Zhang K., Li D. Electromagnetic Theory for Microwaves and Optoelectronics

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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: zhangkq@tsinghua.edu.cn

lidj@ee.tsinghua.edu.cn

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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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 indepen-

dent and irrelevant topics. Then, in the sixties of the 19th century, incon-

sequence 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 cur-

rent, 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, infra-

red, visible and ultra-violet lights, and even X- and γ-ray radiations. Their

frequency range covers from 10

Hz to 10

Hz, the widest for a physical

quantity.

Using damping wave in the ultra-short wave band, H. Hertz experimen-

tally 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, op-

tical 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 propaga-

tion 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. Con-

sequently, 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 analy-

sis. 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 dis-

cussions 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 re-

searchers 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 Elec-

trodynamics” given by the authors at Tsinghua University. More than 300

students from the Department of Electronic Engineering and the Depart-

ment 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 light-

wave technology. However, the b ook 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 transmission-

line and network simulations of wave process are introduced. They are pow-

erful 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 Gaus-

sian 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 anal-

ysis, 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 writ-

ing 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 hospitali-

ties 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 chap-

ter: 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 cir-

cular 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 circular-

harmonics 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

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 Ts-

inghua University, Chinese Academy of Telecommunication Technology and

many institutes on microwave electronics, high-power-microwaves, optoelec-

tronics 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