 K, but which is only because the radiation energy emitted by the blackbody below 700 K is very low and the radiation wavelength is kept out of the visible light range. If the temperature of the blackbody is higher than the above mentioned, it will no longer be black. It will start to turn red, and with the increase of the temperature, to orange, yellow, white, etc., namely, the absorption and emission of electromagnetic waves by the blackbody are consistent with the spectrum, showing a Planck’s trajectory (or blackbody trajectory). The blackbody radiation refers actually to the thermal radiation. In the blackbody spectrum, high temperature can cause high frequency, namely, short wavelength, so those blackbodies with higher temperature are shown

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Fig. 9.19 Near-infrared transmission images of the metamaterial devices. a Near-infrared transmission image of the metamaterial acquired when the near-infrared laser source is 50 cm away from the metamaterial; b 3D intensity distribution of transmission image; c intensity distribution of transmission image in horizontal direction; vertical intensity distribution of transmission image

Fig. 9.20 Enlarged view of transmission image shown in Fig.9.19. a Enlarged view of area 1 in the transmission image; b enlarged view of area 2 in the transmission image

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Fig. 9.21 Near-infrared transmission images of the metamaterial devices. a Near-infrared transmission image of the metamaterial collected when the near-infrared laser source is at a horizontal distance of 65 cm from the circuit board of the metamaterial device; b 3D intensity distribution of transmission image; c intensity distribution of transmission image in the horizontal direction; d intensity distribution of transmission image in the vertical direction

Fig. 9.22 Enlarged view of transmission image shown in Fig.9.21. a Enlarged view of area 1 in the transmission image; b enlarged view of area 2 in the transmission image

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close to the blue area at the end of the spectrum, while those with lower temperature, to the red area. At room temperature, the energy of blackbody radiation is concentrated in longwave electromagnetic radiation and far infrared wave bands; after the blackbody temperature reaches hundreds of degrees Celsius, the blackbody will emit visible light. Taking a steel piece as an example, with the rise of temperature, it turns red, orange and yellow respectively. When the temperature exceeds 1300 °C, it will become white and blue. When turning white, the black body will also emit UV rays heavily. The term blackbody was first named by Kirchhoff in 1862 and introduced into the thermodynamics. The light emitted by blackbody is called blackbody radiation. The radiation power P per unit surface area of a blackbody is proportional to the fourth power of its temperature T. The radiation process of blackbodies arouses physicists’ interest in the thermal equilibrium state in the quantum field. For classical physics, all Fourier models regarding heat balance follow the equipartition theorem of energy. When physicists adopt classical physics to explain blackbodies, a UV disaster occurred inevitably, namely, the Rayleigh Kings law used to calculate the radiation intensity of blackbodies tends to infinity when the radiation frequency tends to infinity. Blackbodies can be used to test the properties of thermal equilibrium and the radiation they emit follow the thermodynamic scattering law, so the research on blackbodies in history has become an opportunity to start the study on quantum physics. Planck established the Blackbody Radiation Law in 1900, which distinguishes the energy in an electromagnetic field according to the different vibration modes of charged vibrators in matters. The blackbody emissivity is a function of frequency and can be defined by Eq. (9.6). I (ω, T ) =

1 2hω3 • hω/kT c2 e −1

(9.6)

where I (ω, T ) is the emissivity indicating the energy radiated from a unit frequency interval. h is the Planck constant; c is the light velocity; e is the natural logarithm; T is the temperature expressed in K; k is the Boltzmann constant expressed in J/K. After converting into the function of wavelength, the emissivity in unit solid angle will be: I (λ, T ) =

1 2hc2 • hc/λkT λ5 e −1

(9.7)

where: I (λ, T ) is the emissivity indicating the energy radiated from a unit frequency interval expressed in Joule·s−1 m−2 ·Sphericity−1 m−1 . The relationship between Eqs. (9.6) and (9.7) is: I (ω, T )dω = −I (λ, T )dλ

(9.8)

9.3 Induction and Detection of Blackbody Infrared Wave by Metamaterials

185

9.3.1 Sensing Properties of Metamaterials to Blackbody Radiation Figure 9.23 shows the common blackbody radiation source. Its infrared radiation wavelength is related to the temperature. When the temperature of the blackbody is set to 1000 °C, the intensity distribution of the output infrared wave spots is shown in Fig. 9.24. As shown in Fig. 9.25, after the infrared wave radiated by the blackbody irradiate the top metal SRR array of a metamaterial device, there will be uniformly distributed diffraction spots in the metal-free area. According to Fig. 9.26, interference fringes appear in the gaps inside the SRR elements and between SRRs, and the intensity of the fringes is higher than the light intensity of other areas shown in the figure. The experiment shows that the metamaterial device can be used for sensing infrared light radiated by blackbodies. Therefore, designing an appropriate SRR array pattern can help to realize and improve the infrared sensing function of metamaterials. Fig. 9.23 Typical blackbody radiation source

Fig. 9.24 3D intensity distribution of blackbody radiation spots

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9 Induction and Detection of Optical Frequency Infrared Signals …

Fig. 9.25 Optical 20 × magnification image of infrared wave radiated by blackbody sensed by metamaterial. a 2D transmission intensity distribution; b 3D transmission intensity distribution Fig. 9.26 Partial optical 40 × magnification image of infrared wave radiated by blackbody sensed by metamaterial

9.4 Summary Metamaterial devices can be used for sensing near infrared laser and infrared wave radiated by blackbodies. Laser beam profilers can be used for acquiring the corresponding optical transmission images. The closely arranged cyclical micro/nano characteristic dimension metal SRR array is provided with high sensitivity induction of electromagnetic wave field. The corresponding SRR arrays used for making metamaterial devices can help to effectively sense optical infrared frequency signals.

References

187

References 1. O’Hara JF, Singh R, Brener I, et al. Thinfilm sensing with planar terahertz metamaterials: sensitivity and limitations. Opt Express. 2008;16(3):1786–95. 2. Chiam S-Y, Singh R, Gu J, et al. Increased frequency shifts in high aspect ratio terahertz split ring resonators. Appl Phys Lett. 2009;94(6): 064102. 3. Tao H, Strikwerda AC, Fan K, et al. Terahertz metamaterials on free-standing highly-flexible polyimide substrates. J Phys D Appl Phys. 2008;41(23): 232004. 4. Peralta XG, Wanke MC, Arrington CL, et al. Large-area metamaterials on thin membranes for multilayer and curved applications at terahertz and higher frequencies. Appl Phys Lett. 2009;94(16): 161113. 5. Elhawil A, Stiens J, Tandt C, et al. Thin-film sensing using circular split-ring resonators at mm-wave frequencies. Appl Phys A. 2011;103(3):623–6. 6. Chen H-T, Padilla WJ, Cich MJ, et al. A metamaterial solid-state terahertz phase modulator. Nat Photonics. 2009;3:148–51. 7. Chen H-T, Padilla WJ, Zide JMO, et al. Active terahertz metamaterial devices. Nature. 2006;444(30):597–600. 8. Landy NI, Bingham CM, Tyler T, et al. Design, theory, and measurement of a polarizationinsensitive absorber for terahertz imaging. Phys Rev B. 2009;79(12): 125104. 9. Tao H, Landy NI, Bingham CM, et al. A metamaterial absorber for the terahertz regime: design, fabrication and characterization. Opt Express. 2008;16(10):7181–8. 10. Wen QiYe, Zhang HuaiWu, Xie YunSong, et al. Dual band terahertz metamaterial absorber: design, fabrication, and characterization. Appl Phys Lett. 2009;95: 241111.

Chapter 10

Induction and Detection of RF Millimeter Wave Signals by Metamaterials

The important breakthrough of the millimeter wave target detection technology was that in the 1930s when the electromagnetic radiation energy of solar, moon and other outer space radiation sources is measured through millimeter wave radiation. In the late 1950s, the first generation millimeter wave radiometer was developed in the British National Defense Research Institute. At that time, these systems were large and only had a very low spatial resolution and temperature sensitivity. One of the most famous radiometers—“Green Minnow”, was a 35 GHz Dicke switch radiometer. This imaging system (about 500 kg) was installed on aircraft. Later, with the development of solid-state millimeter wave semiconductor devices, the size and volume of these systems were also greatly reduced. When the microwave integrated monochip appeared, the millimeter wave detection technology was gradually developed to a new stage [1]. In order to design a new type of millimeter wave signal sensing device, the metamaterial technology can be used to sense millimeter wave signals in experiments. This closely arranged metamaterial array with micro/nano characteristic dimension metal pattern structure is characterized by high sensitivity induction to and high gain amplification of electromagnetic wave field. It is a new detection mode and architecture that efficiently couples and responds electromagnetic waves through induction [2–5].

10.1 RF Millimeter Wave Characteristics The millimeter wave band, with a frequency range of 30–300 GHz and a corresponding wavelength range of 1–10 mm, is between light wave and radio wave bands. According to the research on the quasi-optical technology, millimeter waves have similar characteristics to radio waves and light waves. The target information obtained through millimeter wave radiation measurement is different from that © National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_10

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obtained through visible light and infrared methods. It can help us understand and study the characteristics of objects more comprehensively. The millimeter wave radiation intensity of common objects is far lower than their infrared radiation intensity, however, due to the continuous improvement of the receiving performance of millimeter wave detectors, the high-frequency front ends of receivers are provided with lower noise coefficient, higher power gain and wider frequency bandwidth. The detection sensitivity of millimeter wave detection systems has been significantly improved, which, to some extent, also makes up for the shortcomings. Since the wavelength of a millimeter wave is far higher than that of infrared and visible light, its capability to distinguish target shapes is inferior to that of the infrared or visible light technology. However, millimeter waves have unique radiation characteristics, which can realize those functions that infrared or visible light does not have sometimes. The millimeter wave target detection technology is related to active millimeter wave target detection and passive millimeter wave target detection. Active millimeter wave target detection aims to receive electromagnetic waves reflected from a target through emitting millimeter wave radiation by the system itself. For functions, the active millimeter wave detection system should have a transmitter, a receiver and their common antenna. The passive millimeter wave target detection system does not emit millimeter wave itself, but receives millimeter wave radiation emitted or scattered by a target, which can help to appropriately overcome the angular glint effect of the target. The passive millimeter wave detector, also known as millimeter wave radiometer, is composed of a millimeter wave receiver and a antenna, which is provided with a better radiation measurement capability thanks to its relatively small size. The millimeter wave detection mechanisms mainly include: (1) Single-beam scanning. Using the antenna to scan the vision field through mechanical motion to obtain information. Only one receiver with a low resolution is provided; (2) Phased array scanning. The radiation elements of the system is complex, and the loss of the feed system is too high, hindering the application of its millimeter wave detection; (3) Interference array. The large space required by the interference array leads to the high cost of the system, which is currently mainly used in radio astronomy; (4) Focal plane array. Several microstructure element arrays for receiving signals are arranged on the focal plane and directed at the incident beam. Among these detection systems, the focal plane array system is the most popular one, but it is large, power consuming and slow in response. In order to design and fabricate a more efficient new type of RF millimeter wave detector, according to the design idea of the planar array terahertz SRR device described above, a method using Schottky metamaterials to sense RF millimeter wave signals is proposed. The above mentioned has shown that the SRR array will generate an induction effect through electromagnetic resonance when sensing an incident electromagnetic wave and can stimulate the resonance of plasma polaritons during resonance to generate highly

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191

possible new micro-optics effects By taking this principle as the basic starting point, a preliminary sensing experiment is carried out on millimeter wave signals with a metamaterial to explore the corresponding sensing performance of the metamaterial device within an RF millimeter wave band, which is a beneficial preliminary exploration to realize a new architecture type of RF millimeter wave detector with small size, low power consumption and quick response.

10.2 Millimeter Wave Sensing of Metamaterials 10.2.1 Scheme and Apparatus 1. Millimeter-wave signal generator The millimeter-wave signal generator is composed of a synthetic microwave signal generator and a millimeter wave frequency multiplier module. RF signals required by a frequency multiplier module are input from the synthetic signal generator through the RF cable. The software control is realized through the special connecting cable of the frequency multiplier module. Parameters such as frequency and power can be controlled by the synthetic signal source when the frequency multiplier module is used. The DC drive is provided through a special power adapter. The standard waveguide sections can be divided by the frequency multiplier module, and signals within the 50–325 GHz frequency band can be generated by replacing frequency multiplier modules for different frequency bands, see Table 10.1. The test port of the millimeter wave frequency multiplier module (model: AV82406B) is a standard rectangular waveguide interface, see Fig. 10.1. The drive voltage of this millimeter wave frequency multiplier is 220 V, and the effective output frequency range is 110–170 GHz, see Fig. 10.2. 2. Detection scheme RF millimeter waves with electromagnetic wave signals of 1–2 mm wavelength can be send to the surface of a metamaterial metal array through a waveguide. The metal SRR array on the top layer of the metamaterial device and the Schottky contact region will produce some form of induction characteristics, which can be probably observed in the form of images in the optical CCD after the signals are amplified by a microscopic objective. Table 10.1 Typical millimeter wave signal generator Model

AV82406

AV82406A

AV82406B

AV82406C

Freq. range (GHz)

50–75

75–110

110–170

170–220

Output power (dBm)

14

12

3

−1

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10 Induction and Detection of RF Millimeter Wave Signals by Metamaterials

Fig. 10.1 Rectangular millimeter wave waveguide

Fig. 10.2 Millimeter wave signal frequency multiplier

In order to clearly show the relative position of the metamaterial in an optical path, Fig. 10.3 shows the operating area of the metamaterial device. The microscopic objective is kept very close to the top metal SRR array area of the metamaterial device, which can be controlled within 0.1–10 mm. The microscopic objective can be used to magnify the optical changes of the metal array surface on the top layer of the metamaterial device, and then perform an observation through the magnified images.

10.2.2 Sensing Properties and Analysis of Metamaterials to Millimeter Waves Before the experiment, select the 170 GHz millimeter wave source as shown in Fig. 10.2. The corresponding wavelength should be 1.76 mm. Use the detection system shown in Fig. 10.3 for the experiment. Use the CCD sensor of a laser beam profiler to acquire the optical images of the metamaterial sensed millimeter waves. 1. 170-GHz millimeter wave detection Before the experiment of acquiring images of metamaterial sensed millimeter wave signals, the optical signals of the 170 GHz millimeter wave signal source shall be

10.2 Millimeter Wave Sensing of Metamaterials Camera lens

193 Objective

Metamaterial device Laser beam profiler

Fig. 10.3 Operating area of metamaterial device

taken as the background reference. According to the response band range of the CCD sensor of the laser beam profiler, the sensor cannot be used to detect millimeter wave signals, so it can be predicted that the acquired images should be reference images containing weak noise. In order to observe the reference image signals of the millimeter wave source more comprehensively, the exposure time settings of the camera are 100 ms and 200 ms respectively in the experiment, and the corresponding results are shown in Fig. 10.4a, b, respectively. It must be noted that the images shown in Fig. 10.4 are the result of the 20 × magnification by the objective. The images show that the optical CCD does not sense any effective millimeter wave signal, and the weak low intensity bright lines in the

Fig. 10.4 Reference images relating to optical intensity of millimeter wave source. a Optical intensity image of millimeter wave source at exposure time of 100 ms; b Optical intensity image of millimeter wave source at exposure time of 200 ms

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10 Induction and Detection of RF Millimeter Wave Signals by Metamaterials

images are all background noise data. This result also proves that the optical CCD sensor cannot be used to detect the characteristics of millimeter wave signals. (1) Millimeter wave signal sensing of square single-opening metamaterial devices In order to verify the performance of the designed and fabricated Schottky metamaterial device in sensing RF millimeter waves, a square single-opening SRR element pattern shown in Fig. 10.5 is selected. Figure 10.6 shows its characteristic dimension parameters. According to the placement mode of the metamaterial set in Fig. 10.5 and its operating area in the system, the exposure time of the CCD sensor of the laser beam profiler is set to 200 ms. In the experiment, a 20 × magnification objective is selected for image acquisition. The experimental results are shown in Fig. 10.6. It can be found in Fig. 10.6 that the first acquisition occurred at Time t1, and two bright lines with high intensity appeared in the images acquired by the CCD sensor of the laser beam profiler, see Fig. 10.6a; The second acquisition occurred Fig. 10.5 Optical micrograph of square single-opening SRR element under d = 6 µm, h = 3 µm, t = 10 µm, l = 130 µm

Fig. 10.6 Optical intensity images of metamaterial induced millimeter waves acquired at different times. a Optical intensity image at Time t1; b optical intensity image at Time t1 + 10 s; c optical intensity image at Time t1 + 20 s

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195

10 s after the first acquisition, and only one bright line with high intensity appeared in the images acquired by the CCD sensor of the laser beam profiler, see Fig. 10.6b; The third acquisition occurred 20 s after the first acquisition, and two bright lines with high intensity appeared in the images acquired by the CCD sensor of the laser beam profiler, see Fig. 10.6c. The three image acquisitions can be regarded as an operation mode of equal time interval. According to the comparison among the three acquired images, the bright spots are cyclical and obviously different from the reference images. Therefore, the SRR array on the top layer of the metamaterial has a certain sensing capability to the millimeter wave signals to the surface. (2) Millimeter wave signal sensing of circular four-opening metamaterial devices In Fig. 10.7, a circular four-opening SRR element pattern is selected to verify the Schottky metamaterial device’s performance in sensing RF millimeter waves, its characteristic dimension parameters can be seen in Fig. 10.5. According to the placement mode of the metamaterial set in Fig. 10.3 and its operating area in the system, the exposure time of the CCD sensor of the laser beam profiler is set to 200 ms. In the experiment, a 20 × magnification objective is selected for image acquisition. The experimental results are shown in Fig. 10.8. Fig. 10.7 Optical micrograph of circular four-opening SRR element structure

Fig. 10.8 Optical intensity images of metamaterial-induced millimeter waves acquired at different times. a Acquisition time t1; b acquisition moment t1 + 10 s; c acquisition moment t1 + 20 s

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10 Induction and Detection of RF Millimeter Wave Signals by Metamaterials

It can be found in Fig. 10.8 that the first acquisition occurred at Time t1. Two bright lines with high intensity appeared in the images acquired by the CCD sensor of the laser beam profiler, as shown in Fig. 10.8a. The second acquisition occurred 10 s after the first acquisition, and only one bright line with high intensity appeared in the images acquired by the CCD sensor of the laser beam profiler, see Fig. 10.8b; the third acquisition occurred 20 s after the first acquisition, and two bright lines with high intensity appeared in the images acquired by the CCD sensor of the laser beam profiler, see Fig. 10.8c. The three image acquisitions can be regarded as an operation mode of an equal time interval. The comparison among the three acquired images shows that the bright spots are cyclical and different from the reference images. Therefore, the SRR array on the top layer of the metamaterial has a particular sensing capability for the millimeter wave signals to the surface. 2. X-wave detection with radars Current RF signal detection devices are structurally complex and extensive. This chapter tests RF radar signal sensing with a metamaterial optical antenna to design a new-type device for millimeter wave signal sensing. Such a closely arranged special metal pattern structure array with micro/Nano characteristic scales is characterized by its high-sensitivity induction and high-gain amplification. It is a new-type optical frequency-RF-integrated detection mode and structure that efficiently couples and responds to electromagnetic waves through induction. A radar band is a frequency range of radio waves emitted from radar, in Hz. Most radar sets work in ultra-short wave and microwave bands, with a frequency range of 30–300,000 MHz and wavelength of 1 mm–10 m, containing 4 wave bands, including very high frequency (VHF), ultrahigh-frequency (UHF), superhigh frequency (SHF) and extremely high frequency (EHF). Below 1 GH, radar is in general rarely used because the spectrum is congested by communication and television signals. This frequency range is adopted for a few long-range and over-the-horizon radar sets only. Above 15 GHz, signals are absorbed mainly by water molecules in the air; above 30 GHz, atmospheric absorption increases sharply, making it difficult for radar to work, with heavy noise inside the receiver. So, this frequency range is adopted for only a few milli-meter wave radar sets only. Table 10.2 shows typical radar band characteristics. The earliest radar worked in a P-band metric wave range (Previous band). Germany independently developed its own radar and selected 1.5 cm as the central wavelength of the radar. The electromagnetic waves of this wavelength were called K-band (Kurtz band), which couldn’t be used in rainy or foggy weather because it was highly absorbable to water vapor. A bar (Ka, K-above, i.e., above K-band) slightly higher than K-band and a band (Ku, K-under, i.e., under K-band) were usually adopted to avoid this absorption peak. When an electromagnetic wave with a wavelength of 10 cm was used, its band was defined as an S-band. The letter S is the initial letter of the English word Short, meaning an electromagnetic wave with a shorter wavelength than the original. After the birth of fire-control radar, for which 3-cm-long electromagnetic waves were primarily adopted, the wavelength of 3 cm was named X-band, where X represents

10.2 Millimeter Wave Sensing of Metamaterials Table 10.2 Radar band frequency and wavelength characteristics

197

Band code

Frequency (GHz)

P

0.3–1

100–30

L

1–2

30–15

Wavelength (cm)

S

2–4

15–7.5

C

4–8

7.5–3.75

X

8–12

3.75–2.5

Ku

12–18

2.5–1.67

K

18–27

1.67–1.11

Ka

27–40

1.11–0.75

U

40–60

0.75–0.5

V

60–80

0.5–0.375

W

80–100

0.375–0.3

a certain point on the coordinates. To combine the advantages of the X-band and S-band, a type of radar with a central wavelength of 5 cm was gradually developed, named C-band, where the letter C means “combination”. This chapter focuses on the S, C and X-bands. The Cassegrain antenna is a type of antenna commonly used for microwave communication. Evolved from the parabola, it consists of three parts, i.e., the main reflector, the sub-reflector and the radiation source, as shown in Fig. 10.9. The main reflector of the Cassegrain antenna is a paraboloid of revolution while the sub-reflector is a hyperboloid of revolution. Structurally, one focus of the hyperboloid coincides with the focus of the paraboloid, and the focal axis of the hyperboloid coincides with that of the paraboloid. At the same time, the radiation source is located at the other focus of the hyperboloid. Its sub-reflector can be used to promote the primary reflection of an electromagnetic wave emitted from the radiation source, with the electromagnetic wave reflected to the main reflector. Then, the main reflector acquires a plane wave beam in the corresponding direction after reflection to realize directional transmission. Fig. 10.9 Schematic diagram of Cassegrain antenna

main reflector sub-reflector F1 radiation source

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10 Induction and Detection of RF Millimeter Wave Signals by Metamaterials

When the radiator is located at the real focus F1 of the hyperboloid of revolution, the ray emitted from F1 is equivalent to the ray directly emitted from the virtual focus of the hyperboloid. Therefore, as long as the hyperboloid’s virtual focus coincides with the paraboloid’s focus, the rays reflected from the sub-reflector to the primary reflector can be reflected as plane waves by the paraboloid and then radiated out. Compared with the parabolic antenna, the Cassegrain antenna has the radiation mode of its feed source changed from the parabolic feedforward mode to the parabolic feed backward mode, compacting the structure of the antenna and making it easier to produce such an antenna. In addition, the Cassegrain antenna can be equivalent to a parabolic antenna with a long focal length. Because of the long focal length, the distance from the focus to each point on the aperture plane is close to a constant. Thus, spatial attenuation has little effect on feed radiation, so that the efficiency of the Cassegrain antenna is higher than that of the standard parabolic antenna. X-band RF radar waves send 8–12-GHz planar electromagnetic wave signals to the metal array surface of metamaterial optical antennas. Figure 10.10 shows the corresponding optical antenna device and structural layout. The electrodes of the optical antenna are welded with pins, the central opening is the test target of the micron-tip array optical antenna, and the optical antenna is a 41 × 41 micron structure array element. Figure 10.5 shows its SRR characteristic size parameters. For transmission and reflection experiments, the schemes shown in Figs. 10.11 and 10.12 are used to test the signals from metamaterial optical antennas, respectively. By irradiating the central opening of the optical antenna without electrification, we can test the optical antenna’s transmittance/reflection spectrum characteristics. Then, DC ± 1 V, ± 2 V, ± 4 V, etc. are applied to test the optical antenna’s transmittance/ reflection spectrum characteristics; the polarization direction of X-band radar waves, is adjusted to retest the transmission/reflection spectrum characteristics of the optical antenna. Before testing, X-band transmitted and reflected X-band signals are collected without the optical antenna device, as shown in Figs. 10.13 and 10.14. Fig. 10.10 Optical antenna device

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199

Fig. 10.11 Transmission test

Fig. 10.12 Reflection test

After the optical antenna device is put in place, the transmitted and reflected Xband signals corresponding to metamaterials of typical SRR structure are shown in Figs. 10.15, 10.16, 10.17 and 10.18.

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10 Induction and Detection of RF Millimeter Wave Signals by Metamaterials

Fig. 10.13 Transmitted reference X-band signal in the absence of the optical antenna

Fig. 10.14 Reflected reference X-band signal in the absence of the optical antenna

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Fig. 10.15 Transmission characteristics of Nano-tip elements with standard four-opening microstructure

Fig. 10.16 Transmission characteristics of Nano-tip elements with standard narrow-edge and fouropening microstructure

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10 Induction and Detection of RF Millimeter Wave Signals by Metamaterials

Fig. 10.17 Nano-tip elements with standard two-opening microstructure

Fig. 10.18 Nano-tip elements with standard narrow-edge and four-opening microstructure

References

203

10.3 Summary This chapter discusses the sensing of RF millimeter waves by using a metamaterial device, and the corresponding optical images are acquired with a laser beam profiler. The results are of reference significance. (1) The optical reference signals of a 170 GHz millimeter wave signal source are acquired through the CCD sensor of the laser beam profiler under the exposure time settings of 100 ms and 200 ms, respectively. (2) A 20 × magnification objective is used for image acquisition under the exposure time setting of 200 ms. The CCD sensor of the laser beam profiler is used to acquire images of millimeter waves passing through the square single-opening metamaterial three times at an interval of 10 s. According to the comparison among the three acquired images, the bright spots are cyclical and obviously different from the reference images; (3) A 20 × magnification objective is used for image acquisition under the exposure time setting of 200 ms. The CCD sensor of the laser beam profiler is used to acquire images of millimeter waves passing through the round four-opening metamaterial three times at an interval of 10 s. According to the comparison among the three acquired images, the bright spots are cyclical and obviously different from the reference images; Therefore, the SRR array on the top layer of the metamaterial has a certain sensing capability to the millimeter wave signals to the surface, further improving the corresponding metamaterial array. The fabrication of metamaterial devices will be a great help for sensing RF millimeter wave signals.

References 1. Elhawil A, Stiens J, Tandt C, et al. Thin-film sensing using circular split-ring resonators at mm-wave frequencies. Appl Phys A. 2011;103(3):623–6. 2. Li M, Wen Z, Fu J et al. Composite metamaterials with dual-band magnetic resonances in the terahertz frequency regime. J Phys D Appl Phys. 2009;42:115420. 3. Jun L, Yehua B, Xinyu Z, et al. Voltage adjusting characteristics in terahertz transmission through Fabry-Pérot-based metamaterials. J Vac Sci Technol, B. 2015;33:020605. 4. Azad AK, Dai J, Zhang W. Transmission properties of terahertz pulses through subwavelength double split-ring resonators. Opt Lett. 2006;31(5):634–6. 5. He XJ, Qiu L, Wang Y, et al. A compact thin-film sensor based on nested split-ring-resonator (SRR) metamaterials for microwave applications. J Infrared Millimeter Terahertz Waves. 2011;32(7):902–13.

Chapter 11

Subwavelength Stealth Technology of Metamaterials

Adjusting the reflection, transmission and absorption characteristics of materials is an important research on optical devices, which plays a key role in imaging detection [1], electromagnetic stealth [2] and detection enhancement [3, 4], etc. Traditional electromagnetic devices convert the energy of electromagnetic waves into electric energy, thermal energy or light energy mainly by utilizing material properties, such as the energy level transition and ohmic loss of electrons. For this energy conversion, the absorption characteristics are mainly dependent on the response frequency bands of materials, which is applicable to specific frequency bands since the bandwidths are very narrow generally and not suitable for making broadband devices. Subwavelength structures can help to significantly enhance the electromagnetic absorption efficiency and bandwidth. Response frequency bands can be controlled through structure design, including structure parameters and the pattern cycles, breaking the limitations of traditional absorption technology. This chapter introduces the infrared antireflection technology based on nano-tips (nano-tip structures) and the electrically controlled nano-tip infrared transmittance technology.

11.1 Metamateria-Based Antireflection Technology The antireflection characteristics of tip structures are mainly achieved through the following two aspects. Tip structures, on one hand, can regulate local electrons and incident light and, on the other hand enhance the refraction and reflection of light structures thanks to the gradient effect, improving the light transmission and absorption. When the incident light radiates a metal surface, electric dipoles will be excited on the nano-tip structures, and the radiation of the electric dipoles will help to enhance the light transmission. At the same time, the incident light and excited surface wave propagated to the tips will continuously reflect and transmit at the boundary, enhancing the absorption and transmission of light by materials. © National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_11

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11.1.1 Nano-Tip-Structure Based Electromagnetic Antireflection Technology Electromagnetic fields can be localized according to subwavelength structures. When satisfying the coupling conditions of surface plasmon polariton (SPP), for example, if the metal grating shown in Fig. 11.1a is used for excitation, the incident electromagnetic wave can be converted into SPP. SPP is propagated at metal-medium interfaces, and reflection/transmission can occur when encountering metal-medium boundaries. When a tip structure is used, as shown in Fig. 11.1b, SPP will be reflected several times under the constraint of the tip structure, enhancing the dissipation of SPP, achieving the electromagnetic absorption and reducing the reflectivity. At the same time, the tangential component of SPP will be propagated along the tip structure and converged at the tips, forming a strong electric dipole. The electric dipole radiation can enhance the transmission. In addition, as shown in Fig. 11.1–1c, d, the incident light can be reflected back and forth in the tip structure thanks to the gradient effect, increasing the optical path of light propagation in the medium, improving the medium light absorption and reducing the reflectivity. As shown in Fig. 11.2, designed nano-tip arrays can localize the incident light field and reduce the infrared reflectivity. Si coated with Al film is used as the substrate. The Al film is etched with nano-tip patterns. Figure 11.2c shows an electron micrograph of a designed tip-array structure composed of 1D gratings and nano-tip arrays. The grating cycle is 1.1 µm. Both sides of each grating line are designed with nano-tip

Fig. 11.1 Enhanced absorption of electromagnetic wave by tip structure. a Surface plasma excitation in cyclical structure; b propagation of SPP at tips; c reflection and transmission of incident light at tips (back incidence); d reflection and transmission of incident light at tips (normal incidence)

11.1 Metamateria-Based Antireflection Technology

207

Fig. 11.2 Scanned electron micrographs of typical tip-structures. a Inner-circled structure; b fourtip structure; c tip-array structure

arrays. The cycle of one nano-tip array is 0.3 µm. Figure 11.3c shows the optical nearfield distribution of a tip-array structure under laser irradiation. Under the 633 nm red light irradiation, strong optical near-field signals exist near the tips, indicating that the tips excite a strong electric dipole and the charge is densely distributed. Figure 11.3f shows the optical near-field distribution of the tip-array structures at 10 µm under the infrared light irradiation. The near field light is localized into the tip-array structures, enhancing the absorption of metal to incident light. It can be seen from the reflectivity curve in Fig. 11.4 that the tip-array structures have a very low reflectivity (below 0.4) within the band of 3–14 µm. Figure 11.2a, b show the electron micrographs of the inner-circled-tip and four-tip structures. The inner-circled-tip and four-tip structures are cyclical array structures. Both the transverse and longitudinal cycles are 1.1 µm. A four-tip structure has four tips. An inner-circled tip structure has four tips and one centre circle. It can be seen from the optical near-field Fig. 11.3a, b that the near-field light is focused near the tips under 633 nm red light irradiation. Optical near-field signals represent the intensity of plasmon signals excited by the incident light, which reflects the intensity of electric dipoles excited by the metal surface. It is obvious that the metal tips can excite the electric dipoles, and the central circles can help to enhance the excited electric dipoles. As shown in Fig. 11.3d, e, under the irradiation of the 10 µm infrared light, the energy of near-field light is also localized to the metal. At the same time, the optical near-field signals are very weak at the structure edges. From the reflectivity diagram, both the reflectivities of the structures in the infrared band are lower than 0.6. The four-tip structure has a relatively gentle reflectivity valley with a valley wavelength of about 4.5 µm. The reflectivity curve of the inner-circledtip structure has a reflectivity valley wavelength of about 4.2 µm, and this reflectivity valley is split into two small reflectivity valleys. The center circle is the reason why two small reflectivity valleys exist, which causes the shift of the reflectivity valley value. The structure has a low reflectivity within 3–14 µm, because the incident light is localized to the metal surface under the irradiation, enhancing the absorption of the incident light by the material. At the same time, a strong electric dipole is excited

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Reflectivity

Fig. 11.3 Optical Near-field micrographs of typical tip structures. a Inner-circled-tip structure under 633 nm red light irradiation; b four-tip structure under 633 nm red light irradiation; c tiparray structure under 633 nm red light irradiation; d inner-circled-tip structure under 10 nm infrared laser irradiation; e four-tip structure under 10 nm infrared laser irradiation; f tip-array structure under 10 nm infrared laser irradiation

Inner-circl ed-tip Tip-array Four-tip structure

Wavelength / μm

Fig. 11.4 Infrared reflection characteristics of typical tip structures

at the nano-tip, enhancing the transmission of light. It should be noted here that the metal has a very low infrared transmittance. When the nano-tip structure mentioned above is made on the metal, the transmittance will increase a little, but not high. Most of the energy of the incident light will be absorbed and reflected by the material.

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11.1.2 Inner-Ring-Tip Antireflection Film Figure 11.5 shows the designed inner-ring-tip antireflection film, whose reflectivity can be reduced to less than 0.2 within a specific frequency band. It has a cylinder in the center, and the nano-tip structures are evenly distributed around the cylinder. Each element contains a center circle and eight nano-tips. There are two connection points between the cylinder and the nano-tip array. The structure is a cyclical array, and both the transverse and longitudinal cycles are 1.5 µm. The metal and substrate materials are Al and Si, respectively. By changing the structural parameters of inner-ring-tip antireflection films, the optical near-field properties and reflectivity of films are studied under different parameters. Inner-Ring-Tip-1, Inner-Ring-Tip-2 and Inner-Ring-Tip-3 are designed by keeping the cycle of an antireflection film and the number of nano-tips, and changing the radius of the center circle and the angles of tips, see Fig. 11.5a–c. The angles of nano-tips are 48°, 56° and 90°, respectively, and the distances between two adjacent tips of two adjacent pattern elements are 400 nm, 100 nm and 90 nm, respectively. Figure 11.6 shows the optical near-field micrographs of inner-ring-tip structures. Compared with Inner-Ring-Tip-2, the tip angles of Inner-Ring-Tip-1 are almost the same, however the center circle of Inner-Ring-Tip-2 is bigger, and the tip distance between the elements is closer. It can be seen that Inner-Ring-Tip-2 can localize the light to the tips under 633 nm laser irradiation. Figure 11.6a shows that there are some strong near-field focusing spots below the cylinder of Inner-Ring-Tip1. Figure 11.6b shows that there are some strong near-field focusing spots on the uppermost and leftmost tips of Inner-Ring-Tip-2. Figure 11.6c shows that there are some strong near-field focusing spots above the cylinder of Inner-Ring-Tip-3. The focusing spots at different positions represents different plasmon modes. Under the same wavelength of incident light radiation, the mode of plasmon varies with different structural parameters, which can also be reflected in the reflectivity curve.

Fig. 11.5 Scanned electron microscope micrographs of inner-ring-tip antireflection film. a InnerRing-Tip-1; b Inner-Ring-Tip-2; c Inner-Ring-Tip-3

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Fig. 11.6 Optical near-field micrographs of inner-ring-tip structures. a Photograph of Inner-RingTip-1 under 633 nm red light irradiation; b photograph of Inner-Ring-Tip-2 under 633 nm red light irradiation; c photograph of Inner-Ring-Tip-3 under 633 nm red light irradiation; d photograph of Inner Inner-Ring-Tip-1 at 10 µm infrared laser irradiation; e photograph of Inner Inner-Ring-Tip-2 at 10 µm infrared laser irradiation; f photograph of Inner Inner-Ring-Tip-3 at 10 µm infrared laser irradiation

Figure 11.3d–f show the optical near-field distribution of inner-ring-tip structures under 10 µm infrared light irradiation. The optical near-field patterns of the three structures under infrared light irradiation are similar except those properties of different mediums. The signal of Al in the structure is weaker than that of Si, and the plasmon signal is not strong. It can also be seen from the reflectivity curve of Fig. 11.7 that there is no any obvious reflectivity peak valley value at 10 µm, and the plasmon frequency is kept within 5–7 µm. Figure 11.7 shows the infrared reflection characteristics of inner-ring-tip structures. The duty ratios of Inner-Ring-Tip-1 and Inner-Ring-Tip-3 are the lowest and highest, respectively. Al is also highly reflective in the infrared band, so the reflectivity of a structure with a higher duty ratio will be higher as a whole. It can be seen from Fig. 11.7 that the reflectivity curve values of Inner-Ring-Tip-1 are generally low, while those of Inner-Ring-Tip-3, generally high. At the same time, with the change of the parameters of an inner-ring-tip structure, the plasmon frequency also shifts, showing the shift of the emissivity valley value. It can be seen from the reflectivity curves that the lower the tip distance is, the higher the reflectivity valley wavelength becomes. The tip distance of Inner-Ring-Tip-1 is 400 nm, and the valley wavelength is 5.5 µm; The tip distance of Inner-Ring-Tip-2 is 100 nm, and the valley wavelength is 6.1 µm; The tip distance of Inner-Ring-Tip-3 is 90 nm, and the valley wavelength is 6.5 µm.

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Reflectivity

11.2 Vertical-Tip Metamaterials

Inner-Ring-Tip-1 Inner-Ring-Tip-2 Inner-Ring-Tip-3

Wavelength / μm

Fig. 11.7 Infrared reflection characteristics of inner-ring-tip structures

11.2 Vertical-Tip Metamaterials The planar-tip metamaterials have near-field focusing and far-field antireflection properties. Vertical-tip metamaterials also have near-field focusing and far-field antireflection properties. This section introduces the optical near-field properties and infrared reflection properties of vertical-tip metamaterials.

11.2.1 Fabrication of Vertical-Tip Metamaterials For a planar-tip structure, the edge should be as steep as possible, while for a verticaltip structure, the edge should have a depth gradient, the center should be the highest and the surroundings should be lowered and deepened gently, forming a conical structure. Two methods can be adopted to fabricate vertical-tip metamaterial structures, one is focused ion beam etching, and the other is electron beam photolithographing + inductively coupled plasma etching. For the focused ion beam etching method, different etching gradients can be mainly set to make the processed patterns have a conical structure. For the method of electron beam photolithographing + inductively coupled plasma etching method, the gas concentration for inductively coupled plasma etching can be mainly adjusted to make the etched edge be smooth. Figure 11.8 shows the steps for processing a vertical-tip optical antenna according to the focused ion beam etching method. The left side of the figure shows the processed pattern file, while the right side shows the appearances after processing. Focused ion beam etching is a micro/nano processing technology that uses focused ion beam to directly bombard materials and directly process the surface of materials.

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Fig. 11.8 Steps of focused ion beam etching method for processing vertical tips. a Steps of focused ion beam etching for single vertical tip processing; b steps of focused ion beam etching for vertical -tip array processing

Focused ion beam etching has an edge effect, and therefore a certain depth gradient can achieve at edges of etched structures. As shown in Fig. 11.8a, when the etched pattern file is a ring, a single vertical tip structure will be processed in the middle, and a certain depth gradient will appear at the outer boundary of the ring. In order to process an arrayed vertical tip structure, the processing steps shown in Fig. 11.8b are adopted, first process a square array pattern with inner circles, and then modify the bulges between the tips to obtain the final vertical-tip array pattern. In the square pattern with inner circles, each white circle in the middle will be provided with a vertical tip structure, and an obvious bulge will appear between each two tips. These bulges are caused by the accumulation of Si between tips after etching the vertical tip structure, which can be eliminated after a grating structure is made through secondary etching. Figure 11.9 shows the steps for processing a vertical tip array according to the electron beam photolithographing + inductively coupled plasma etching method. First, coat the negative photoresist uniformly on the Si substrate with a homogenizer, expose the photoresist into a square array through electron beam photolithographing, and then form a vertical tip array on the Si substrate through inductively coupled plasma etching. Different cone tip angles can be obtained by adjusting the concentration and proportion of SF6 and C4F8 during etching. Different tip depths can be achieved by controlling the etching time. The Si cone tips are coated with a layer of metal by a magnetron sputtering machine. Figure 11.10 shows the electron micrographs after processing.

11.2 Vertical-Tip Metamaterials

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Negative photoresist Si substrate

Electron beam photolithographing Electron beam photolithographed pattern

Inductively coupled plasma etching Fig. 11.9 Steps of electron beam photolithographing + inductively coupled plasma etching for processing vertical tips

Fig. 11.10 Vertical tips processed through inductively coupled plasma etching after electron beam photolithographing. a Si cone tip; b Si cone tip; c Si–Al cone tip

11.2.2 Optical Near-Field Properties of Vertical-Tip Metamaterials Figure 11.11 shows the electron micrographs of two kinds of conical structures fabricated according to the electron beam photolithographing + inductively coupled plasma etching method, and their optical near-field micrographs obtained under

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Fig. 11.11 Optical near-field micrographs of vertical nano tips. a Cone tips; b near-field characteristics of cone tips under 633 nm light irradiation; c near-field characteristics of cone tips under 10 µm light irradiation; d square truncated cone tips; e near-field characteristics of square truncated cone tips under 633 nm light irradiation; f near-field characteristics of square truncated cone tips under 10 µm light irradiation

633 nm and 10 µm incident light radiation. The cycles of conical array and square truncated cone array are 500 nm and 1 µm, respectively. The substrate material and metal materials are Si and Au, respectively. It can be seen that the sample structures processed according to this method have clear edges, good uniformity and excellent appearance. For a conical structure, near-field focusing spots can be formed at the upper left and lower right parts under the 633 nm red light irradiation. The focusing spot at the lower right is stronger, because the incident light is irradiated at an angle of 135° mainly. For near-field distribution, stripe-like bright spots can be found, indicating that the conical array can excite the propagating plasmon. Under the irradiation 10 µm laser, there are some shadows on the left side of the structure, which are some errors caused by probe scanning. Near the vertex of the nano cones, there is a streak spot. For a circular truncated cone, the near-field spot intensity at the upper left corner is higher under the 633 nm red light irradiation, because the bottom diameter of one cone is 200 nm, while the bottom edge length of a square truncated cone is 500 nm. Different structure sizes will form near-field spots at different positions. Under the irradiation of 10 µm laser, similar to the conical structure, shadows and streak spots can also be found on the left side of the square truncated cones and near the vertex, respectively.

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11.2.3 Reflection Characteristics of Vertical-Tip Metamaterials We also studied the infrared reflection characteristics of vertical tips, and measured the infrared reflection characteristics of three vertical tip structures with a Fourier transform infrared spectrometer, including the Al-film coated Si cone tip structure (cone bottom dia.: 150 nm; Cycle: 1 µm), the Si cone tip structure (cone bottom dia.: 100 nm; Cycle: 300 nm) and the Al-film coated Si cone tip structure (cone bottom dia.: 100 nm; Cycle: 300 nm). Figure 11.12 shows the infrared reflection curves of a vertical-tip metamaterial. When the size and cycle are150nm and 1 µm, respectively, the reflectivity curve of the vertical-tip metamaterial will be relatively smooth. In the 3–14 µm band, the reflectivity of the vertical-tip metamaterial is kept within 0.4–0.6. When the size and cycle are100nm and 300 nm, respectively, the reflectivity curve of the vertical-tip metamaterial will have obvious peak and valley values besides the reflectivity peaks at 8 and 10.6 µm. Therefore, only when the duty ratio is relatively higher can a relatively obvious reflectivity peak appear in the reflectivity curve. Al is also highly reflective in the infrared band, which can be reduced greatly through vertical-tip arrays.

Fig. 11.12 Infrared reflection characteristics of vertical nanotip structures

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11.3 Electrically Controlled Infrared Transmittance Metamaterials Once a metamaterial is fabricated, its optical properties will be determined and cannot be changed, limiting its application. Dynamically adjusting the optical properties of materials is an urgent need. This section will introduce an electrically controlled infrared transmission metamaterial. By applying voltage to the metamaterial, the infrared transmission characteristics can be controlled.

11.3.1 Electrically Controlled Infrared Transmittance Metamaterial Metals are highly reflective in the infrared band, the main reason for this being that when light radiates a metal surface, free electrons on the surface will oscillate. This oscillation will reflect the incident light back, making it difficult for the incident light to pass through the metal. When a metal contacts a semiconductor, if the work function of the metal is higher than that of the semiconductor, a Schottky barrier will be formed at the metal–semiconductor interface. The electrons in the semiconductor will flow to the metal, making the metal surface negatively charged and the semiconductor surface positively charged. These positive charges are distributed in the spatially-charged region of the semiconductor surface. The spatially-charged region has a certain electric field, which can cause band bending, forming a Schottky barrier. Applying voltage to the device can help to adjust and control the Schottky barrier on semiconductor side, thus changing the electronic concentration of the metal. When the electron density in the metal becomes lower, the reflection of the metal on the incident light will be weakened, and the transmissivity of the device will be enhanced. Based on this principle, an electrically controlled infrared transmission device is fabricated. See Fig. 11.13 for the device architecture. Au film Pattern region Si cone

Upper electrode Au film

Conductive Al foil

(a)

Lower electrode

Si substrate

Si substrate

Conductive Al foil

PCB

(b)

(c)

Fig. 11.13 Electrically controlled infrared device. a Partial hierarchical structure of device; b front view of device; c back view of device

11.3 Electrically Controlled Infrared Transmittance Metamaterials

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Fig. 11.14 Measurement

As shown in Fig. 11.13, the device is composed of Si nano cones. The upper surface of the Si cones is coated with Au film, and the back of the Si chip is secured to conductive Al foil, which is also used as the lower electrode. A sample should be fixed on the PCB, and a conductive tape, stuck on the Au film and conductive Al foil for the sake of easy measurement. The electrically controlled transmissivity can be tested by the self-setting measuring equipment, see Fig. 11.14. The 2.2 µm laser is emitted through optical fibers to the Si cone pattern region of the sample, and is received by an optical power meter through the sample. The electrically controlled transmission and current–voltage characteristics of the sample can be measured by applying a voltage between the upper and lower electrodes of the sample, controlling the voltage at both ends of the sample through a DC voltage stabilizing source, and then using a multimeter to measure the current passing through the sample.

11.3.2 Electrically Controlled Transmission Characteristics of Electrically Controlled Infrared Transmittance Metamaterials Figure 11.15 shows the electrically controlled infrared characteristics of the sample. The abscissa represents the voltage applied at both ends of the sample, the “Positive” represents the positive voltage applied at the Au film end, and the “Negative” represents the negative voltage applied at the Au film end. It can be seen that when a positive voltage is applied to the Au film end, the electrically controlled transmission characteristics of the sample almost do not change. When a negative voltage is applied to the Au film end, the transmission of the sample increases as the voltage increases. Figure 11.16 shows the electrically controlled transmission characteristic curve when a negative voltage is applied to the Au film end. In order to eliminate the

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Fig. 11.16 IR Electrically controlled infrared transmission characteristic curve when negative voltage is applied to Au film

Optical power (mW)

Fig. 11.15 Electrically-controlled transmission characteristic curve of sample

Optical power (mW) without laser emission Optical power (mW) with laser emission

Voltage (V)

influence, only the case of a voltage being applied without emitting the laser is also measured. The optical power measured by the optical power meter will be zero when no laser is emitted. When no any voltage is applied, the transmitting light power will be 1.1 mW. As the voltage increased, the transmitting light power at first remained nearly unchanged; when the voltage signal is higher than or equal to 1 V, the transmitting light power will increase linearly with the voltage; when the voltage is higher than 4 V, the light transmission power will increase sharply. This is because a tunneling effect occurs when the voltage is greater than 4 V, resulting in a sharp increase of the current, a loss of heat and a sharp increase of the measured optical power.

11.3.3 Current–Voltage Characteristics of Electrically Controlled Infrared Reflectivity Metamaterials The current–voltage characteristics of the sample are measured by with a DC voltage stabilizing source and an ammeter. For comparison, the current–voltage characteristics without emitting laser are also measured, see Fig. 11.17 for the results.

11.3 Electrically Controlled Infrared Transmittance Metamaterials

Current (mA) without laser emission

Current (mA)

Fig. 11.17 Current–voltage characteristic curve of sample when negative voltage is applied to Au film

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Current (mA) with laser emission

Voltage (V)

The current values of the sample with and without laser emission are almost the same, indicating that the influence of laser on the current–voltage characteristics of the sample is very low, and the photocurrent of the sample is also very low. When the voltage is less than 1 V, there is no current; when the voltage is higher than 1 V, the current will increase slowly first with the increase of voltage. When the voltage reaches 2.4 V, the current will tend to be saturated, i.e. at about 2.5 mA. When the voltage is higher than 3.2 V, the current will increase sharply, which is mainly caused by the rectification effect caused by metal- semiconductor contact.

11.3.4 Controlling Principle of Electronically Controlled Infrared Transmission Metamaterials At the interface between Si and Au, since the work function of Au is higher than that of Si, the electrons of Si will flow into Au, forming a positive spatially-charged region on the Si side of the Si-Au interface. At room temperature, due to thermal excitation, Si electrons flow to Au, with Au electrons also flowing to Si. When there is no voltage is applied, the two thermally excited flows are balanced, namely, the number of electrons flowing from Si to Au is equal to that flowing from Au to Si. When a positive voltage is applied to Au, the Fermi energy of the Si electrons will increase, and the barrier height on the Si side will decrease. At this time, the number of Si electrons flowing to Au will increase due to thermal excitation, which will be higher than that of Au flowing to Si. As a whole, the number Au electrons will be greater than the electrons flowing from Si. When a negative voltage is applied to Au, the barrier height on the Si side will increase. At this time, the number of Si electrons flowing to Au will decrease due to thermal excitation, which will be less than that of Au flowing to Si. As a whole, when electrons flow from Au to Si, the number of Au electrons will decrease. As shown in Fig. 11.17, when a reverse bias is applied, the current will increase slowly at first. When the applied voltage reaches 2.4 V, the current will tend to be stable, i.e. 2.2 mA. This is because when the potential barrier on the Si side is high

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enough, the number of electrons from Si to Au will be almost zero after passing the barrier. When the reverse voltage increases, the electron flow from Si to Au can be ignored, and the reverse current will tend to be saturated. When the voltage continues to increase, Si electrons will directly flow through the potential barrier to Au, which means that a tunneling effect will occur and the current will increase sharply. When the voltage is higher than 3.2 V, the current will increase sharply.

11.4 Electrically Controlled Infrared Reflective Liquid Crystal (LC) Metamaterial Devices This section will introduce an electrically controlled infrared reflective metamaterial. The device is composed of metamaterial and LC. The infrared reflective characteristics of the device can be controlled by applying a voltage between the upper and lower electrodes of the device.

11.4.1 Electrically Controlled Infrared Reflective LC Metamaterials The reflective properties of the metamaterial device are mainly affected by two parameters: one is the structural parameters of the metamaterial, including element size and cycle; the other is the medium parameters around the metamaterial, including refractive index and permeability, etc. LC is a type of material with electrical and optical anisotropies. LC is an ellipsoidal molecule, and its refractive index along the long axis is different from that of the short axis. Under an applied voltage, the arrangement of LC molecules will become orderly, which will rotate in the direction of the electric field. By combining LC molecules with the metamaterial, the deflection of LC can be controlled using voltage, which can change the refractive index of the metamaterial environment medium and cause a change of infrared reflection characteristics of certain devices. As shown in Fig. 11.18, the device is composed of metamaterial and LC. The Al 2D grating is made on the conductive glass. There is LC on the Al 2D grating, and the LC is covered with a conductive glass with an oriented layer. Al 2D grating is used as the lower electrode, and the ITO in the upper conductive glass is used as the upper electrode. The LC is initially oriented through friction orientation, with the orientation material being friction polyimide. A Fourier transform infrared spectrometer is used to measure the infrared reflection spectrum of the device. Figure 11.19c shows the reflection curve of a Thorlabs silver reflector used as the benchmark. The reflectivity of the Thorlabs silver reflector within the visible and infrared bands is higher than 95%.

11.4 Electrically Controlled Infrared Reflective Liquid Crystal (LC) …

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SiO2 substrate

ITO orientation layer LC Al 2D grating

SiO2 substrate

Fig. 11.18 Electrically-controlled infrared reflector. a Electrically-controlled infrared reflective device architecture; b structural parameters of the metamaterial; c optical micrograph of metamaterial; d device

Figure 11.19 shows the infrared reflection curves of two 2D gratings. One is 600 nm long and 400 nm wide, and the other is 800 nm long and 600 nm wide. Both the transverse and longitudinal cycles of the two 2D gratings are 1 µm. The cycles of the two metamaterials are the same, so the reflectivity characteristics of the two metamaterials are basically the same. The infrared reflectivity of the 600 nm long and 400 nm wide Al 2D grating is higher than that of the Thorlabs silver mirror. The infrared reflectivity peaks of the two metamaterials are basically the same. Their different elemental structures will make the reflectivity peaks slightly different. Near the two reflectivity peaks (3.1 and 3.25 µm), the reflectivity curve of the 800 nm long and 600 nm wide Al 2D grating jitter. The reflectivity of the 600 nm long and 400 nm wide Al 2D grating is higher than that of the 800 nm long and 600 nm wide Al 2D grating.

11.4.2 Electrical Control Characteristics of LC Metamaterial Devices The equivalent refractive index of the surface plasmon is determined by the refractive indexes of the metal and metamaterial environment medium, which is defined by Eq. (11.1).

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Reflectivity

Reflectivity

L 800nm, W 600nm

Wavelength / μm

Wavelength / μm

Reflectivity / %

Thorlabs silver reflector

Wavelength / μm

Fig. 11.19 Infrared reflectivity curve of the metamaterial. a Infrared reflection curve of 600 nm long and 400 nm wide Al 2D grating metamaterial; b infrared reflection curve of 800 nm long and 600 nm wide Al 2D grating metamaterial; c infrared reflection curve of Thorlabs silver mirror

 ne f f =

εm εd εm + εd

(11.1)

where Em and Ed are the dielectric constants of metal and dielectric, respectively. The propagation constant of the surface plasmon can be defined by Eq. (11.2).  β = k0

εm εd = k0 n e f f εm + εd

(11.2)

where k 0 is the wave number in vacuum. When the wave vector satisfies the requirements, the surface plasmon will be excited. The propagation constant of the surface plasmon is related to the dielectric constant of the environment medium, which, together with the infrared reflection characteristics of the device, can be controlled by changing the dielectric constant of the metamaterial environment’s mediums. Figure 11.20 shows the device states with and without voltage application. When no voltage is applied, the LC molecules being parallel to the metamaterial lie in the oriented layer. The dielectric constant of the metamaterial environment medium is ne . When a voltage is applied, the LC molecules will rotate under the electric field and be perpendicular to the distribution of the metamaterial, and the dielectric constant of the metamaterial environment medium will become n0 . The refractive index of

11.4 Electrically Controlled Infrared Reflective Liquid Crystal (LC) …

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Fig. 11.20 Liquid crystal(LC) Metamaterial Device. a With voltage application; b without voltage application

the metamaterial environment medium can be changed with the voltage, causing changes of the plasmon mode as well as the infrared reflection characteristics of the device. Figure 11.21 shows the electrically controlled infrared reflection characteristic curves of the device. Due to the different structural parameters of the metamaterials, the peak reflectivities of the 600 nm long and 400 nm wide devices are at about 3.53 µm, 3.72 µm and 3.97 µm, respectively, while the peak reflectivities of the 800 nm long and 600 nm wide devices are at about 3.57 µm, 3.8 µm and 4.2 µm, respectively. Since the cycles of the two metamaterials are the same, there is little difference in the positions of the peak wavelengths. It can be seen from Fig. 11.21 that under the control of voltage signals, the wavelength points of reflectivity peaks have shifted. When the voltage signal increases, the wavelength points of the reflectivity peaks move to the short wave direction. For the 600 nm long and 400 nm wide Al 2D grating LC metamaterial device, when the voltage signal increases from 0 to 10 V, the peak wavelength point of ~ 3.72 µm shifts from 3.73 to 3.7 µm, and the peak wavelength point of ~ 3.97 µm shifts from 3.98 to 3.95 µm. For the 800 nm long and 600 nm wide Al 2D grating LC metamaterial device, when the voltage signal increases from 4.1 to 16.1 V, the peak wavelength point of ~ 3.57 µm shifts from 3.58 to 3.26 µm, and the peak wavelength point of ~ 3.8 µm shifts from 3.82 to 3.8 µm. The 600 nm long and 400 nm wide Al 2D grating LC metamaterial device has a higher control capability. Therefore, the closer the duty ratio is to 0.5, the better the control capabilities will be.

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Fig. 11.21 Electrically-controlled infrared reflection characteristics of devices. a Electricallycontrolled infrared reflection characteristic curves of Al 2D grating LC metamaterial device (L 600 nm, W 400 nm); b electrically-controlled infrared reflection characteristic curves of Al 2D grating LC metamaterial device (L 800 nm, W 600 nm)

References 1. Debus C, Bolivar PH. Frequency selective surfaces for high sensitivity terahertz sensing. Appl Phys Lett. 2007;91(18):184102. 2. Al-Naib IAI, Jansen C, Koch M. Thin-film sensing with planar asymmetric metamaterial resonators. Appl Phys Lett. 2008;93(8):083507. 3. Ibraheem IA, Koch M. Coplanar waveguide metamaterials: the role of bandwidth modifying slots. Appl Phys Lett. 2007;91(11):113517. 4. Chen WC, Mock J, Smith D, et al. Controlling gigahertz and terahertz surface electromagnetic waves with metamaterial resonators. Phys Rev X. 2011;1(2):1–6.

Chapter 12

Optical Frequency-RF Integrated Detection Architecture Based on Metamaterials

A metamaterial-based Schottky terahertz signal detector, from bottom to top, is composed of semiconductor substrate layer, doped semiconductor layer, SiO2 layer and metamaterial layer, ohmic electrode and Schottky electrode; the metamaterial layer is a metal split-ring resonance element array with a cyclical micro/nano structure. The metal split-ring resonance element array contains a variety of patterns and their characteristic dimension parameters. Each pattern has complete absorption characteristics for specific electromagnetic waves. The corresponding electromagnetic wave absorption frequency band can be controlled by changing the structure and size parameters of the metal split-ring resonance element. The electromagnetic wave absorption intensity of the metal split-ring resonance element array in the metamaterial layer can be adjusted by changing the depletion layer width of N-GaAs. The detector can work within a single or several wavebands from optical frequency to the RF by selecting the structures of different metal split-ring resonance elements and performing monolithic integration. Metamaterials with artificial pattern structures are available for detecting signals in relation to infrared optical radiation, terahertz waves and RF millimeter waves through resonance. SRR arrays are reasonably configured for sensing electromagnetic wave fields of different wavebands, which meets the binary physical structure requirement of optical frequency and RF electromagnetic-wave fields, reflecting the small-size and facility features of the optical frequency band, and realizing the remote and penetrating detection capabilities of the RF band.

12.1 Optical Frequency-RF Detection Architecture Surface plasmon polariton (SPP), which is an objective vibration mode composed of surface electron density waves and the excited electromagnetic field, can be significantly excited, effectively transported, and functionally arranged on metamaterials. © National Defense Industry Press 2023 J. Luo et al., Metamaterial-Based Optical and Radio Frequency Sensing, Advances in Optics and Optoelectronics, https://doi.org/10.1007/978-981-99-2965-8_12

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Research indicates that a metamaterial with sub-wavelength characteristics can efficiently constrain incident light energy to medium interfaces, such as a typical metal– dielectric interface, thus realizing effective reflection and transmission of incident light waves. High-density surface states exist in tip structures, such as the standard Nano-tip surface, making it possible to significantly increase the distribution density of tip charges by gathering large amounts of charges such as tip electrons. Surface waves can be transported and even gathered through tip boundaries to enhance local light wave amplitude, i.e., light intensity. High-density charge distribution and largeamplitude electromagnetic fields are achievable through Nano-tips, which implies that light waves can go beyond the diffraction limit and get further gathered through the tips. Therefore, by rationally designing a Nano-tip structure and shape parameters, we can effectively control charge distribution in Nano-tip metamaterials, making it possible to conduct effective control over the near-field optical characteristics of Nano-tip metamaterials. Local SPP is formed on the surface of the optical antenna under the excitation of incident electromagnetic signals. With the constant change of the electromagnetic field, energy is radiated outward, with the optical antenna bringing about local strong surface plasmon resonance sharp corners and intersections. In Fig. 12.1, the microtip is 20 μm high, and the sharp corner is at 10 degrees, with a Nano characteristic scale formed at the tip, achieving a noticeable electron aggregation effect. Local SPP is formed on the surface of the metamaterial optical antenna under the exception of incident electromagnetic signals at 0.1–3THz, creating an induction effect with the constant change of the electromagnetic field. Figure 12.2 shows the SPP effect achieved at the tips and edges. Figure 12.3 shows the SPP effect achieved at the tips and edges of the metamaterial optical antenna under the excitation of 5–10-μm infrared signals. Fig. 12.1 Independent nano-tip electron aggregation effect

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Fig. 12.2 THz signal simulation of local SPP on the surface of the metamaterial optical antenna. a Electric field; b magnetic field; c surface current

Fig. 12.3 Infrared signal simulation of local SPP on the surface of the metamaterial optical antenna. a electric field; b magnetic field; c surface current

Figure 12.4 shows the SPP effect achieved at the tips and edges of the metamaterial optical antenna under the excitation of 400–600-nm infrared signals. Figure 12.5 shows a detection array using the metamaterial micro/nano structure to detect optical frequency-RF integrated ultra-wideband wave fields. As shown in Fig. 12.5, several metamaterial structure subarrays for respectively sensing electromagnetic wave fields with different spectral components are arranged in order to form a complete array detector. The central wavelength λ sensed by each subarray can shift to a certain extent with the change of electrical parameters of the bias circuit. The subarray layout, the subarray element metamaterial micro/nano structure and the pattern form, structure parameter and electronic configuration, as well as the influence of the cascading and coupling modes between sub-structures on the induction detection efficiency are all integrated into the design, simulation, fabrication, testing, evaluation and optimization of principle devices. The metal layers of each cyclical micro/nano structure in the metamaterial layer for optical frequency-RF integrated detection have complete absorption characteristics for specific electromagnetic waves. The fabrication of metamaterials can be subject

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Fig. 12.4 Visible band simulation of local SPP on the surface of the metamaterial optical antenna. a electric field; b magnetic field; c surface current

Fig. 12.5 Optical frequency-RF integrated detection array based on artificial metamaterial

to the Schottky process standard. The substrate can be but not limited to SI-GaAs, Si and Al2 O3 , etc. The ohmic electrode of Schottky diodes can be but not limited to Ni, Ge and Au; The Schottky electrode can be but not limited to Ti and Au. Figure 12.6 shows a schematic diagram of the longitudinal section of an optical frequency-RF detection device. In the figure, 1 is the substrate layer, 2 is the N-GaAs layer, 3 is the SiO2 layer, 4 is the metal layer of the cyclical micro/nano structure, 5 is the ohmic electrode, 6 is the Schottky electrode and 7 is the incident electromagnetic wave signal. As shown in Fig. 12.7, the above-mentioned metal split-ring resonance element SRR array composed of different patterns is equivalent to multiple LC resonance circuits. When the target electromagnetic wave signal is vertically propagated to the metamaterial layer, these LC resonance circuits will resonate with the electromagnetic wave with a specific wavelength and absorb the energy of the corresponding

12.2 Detected Microstructure Characteristics Fig. 12.6 Longitudinal section of optical frequency-RF integrated detector

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7 5 4

3 2

6

1

wavelength in the incident electromagnetic wave. If the above-mentioned several metal split-ring resonance element arrays are grouped and numbered, they would respectively correspond to Infrared Wavelength 1, Infrared Wavelength 2,……, Infrared Wavelength N1, Terahertz Wavelength 1, Terahertz Wavelength 2,……, Terahertz Wavelength N2, Millimeter Wavelength 1, Millimeter Wavelength 2,……, Millimeter Wavelength N3, where N1, N2 and N3 are respectively corresponding to the number of metal split-ring resonance SRR element arrays for sensing infrared radiation, terahertz wave fields and RF millimeter waves.

12.2 Detected Microstructure Characteristics The pattern features as shown in Figs. 12.8, 12.9 and 12.10 can be obtained by magnifying the microstructural elements of the optical frequency infrared radiation, terahertz wave field and RF millimeter wave regions. The metal split-ring resonance elements of the metal split-ring resonance element array area are made of Ti and Au (20–30 nm and 200–250 nm thick respectively), which form a Schottky contact with the N-GaAs layer. When operating within the far infrared band, the opening spacing, line width, cycle, middle line inclination, middle line length and middle line width are t = 80–200 nm, d = 200–600 nm, L = 500–2000 nm, θ = 0–90°, p = 300–2000 nm, f ≤ d/4, respectively. The metal split-ring resonance elements of the metal split-ring resonance element array area are made of Ti and Au (20–30 nm and 200–250 nm thick respectively), which form a Schottky contact with the N-GaAs layer. When operating within the terahertz band, the opening spacing, line width, cycle, middle line inclination, middle line length and middle line width are t = 2–8 μm, d = 4–14 μm, L = 36–100 μm, θ = 0–90°, p = 10–100 μm, f ≤ d/4, respectively. The metal split-ring resonance elements of the metal split-ring resonance element array area are made of Ti and Au (20–30 nm and 200–250 nm thick respectively), which form a Schottky contact with the N-GaAs layer. When operating within the

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12 Optical Frequency-RF Integrated Detection Architecture Based … Optical frequency infrared band

Terahertz band RF millimeter band

Ohmic electrode

Schottky electrode

Schottky electrode

Fig. 12.7 Top view of optical frequency-RF integrated detector

Fig. 12.8 Magnified view of metal split-ring resonance element array for sensing optical frequency infrared radiation

millimeter wave, the opening spacing, line width, cycle, middle line inclination, middle line length and middle line width are t = 10–20 μm, d = 20–60 μm, L = 200–300 μm, θ = 0–90°, p = 50–300 μm, f ≤ d/4, respectively. As shown in Fig. 12.6, the key method for preparing Ohmic Electrode 5 and Schottky Electrode 6 is the same as the above mentioned. Through the proposed preparation scheme, the above mentioned composite broadband SRR pattern array is integrated into a Schottky diode on a monolithic semiconductor substrate to achieve an optical frequency-RF integrated broad spectrum signal detector.

12.2 Detected Microstructure Characteristics

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Fig. 12.9 Magnified view of metal split-ring resonance element array for sensing terahertz wave field

Fig. 12.10 Magnified view of metal split-ring resonance element array for sensing RF millimeter waves

Planar and vertical Nano-tip metamaterials can be developed when Nano-tip technology is applied to all metamaterial microstructures. The metamaterial optical antenna layer is an array structure composed of multiple metal layers spaced apart from one another, used for signal detection of the local SPP effects generated by incident optical infrared, THz waves and RF-band electromagnetic signals; the metal layers are connected in parallel with each other, one end associated with the Schottky electrode, the other with the common electrode; there are two metal layers, i.e., the first metal layer and the second metal layer. Specifically, the first metal layer is a metal Nano-tip array with a width of 0.5– 5 mm, which has local SPP characteristics about incident infrared electromagnetic waves. The metal Nano-tip array is a metal array has a periodic Nano-tip structure; the Nano-tip structure is a Nano-scale tip structure composed of metal Nano-tips. The second metal layer is a metal array with a width of 5–100 mm, which has a local SPP effect on the incident electromagnetic signals in the S-band, C-band or X-band; moreover, the second metal layer is composed of micron elements arranged periodically; in the micron, elements are of the micron structure. Further, the first and second metal layers are distributed on the same plane to form an array structure. The two layers can be located in two different planes, with the first metal layer on the first plane, forming an array structure on the first plane, the second metal layer on the second plane, creating an array structure on the second plane, and both planes

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superimposed on each other. When distributed on the same plane, the first and second layers can be arranged separately to receive corresponding signals independently; specifically, they can be arranged as shown in Fig. 12.11a. At this point, all the first metal layers 41 and second metal layers 42 can be concentrated separately to form the first metal block and the second metal block, respectively. The first metal block and the second metal block are arranged independently to jointly form an array structure, with the first metal block located at the left half of the array structure and the second metal block at the right half of the array structure. Alternatively, they can be arranged as shown in Fig. 12.11b, with the first metal layers 41 intensively distributed in the middle region and the second metal layers 42 in the peripheral region to surround the first metal layers as a whole to form an array structure. Besides, the first and second metal layers can also be mixed and arranged in an arbitrary to facilitate the function extension of the entire optical antenna. The first and second layers are nested when located in two different planes. At this point, the direction and position needn’t be considered for signal reception, thus ensuring higher efficiency. As shown in Fig. 12.12, the first metal layer 41 is superimposed on the second metal layer 42 to form an array structure in two planes, respectively. As shown in Fig. 12.12, the first metal layer 41 is superimposed on the second metal layer 42

Fig. 12.11 Array arrangement of metamaterial a separate arrangement; b wraparound arrangement

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Fig. 12.12 Cascade arrangement of metamaterial array

to form an array structure in two planes, respectively, with the metamaterial optical antenna layer composed of two metal layers superimposed. It should be noted that the structure shown in Fig. 12.12 is for reference only. Since the size of the array formed by the second metal layers is large, the first metal layers can also be nested and superimposed on each other in the internal spare space of the array formed by the second metal layers. Signals in different bands differ in wavelength and resolution, and the spot diameter of infrared signals is small (millimeter-scale). In contrast, the spot diameter of RF signals is large (centimeter-scale). Therefore, to detect signals from the infrared band to the RF band, the detector can fully receive electromagnetic signals of different wavelengths based on the above scheme, making it possible to detect signals of all wavelengths. In the actual detection process, under the conventional background with low environmental signal interference, a voltage of 2 V with load resistance can be applied to the Schottky electrode to enhance Nano-tip electron concentration and signal strength, including the signal strength on micron elements, to detect infrared and RF signals accurately. Given weak incident electromagnetic wave signals, a reverse DC bias voltage of 0.1–5 V can be applied to the ohmic electrode and Schottky electrode to increase the width of the depletion region in the contact area between the metal and doping layer of the metamaterial optical antenna layer, to enhance the signal strength at the Nano-tips and micron elements of the metamaterial optical antenna layer. Thereby making it possible to accurately detect infrared, THz, and RF signals. The metal Nano-tip array in the first metal layer comprises a several identical metal Nano-units. In contrast, the silicon dioxide in the silicon dioxide layer insulates the gaps between and inside the metal Nano units. Specifically, the metal Nano-units comprise one or more metal Nano-tips parallel or perpendicular to the doping layer; moreover, the metal Nano-units are of the Nano-structure and made of titanium and gold, with a thickness of 20–80 nm and 100–250 nm respectively. When the metal Nano-tips parallel the doping layer, the abovementioned metal Nano-tip array is of the planar structure. Thus, the metal Nano-tip array is a pure Nano-structure or a microNano structure; for the pure Nano-structure. Figure 12.13 shows its metal Nano-tip array and detailed structural schematic diagram for the pure Nano-structure. A metal Nano-unit comprises a planar metal Nano-tip, and all the planar metal Nano-tip are

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isosceles triangles in the sharp angle orientation. A metal sheet or wire connects two adjacent metal Nano units. The spacing between the metal Nano-units, p = 10– 300 nm, the peripheral width of planar metal Nano-tip elements, L = 50–300 nm, the width of planar metal Nano-tips, d = 20–150 nm, height h = 80–500 nm, and sharp angle θ = 10–60°, respectively. For a micro-Nano structure, the metal Nano-tip array contains not only metal Nano-units but also a plurality of identical micron elements, which are of the micron structure and polygonal in shape, made of titanium and gold; all metal Nano-units are distributed on the outer or inner side, jointly forming a micro-Nano structure, significantly saving the cost infrared RF signal detection. Figure 12.14 shows a metal Nano-tip array of the micro-Nano structure with square micron elements. In contrast, each metal Nano-unit is composed of a planar metal Nano-tip that exists as an isosceles triangle, and each metal Nano-unit is distributed on the inner side of the micron of a micron element along each side of the micron element. At this point, two adjacent micron elements are connected through a metal sheet or wire, while two adjoining metal Nano units needn’t be combined. When the metal Nano-tips are perpendicular to the doping layer, the abovementioned metal Nano-tip array is of the 3D structure, specifically vertical prismatic structure, and the number of edges, N ≥ 6. As shown in Fig. 12.15, the number of edges is 6, and the sharp angle α formed by extended reverse lines of all the edges

Fig. 12.13 Magnified view of planar Nano-tip element array for sensing electromagnetic waves Fig. 12.14 Nano-tip array of the micro-Nano structure with square micron elements

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Fig. 12.15 Magnified view of vertical prismatic Nano-tip element array for sensing electromagnetic waves Fig. 12.16 Arc-shaped planar micron structure

is 10–40°; the side length of the upper surface, a1, is 30–200 nm, the side length of the upper surface, a2, is 10–100 nm, the slant height, h, is 80 –300 nm, and the metal Nano-tip spacing, p = 10–100 nm. Further, in the second metal layer, the silicon dioxide in the silicon dioxide layer insulates the gap between the micron elements. The micron elements are of the micron structure and can be made of titanium and gold; metal sheets or wires connect the micron elements, and their spacing is 50–500 μm. Specifically, the metal array is of the planar structure when the micron elements parallel the doping layer. At this point, the micron elements are of the arc-shaped planar structure, as shown in Fig. 12.16, with a radian of 10–120°, length of 10–500 μm, and width of 50–500 μm. When the micron elements are perpendicular to the doping layer, the metal array is of the 3D structure. At this point, the second metal layer is a vertical metal array. The micron elements are of the conical structure or arc-shaped prismatic structure on the upper and lower surfaces. The number of edges for a micron element with an upper surface of the arc-shaped prismatic structure is 3 or 4. Figure 12.17 shows a vertical metal array and its detailed structural diagram. The number of edges is 4; the radian β is 10–180°; the side length of the lower surface, a1 and b1, is 10–100 μm; the slant height, h, is 1–100 μm. For a micron element of the conical structure, its bottom diameter is 10–100 μm, height is 1–100 μm, and cone angle is 10–60°.

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Fig. 12.17 Magnified view of arc-shaped prismatic Nano-tip element array for sensing electromagnetic waves

12.3 Summary Optical frequency imaging technology is characterized by higher imaging resolution, range resolution and sensitivity, smaller equipment size, lower mass and power consumption, and better structure and system compatibility than RF imaging technology. This is because the wavelength is far shorter than the RF electromagnetic radiation range. However, it is subject to short observation distance, weak target penetration (perspective), and influence of the atmospheric window effect, climate, weather, solar radiation and other interference. At present, it is widely used in missile (terminal) guidance, medium/short range imaging observation, battlefield imaging detection, etc. RF imaging technology adopted by synthetic aperture radars etc. is characterized by its strong imaging detection, long observation distance, all-weather 24 h operation, better target penetration and camouflage recognition when compared to optical frequency detection, in addition to its good environmental adaptability. It has been widely used in remote measurement, ocean surveillance, moving target indication, moving/static target interception, identification, camouflage recognition and detection, high orbit imaging satellite and deep space exploration, etc. However, defects such as imaging definition being still far lower than that of optical frequency electromagnetic mediums, higher equipment’s overall size, mass and power consumption, complex system structures, antennas requiring far higher receiving and transmitting capabilities than the objectives of optical frequency systems, as well as the hard integration of the current technical system with the optical frequency imaging systems, etc. still exist. The difference in physical behavior between optical and RF electromagnetic waves is in their distinct wavelengths. Optical signals have wavelengths measured in the micrometer/submicron range, while RF signals are measured in the millimeter/ centimeter or even higher ranges. Because of this, both have the physical capability to convert from spatial electromagnetic field data to image information, and stateof-the-art technology can help realize efficient image detection in optical and RF frequencies. Therefore, a key step to achieve the real optical frequency-RF integrated imaging detection is to find the theoretical system and physical sensitive architecture being available for both optical frequency and RF electromagnetic wave fields at the

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same time for the sake of miniaturized, handy and high-definition imaging being similar to or even better than the optical frequency system, as well as strong remote detection capability under the RF system. Fortunately, such physical architecture has been proposed in recent years in several rapidly developed typical photoelectric conversion methods based on the terahertz electromagnetic wave field imaging detection technology. Nowadays, the rapid development of terahertz imaging technology shows that the optical frequency and RF imaging detection operations can coexist under the same physical architecture. The metamaterials made with SRR structures and being compatible with the micro/nano semiconductor technology are obviously available for sensing electromagnetic waves, and have additional radiation characteristics during electromagnetic wave transmission, namely the designed metamaterials integrate the functions for sensing and radiating broad spectrum electromagnetic waves, which are also necessary in current military applications. At the same time, the proposed design model and fabrication method based on artificial metamaterials can be extended to the ultrawide spectrum domain of optical frequency-RF integration, so as to achieve practical and feasible optical frequency-to-RF integration signal detection. According to the artificially optimized SRR structure, as well as the existing technology and models, they can be used to detect extremely weak signals, and microwatt level results can be obtained relying on the overall capability for sensing signals. Therefore, electrically controlled artificial metamaterial micro/nano structures and their arrays based on special materials and structures can be used to conduct highly sensitive quantitative control of parameters such as amplitudes, spectra and phases of electromagnetic wave fields through resonance induction with electromagnetic wave fields. The above research indicates the extensive development prospects of electrically controlled artificial metamaterial structures in electromagnetic wave field phased-arrays, optical antennas, wavefront detectors, photocells, stealth and miniaturized optical frequency-RF integrated inductive detection, etc.