**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
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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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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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