Chapter 1.FUNDAMENTALS 1
1.1 Maxwell Equations in Free Space 3
A.Spatial Frequency k 8
B.Vector Analysis and Boundary Conditions 13
1.2 Polarization 39
Topic 1.2A Stokes Parameters and Poincare Sphere 44
1.3 Lorentz Force Law 54
A.Poynting’s Theorem and Poynting’s Vector 60
B.Momentum Conservation Theorem 63
1.4 Hertzian Waves 67
Topic 1.4A Electric Field Pattern 75
1.5 Waves in Media 84
A.Wave Vector k 84
B.Waves in Conducting Media 87
C.Waves in Plasma Media 90
D.Waves in Uniaxial Media 95
1.6 Wave Reflections 101
1.7 Wave Guidance 122
A.Guidance by Conducting Parallel Plates 122
B.Guidance by Rectangular Waveguides 129
C.Rectangular Cavity Resonators 134
1.8 Constitutive Relations 144
A.Anisotropic and Bianisotropic Media 146
Topic 1.8A Constitutive Matrices 149
1.9 Boundary Conditions 155
Topic 1.9A Derivation of Boundary Conditions 155
Topic 1.9B Boundary Conditions for Moving Boundaries 157
Answers 162
Chapter 2.TRANSMISSION LINES 179
2.1 Transmission Line Theory 180
A.Wave Equations and Wave Solutions 183
B.Poynting’s Theorem 185
Topic 2.1A Circuit Theory 186
2.2 Transients on Transmission Lines 191
2.3 Sinusoidal Steady State Transmission Lines 206
A.Reflection from a Terminated Transmission Line 209
B.Input Impedance 210
C.Generalized Reflection Coefficient 212
Topic 2.3A Smith Chart 215
2.4 Lumped Element Transmission Lines 224
2.5 Normal modes on Transmission Lines 245
A.Normal Modes and Natural Frequencies 245
B.Initial Value Problem 247
2.6 Transmission Line Modeling 261
A.Modeling Reflection and Transmission 261
B.Modeling Antenna Radiation 266
Topic 2.6A Pattern Multiplication Technique 275
C.Modeling Radiation by Current Sheets 279
Topic 2.6B Equivalence Principle 280
Answers 296
Chapter 3.PROPAGATION AND GUIDANCE 303
3.1 Time-Harmonic Fields 305
A.Maxwell Equations for Time-Harmonic Fields 305
B.Constitutive Relations and Dispersive Media 306
C.Time-Average Poynting Power Vector 311
Topic 3.1A Symmetry Conditions for Lossless Media 314
3.2 Plane Wave Solutions 319
A.Phase and Group Velocities 321
B.Penetration Depth in Lossy Media 324
C.Evanescent Waves in Lossless Media 325
3.3 Waves in Media and the kDB System 331
A.kDB System 331
B.Maxwell Equations in kDB System 335
C.Plane Waves in Uniaxial Media 338
Topic 3.3A Plane Waves in Gyrotropic Media 345
Topic 3.3B Plane Waves in Bianisotropic Media 350
Topic 3.3C Plane Waves in Nonlinear Media 353
3.4 Reflection and Transmission 370
A.Phase Matching 370
B.Reflection and Transmission at a Plane Boundary 376
C.Reflection and Transmission by a Layered Medium 385
3.5 Guidance 407
A.Guidance by Conducting Parallel Plates 407
B.Guided Waves in a Slab Dielectric Waveguide 424
C.Guided Waves in Layered Media 429
D.Cylindrical Rectangular Waveguides 439
E.Cylindrical Circular Waveguides 444
3.6 Resonance 466
A.Rectangular Cavity Resonator 466
B.Circular Cavity Resonator 469
C.Spherical Cavity Resonator 471
Topic 3.6A Cavity Perturbation 474
Answers 481
Chapter 4.RADIATION 497
4.1 Cerenkov Radiation 499
4.2 Green’s Functions 505
A.Dyadic Green’s Functions 505
B.Radiation Field Approximation 509
4.3 Hertzian Dipoles 515
A.Hertzian Electric Dipole 515
B.Hertzian Magnetic Dipole and Small Loop Antenna 520
4.4 Linear Dipole Arrays 526
A.Uniform Array Antenna with Progressive Phase Shift 526
B.Array Antennas with Nonuniform Current Distributions 533
C.Dolph-Chebyshev Arrays 536
D.Array Pattern Synthesis 542
4.5 Linear Antennas 555
4.6 Biconical Antennas 564
A.Formulation and Wave Solutions 564
B.Solution in the Air Region and Dipole Fields 568
C.Solution in the Antenna Region 570
D.Transmission Line Model 572
E.Formal Solution of the Biconical Antenna Problem 578
4.7 Dipole Antennas in Layered Media 582
A.Integral Formulation 582
B.Contour Integration Methods 591
Topic 4.7A Dipole on a Two-Layer Medium 612
Answers 640
Chapter 5.THEOREMS OF WAVES AND MEDIA 649
5.1 Equivalence Principle 651
A.Electric and Magnetic Dipole Sources 651
B.Image Sources 652
C.Electric and Magnetic Current Sheets 653
D.Impressed and Induced Current Sheets 655
Topic 5.1A Uniqueness Theorem 663
Topic 5.1B Duality and Complementarity 664
Topic 5.1C Mathematical Formulations ofHuygens’ Principle 672
Topic 5.1D Fresnel and Fraunhofer Diffraction 682
5.2 Reaction and Reciprocity 702
A.Reaction 702
B.Reciprocity 703
C.Reciprocity Conditions 707
D.Modified Reciprocity Theorem 709
Topic 5.2A Stationary Formulas and Rayleigh-Ritz Procedure 710
Topic 5.2B Method of Moments 718
5.3 Quasi-Static Limits 723
5.4 Geometrical Optics Limit 729
5.5 Paraxial Limit 750
Topic 5.5A Gaussian Beam 750
5.6 Quantization of Electromagnetic Waves 758
A.Uncertainty Principle 758
B.Annihilation and Creation Operators 761
C.Wave Quantization in Bianisotropic Media 769
Answers 776
Chapter 6.SCATTERING 781
6.1 Scattering by Spheres 783
A.Rayleigh Scattering 783
B.Mie Scattering 786
6.2 Scattering by a Conducting Cylinder 792
A.Exact Solution 792
B.Watson Transformation 794
C.Creeping Waves 796
6.3 Scattering by Periodic Rough Surfaces 803
A.Scattering by Periodic Corrugated Conducting Surfaces 803
B.Scattering by Periodic Dielectric Surfaces 807
6.4 Scattering by Random Rough Surfaces 816
A.Kirchhoff Approximation 818
B.Geometrical Optics Solution 826
C.Small Perturbation Method 829
6.5 Scattering by Periodic Media 839
A.First-Order Coupled-Mode Equations 841
B.Reflection and Transmission by Periodically-Modulated Slab 843
C.Far-Field Diffraction of a Gaussian Beam 847
6.6 Scattering by Random Media 849
A.Dyadic Green’s Function for Layered Media 850
B.Scattering by a Half-Space Random Medium 856
6.7 Effective Permittivity for a Volume Scattering Medium 860
A.Random Discrete Scatterers 862
B.Effective Permittivity for a Continuous Random Medium 867
Answers 878
Chapter 7.ELECTROMAGNETIC WAVE THEORY AND SPECIAL RELATIVITY 883
7.1 Maxwell-Minkowski Theory 885
Topic 7.1A Amperian Formulation 886
Topic 7.1B Boffi Formulation 887
Topic 7.1C Chu Formulation 887
7.2 Lorentz Transformation 889
Topic 7.2A Derivation of Electromagnetic Field Transformation 893
Topic 7.2B Lorentz Invariants 898
Topic 7.2C Electromagnetic Field Classification 900
Topic 7.2D Transformation of Frequency and Wave Vector 902
Topic 7.2E Aberration Effect 903
Topic 7.2F Doppler Effect 904
7.3 Waves in Moving Media 913
A.Transformation of Constitutive Relations 913
Topic 7.3A Plane Waves in Moving Uniaxial Media 918
Topic 7.3B Phase Matching at Moving Boundaries 923
Topic 7.3C Force on a Moving Dielectric Half-space 925
Topic 7.3D Guided Waves in a Moving Dielectric Slab 928
Topic 7.3E Guided Waves in Moving Gyrotropic Media 931
7.4 Maxwell Equations in Tensor Form 936
Topic 7.4A Contravariant and Covariant Vectors 938
Topic 7.4B Field Tensor and Excitation Tensor 944
Topic 7.4C Constitutive Relations in Tensor Form 946
7.5 Hamilton’s Principle and Noether’s Theorem 948
A.Action Integral 948
B.Hamilton’s Principle and Maxwell Equations 948
C.Noether’s Theorem and Energy Momentum Tensors 950
Answers 955
REFERENCES 959
INDEX 981