Electromagnetic Theory for Microwaves and Optoelectronics 2008.pdf

Electromagnetic Theory for Microwaves and Optoelectronics 2008.pdf

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Unformatted text preview: Keqian Zhang · Dejie Li Electromagnetic Theory for Microwaves and Optoelectronics Keqian Zhang · Dejie Li Electromagnetic Theory for Microwaves and Optoelectronics Second Edition With 280 Figures and 13 Tables 123 Professor Keqian Zhang Professor Dejie Li Department of Electronic Engineering Tsinghua University Beijing 100084 China e-mail: [email protected] [email protected] Library of Congress Control Number: 2007934278 DOI: 10.1007/978-3-540-74296-8 ISBN 978-3-540-74295-1 Springer Berlin Heidelberg New York ISBN 978-3-540-63178-1 1st ed. Springer Berlin Heidelberg New York 1998 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2008 The use of general descriptive names, registered names, trademarks, 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. Typesetting: supplied by the authors Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig, Germany Cover Design: eStudio Calamar, Girona, Spain Printed on acid-free paper 60/3180/YL 543210 Preface by Dr. C.Y.Meng Preliminary and qualitative knowledge of static magnetism and electricity were acquired by mankind since very ancient times. However, an in-depth and quantitative analysis was not available until the beginning of the 19th Century, while magnetism and electricity are still recognized as two independent and irrelevant topics. Then, in the sixties of the 19th century, inconsequence and non-self-consistency was discovered by J. C. Maxwell when he tried to sum up the known laws of electricity and magnetism. However, this was eliminated after his creative introduction of the idea of displacement current, and the well known Maxwell equations were formed consequently as the foundation of electromagnetism. From these equations, it is understood that electricity and magnetism are by no means non-related, but two aspects of just one thing. Maxwell not only unified electricity and magnetism, but also proved that light is actually a part of the electromagnetic spectrum, which extends from super long, long, medium, short, ultra short, meter, decimeter, centimeter and millimeter waves all the way down to far infra-red, infrared, visible and ultra-violet lights, and even X- and γ-ray radiations. Their frequency range covers from 101 Hz to 1020 Hz, the widest for a physical quantity. Using damping wave in the ultra-short wave band, H. Hertz experimentally confirmed the existence of electromagnetic wave, and measured some of its properties. However, the first application of electromagnetic wave was in the long wave range. In the following decades, scientists tried to use shorter radio waves and extend the optical wavelength range on both sides of the visible light waves. Now, radio and light waves have met in the far-infrared band, and the full electromagnetic spectrum has been connected together. The wavelength range involved in this book covers microwave and part of the optical waves. Microwave deals with wavelengths in the order from meters to millimeters, the shortest part in the radio-wave spectrum. It was studied only by few scientists before the World War II, followed by fast development during the war as desired by applications in radar, then post-war applications in communications, industrial and scientific research. On the other hand, optical wavelengths involved in this book lie in the micrometer or near-infrared range, mainly for information transmission experiencing rapid development in the recent decades. In fact, this part of electromagnetic spectrum shifts to vi Preface center stage only after the invention of laser diode and low-loss optical fiber in the late sixties of the 20th century. The basic reason that microwave and optical wave are so prevailing is that they can carry huge amount of information. All information requires a certain amount of bandwidth. Wider bandwidth is needed for more complicated information (such as video image). As the carrier frequency must be times higher than the information bandwidth, very high carrier frequency or very short carrier wavelength must be used to carry more information. Another feature of microwave and optical wave is related to their propagation characteristics. It’s quite easy to confine them into a very narrow beam, so to avoid mutual interference. At the same time, appropriate waveguide can be used to realize long distance low loss transmission. These characteristics enable microwave and optical wave very suitable to accommodate the modern societal need under information explosion. Consequently, through flourishing development, an advanced academic field – microwave and optic wave, or microwave and optoelectronics, is formed. As part of electromagnetic wave, both microwave and optical wave share identical or similar behavior and characteristics, as well as tools for analysis. But traditionally they belong to two different subjects, and there still lacks a unified monograph in this field to guide serious entry level researchers. Published books on electrodynamics or electromagnetic theory are basically fundamentals, and after reading these books, the readers are still difficult to understand the most advanced papers and engage in further research. This book, Electromagnetic Theory for Microwaves and Optoelectronics authored by Keqian and Dejie, just met this demand. Basic theory of electromagnetic field and wave are given with relevant knowledge of mathematical treatment to keep the readers’ legs for their first step, while detailed and in-depth discussions are given on various aspects of microwaves and optical waves. Along with rigid mathematical analysis, clear and vivid descriptions on physical ideas relevant to various issues are presented. Through this book, readers are anticipated to go through current literature with ease, to grasp basic ideas and methodology of analysis in conducting research in these areas, and in a mood to explore treasures. Through decades of teaching and research, the authors summarized their experience into this million-word distinctive monograph. I am really happy for its publication, and also for those researchers in this and adjacent fields in having such a textbook or reference book. Tsinghua Campus, 1994 Dr. Chao -Ying Meng (1906–1995) Translated by Chongcheng Fan, Professor, Tsinghua University Preface to the First Edition This book is a first year graduate text on electromagnetic fields and waves. It is the translated and revised edition of the Chinese version with the same title published by the Publishing House of Electronic Industry (PHEI) of China in 1994. The text is based on the graduate course lectures on “Advanced Electrodynamics” given by the authors at Tsinghua University. More than 300 students from the Department of Electronic Engineering and the Department of Applied Physics have taken this course during the last decade. Their particular fields are microwave and millimeter-wave theory and technology, physical electronics, optoelectronics and engineering physics . As the title of the book shows, the texts and examples in the book concentrate mainly on electromagnetic theory related to microwaves and optoelectronics, or lightwave technology. However, the book can also be used as an intermediate-level text or reference book on electromagnetic fields and waves for student and scientists engaged in research in neighboring fields. The purpose of this book is to give a unified formulation and analysis of the electromagnetic problems in microwave and light-wave technologies and other wave systems. The book should enable readers to reach the position of being able to read the modern literature and to engage in theoretical research in electromagnetic theory without much difficulty. In this book, the behavior and the characteristics of a large variety of electromagnetic waves, which relate to the problems in various different technological domains, are formulated. The purpose is to give the reader a wide scope of knowledge, rather than merely to confine them in a narrow domain of a specific field of research. The authors believe that the scope is just as important as the depth of knowledge in training a creative scientist. Chapters 1 through 3 provide the physical and mathematical foundations of the theory of fields and waves. The concepts introduced in these chapters are helpful to the understanding of the physical process in all wave systems. In Chap. 2, in addition to the plane waves in simple media, the transmissionline and network simulations of wave process are introduced. They are powerful and useful tools for the analysis of all kinds of wave systems, i.e., the equivalent circuit approach. The necessary mathematical tools for solving electromagnetic field problems are given in Chap. 3. viii Preface Chapters 4 through 6 cover the field analysis of electromagnetic waves confined in material boundaries, or so-called guided waves. The category of the boundaries are conducting boundaries in Chap. 4, dielectric boundaries in Chap. 5, and the periodic boundaries in Chap. 6. The mode-coupling theory and the theory of distributed feedback structures (DFB) are also included in Chap. 6. Chapters 7 through 9 are a subjective continuation of Chap. 2. They deal with electromagnetic waves in open space, including waves in dispersive media (in Chap. 7), waves in anisotropic media (Chap. 8), and the theory of Gaussian beams (Chap. 9). All these are topics related to modern microwave and light-wave technologies. Scalar diffraction theory is given in Chap. 10. In addition to the scalar diffraction theory for plane waves in isotropic media, the diffraction of Gaussian beams and the diffraction in anisotropic media are also given, which are important topics in light-wave and millimeter-wave problems. It is assumed that the readers have undergraduate knowledge of field and circuit theories, and the mathematical background of calculus, Fourier analysis, functions of complex variables, differential equations, vector analysis, and matrix theory. Chapters 1 through 8 are written by Keqian Zhang. Chapters 9 and 10 are written by Dejie Li. Keqian Zhang also went through the whole manuscript so as to make it a unified volume. During the time period involved in preparing the subject matter and writing the book, the authors discussed and debated with colleagues and students at the physical electronics group of Tsinghua University, and this was very fruitful in many respects. Professor Lian Gong of electrical engineering at Tainghua University read both the Chinese and the English versions of the manuscript with care and offered many helpful suggestions. Ms. Cybil X.-H. Hu, alumnus 1985 from Tsinghua University and currently on leave from the University of Pennsylvania read and corrected the preliminary version of the English manuscript. The copy editor, Dr. Victoria Wicks of Springer-Verlag, not only did the editorial work carefully but also gave a lot of help in English writing. The authors should like to acknowledge with sincere thanks all the mentioned contributions to this volume. Our thanks are also extended to Professors Xianglin Yang of Nanjing Post and Telecommunication University, Wen Zhou of Zhejiang University, Chenghe Xu of Peking University, and Mr. Jinsheng Wu of PHEI for their contributions in the publishing of the Chinese edition. We are also grateful to persons in various countries for their kind hospitalities during our visits to their institutions or for giving talks in our department and for the helpful discussions. Tsinghua University, 1997 Keqian Zhang and Dejie Li Preface to the Second Edition It has been nine years since the first English edition of this monograph was published in 1998. During these years, the second Chinese edition and a new edition in traditional Chinese characters were published in Beijing, 2001 and Taipei, 2004, respectively. Compared with the first edition, this second English edition is different in rearranged and revised chapters and sections, improved explanations and new contents. Some misprints, errors and inadequacies are also remedied. Major revisions include 1. Chapter 2 in the first edition is separated into two chapters: Chapter 2 – Introduction to waves and Chapter 3 – Transmission-Line Theory and Network Theory for Electromagnetic Waves. 2. Chapters 7 and 8 in the first edition are combined into one chapter: Chapter 8 – Electromagnetic Waves in Dispersive Media and Anisotropic Media. 3. Consequently, Chapters 3 to 6 in the first edition are changed into Chapters 4 to 7, respectively, and the total number of chapters remains unchanged. 4. Basic theory of dielectric layers and impedance transducers is moved to the end of Chapter 2. 5. In Chapter 2, discussion on the reflection, transmission and refraction of plane waves is rearranged. 6. In Chapter 6, discussion on the behavior of EH and HE modes in circular dielectric waveguides is improved and a relevant figure added. Major content expansion include 1. LSE and LSM modes in rectangular metal waveguide in Chapter 5. 2. Solution of rectangular dielectric waveguide by means of circularharmonics in Chapter 6. x Contents 3. Disk-loaded waveguide with edge coupling hole in Chapter 7. 4. General formulation of the contra-directional mode coupling in Chapter 7. 5. Some new problems in Chapters 2, 3, 4, 6 and 7. Last year, 2006, was the centennial of the birth of our mentor Professor Dr. C. Y. Meng (Zhaoying Meng). Through his guidance, our team entered the fields of microwaves and optoelectronics half a century ago. We were highly privileged and honored that Prof. Meng wrote a Preface for the first Chinese edition in 1994. Now, we would like very much to put its English version, translated by Prof. Chongcheng Fan, at the beginning of this edition to commemorate the 100th anniversary of Prof. Meng’s birth. Our thanks are extended to a large number of graduate students from Tsinghua University, Chinese Academy of Telecommunication Technology and many institutes on microwave electronics, high-power-microwaves, optoelectronics and optical-fiber communications in China and abroad, who pointed out many errors and inconsistencies in the first edition, and gave us many beneficial comments. The authors would like to acknowledge with sincere thanks to Dr. Dieter Merkle, Dr. Christoph Baumann, Ms. Petra Jantzen, Ms. Carmen Wolf of the Engineering Editorial, Springer-Verlag, and Mr. Martin Weissgerber of LE-TeX for their excellent editorial work. We will be most grateful to those readers to bring to our attention any error, misprint or inconsistency that may remain in this edition, which will be corrected in the next edition. Tsinghua University, Beijing, 2007 Keqian Zhang and Dejie Li Contents 1 Basic Electromagnetic Theory 1.1 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . 1.1.1 Basic Maxwell Equations . . . . . . . . . . . . . . 1.1.2 Maxwell’s Equations in Material Media . . . . . . 1.1.3 Complex Maxwell Equations . . . . . . . . . . . . 1.1.4 Complex Permittivity and Permeability . . . . . . 1.1.5 Complex Maxwell Equations in Anisotropic Media 1.1.6 Maxwell’s Equations in Duality form . . . . . . . . 1.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 1.2.1 General Boundary Conditions . . . . . . . . . . . . 1.2.2 The Short-Circuit Surface . . . . . . . . . . . . . . 1.2.3 The Open-Circuit Surface . . . . . . . . . . . . . . 1.2.4 The Impedance Surface . . . . . . . . . . . . . . . 1.3 Wave Equations . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Time-Domain Wave Equations . . . . . . . . . . . 1.3.2 Solution to the Homogeneous Wave Equations . . 1.3.3 Frequency-Domain Wave Equations . . . . . . . . 1.4 Poynting’s Theorem . . . . . . . . . . . . . . . . . . . . . 1.4.1 Time-Domain Poynting Theorem . . . . . . . . . . 1.4.2 Frequency-Domain Poynting Theorem . . . . . . . 1.4.3 Poynting’s Theorem for Dispersive Media . . . . . 1.5 Scalar and Vector Potentials . . . . . . . . . . . . . . . . . 1.5.1 Retarding Potentials, d’Alembert’s Equations . . . 1.5.2 Solution of d’Alembert’s Equations . . . . . . . . . 1.5.3 Complex d’Alembert Equations . . . . . . . . . . . 1.6 Hertz Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.1 Instantaneous Hertz Vectors . . . . . . . . . . . . . 1.6.2 Complex Hertz Vectors . . . . . . . . . . . . . . . 1.7 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Reciprocity . . . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 6 13 15 17 18 19 19 21 22 23 24 24 25 29 30 30 32 35 41 41 43 45 46 46 49 50 51 52 xii Contents 2 Introduction to Waves 2.1 Sinusoidal Uniform Plane Waves . . . . . . . . . . . . . . . . 2.1.1 Uniform Plane Waves in Lossless Simple Media . . . . 2.1.2 Uniform Plane Waves with an Arbitrary Direction of Propagation . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Plane Waves in Lossy Media: Damped Waves . . . . . 2.2 Polarization of Plane Waves . . . . . . . . . . . . . . . . . . . 2.2.1 Combination of Two Mutually Perpendicular Linearly Polarized Waves . . . . . . . . . . . . . . . . . . . . . 2.2.2 Combination of Two Opposite Circularly Polarized Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Stokes Parameters and the Poincar´e Sphere . . . . . . 2.2.4 The Degree of Polarization . . . . . . . . . . . . . . . 2.3 Normal Reflection and Transmission of Plane Waves . . . . . 2.3.1 Normal Incidence and Reflection at a PerfectConductor Surface, Standing Waves . . . . . . . . . . 2.3.2 Normal Incidence, Reflection and Transmission at Nonconducting Dielectric Boundary, Traveling-Standing Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Oblique Reflection and Refraction of Plane Waves . . . . . . 2.4.1 Snell’s Law . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Oblique Incidence and Reflection at a PerfectConductor Surface . . . . . . . . . . . . . . . . . . . . 2.4.3 Fresnel’s Law, Reflection and Refraction Coefficients . 2.4.4 The Brewster Angle . . . . . . . . . . . . . . . . . . . 2.4.5 Total Reflection and the Critical Angle . . . . . . . . 2.4.6 Decaying Fields and Slow Waves . . . . . . . . . . . . 2.4.7 The Goos–H¨anchen Shift . . . . . . . . . . . . . . . . 2.4.8 Reflection Coefficients at Dielectric Boundary . . . . . 2.4.9 Reflection and Transmission of Plane Waves at the Boundary Between Lossless and Lossy Media . . . . . 2.5 Transformission of Impedance for Electromagnetic Waves . . 2.6 Dielectric Layers and Impedance Transducers . . . . . . . . . 2.6.1 Single Dielectric Layer, The λ/4 Impedance Transducer 2.6.2 Multiple Dielectric Layer, Multi-Section Impedance Transducer . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 A Multi-Layer Coating with an Alternating Indices. . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Transmission-Line Theory and Network Theory magnetic Waves 3.1 Basic Transmission Line Theory . . . . . . . . . . 3.1.1 The Telegraph Equations . . . . . . . . . 3.1.2 Solution of the Telegraph Equations . . . 3.2 Standi...
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