Electromagnetic fields

Contents
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
vii
viii Contents
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
ConductingWedge 171
5.3 Field Behavior at a
DielectricWedge 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 TheWave 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 LinearWire Antennas 327
7.14 CurvedWire Antennas:
Radiation 333
7.15 Transient Sources 337
8. Radiation in a Material
Medium 357
8.1 Constitutive Equations 357
8.2 PlaneWaves 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
Contents ix
9. Plane Boundaries 423
9.1 PlaneWave 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
x Contents
14.5 Scattering byWedges 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
15. CylindricalWaveguides 813
15.1 Field Expansions in a
ClosedWaveguide 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 GuidedWaves in
General Media 859
15.8 Orthogonality and
Normalization 865
15.9 DielectricWaveguides 873
15.10 Other Examples
ofWaveguides 882
16. Axisymmetric and Conical
Boundaries 905
16.1 Field Expansions for
Axisymmetric Geometries 905
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 ConicalWaveguide 918
16.6 Singularities at the
Tip of a Cone 926
16.7 Radiation and Scattering
from Cones 930
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
Contents xi
Appendix 1. Vector Analysis in Three
Dimensions 1001
Appendix 2. Vector Operators in
Several Coordinate Systems 1011
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
Appendix 9. Some Eigenfunctions
and Eigenvectors 1105
Appendix 10. Miscellaneous Data 1111
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