Electromagnetic Boundary Problems

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, F, F, ?) 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

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.