1st Edition

Electromagnetic Boundary Problems

By Edward F. Kuester, David C. Chang Copyright 2016
    363 Pages 8 Color & 63 B/W Illustrations
    by CRC Press

    Electromagnetic Boundary Problems introduces the formulation and solution of Maxwell’s equations describing electromagnetism. Based on a one-semester graduate-level course taught by the authors, the text covers material parameters, equivalence principles, field and source (stream) potentials, and uniqueness, as well as:

    • Provides analytical solutions of waves in regions with planar, cylindrical, spherical, and wedge boundaries
    • Explores the formulation of integral equations and their analytical solutions in some simple cases
    • Discusses approximation techniques for problems without exact analytical solutions
    • Presents a general proof that no classical electromagnetic field can travel faster than the speed of light
    • Features end-of-chapter problems that increase comprehension of key concepts and fuel additional research

    Electromagnetic Boundary Problems uses generalized functions consistently to treat problems that would otherwise be more difficult, such as jump conditions, motion of wavefronts, and reflection from a moving conductor. The book offers valuable insight into how and why various formulation and solution methods do and do not work.

    List of Figures

    List of Tables

    Preface

    Author Bios

    Maxwell's Equations and Sources

    Maxwell Equations in Free Space

    Energy Transfer and Poynting's Theorem

    Macroscopic Maxwell Equations in Material Media

    Multipole Expansions for Charges and Currents

    Averaging of Charge and Current Densities

    Conduction, Polarization, and Magnetization

    Time-Harmonic Problems

    Duality; Equivalence; Surface Sources

    Duality and Magnetic Sources

    Stream Potentials

    Equivalence Principles

    Jump Conditions

    General Jump Conditions at a Stationary Surface

    Example: Thin-Sheet Boundary Conditions

    Jump Conditions at a Moving Surface

    Force on Surface Sources

    Example: Charge Dipole Sheet at a Dielectric Interface

    Problems

    Potential Representations of the Electromagnetic Field

    Lorenz Potentials and their Duals (A, Φ, F, Ψ)

    Hertz Vector Potentials

    Jump Conditions for Hertz Potentials

    Time-Harmonic Hertz Potentials

    Special Hertz Potentials

    Whittaker Potentials

    Debye Potentials

    Problems

    Fundamental Properties of the Electromagnetic Field

    Causality; Domain of Dependence

    Domain of Dependence

    Motion of Wavefronts

    The Ray Equation and the Eikonal

    Passivity and Uniqueness

    Time-Domain Theorems

    Radiation Conditions

    Time-Harmonic Theorems

    Equivalence Principles and Image Theory

    Lorentz Reciprocity

    Scattering Problems

    Aperture Radiation Problems

    Classical Scattering Problems

    Aperture Scattering Problems

    Planar Scatterers and Babinet's Principle

    Problems

    Radiation by Simple Sources and Structures

    Point and Line Sources in Unbounded Space

    Static Point Charge

    Potential of a Pulsed Dipole in Free Space

    Time-Harmonic Dipole

    Line Sources in Unbounded Space

    Alternate Representations for Point and Line Source Potentials

    Time-Harmonic Line Source

    Time-Harmonic Point Source

    Radiation from Sources of Finite Extent; The Fraunhofer Far Field Approximation

    Far Field Superposition

    Far Field via Fourier Transform

    The Stationary Phase Principle

    Radiation in Planar Regions

    The Fresnel and Paraxial Approximations; Gaussian Beams

    The Fresnel Approximation

    The Paraxial Approximation

    Gaussian Beams

    Problems

    Scattering by Simple Structures

    Dipole Radiation over a Half-Space

    Reflected Wave in the Far Field

    Transmitted Wave in the Far Field

    Other Dipole Sources

    Radiation and Scattering from Cylinders

    Aperture Radiation

    Plane Wave Scattering

    Diffraction by Wedges; The Edge Condition

    Formulation

    The Edge Condition

    Formal Solution of the Problem

    The Geometrical Optics Field

    The Diffracted Field

    Uniform Far-Field Approximation

    Spherical Harmonics

    Problems

    Propagation and Scattering in More Complex Regions

    General Considerations

    Waveguides

    Parallel-Plate Waveguide: Mode Expansion

    Parallel-Plate Waveguide: Fourier Expansion

    Open Waveguides

    Propagation in a Periodic Medium

    Gel'fand's Lemma

    Bloch Wave Modes and Their Properties

    The Bloch Wave Expansion

    Solution for the Field of a Current Sheet in Terms of Bloch Modes

    Problems

    Integral Equations in Scattering Problems

    Green's Theorem and Green's Functions

    Scalar Problems

    Vector Problems

    Dyadic Green's Functions

    Relation to Equivalence Principle

    Integral Equations for Scattering by a Perfect Conductor

    Electric-Field Integral Equation (EFIE)

    Magnetic-Field Integral Equation (MFIE)

    Nonuniqueness and Other Difficulties

    Volume Integral Equations for Scattering by a Dielectric Body

    Integral Equations for Static "Scattering" by Conductors

    Electrostatic Scattering

    Magnetostatic Scattering

    Electrostatics of a Thin Conducting Strip

    Electrostatics of a Thin Conducting Circular Disk

    Integral Equations for Scattering by an Aperture in a Plane

    Static Aperture Problems

    Electrostatic Aperture Scattering

    Magnetostatic Aperture Scattering

    Example: Electric Polarizability of a Circular Aperture

    Problems

    Approximation Methods

    Recursive Perturbation Approximation

    Example: Strip over a Ground Plane

    Physical Optics Approximation

    Operator Formalism for Approximation Methods

    Example: Strip over a Ground Plane (Revisited)

    Variational Approximation

    The Galerkin-Ritz Method

    Example: Strip over a Ground Plane (Re-Revisited)

    Problems

    Appendix A: Generalized Functions

    Introduction

    Multiplication of Generalized Functions

    Fourier Transforms and Fourier Series of Generalized Functions

    Multidimensional Generalized Functions

    Problems

    Appendix B: Special Functions

    Gamma Function

    Bessel Functions

    Spherical Bessel Functions

    Fresnel Integrals

    Legendre Functions

    Chebyshev Polynomials

    Exponential Integrals

    Polylogarithms

    Problems

    Appendix C: Rellich's Theorem

    Appendix D: Vector Analysis

    Vector Identities

    Vector Differentiation in Various Coordinate Systems

    Rectangular (Cartesian) Coordinates

    Circular Cylindrical Coordinates

    Spherical Coordinates

    Poincaré's Lemma

    Helmholtz’s Theorem

    Generalized Leibnitz Rule

    Dyadics

    Problems

    Appendix E: Formulation of Some Special Electromagnetic Boundary Problems

    Linear Cylindrical (Wire) Antennas

    Transmitting Mode

    Receiving Mode

    Static Problems

    Electrostatic Problems

    The Capacitance Problem

    The Electric Polarizability Problem

    Magnetostatic Problems

    The Inductance Problem

    The Magnetic Polarizability Problem

    Problems

    Index

    Biography

    Edward F. Kuester received a BS degree from Michigan State University, East Lansing, USA, and MS and Ph.D degrees from the University of Colorado Boulder (UCB), USA, all in electrical engineering. Since 1976, he has been with the Department of Electrical, Computer, and Energy Engineering at UCB, where he is currently a professor. He also has been a summer faculty fellow at the Jet Propulsion Laboratory, Pasadena, California, USA; visiting professor at the Technische Hogeschool, Delft, The Netherlands; invited professor at the École Polytechnique Fédérale de Lausanne, Switzerland; and visiting scientist at the National Institute of Standards and Technology (NIST), Boulder, Colorado, USA. Widely published, Dr. Kuester is a fellow of the Institute of Electrical and Electronics Engineers (IEEE), and a member of the Society for Industrial and Applied Mathematics (SIAM) and Commissions B and D of the International Union of Radio Science (URSI).

    David C. Chang holds a bachelor's degree in electrical engineering from National Cheng Kung University, Tainan, Taiwan, and MS and Ph.D degrees in applied physics from Harvard University, Cambridge, Massachusetts, USA. He was previously full professor of electrical and computer engineering at the University of Colorado Boulder (UCB), USA, where he also served as chair of the department and director of the National Science Foundation Industry/University Cooperative Research Center for Microwave/Millimeter-Wave Computer-Aided Design. He then became dean of engineering and applied sciences at Arizona State University, Tempe, USA; was named president of Polytechnic University (now the New York University Polytechnic School of Engineering (NYU Poly)), Brooklyn, USA; and was appointed as NYU Poly chancellor. He retired from that position in 2013, and is now professor emeritus at the same university. Dr. Chang is a life fellow of the Institute of Electrical and Electronics Engineers (IEEE); stays active in the International Scientific Radio Union (URSI); has been named an honorary professor at five major Chinese universities; serves as chairman of the International Board of Advisors at Hong Kong Polytechnic University, Hung Hom; and was appointed special advisor to the president of Nanjing University, China.

    "… a unique title by two authors whose in-depth knowledge of this material and ability to present it to others are hardly matched. While the book provides distinguishing coverage and presentation of many topics, some discussions cannot be found elsewhere. I highly recommend this outstanding piece, bringing great value as both a textbook and reference text."
    —Branislav M. Notaros, Colorado State University, Fort Collins, USA

    "… useful for students, researchers, engineers, and teachers of electromagnetics. Today, in many universities, this discipline is taught by teachers who do not have much research experience in electromagnetism. That is why this textbook, written by world-known specialists and showing how electromagnetics courses should be built and taught, is very important. The authors have made clearer several aspects of electromagnetism which are poorly highlighted in earlier-published literature."
    —Guennadi Kouzaev, Norwegian University of Science and Technology, Trondheim

    "Graduate students and learners of electromagnetics of any age and status: If you have not had a chance to attend graduate-level courses taught by great professors like Edward F. Kuester and David C. Chang, here comes opportunity knocking on your door. Electromagnetic Boundary Problems is borne out of course notes prepared, used, corrected, and perfected by the authors over the years at the University of Colorado, Boulder. This is a book of gems."
    IEEE Antennas and Propagation, October 2016