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.
Author(s): Akira Ishimaru
Series: The IEEE Press Series on Electromagnetic Wave Theory
Edition: 2
Publisher: Wiley-IEEE Press
Year: 2017
Language: English
Pages: 945
City: Piscataway, NJ
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
vii
viii CONTENTS
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 Relection / 44
3.7 Waves in Layered Media / 47
3.8 Acoustic Relection 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 Proile / 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–β Diagram and Phase and Group Velocities / 95
4.7 Rectangular Waveguides / 98
4.8 Cylindrical Waveguides / 100
4.9 TEM Modes / 104
CONTENTS ix
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
x CONTENTS
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
CONTENTS xi
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
xii CONTENTS
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
CONTENTS xiii
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 ofWaves 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 Relected 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
xiv CONTENTS
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
CONTENTS xv
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
Relectivity / 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 Speciic 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
xvi CONTENTS
21 WAVES IN METAMATERIALS AND PLASMON 685
21.1 Refractive Index n and μ–ε 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
Classiication) / 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
CONTENTS xvii
23.8 Modiied 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
xviii CONTENTS
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
