A comprehensive survey of boundary conditions as applied in antenna and microwave engineering, material physics, optics, and general electromagnetics research.
Boundary conditions are essential for determining electromagnetic problems. Working with engineering problems, they provide analytic assistance in mathematical handling of electromagnetic structures, and offer synthetic help for designing new electromagnetic structures. Boundary Conditions in Electromagnetics describes the most-general boundary conditions restricted by linearity and locality, and analyzes basic plane-wave reflection and matching problems associated to a planar boundary in a simple-isotropic medium.
This comprehensive text first introduces known special cases of particular familiar forms of boundary conditions - perfect electromagnetic conductor, impedance, and DB boundaries - and then examines various general forms of boundary conditions. Subsequent chapters discuss sesquilinear boundary conditions and practical computations on wave scattering by objects defined by various boundary conditions. The practical applications of less-common boundary conditions, such as for metamaterial and metasurface engineering, are referred to throughout the text. This book:
- Describes the mathematical analysis of fields associated to given boundary conditions
- Provides examples of how boundary conditions affect the scattering properties of a particle
- Contains ample in-chapter exercises and solutions, complete references, and a detailed index
- Includes appendices containing electromagnetic formulas, Gibbsian 3D dyadics, and four-dimensional formalism
Boundary Conditions in Electromagnetics is an authoritative text for electrical engineers and physicists working in electromagnetics research, graduate or post-graduate students studying electromagnetics, and advanced readers interested in electromagnetic theory.
Table of Contents
Preface ix
1 Introduction 1
1.1 Basic Equations 1
1.2 Duality Transformation 3
1.3 Plane Waves 5
1.4 TE/TM Decomposition 8
1.5 Problems 10
2 Perfect Electromagnetic Conductor Boundary 11
2.1 PEMC Conditions 11
2.2 Eigenproblem of Dyadic Jt 12
2.3 Reflection from PEMC Boundary 14
2.4 Polarization Rotation 17
2.5 Point Source and PEMC Plane 18
2.6 Waveguide with PEMC Walls 20
2.7 Parallel-Plate PEMC Resonator 22
2.8 Modeling Small PEMC Particles 24
2.9 Problems 29
3 Impedance Boundary 33
3.1 Basic Conditions 33
3.2 Subclasses of Impedance Boundaries 36
3.3 Reflection from Impedance Boundary 38
3.4 Matched Waves 40
3.5 Simple-Isotropic Impedance Boundary 41
3.6 General Isotropic Boundary 48
3.7 Perfectly Anisotropic Boundary 52
3.8 Generalized Soft-and-Hard (GSH) Boundary 55
3.9 Duality Transformation of Impedance Boundaries 62
3.10 Realization of Impedance Boundaries 64
3.11 Problems 67
4 DB Boundary 71
4.1 Boundary Conditions Involving Normal Field Components 71
4.2 Reflection from DB Boundary 72
4.3 Realization of DB Boundary 75
4.4 Spherical DB Resonator 81
4.5 Circular DB Waveguide 84
4.6 D’B’ Boundary 92
4.7 Mixed-Impedance (DB/D’B’) Boundary 96
4.8 Problems 98
5 General Boundary Conditions 101
5.1 Electromagnetic Sheet as Boundary Surface 101
5.2 General Boundary Conditions (GBC) 102
5.3 Decomposition of Plane Waves 104
5.4 Reflection from GBC Boundary 106
5.5 Matched Waves 108
5.6 Eigenwaves 110
5.7 Duality Transformation 112
5.8 Soft-and-Hard/DB (SHDB) Boundary 113
5.9 Generalized Soft-and-Hard/DB (GSHDB) Boundary 122
5.10 GBC Boundaries with PEC/PMC Equivalence 127
5.11 Some Special GBC Boundaries 128
5.12 Summary of GBC Conditions 133
5.13 Reciprocity of GBC Boundaries 134
5.14 Realization of the GBC Boundary 139
5.15 Problems 140
6 Sesquilinear Boundary Conditions 143
6.1 Isotropic and Anisotropic SQL Boundaries 144
6.2 Reflection from Isotropic SQL Boundary 145
6.3 Eigenfields 149
6.4 Power Balance 151
6.5 Image theory 153
6.6 Problems 155
7 Scattering by Objects Defined by Boundary Conditions 157
7.1 Cross Sections and Efficiencies 157
7.2 PEC, PMC, and PEMC Objects 159
7.3 DB and D’B’-Boundary Objects 165
7.4 Impedance-Boundary Objects 169
7.5 Problems 176
A Electromagnetic Formulas 179
B Dyadics 183
C Four-Dimensional Formalism 189
D Solutions to Problems 197
References 247
Index 256
