book

Electromagnetic Boundary Problems

Name: Electromagnetic Boundary Problems
ISBN: 9781498730280

by Edward F. Kuester, David C. Chang

October 2015

Intermediate to advanced

363 pages

7h 54m

English

CRC Press

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Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of Figures
List of Tables
Series Preface
Preface

Authors
Chapter 1 Maxwell’s Equations and Sources
1.1 Maxwell Equations in Free Space1.1.1 Energy Transfer and Poynting’s Theorem1.2 Macroscopic Maxwell Equations in Material Media1.2.1 Multipole Expansions for Charges and Currents1.2.2 Averaging of Charge and Current Densities1.2.3 Conduction, Polarization, and Magnetization1.2.4 Material Properties and Constitutive Equations1.3 Time-Harmonic Problems
1.4 Duality; Equivalence; Surface Sources
1.4.1 Duality and Magnetic Sources1.4.2 Stream Potentials1.4.3 Equivalence Principles1.5 Jump Conditions1.5.1 General Jump Conditions at a Stationary Surface1.5.2 Example: Thin-Sheet Boundary Conditions1.5.3 Jump Conditions at a Moving Surface1.5.4 Force on Surface Sources1.5.5 Example: Charge Dipole Sheet at a Dielectric Interface1.6 Problems
Chapter 2 Potential Representations of the Electromagnetic Field
2.1 Lorenz Potentials and their Duals (A, Φ, F, Ψ)2.2 Hertz Vector Potentials2.2.1 Jump Conditions for Hertz Potentials2.2.2 Time-Harmonic Hertz Potentials2.3 Special Hertz Potentials2.3.1 Whittaker Potentials2.3.2 Debye Potentials2.4 Problems
Chapter 3 Fundamental Properties of the Electromagnetic Field
3.1 Causality; Domain of Dependence3.1.1 Domain of Dependence3.1.2 Motion of Wavefronts3.1.3 The Ray Equation and the Eikonal3.2 Passivity and Uniqueness3.2.1 Time-Domain Theorems3.2.2 Radiation Conditions3.2.3 Time-Harmonic Theorems3.2.4 Equivalence Principles and Image Theory3.3 Lorentz Reciprocity3.4 Scattering Problems3.4.1 Aperture Radiation Problems3.4.2 Classical Scattering Problems3.4.3 Aperture Scattering Problems3.5 Planar Scatterers and Babinet’s Principle3.6 Problems
Chapter 4 Radiation by Simple Sources and Structures
4.1 Point and Line Sources in Unbounded Space4.1.1 Static Point Charge4.1.2 Potential of a Pulsed Dipole in Free Space4.1.3 Time-Harmonic Dipole4.1.4 Line Sources in Unbounded Space4.2 Alternate Representations for Point and Line Source Potentials4.2.1 Time-Harmonic Line Source4.2.2 Time-Harmonic Point Source4.3 Radiation from Sources of Finite Extent; The Fraunhofer Far-Field Approximation4.3.1 Far Field by Superposition4.3.2 Far Field via Fourier Transform4.3.3 The Stationary Phase Principle4.4 Radiation in Planar Regions4.5 The Fresnel and Paraxial Approximations; Gaussian Beams4.5.1 The Fresnel Approximation4.5.2 The Paraxial Approximation4.5.3 Gaussian Beams4.6 Problems
Chapter 5 Scattering by Simple Structures
5.1 Dipole Radiation over a Half-Space5.1.1 Reflected Wave in the Far Field5.1.2 Transmitted Wave in the Far Field5.1.3 Other Dipole Sources5.2 Radiation and Scattering from Cylinders5.2.1 Aperture Radiation5.2.2 Plane Wave Scattering5.3 Diffraction by Wedges; The Edge Condition5.3.1 Formulation5.3.2 The Edge Condition5.3.3 Formal Solution of the Problem5.3.4 The Geometrical Optics Field5.3.5 The Diffracted Field5.3.6 Uniform Far-Field Approximation5.4 Spherical Harmonics5.5 Problems
Chapter 6 Propagation and Scattering in More Complex Regions
6.1 General Considerations6.2 Waveguides6.2.1 Parallel-Plate Waveguide: Mode Expansion6.2.2 Parallel-Plate Waveguide: Fourier Expansion6.2.3 Open Waveguides6.3 Propagation in a Periodic Medium6.3.1 Gel’fand’s Lemma6.3.2 Bloch Wave Modes and Their Properties6.3.3 The Bloch Wave Expansion6.3.4 Solution for the Field of a Current Sheet in Terms of Bloch Modes6.4 Problems
Chapter 7 Integral Equations in Scattering Problems
7.1 Green’s Theorem and Green’s Functions7.1.1 Scalar Problems7.1.2 Vector Problems7.1.3 Dyadic Green’s Functions7.1.4 Relation to Equivalence Principle7.2 Integral Equations for Scattering by a Perfect Conductor7.2.1 Electric-Field Integral Equation (EFIE)7.2.2 Magnetic-Field Integral Equation (MFIE)7.2.3 Nonuniqueness and Other Difficulties7.3 Volume Integral Equations for Scattering by a Dielectric Body
7.4 Integral Equations for Static “Scattering” by Conductors
7.4.1 Electrostatic Scattering7.4.2 Magnetostatic Scattering7.5 Electrostatics of a Thin Conducting Strip7.6 Electrostatics of a Thin Conducting Circular Disk7.7 Integral Equations for Scattering by an Aperture in a Plane7.8 Static Aperture Problems7.8.1 Electrostatic Aperture Scattering7.8.2 Magnetostatic Aperture Scattering7.8.3 Example: Electric Polarizability of a Circular Aperture7.9 Problems
Chapter 8 Approximation Methods
8.1 Recursive Perturbation Approximation8.1.1 Example: Strip over a Ground Plane8.1.2 Physical Optics Approximation8.2 Operator Formalism for Approximation Methods8.2.1 Example: Strip over a Ground Plane (Revisited)8.3 Variational Approximation8.3.1 The Galerkin-Ritz Method8.3.2 Example: Strip over a Ground Plane (Re-Revisited)8.4 Problems
Appendix A Generalized Functions
A.1 IntroductionA.2 Multiplication of Generalized FunctionsA.3 Fourier Transforms and Fourier Series of Generalized FunctionsA.4 Multidimensional Generalized FunctionsA.5 Problems
Appendix B Special Functions
B.1 Gamma FunctionB.2 Bessel FunctionsB.3 Spherical Bessel FunctionsB.4 Fresnel IntegralsB.5 Legendre FunctionsB.6 Chebyshev PolynomialsB.7 Exponential IntegralsB.8 PolylogarithmsB.9 Problems
Appendix C Rellich’s Theorem
Appendix D Vector Analysis
D.1 Vector IdentitiesD.2 Vector Differentiation in Various Coordinate SystemsD.2.1 Rectangular (Cartesian) CoordinatesD.2.2 Circular Cylindrical CoordinatesD.2.3 Spherical CoordinatesD.3 Poincare’s LemmaD.4 Helmholtz’s TheoremD.5 Generalized Leibnitz RuleD.6 DyadicsD.7 Problems
Appendix E Formulation of Some Special Electromagnetic Boundary Problems
E.1 Linear Cylindrical (Wire) AntennasE.1.1 Transmitting ModeE.1.2 Receiving ModeE.2 Static ProblemsE.2.1 Electrostatic ProblemsE.2.2 The Capacitance ProblemE.2.3 The Electric Polarizability ProblemE.2.4 Magnetostatic ProblemsE.2.5 The Inductance ProblemE.2.6 The Magnetic Polarizability ProblemE.3 Problems
Index

Content preview from Electromagnetic Boundary Problems

E Formulation of Some Special Electromagnetic Boundary Problems

The most common scattering problems of electromagnetics were stated in Section 3.4. Some of the more specialized problems are given in this Appendix.

E.1 LINEAR CYLINDRICAL (WIRE) ANTENNAS

Because they can serve in either a transmitting or receiving mode, antenna problems are a rather special mixture of radiation and scattering type problems.¹ We will assume for simplicity that the antenna structure is embedded in otherwise infinite, uniform free space.

E.1.1 TRANSMITTING MODE

We consider first an idealized transmitting antenna as shown in Figure E.1. The antenna itself is a thin tubular perfect conductor of radius a and length 2l driven by an ideal voltage source ...

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