# Electromagnetic Wave Propagation, Radiation, and Scattering

## From Fundamentals to Applications

IEEE/OUP Series on Electromagnetic Wave Theory (formerly IEEE only), Series Editor: Donald G. Dudley. (Series Nr. 1)

2. Edition October 2017

968 Pages, Hardcover*Wiley & Sons Ltd*

**978-1-118-09881-3**

### Short Description

Written by an expert in electromagnetic research, this book provides a thorough treatment of electromagnetic waves that delves into mathematical formulas, delta functions, matrix algebra, and optical theorems. Organized into two sections, the book covers the tenets of electromagnetic wave propagation, radiation, and scattering before illustrating its function in radiometry, geophysical remote sensing and imaging, and biomedical and signal processing applications. The text is intended for graduate students and practicing engineers. To obtain the solutions manual, please send an email to: ieeeproposals@wiley.com.

One of the most methodical treatments of electromagnetic wave propagation, radiation, and scattering--including new applications and ideas

Presented in two parts, this book takes an analytical approach on the subject and emphasizes new ideas and applications used today. Part one covers fundamentals of electromagnetic wave propagation, radiation, and scattering. It provides ample end-of-chapter problems and offers a 90-page solution manual to help readers check and comprehend their work. The second part of the book explores up-to-date applications of electromagnetic waves--including radiometry, geophysical remote sensing and imaging, and biomedical and signal processing applications.

Written by a world renowned authority in the field of electromagnetic research, this new edition of Electromagnetic Wave Propagation, Radiation, and Scattering: From Fundamentals to Applications presents detailed applications with useful appendices, including mathematical formulas, Airy function, Abel's equation, Hilbert transform, and Riemann surfaces. The book also features newly revised material that focuses on the following topics:

* Statistical wave theories--which have been extensively applied to topics such as geophysical remote sensing, bio-electromagnetics, bio-optics, and bio-ultrasound imaging

* Integration of several distinct yet related disciplines, such as statistical wave theories, communications, signal processing, and time reversal imaging

* New phenomena of multiple scattering, such as coherent scattering and memory effects

* Multiphysics applications that combine theories for different physical phenomena, such as seismic coda waves, stochastic wave theory, heat diffusion, and temperature rise in biological and other media

* Metamaterials and solitons in optical fibers, nonlinear phenomena, and porous media

Primarily a textbook for graduate courses in electrical engineering, Electromagnetic Wave Propagation, Radiation, and Scattering is also ideal for graduate students in bioengineering, geophysics, ocean engineering, and geophysical remote sensing. The book is also a useful reference for engineers and scientists working in fields such as geophysical remote sensing, bio-medical engineering in optics and ultrasound, and new materials and integration with signal processing.

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 LOW FREQUENCY 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 mu-epsilon 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-Reversal 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