PREFACE

This book is primarily intended as a graduate-level text for students who wish to specialize in electromagnetic (EM) wave radiation, scattering, and diffraction for engineering applications. The book is also suitable for use in these areas by practicing EM engineers and researchers in industry. EM theory is a classical subject; however, the need for a strong background in EM wave theory at the basic as well as advanced levels is ever-present, because of its continued applications to modern technologies, e.g., to the design of antennas for communications as well as for various types of sensing including biomedical sensors; to the prediction of antenna wave interactions with their complex platforms (such as aerospace, naval, satellite, and others); and to the analysis/synthesis of conformal phased-array antennas as well as predicting radar target returns, etc. Furthermore, the possibility of creating engineered materials with desired EM properties, and the push to higher wave frequencies for increased bandwidth applications, etc., are also factors that are influencing some of the directions for future developments in EM. The present book is therefore designed to provide an understanding of the behavior of EM fields in radiation, scattering, and guided wave environments, from first principles and from low to high frequencies, to meet some of the challenges of current and future EM technology.

Most electrical engineering students admitted into graduate school have typically completed only one semester course on introductory EM as part of their undergraduate curriculum. Quite often, graduate students with a limited EM background, but who have chosen to perform research in EM radiation, scattering, and guided wave or propagation problems, may use available EM commercial software to simulate their research problems without having a sufficient knowledge of what numerical results might be expected from their simulations or if the results make good sense. The present book can facilitate students with a somewhat limited undergraduate EM background to rapidly and systematically advance their understanding of EM wave theory that is useful and important for doing graduate-level research on EM wave problems. This book can therefore also be useful for gaining a better understanding of problems they are trying to simulate with commercial EM software.

The material in the book is mostly self-contained since the necessary mathematical tools are also developed in sufficient detail; it is assumed that the reader has some familiarity with vector calculus, complex variables, and matrix algebra at the undergraduate level. All of the material is presented in substantial detail, and with sufficient explanations so that it can be followed with relative ease. The latter feature is preserved throughout the book. Physical interpretations of the EM wave phenomena are stressed along with their underlying mathematics. Several examples are included to illustrate the concepts. It is therefore hoped that this book would be particularly convenient for teaching EM wave theory at the graduate level, and also convenient for self-study as a refresher for interested EM industry professionals. This book also contains many results that may be found only in research papers and reports from research labs. The majority of the book deals with time harmonic EM wave phenomena; however, an analysis of EM waves directly in the time domain is also included in a few places. An analytical study of transient time EM phenomena is important with the ability to generate short pulses and pulses with significant high-frequency content; it is also useful for radiating special waveforms and for target identification and other applications.

A part of the book is based on the lectures given by Prof. Pathak; it was offered as a graduate level, three-course sequence on EM wave theory, at The Ohio State University, in the Department of Electrical and Computer Engineering (ECE). While originally the course was offered over three quarters during an academic year, it can also be offered as a two-semester course in which Chapters 1-9 would form the material for the first semester and the remaining Chapters 10-18 could be completed in the second semester. Of course, the instructor could choose which topics to include or omit, from any chapter, as desired.

The major emphasis in the book is on analytical methods in EM and in particular ray methods; such methods are included, in particular because they generally provide useful physical insights into the mechanisms of EM wave radiation, scattering, and diffraction, by relatively complex structures, in terms of rays. Ray methods are useful and valid especially at moderate-to-high frequencies. The physical insights provided to EM design engineers by such analytically based solutions to EM problems can hardly be overemphasized. At low frequencies, the ray picture tends to break down; on the other hand, numerical methods are highly suitable in these moderate- to low-frequency regimes where they become more efficient and can solve more general problems than analytical methods; thus, they are also crucial to EM design engineers. Only integral equation-based numerical methods in EM are included here. It is noted that other numerical methods such as those based on partial differential equation methods, namely, finite difference and finite element methods are not included, as they are readily available in many excellent books solely devoted to them. On the other hand, a detailed analytical treatment of modern high-frequency problems using asymptotic methods of solution and their ray interpretation is not so readily available in graduate-level EM texts; it is hence developed here in a systematic and detailed fashion, and its inclusion may be viewed as one of the special features of this book. Engineered materials are gaining more interest in applications because they appear to be useful for designing structures with special EM properties. Such structures may be classified broadly as electromagnetic band gap (EBG) structures. A discussion of such EBG structures and metasurfaces is not included in the book as it can also be found in books fully devoted to these topics. EBG structures are typically periodic structures, and an analysis of periodic structures is certainly included in the book. The list of topics included in this book are briefly summarized below; the range of topics is kept reasonably broad and the material is quite detailed to provide an overall EM background containing both breadth and depth for the graduate students so that they can then embark on their EM research with sufficient confidence.

Chapter 1 provides an introduction to Maxwell's equations and constitutive relations. The Kramer's-Kronig relationship is developed. The wave equation is obtained from Maxwell's equations, and EM plane waves are introduced as solutions to the source-free wave equation in rectangular coordinates. Polarization of plane waves is discussed in detail and its representation using the Poincaré sphere is described. Phase and group velocity of waves are discussed. Cylindrical and spherical waves are obtained as solutions to the source-free wave equation in cylindrical and spherical coordinates, respectively.

Chapter 2 develops EM boundary conditions for both stationary and moving boundaries. The special theory of relativity is employed for moving boundaries; also constitutive relations are obtained for a moving medium. Use of relativity in EM is demonstrated, e.g., in the analysis of Doppler-shifted EM signal received from a fast moving object, and via other examples.

In Chapter 3, plane waves reflecting from a medium half space are studied. Snell's laws, as well as Brewster and Critical angles are defined. Expressions for the reflection and transmission of plane waves incident on a planar layered medium are obtained. Characteristic plane waves in a cold magneto plasma as well as in a general bi-anisotropic media are studied. Plane waves in planar anisotropic-layered media are also treated.

Chapter 4 presents a representation of EM fields in terms of a plane wave spectral expansion. The utility of such a plane wave spectral representation is demonstrated via the problem of transmission of EM plane waves through apertures in perfectly conducting planar screens.

Chapter 5 introduces the concept of EM potentials for representing EM fields of sources in unbounded media. Potentials using the Lorenz and Coulomb gauges are considered. Potentials are employed to represent fields of antennas, and the near and far zone regions of antennas are defined. Also, an expression for the fields of a charged particle in motion is given. A discussion on Cerenkov radiation due to a fast moving charged particle in a dense medium is included, as it can be predicted accurately by Maxwell's equations. It is shown that fields due to a source can also be represented directly in terms of a Green's dyadic; its regularization at the source singularity is discussed. Finally, a Green's dyadic for fields of a source in bi-anisotropic media is presented.

Chapter 6 is devoted to EM theorems. An understanding of these powerful theorems, especially the reciprocity and reaction theorems, is important for solving a variety of EM problems of engineering interest; they can offer useful information on the underlying physics and on the simplifications for solving such problems. Several examples are given on the application of theorems in this and later chapters; such wide-ranging applications do not appear to be readily available in most graduate-level texts. Examples presented on the application of theorems include calculation of EM radiation pressure on...