Preface xiii
1. Linear Analysis 1
1.1 Linear Spaces 2
1.2 Linear Transformations 5
1.3 The Inversion Problem 8
1.4 Green’s Functions 11
1.5 Reciprocity 14
1.6 Green’s Dyadics 17
1.7 Convergence of a Series 19
1.8 Eigenfunctions 20
1.9 Integral Operators 23
1.10 Eigenfunction Expansions 26
1.11 Discretization 30
1.12 Matrices 33
1.13 Solution of Matrix Equations: Stability 36
1.14 Finite Differences 38
1.15 Perturbations 43
2. Variational Techniques 51
2.1 Stationary functionals 52
2.2 A Suitable Functional for the String Problem 53
2.3 Functionals for the General l Transformation 55
2.4 Euler’s Equations of Some Important Functionals 58
2.5 Discretization of the Trial Functions 60
2.6 Simple Finite Elements for Planar Problems 62
2.7 More Finite Elements 65
2.8 Direct Numerical Solution of Matrix Problems 69
2.9 Iterative Numerical Solution of Matrix Problems 70
3. Electrostatic Fields in the Presence of Dielectrics 77
3.1 Volume Charges in Vacuum 77
3.2 Green’s Function for Infinite Space 80
3.3 Multipole Expansion 83
3.4 Potential Generated by a Single Layer of Charge 86
3.5 Potential Generated by a Double Layer of Charge 91
3.6 Potential Generated by a Linear Charge 94
3.7 Spherical Harmonics 98
3.8 Dielectric Materials 102
3.9 Cavity Fields 105
3.10 Dielectric Sphere in an External Field 108
3.11 Dielectric Spheroid in an Incident Field 111
3.12 Numerical Methods 115
4. Electrostatic Fields in the Presence of Conductors 125
4.1 Conductivity 125
4.2 Potential Outside a Charged Conductor 127
4.3 Capacitance Matrix 133
4.4 The Dirichlet Problem 134
4.5 The Neumann Problem 137
4.6 Numerical Solution of the Charge Density Problem 139
4.7 Conductor in an External Field 142
4.8 Conductors in the Presence of Dielectrics 146
4.9 Current Injection into a Conducting Volume 148
4.10 Contact Electrodes 153
4.11 Chains of Conductors 158
5. Special Geometries for the Electrostatic Field 167
5.1 Two-Dimensional Potentials in the Plane 167
5.2 Field Behavior at a Conducting Wedge 171
5.3 Field Behavior at a Dielectric Wedge 175
5.4 Separation of Variables in Two Dimensions 177
5.5 Two-Dimensional Integral Equations 181
5.6 Finite Methods in Two Dimensions 185
5.7 Infinite Computational Domains 188
5.8 More Two-Dimensional Techniques 192
5.9 Layered Media 196
5.10 Apertures 199
5.11 Axisymmetric Geometries 203
5.12 Conical Boundaries 207
6. Magnetostatic Fields 221
6.1 Magnetic Fields in Free Space: Vector Potential 221
6.2 Fields Generated by Linear Currents 224
6.3 Fields Generated by Surface Currents 227
6.4 Fields at Large Distances from the Sources 229
6.5 Scalar Potential in Vacuum 232
6.6 Magnetic Materials 234
6.7 Permanent Magnets 236
6.8 The Limit of Infinite Permeability 239
6.9 Two-Dimensional Fields in the Plane 244
6.10 Axisymmetric Geometries 249
6.11 Numerical Methods: Integral Equations 251
6.12 Numerical Methods: Finite Elements 253
6.13 Nonlinear Materials 258
6.14 Strong Magnetic Fields and Force-Free Currents 260
7. Radiation in Free Space 277
7.1 Maxwell’s Equations 277
7.2 The Wave Equation 280
7.3 Potentials 282
7.4 Sinusoidal Time Dependence: Polarization 286
7.5 Partially Polarized Fields 290
7.6 The Radiation Condition 293
7.7 Time-Harmonic Potentials 296
7.8 Radiation Patterns 300
7.9 Green’s Dyadics 303
7.10 Multipole Expansion 307
7.11 Spherical Harmonics 313
7.12 Equivalent Sources 320
7.13 Linear Wire Antennas 327
7.14 Curved Wire Antennas: Radiation 333
7.15 Transient Sources 337
8. Radiation in a Material Medium 357
8.1 Constitutive Equations 357
8.2 Plane Waves 370
8.3 Ray Methods 377
8.4 Beamlike Propagation 388
8.5 Green’s Dyadics 392
8.6 Reciprocity 397
8.7 Equivalent Circuit of an Antenna 402
8.8 Effective Antenna Area 409
9. Plane Boundaries 423
9.1 Plane Wave Incident on a Plane Boundary 423
9.2 Propagation Through a Layered Medium 442
9.3 The Sommerfeld Dipole Problem 448
9.4 Multilayered Structures 452
9.5 Periodic Structures 460
9.6 Field Penetration Through Apertures 478
9.7 Edge Diffraction 490
10. Resonators 509
10.1 Eigenvectors for an Enclosed Volume 509
10.2 Excitation of a Cavity 514
10.3 Determination of the Eigenvectors 517
10.4 Resonances 525
10.5 Open Resonators: Dielectric Resonances 529
10.6 Aperture Coupling 540
10.7 Green’s Dyadics 544
11. Scattering: Generalities 563
11.1 The Scattering Matrix 563
11.2 Cross Sections 568
11.3 Scattering by a Sphere 574
11.4 Resonant Scattering 582
11.5 The Singularity Expansion Method 586
11.6 Impedance Boundary Conditions 598
11.7 Thin Layers 601
11.8 Characteristic Modes 604
12. Scattering: Numerical Methods 617
12.1 The Electric Field Integral Equation 617
12.2 The Magnetic Field Integral Equation 624
12.3 The T-Matrix 629
12.4 Numerical Procedures 633
12.5 Integral Equations for Penetrable Bodies 639
12.6 Absorbing Boundary Conditions 646
12.7 Finite Elements 651
12.8 Finite Differences in the Time Domain 654
13. High- and Low-Frequency Fields 671
13.1 Physical Optics 671
13.2 Geometrical Optics 676
13.3 Geometric Theory of Diffraction 681
13.4 Edge Currents and Equivalent Currents 689
13.5 Hybrid Methods 692
13.6 Low-Frequency Fields: The Rayleigh Region 695
13.7 Non-Conducting Scatterers at Low Frequencies 696
13.8 Perfectly Conducting Scatterers at Low Frequencies 699
13.9 Good Conductors 707
13.10 Stevenson’s Method Applied to Good Conductors 711
13.11 Circuit Parameters 715
13.12 Transient Eddy Currents 719
14. Two-Dimensional Problems 733
14.1 E and H Waves 733
14.2 Scattering by Perfectly Conducting Cylinders 738
14.3 Scattering by Penetrable Circular Cylinders 743
14.4 Scattering by Elliptic Cylinders 746
14.5 Scattering by Wedges 749
14.6 Integral Equations for Perfectly Conducting Cylinders 751
14.7 Scattering by Penetrable Cylinders 759
14.8 Low-Frequency Scattering by Cylinders 764
14.9 Slots in a Planar Screen 770
14.10 More Slot Couplings 778
14.11 Termination of a Truncated Domain 786
14.12 Line Methods 792
16.2 Scattering by Bodies of Revolution: Integral Equations 908
16.3 Scattering by Bodies of Revolution: Finite Methods 912
16.4 Apertures in Axisymmetric Surfaces 915
16.5 The Conical Waveguide 918
16.6 Singularities at the Tip of a Cone 926
16.7 Radiation and Scattering from Cones 930
15. Cylindrical Waveguides 813
15.1 Field Expansions in a Closed Waveguide 814
15.2 Determination of the Eigenvectors 818
15.3 Propagation in a Closed Waveguide 822
15.4 Waveguide Losses 832
15.5 Waveguide Networks 837
15.6 Aperture Excitation and Coupling 844
15.7 Guided Waves in General Media 859
15.8 Orthogonality and Normalization 865
15.9 Dielectric Waveguides 873
15.10 Other Examples of Waveguides 882
16. Axisymmetric and Conical Boundaries 905
16.1 Field Expansions for Axisymmetric Geometries 905
17. Electrodynamics of Moving Bodies 943
17.1 Fields Generated by a Moving Charge 943
17.2 The Lorentz Transformation 946
17.3 Transformation of Fields and Currents 950
17.4 Radiation from Sources: the Doppler Effect 955
17.5 Constitutive Equations and Boundary Conditions 958
17.6 Material Bodies Moving Uniformly in Static Fields 960
17.7 Magnetic Levitation 962
17.8 Scatterers in Uniform Motion 966
17.9 Material Bodies in Nonuniform Motion 972
17.10 Rotating Bodies of Revolution 974
17.11 Motional Eddy Currents 979
17.12 Accelerated Frames of Reference 984
17.13 Rotating Comoving Frames 988
Appendix 1. Vector Analysis in Three Dimensions 1001
Appendix 9. Some Eigenfunctions and Eigenvectors 1105
Appendix 2. Vector Operators in Several Coordinate Systems 1011
Appendix 10. Miscellaneous Data 1111
Appendix 3. Vector Analysis on a Surface 1025
Appendix 4. Dyadic Analysis 1035
Appendix 5. Special Functions 1043
Appendix 6. Complex Integration 1063
Appendix 7. Transforms 1075
Appendix 8. Distributions 1089
Bibliography 1117
General Texts on Electromagnetic Theory 1117
Texts that Discuss Particular Areas of Electromagnetic Theory 1118
General Mathematical Background 1122
Mathematical Techniques Specifically Applied to Electromagnetic Theory 1123
Acronyms and Symbols 1127
Author Index 1133
Subject Index 1149
