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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
Many advances in electromagnetic theory were made in recent years in response to new applications of the theory to microwaves, millimeter waves, optics, and acoustics; as a result, there is a need to present a cohesive account of these advances with sufficient background material. In this book we present the fundamentals and the basic formulations of electromagnetic theory as well as advanced analytical theory and mathematical techniques and current new topics and applications.
In Chapter 2, we review the fundamentals, starting with Maxwell's equations and covering such fundamental concepts and relationships as energy relations, potentials, Hertz vectors, and uniqueness and reciprocity theorems. The chapter concludes with linear acoustic-wave formulation. Plane-wave incidence on dielectric layers and wave propagation along layered media are often encountered in practice. Examples are microwaves in dielectric coatings, integrated optics, waves in the atmosphere, and acoustic waves in the ocean. Chapter 3 deals with these problems, starting with reviews of plane waves incident on layered media, Fresnel formulas, Brewster's angle, and total reflection. The concepts of complex waves, trapped surface waves, and leaky waves are presented with examples of surface-wave propagation along dielectric slabs, and this is followed by discussion on the relation between Zenneck waves and plasmons. The chapter concludes with Wentzel-Kramers-Brillouim (WKB) solutions and the Bremmer series for inhomogeneous media and turning points, and WKB solutions for the propagation constant of guided waves in inhomogeneous media such as graded-index fibers.
Chapter 4 deals with microwave waveguides, dielectric waveguides, and cavities. Formulations for transverse magetic (TM), transverse electric (TE), and transverse electromagnetic (TEM) waves, eigenfunctions, eigenvalues, and the k-ß diagram are given, followed by pulse propagation in dispersive media. Dielectric waveguides, step-index fibers, and graded-index fibers are discussed next with due attention to dispersion. It concludes with radial and azimuthal waveguides, rectangular and cylindrical cavities, and spherical waveguides and cavities. This chapter introduces Green's identities, Green's theorem, special functions, Bessel and Legendre functions, eigenfunctions and eigenvalues, and orthogonality.
One of the most important and useful tools in electromagnetic theory is Green's functions. They are used extensively in the formulation of integral equations and radiation from various sources. Methods of constructing Green's functions are discussed in Chapter 5. First, the excitation of waves by electric and magnetic dipoles is reviewed. Three methods of expressing Green's functions are discussed. The first is the representation of Green's functions in a series of eigenfunctions. The second is to express them using the solutions of homogeneous equations. Here, we discuss the important properties of Wronskians. The third is the Fourier transform representation of Green's functions. In actual problems, these three methods are often combined to obtain the most convenient representations. Examples are shown for Green's functions in rectangular waveguides and cylindrical and spherical structures.
Chapter 6 deals with the radiation field from apertures. We start with Green's theorem applied to the field produced by the sources and the fields on a surface. Here, we discuss the extinction theorem and Huygens' formula. Next, we consider the Kirchhoff approximation and Fresnel and Fraunhofer diffraction formulas. Spectral representations of the field are used to obtain Gaussian beam waves and the radiation from finite apertures. The interesting phenomenon of the Goos-Hanchen shift of a beam wave at an interface and higher-order beam waves are also discussed. The chapter concludes with the electromagnetic vector Green's theorem, Stratton-Chu formula, Franz formula, equivalence theorem, and electromagnetic Kirchhoff approximations.
The periodic structures discussed in Chapter 7 are used in many applications, such as optical gratings, phased arrays, and frequency-selective surfaces. We start with the Floquet-mode representation of waves in periodic structures. Guided waves along periodic structures and plane-wave incidence on periodic structures are discussed using integral equations and Green's function. An interesting question regarding the Rayleigh hypothesis for scattering from sinusoidal surfaces is discussed. Also included are the coupled-mode theory and co-directional and contra-directional couplers.
Chapter 8 deals with material characteristics. We start with the dispersive characteristics of dielectric material, the Sellmeier equation, plasma, and conductors. It also includes the Maxwell-Garnett and Polder-van Santen mixing formulas for the effective dielectric constant of mixtures. Wave propagation characteristics in magnetoplasma, which represents the ionosphere and ionized gas, and in ferrite, used in microwave networks, are discussed as well as Faraday rotation, group velocity, warm plasma, and reciprocity relations. This is followed by wave propagation in chiral material. The chapter concludes with London's equations and the two-fluid model of superconductors at high frequencies.
Chapter 9 presents selected topics on antennas, apertures, and arrays. Included in this chapter are radiation from current distributions, dipoles, slots, and loops. Also discussed are arrays with nonuniform spacings, microstrip antennas, mutual couplings, and the integral equation for current distributions on wire antennas. Chapter 10 starts with a general description of the scattering and absorption characteristics of waves by dielectric and conducting objects. Definitions of cross sections and scattering amplitudes are given, and Rayleigh scattering and Rayleigh-Debye approximations are discussed. Also included are the Stokes vector, the Mueller matrix, and the Poincaré sphere for a description of the complete and partial polarization states. Techniques discussed for obtaining the cross sections of conducting objects include the physical optics approximation and the moment method. Formal solutions for cylindrical structures, spheres, and wedges are presented in Chapter 11, including a discussion of branch points, the saddle-point technique, the Watson transform, the residue series, and Mie theory. Also discussed is diffraction by wedges, which will be used in Chapter 13.
Electromagnetic scattering by complex objects is the topic of Chapter 12. We present scalar and vector formulations of integral equations. Babinet's principle for scalar and electromagnetic fields, electric field integral equation (EFIE), and magnetic field integral equation (MFIE) are discussed. The T-matrix method, also called the extended boundary condition method, is discussed and applied to the problem of sinusoidal surfaces. In addition to the surface integral equation, also included are the volume integral equation for two- and three-dimensional dielectric bodies and Green's dyadic. Discussions of small apertures and slits are also included.
Geometric theory of diffraction (GTD) is one of the powerful techniques for dealing with high-frequency diffraction problems. GTD and UTD (uniform geometric theory of diffraction) are discussed in Chapter 13. Applications of GTD to diffraction by slits, knife edges, and wedges are presented, including slope diffraction, curved wedges, and vertex and surface diffractions.
Chapter 14 deals with excitation and scattering by sources, patches, and apertures embedded in planar structures. Excitation of a dielectric slab is discussed, followed by the WKB solution for the excitation of waves in inhomogeneous layers. An example of the latter is acoustic-wave excitation by a point source in the ocean. Next, we give general spectral formulations for waves in patches, strip lines, and apertures embedded in dielectric layers. Convenient equivalent network representations are presented that are applicable to strip lines and periodic patches and apertures.
The Sommerfeld dipole problem is that of finding the field when a dipole is located above the conducting earth. This classical problem, which dates back to 1907, when Zenneck investigated what is now known as the Zenneck wave, is discussed in Chapter 15, including a detailed study of the Sommerfeld pole, the modified saddle-point technique, lateral waves, layered media, and mode representations.
The inverse scattering problem in Chapter 16 is one of the important topics in recent years. It deals with the problem of obtaining the properties of an object by using the observed scattering data. First, we present the Radon transform, used in computed tomography or X-ray tomography. The inverse Radon transform is obtained by using the projection slice theorem and the back projection of the filtered projection. Also included is an alternative inverse Radon transform in terms of the Hilbert transform. For ultrasound and electromagnetic imaging problems, it is necessary to include the diffraction effect. This leads to diffraction tomography, which makes use of back propagation rather than back projection. Also discussed are physical optics inverse scattering and the holographic inverse problem. Abel's integral equations are frequently used in inverse problems. Here, we illustrate this technique...
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