Boundary Conditions in Electromagnetics (eBook)

Ismo V. Lindell, PhD, is Professor Emeritus at Aalto University, Finland. He is recipient of the S.A. Schelkunoff prize, the Maxwell prize, the van der Pol Gold Medal, and is author of Multiforms, Dyadics, and Electromagnetic Media, Differential Forms in Electromagnetics, and Methods for Electromagnetic Field Analysis. Ari Sihvola, PhD, is Professor of Electromagnetics at the Aalto University School of Electrical Engineering, Finland. He was previously a visiting engineer at MIT, visiting scientist at Pennsylvania State University, and visiting professor at the Swiss Federal Institute of Technology and the University of Paris.

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