Electromagnetic Wave Propagation, Radiation, and Scattering

About The Author Xix

Preface Xxi

Preface To The First Edition Xxv

Acknowledgments Xxvii

Part I Fundamentals 1

1 Introduction 3

2 Fundamental Field Equations 7

2.1 Maxwell's Equations / 7

2.2 Time-Harmonic Case / 10

2.3 Constitutive Relations / 11

2.4 Boundary Conditions / 15

2.5 Energy Relations and Poynting's Theorem / 18

2.6 Vector and Scalar Potentials / 22

2.7 Electric Hertz Vector / 24

2.8 Duality Principle and Symmetry of Maxwell's Equations / 25

2.9 Magnetic Hertz Vector / 26

2.10 Uniqueness Theorem / 27

2.11 Reciprocity Theorem / 28

2.12 Acoustic Waves / 30

Problems / 33

3 Waves In Inhomogeneous And Layered Media 35

3.1 Wave Equation for a Time-Harmonic Case / 35

3.2 Time-Harmonic Plane-Wave Propagation in Homogeneous Media / 36

3.3 Polarization / 37

3.4 Plane-Wave Incidence on a Plane Boundary: Perpendicular Polarization (s Polarization) / 39

3.5 Electric Field Parallel to a Plane of Incidence: Parallel Polarization (p Polarization) / 43

3.6 Fresnel Formula, Brewster's Angle, and Total Reflection / 44

3.7 Waves in Layered Media / 47

3.8 Acoustic Reflection and Transmission from a Boundary / 50

3.9 Complex Waves / 51

3.10 Trapped Surface Wave (Slow Wave) and Leaky Wave / 54

3.11 Surface Waves Along a Dielectric Slab / 57

3.12 Zenneck Waves and Plasmons / 63

3.13 Waves in Inhomogeneous Media / 66

3.14 WKB Method / 68

3.15 Bremmer Series / 72

3.16 WKB Solution for the Turning Point / 76

3.17 Trapped Surface-Wave Modes in an Inhomogeneous Slab / 77

3.18 Medium With Prescribed Profile / 80

Problems / 81

4 Waveguides And Cavities 85

4.1 Uniform Electromagnetic Waveguides / 85

4.2 TM Modes or E Modes / 86

4.3 TE Modes or H Modes / 87

4.4 Eigenfunctions and Eigenvalues / 89

4.5 General Properties of Eigenfunctions for Closed Regions / 91

4.6 k-ß Diagram and Phase and Group Velocities / 95

4.7 Rectangular Waveguides / 98

4.8 Cylindrical Waveguides / 100

4.9 TEM Modes / 104

4.10 Dispersion of a Pulse in a Waveguide / 106

4.11 Step-Index Optical Fibers / 109

4.12 Dispersion of Graded-Index Fibers / 116

4.13 Radial and Azimuthal Waveguides / 117

4.14 Cavity Resonators / 120

4.15 Waves in Spherical Structures / 123

4.16 Spherical Waveguides and Cavities / 128

Problems / 133

5 Green's Functions 137

5.1 Electric and Magnetic Dipoles in Homogeneous Media / 137

5.2 Electromagnetic Fields Excited by an Electric Dipole in a Homogeneous Medium / 139

5.3 Electromagnetic Fields Excited by a Magnetic Dipole in a Homogeneous Medium / 144

5.4 Scalar Green's Function for Closed Regions and Expansion of Green's Function in a Series of Eigenfunctions / 145

5.5 Green's Function in Terms of Solutions of the Homogeneous Equation / 150

5.6 Fourier Transform Method / 155

5.7 Excitation of a Rectangular Waveguide / 157

5.8 Excitation of a Conducting Cylinder / 159

5.9 Excitation of a Conducting Sphere / 163

Problems / 166

6 Radiation From Apertures And Beam Waves 169

6.1 Huygens' Principle and Extinction Theorem / 169

6.2 Fields Due to the Surface Field Distribution / 173

6.3 Kirchhoff Approximation / 176

6.4 Fresnel and Fraunhofer Diffraction / 178

6.5 Fourier Transform (Spectral) Representation / 182

6.6 Beam Waves / 183

6.7 Goos-Hanchen Effect / 187

6.8 Higher-Order Beam-Wave Modes / 191

6.9 Vector Green's Theorem, Stratton-Chu Formula, and Franz Formula / 194

6.10 Equivalence Theorem / 197

6.11 Kirchhoff Approximation for Electromagnetic Waves / 198

Problems / 199

7 Periodic Structures And Coupled-Mode Theory 201

7.1 Floquet's Theorem / 202

7.2 Guided Waves Along Periodic Structures / 203

7.3 Periodic Layers / 209

7.4 Plane Wave Incidence on a Periodic Structure / 213

7.5 Scattering from Periodic Surfaces Based on the Rayleigh Hypothesis / 219

7.6 Coupled-Mode Theory / 224

Problems / 229

8 Dispersion And Anisotropic Media 233

8.1 Dielectric Material and Polarizability / 233

8.2 Dispersion of Dielectric Material / 235

8.3 Dispersion of Conductor and Isotropic Plasma / 237

8.4 Debye Relaxation Equation and Dielectric Constant of Water / 240

8.5 Interfacial Polarization / 240

8.6 Mixing Formula / 241

8.7 Dielectric Constant and Permeability for Anisotropic Media / 244

8.8 Magnetoionic Theory for Anisotropic Plasma / 244

8.9 Plane-Wave Propagation in Anisotropic Media / 247

8.10 Plane-Wave Propagation in Magnetoplasma / 248

8.11 Propagation Along the DC Magnetic Field / 249

8.12 Faraday Rotation / 253

8.13 Propagation Perpendicular to the DC Magnetic Field / 255

8.14 The Height of the Ionosphere / 256

8.15 Group Velocity in Anisotropic Medium / 257

8.16 Warm Plasma / 259

8.17 Wave Equations for Warm Plasma / 261

8.18 Ferrite and the Derivation of Its Permeability Tensor / 263

8.19 Plane-Wave Propagation in Ferrite / 266

8.20 Microwave Devices Using Ferrites / 267

8.21 Lorentz Reciprocity Theorem for Anisotropic Media / 270

8.22 Bi-Anisotropic Media and Chiral Media / 272

8.23 Superconductors, London Equation, and the Meissner Effects / 276

8.24 Two-Fluid Model of Superconductors at High Frequencies / 278

Problems / 280

9 Antennas, Apertures, And Arrays 285

9.1 Antenna Fundamentals / 285

9.2 Radiation Fields of Given Electric and Magnetic Current Distributions / 289

9.3 Radiation Fields of Dipoles, Slots, and Loops / 292

9.4 Antenna Arrays with Equal and Unequal Spacings / 296

9.5 Radiation Fields from a Given Aperture Field Distribution / 301

9.6 Radiation from Microstrip Antennas / 305

9.7 Self- and Mutual Impedances of Wire Antennas with Given Current Distributions / 308

9.8 Current Distribution of a Wire Antenna / 313

Problems / 314

10 Scattering Of Waves By Conducting And Dielectric Objects 317

10.1 Cross Sections and Scattering Amplitude / 318

10.2 Radar Equations / 321

10.3 General Properties of Cross Sections / 322

10.4 Integral Representations of Scattering Amplitude and Absorption Cross Sections / 325

10.5 Rayleigh Scattering for a Spherical Object / 328

10.6 Rayleigh Scattering for a Small Ellipsoidal Object / 330

10.7 Rayleigh-Debye Scattering (Born Approximation) / 334

10.8 Elliptic Polarization and Stokes Parameters / 338

10.9 Partial Polarization and Natural Light / 341

10.10 Scattering Amplitude Functions f11, f12, f21, and f22 and the Stokes Matrix / 342

10.11 Acoustic Scattering / 344

10.12 Scattering Cross Section of a Conducting Body / 346

10.13 Physical Optics Approximation / 347

10.14 Moment Method: Computer Applications / 350

Problems / 354

11 Waves In Cylindrical Structures, Spheres, And Wedges 357

11.1 Plane Wave Incident on a Conducting Cylinder / 357

11.2 Plane Wave Incident on a Dielectric Cylinder / 361

11.3 Axial Dipole Near a Conducting Cylinder / 364

11.4 Radiation Field / 366

11.5 Saddle-Point Technique / 368

11.6 Radiation from a Dipole and Parseval's Theorem / 371

11.7 Large Cylinders and the Watson Transform / 373

11.8 Residue Series Representation and Creeping Waves / 376

11.9 Poisson's Sum Formula, Geometric Optical Region, and Fock

Representation / 379

11.10 Mie Scattering by a Dielectric Sphere / 382

11.11 Axial Dipole in the Vicinity of a Conducting Wedge / 390

11.12 Line Source and Plane Wave Incident on a Wedge / 392

11.13 Half-Plane Excited by a Plane Wave / 394

Problems / 395

12 Scattering By Complex Objects 401

12.1 Scalar Surface Integral Equations for Soft and Hard Surfaces / 402

12.2 Scalar Surface Integral Equations for a Penetrable Homogeneous Body / 404

12.3 EFIE and MFIE / 406

12.4 T-Matrix Method (Extended Boundary Condition Method) / 408

12.5 Symmetry and Unitarity of the T-Matrix and the Scattering Matrix / 414

12.6 T-Matrix Solution for Scattering from Periodic Sinusoidal Surfaces / 416

12.7 Volume Integral Equations for Inhomogeneous Bodies: TM Case / 418

12.8 Volume Integral Equations for Inhomogeneous Bodies: TE Case / 423

12.9 Three-Dimensional Dielectric Bodies / 426

12.10 Electromagnetic Aperture Integral Equations for a Conducting Screen / 427

12.11 Small Apertures / 430

12.12 Babinet's Principle and Slot and Wire Antennas / 433

12.13 Electromagnetic Diffraction by Slits and Ribbons / 439

12.14 Related Problems / 441

Problems / 441

13 Geometric Theory Of Diffraction And Lowfrequency Techniques 443

13.1 Geometric Theory of Diffraction / 444

13.2 Diffraction by a Slit for Dirichlet's Problem / 447

13.3 Diffraction by a Slit for Neumann's Problem and Slope Diffraction / 452

13.4 Uniform Geometric Theory of Diffraction for an Edge / 455

13.5 Edge Diffraction for a Point Source / 457

13.6 Wedge Diffraction for a Point Source / 461

13.7 Slope Diffraction and Grazing Incidence / 463

13.8 Curved Wedge / 463

13.9 Other High-Frequency Techniques / 465

13.10 Vertex and Surface Diffraction / 466

13.11 Low-Frequency Scattering / 467

Problems / 470

14 Planar Layers, Strip Lines, Patches, And Apertures 473

14.1 Excitation of Waves in a Dielectric Slab / 473

14.2 Excitation of Waves in a Vertically Inhomogeneous Medium / 481

14.3 Strip Lines / 485

14.4 Waves Excited by Electric and Magnetic Currents Perpendicular to Dielectric Layers / 492

14.5 Waves Excited by Transverse Electric and Magnetic Currents in Dielectric Layers / 496

14.6 Strip Lines Embedded in Dielectric Layers / 500

14.7 Periodic Patches and Apertures Embedded in Dielectric Layers / 502

Problems / 506

15 Radiation From A Dipole On The Conducting Earth 509

15.1 Sommerfeld Dipole Problem / 509

15.2 Vertical Electric Dipole Located Above the Earth / 510

15.3 Reflected Waves in Air / 514

15.4 Radiation Field: Saddle-Point Technique / 517

15.5 Field Along the Surface and the Singularities of the Integrand / 519

15.6 Sommerfeld Pole and Zenneck Wave / 521

15.7 Solution to the Sommerfeld Problem / 524

15.8 Lateral Waves: Branch Cut Integration / 528

15.9 Refracted Wave / 536

15.10 Radiation from a Horizontal Dipole / 538

15.11 Radiation in Layered Media / 541

15.12 Geometric Optical Representation / 545

15.13 Mode and Lateral Wave Representation / 549

Problems / 550

Part II Applications 553

16 Inverse Scattering 555

16.1 Radon Transform and Tomography / 555

16.2 Alternative Inverse Radon Transform in Terms of the Hilbert Transform / 559

16.3 Diffraction Tomography / 561

16.4 Physical Optics Inverse Scattering / 567

16.5 Holographic Inverse Source Problem / 570

16.6 Inverse Problems and Abel's Integral Equation Applied to Probing of the Ionosphere / 572

16.7 Radar Polarimetry and Radar Equation / 575

16.8 Optimization of Polarization / 578

16.9 Stokes Vector Radar Equation and Polarization Signature / 580

16.10 Measurement of Stokes Parameter / 582

Problems / 584

17 Radiometry, Noise Temperature, And Interferometry 587

17.1 Radiometry / 587

17.2 Brightness and Flux Density / 588

17.3 Blackbody Radiation and Antenna Temperature / 589

17.4 Equation of Radiative Transfer / 592

17.5 Scattering Cross Sections and Absorptivity and Emissivity of a Surface / 594

17.6 System Temperature / 598

17.7 Minimum Detectable Temperature / 600

17.8 Radar Range Equation / 601

17.9 Aperture Illumination and Brightness Distributions / 602

17.10 Two-Antenna Interferometer / 604

Problems / 607

18 Stochastic Wave Theories 611

18.1 Stochastic Wave Equations and Statistical Wave Theories / 612

18.2 Scattering in Troposphere, Ionosphere, and Atmospheric Optics / 612

18.3 Turbid Medium, Radiative Transfer, and Reciprocity / 612

18.4 Stochastic Sommerfeld Problem, Seismic Coda, and Subsurface Imaging / 613

18.5 Stochastic Green's Function and Stochastic Boundary Problems / 615

18.6 Channel Capacity of Communication Systems with Random Media Mutual Coherence Function / 619

18.7 Integration of Statistical Waves with Other Disciplines / 621

18.8 Some Accounts of Historical Development of Statistical Wave Theories / 622

19 Geophysical Remote Sensing And Imaging 625

19.1 Polarimetric Radar / 626

19.2 Scattering Models for Geophysical Medium and Decomposition Theorem / 630

19.3 Polarimetric Weather Radar / 632

19.4 Nonspherical Raindrops and Differential Reflectivity / 634

19.5 Propagation Constant in Randomly Distributed Nonspherical Particles / 636

19.6 Vector Radiative Transfer Theory / 638

19.7 Space-Time Radiative Transfer / 639

19.8 Wigner Distribution Function and Specific Intensity / 641

19.9 Stokes Vector Emissivity from Passive Surface and Ocean Wind Directions / 644

19.10 Van Cittert-Zernike Theorem Applied to Aperture Synthesis Radiometers Including Antenna Temperature / 646

19.11 Ionospheric Effects on SAR Image / 650

20 Biomedical Em, Optics, And Ultrasound 657

20.1 Bioelectromagnetics / 658

20.2 Bio-EM and Heat Diffusion in Tissues / 659

20.3 Bio-Optics, Optical Absorption and Scattering in Blood / 663

20.4 Optical Diffusion in Tissues / 666

20.5 Photon Density Waves / 670

20.6 Optical Coherence Tomography and Low Coherence Interferometry / 672

20.7 Ultrasound Scattering and Imaging of Tissues / 677

20.8 Ultrasound in Blood / 680

21 Waves In Metamaterials And Plasmon 685

21.1 Refractive Index n and µ-e Diagram / 686

21.2 Plane Waves, Energy Relations, and Group Velocity / 688

21.3 Split-Ring Resonators / 689

21.4 Generalized Constitutive Relations for Metamaterials / 692

21.5 Space-Time Wave Packet Incident on Dispersive Metamaterial and Negative Refraction / 697

21.6 Backward Lateral Waves and Backward Surface Waves / 701

21.7 Negative Goos-Hanchen Shift / 704

21.8 Perfect Lens, Subwavelength Focusing, and Evanescent Waves / 708

21.9 Brewster's Angle in NIM and Acoustic Brewster's Angle / 712

21.10 Transformation Electromagnetics and Invisible Cloak / 716

21.11 Surface Flattening Coordinate Transform / 720

22 Time-Reversal Imaging 723

22.1 Time-Reversal Mirror in Free Space / 724

22.2 Super Resolution of Time-Reversed Pulse in Multiple

Scattering Medium / 729

22.3 Time-Reversal Imaging of Single and Multiple Targets and DORT (Decomposition of Time- eversal Operator) / 731

22.4 Time-Reversal Imaging of Targets in Free Space / 735

22.5 Time-Reversal Imaging and SVD (Singular Value Decomposition) / 739

22.6 Time-Reversal Imaging with MUSIC (Multiple Signal Classification) / 739

22.7 Optimum Power Transfer by Time-Reversal Technique / 740

23 Scattering By Turbulence, Particles, Diffuse Medium, And Rough Surfaces 743

23.1 Scattering by Atmospheric and Ionospheric Turbulence / 743

23.2 Scattering Cross Section per Unit Volume of Turbulence / 746

23.3 Scattering for a Narrow Beam Case / 748

23.4 Scattering Cross Section Per Unit Volume of Rain and Fog / 750

23.5 Gaussian and Henyey-Greenstein Scattering Formulas / 751

23.6 Scattering Cross Section Per Unit Volume of Turbulence,

Particles, and Biological Media / 752

23.7 Line-of-Sight Propagation, Born and Rytov Approximation / 753

23.8 Modified Rytov Solution with Power Conservation, and Mutual Coherence Function / 754

23.9 MCF for Line-of-Sight Wave Propagation in Turbulence / 756

23.10 Correlation Distance and Angular Spectrum / 759

23.11 Coherence Time and Spectral Broadening / 760

23.12 Pulse Propagation, Coherence Bandwidth, and Pulse Broadening / 761

23.13 Weak and Strong Fluctuations and Scintillation Index / 762

23.14 Rough Surface Scattering, Perturbation Solution, Transition Operator / 765

23.15 Scattering by Rough Interfaces Between Two Media / 771

23.16 Kirchhoff Approximation of Rough Surface Scattering / 774

23.17 Frequency and Angular Correlation of Scattered Waves from Rough Surfaces and Memory Effects / 779

24 Coherence In Multiple Scattering And Diagram Method 785

24.1 Enhanced Radar Cross Section in Turbulence / 786

24.2 Enhanced Backscattering from Rough Surfaces / 787

24.3 Enhanced Backscattering from Particles and Photon

Localization / 789

24.4 Multiple Scattering Formulations, the Dyson and Bethe-Salpeter Equations / 791

24.5 First-Order Smoothing Approximation / 793

24.6 First- and Second-Order Scattering and Backscattering Enhancement / 794

24.7 Memory Effects / 795

25 Solitons And Optical Fibers 797

25.1 History / 797

25.2 KDV (Korteweg-De Vries) Equation for Shallow Water / 799

25.3 Optical Solitons in Fibers / 802

26 Porous Media, Permittivity, Fluid Permeability Of Shales And Seismic Coda 807

26.1 Porous Medium and Shale, Superfracking / 808

26.2 Permittivity and Conductivity of Porous Media, Archie's Law, and Percolation and Fractal / 809

26.3 Fluid Permeability and Darcy's Law / 811

26.4 Seismic Coda, P-Wave, S-Wave, and Rayleigh Surface Wave / 812

26.5 Earthquake Magnitude Scales / 813

26.6 Waveform Envelope Broadening and Coda / 814

26.7 Coda in Heterogeneous Earth Excited by an Impulse Source / 815

26.8 S-wave Coda and Rayleigh Surface Wave / 819

Appendices 821

References 913

Index 929