Electromagnetic wave propagation, radiation, and scattering

Akira Ishimaru9780132490535, 0132490536

Table of contents :
Title page ……Page 1
Date-line ……Page 2
Contents ……Page 3
Preface ……Page 14
1 Introduction ……Page 16
2.1 Maxwell’s Equations ……Page 20
2.2 Time-Harmonic Case ……Page 23
2.3 Constitutive Relations ……Page 24
2.4 Boundary Conditions ……Page 28
2.5 Energy Relations and Poynting Theorem ……Page 30
2.6 Vector and Scalar Potentials ……Page 33
2.7 Electric Hertz Vector ……Page 35
2.8 Duality Principle and Symmetry of Maxwell’s Equations ……Page 36
2.9 Magnetic Hertz Vector ……Page 37
2.10 Uniqueness Theorem ……Page 38
2.11 Reciprocity Theorem ……Page 39
2.12 Acoustic Waves 26 Problems ……Page 44
3.1 Wave Equation for a Time-Harmonic Case ……Page 46
3.2 Time-Harmonic Plane-Wave Propagation in Homogeneous Media ……Page 47
3.3 Polarization ……Page 48
3.4 Plane-Wave Incidence on a Plane Boundary: Perpendicular Polarization ($s$ Polarization) ……Page 51
3.5 Electric Field Parallel to a Plane of Incidence: Parallel Polarization ($p$ Polarization) ……Page 54
3.6 Fresnel Formula, Brewster’s Angle, and Total Reflection ……Page 55
3.7 Waves in Layered Media ……Page 58
3.8 Acoustic Reflection and Transmission from a Boundary ……Page 60
3.9 Complex Waves ……Page 61
3.10 Trapped Surface Wave (Slow Wave) and Leaky Wave ……Page 64
3.11 Surface Waves along a Dielectric Slab ……Page 67
3.12 Zenneck Waves and Plasmons ……Page 72
3.13 Waves in Inhomogeneous Media ……Page 74
3.14 WKB Method ……Page 77
3.15 Bremmer Series ……Page 80
3.16 WKB Solution for the Turning Point ……Page 84
3.17 Trapped Surface-Wave Modes in an Inhomogeneous Slab ……Page 85
3.18 Medium with Prescribed Profile ……Page 87
Problems ……Page 88
4.1 Uniform Electromagnetic Waveguides ……Page 91
4.2 TM Modes or E Modes ……Page 92
4.3 TE Modes or H Modes ……Page 93
4.4 Eigenfunctions and Eigenvalues ……Page 95
4.5 General Properties of Eigenfunctions for Closed Regions ……Page 97
4.6 $k$-$beta$ Diagram and Phase and Group Velocities ……Page 100
4.7 Rectangular Waveguides ……Page 102
4.8 Cylindrical Waveguides ……Page 104
4.9 TEM Modes ……Page 108
4.10 Dispersion of a Pulse in a Waveguide ……Page 109
4.11 Step-Index Optical Fibers ……Page 112
4.12 Dispersion of Graded-Index Fibers ……Page 118
4.13 Radial and Azimuthal Waveguides ……Page 119
4.14 Cavity Resonators ……Page 122
4.15 Waves in Spherical Structures ……Page 125
4.16 Spherical Waveguides and Cavities ……Page 129
Problems ……Page 134
5.1 Electric and Magnetic Dipoles in Homogeneous Media ……Page 136
5.2 Electromagnetic Fields Excited by an Electric Dipole in a Homogeneous Medium ……Page 138
5.3 Electromagnetic Fields Excited by a Magnetic Dipole in a Homogeneous Mediun ……Page 142
5.4 Scalar Green’s Functions for Closed Regions and Expansion of Green’s Function in a Series of Eigenfunctions ……Page 144
5.5 Green’s Function in Terms of Solutions of the Homogeneous Equation ……Page 148
5.6 Fourier Transform Method ……Page 152
5.7 Excitation of a Rectangular Waveguide ……Page 154
5.8 Excitation of a Conducting Cylinder ……Page 156
5.9 Excitation of a Conducting Sphere ……Page 159
Problems ……Page 162
6.1 Huygens’ Principle and Extinction Theorem ……Page 164
6.2 Fields due to the Surface Field Distribution ……Page 168
6.3 Kirchhoff Approximation ……Page 171
6.4 Fresnel and Fraunhofer Diffraction ……Page 172
6.5 Fourier Transform (Spectral) Representation ……Page 175
6.6 Beam Waves ……Page 177
6.7 Goos-Hanchen Effect ……Page 180
6.8 Higher-Order Beam-Wave Modes ……Page 184
6.9 Vector Green’s Theorem, Stratton-Chu Formula, and Franz Formula ……Page 187
6.10 Equivalence Theorem ……Page 189
6.11 Kirchhoff Approximation for Electromagnetic Waves ……Page 190
Problems ……Page 191
7 Periodic Structures and Coupled-Mode Theory ……Page 193
7.1 Floquet’s Theorem ……Page 194
7.2 Guided Waves Along Periodic Structures ……Page 195
7.3 Periodic Layers ……Page 201
7.4 Plane Wave Incidence on a Periodic Structure ……Page 204
7.5 Scattering From Periodic Surfaces Based on the Rayleigh Hypothesis ……Page 210
7.6 Coupled-Mode Theory ……Page 214
Problems ……Page 218
8.1 Dielectric Material and Polarizability ……Page 220
8.2 Dispersion of Dielectric Material ……Page 222
8.3 Dispersion of Conductor and Isotropic Plasma ……Page 224
8.4 Debye Relaxation Equation and Dielectric Constant of Wates ……Page 225
8.6 Mixing Formula ……Page 227
8.7 Dielectric Constant and Permeability for Anisotropic Media ……Page 230
8.8 Magnetoionic Theory for Anisotropic Plasma ……Page 231
8.9 Plane-Wave Propagation in Anisotropic Media ……Page 233
8.10 Plane-Wave Propagation in Magnetoplasma ……Page 234
8.11 Propagation Along the DC Magnetic Field ……Page 235
8.12 Faraday Rotation ……Page 239
8.13 Propagation Perpendicular to the DC Magnetic Field ……Page 240
8.14 The Height of the Ionosphere ……Page 241
8.15 Group Velocity in Anisotropic Medium ……Page 242
8.16 Warm Plasma ……Page 243
8.17 Wave Equations for Warm Plasma ……Page 245
8.18 Ferrite and the Derivation of its Permeability Tensor ……Page 247
8.19 Plane-Wave Propagation in Ferrite ……Page 250
8.20 Microwave Devices Using Ferrites ……Page 251
8.21 Lorentz Reciprocity Theorem for Anisotropic Media ……Page 254
8.22 Bianisotropic Media and Chiral Media ……Page 256
8.23 Superconductors, London Equation, and the Meisner Effects ……Page 259
8.24 Two-Fluid Model of Superconductors at High Frequencies ……Page 260
Problems ……Page 263
9.1 Antenna Fundamentals ……Page 265
9.2 Radiation Fields of Given Electric and Magnetic Current Distributions ……Page 269
9.3 Radiation Fields of Dipoles, Slots, and Loops ……Page 271
9.4 Antenna Arrays with Equal and Nonequal Spacings ……Page 275
9.5 Radiation Fields from a Given Aperture Field Distribution ……Page 280
9.6 Radiation from Microstrip Antennas ……Page 283
9.7 Self- and Mutual Impedances of Wire Antennas with Given Current Distributions ……Page 286
9.8 Current Distribution of a Wire Antenna ……Page 290
Problems ……Page 291
10 Scattering of Waves by Conducting and Dieiectric Objects ……Page 293
10.1 Cross Sections and Scattering Amplitude ……Page 294
10.2 Radar Equations ……Page 296
10.3 General Properties of Cross Sections ……Page 298
10.4 Integral Representations of Scattering Amplitude and Absorption Cross Sections ……Page 300
10.5 Rayleigh Scattering for a Spherical Object ……Page 303
10.6 Rayleigh Scattering for a Small Ellipsoidal Object ……Page 305
10.7 Rayleigh-Deb ye Scattering (Born Approximation) ……Page 309
10.8 Elliptic Polarization and Stokes Parameters ……Page 313
10.9 Partial Polarization and Natural Light ……Page 315
10.10 Scattering Ampitude Functions $f_{11}$, $f_{12}$, $f_{21}$, and $f_{22}$ and the Stokes Matrix ……Page 316
10.11 Acoustic Scattering ……Page 318
10.12 Scattering Cross Section of Conducting Body ……Page 319
10.13 Physical Optics Approximation ……Page 321
10.14 Moment Method : Computer Applications ……Page 323
Problems ……Page 326
11.1 Plane Wave Incident on a Conducting Cylinder ……Page 329
11.2 Plane Wave Incident on a Dielectric Cylinder ……Page 333
11.3 Axial Dipole near a Conducting Cylinder ……Page 335
11.4 Radiation Field ……Page 337
11.5 Saddle-Point Technique ……Page 338
11.6 Radiation from a Dipole and Parseval’s Theorem ……Page 341
11.7 Large Cylinders and The Watson Transform ……Page 343
11.8 Residue Series Representation and Creeping Waves ……Page 345
11.9 Poisson’s Sum Formula, Geometric Optical Region, and Fock Representation ……Page 348
11.10 Mie Scattering by an Dielectric Sphere ……Page 351
11.11 Axial Dipole in the Vicinity of a Conducting Wedge ……Page 357
11.12 Line Source and Plane Wave Incident on a Wedge ……Page 359
11.13 Half-Plane Excited by a Plane Wave ……Page 361
Problems ……Page 362
12 Scattering by Complex Objects ……Page 365
12.1 Scalar Surface Integral Equations for Soft and Hard Surface ……Page 366
12.2 Scalar Surface Integral Equations for a Penetrable Homogeneous Body ……Page 368
12.3 EFIE and MFIE ……Page 369
12.4 T-Matrix Method (Extended Boundary Condition Method) ……Page 371
12.5 Symmetry and Unitarity of the T Matrix and the Scattering Matrix ……Page 376
12.6 T-Matrix Solution for Scattering from Periodic Sinusoidal Surfaces ……Page 379
12.7 Volume Integral Equations for Inhomogeneous Bodies: TM Case ……Page 380
12.8 Volume Integral Equations for Inhomogeneous Bodies: TE Case ……Page 384
12.9 Three-Dimensional Dielectric Bodies ……Page 387
12.10 Electromagnetic Aperture Integral Equations for a Conducting Screen ……Page 388
12.11 Small Apertures ……Page 391
12.12 Babinet’s Principle and Slot and Wire Antennas ……Page 394
12.13 Electromagnetic Diffraction by Slits and Ribbons ……Page 399
Problems ……Page 400
13 Geometric Theory of Diffraction and Low-Frequency Techniques ……Page 402
13.1 Geometrical Theory of Diffraction ……Page 403
13.2 Diffraction by a Slit for Dirichlet’s Problem ……Page 406
13.3 Diffraction by a Slit for Neumann’s Problem and Slope Diffraction ……Page 410
13.4 Uniform Geometrical Theory of Diffraction for an Edge ……Page 413
13.5 Edge Diffraction for a Point Source ……Page 415
13.6 Wedge Diffraction for a Point Source ……Page 419
13.7 Slope Diffraction and Grazing Incidence ……Page 420
13.8 Curved Wedge ……Page 421
13.9 Other High-Frequency Techniques ……Page 422
13.10 Vertex and Surface Diffraction Diffraction ……Page 423
13.11 Low-Frequency Scattering ……Page 424
Problems ……Page 427
14.1 Excitation of Waves in a Dielectric Slab ……Page 429
14.2 Excitation of Waves in a Vertically Inhomogeneous Medium ……Page 436
14.3 Strip Lines ……Page 440
14.4 Waves Excited by Electric and Magnetic Currents Perpendicular to Dielectric Layers ……Page 446
14.5 Waves Excited by Transverse Electric and Magnetic Currents in Dielectric Layers ……Page 450
14.6 Strip Lines Embedded in Dielectric Layers ……Page 454
14.7 Periodic Patches and Apertures Embedded in Dielectric Layers ……Page 456
Problems ……Page 459
15.1 Sommerfeld Dipole Medium ……Page 462
15.2 Vertical Electric Dipole Located Above the Earth ……Page 463
15.3 Reflected Waves in Air ……Page 467
15.4 Radiation Field: Saddle-Point Technique ……Page 469
15.5 Field Along the Surface and the Singularities of the Integrand ……Page 471
15.6 Sommerfeld Pole and Zenneck Wave ……Page 473
15.7 Solution to the Sommerfeld Problem ……Page 476
15.8 Lateral Waves: Branch Cut Integration ……Page 479
15.9 Refracted Wave ……Page 487
15.10 Radiation from a Horizontal Dipole ……Page 489
15.11 Radiation in Layered Media ……Page 492
15.12 Geometrical Optical Representation ……Page 495
15.13 Mode and Lateral Wave Representation ……Page 498
Problems ……Page 500
16.1 Radon Transform and Tomography ……Page 501
16.2 Alternative Inverse Radon Transform in Terms of the Hilber Transform ……Page 505
16.3 Diffraction Tomography ……Page 506
16.4 Physical Optics Inverse Scattering ……Page 512
16.5 Holographic Inverse Source Problem ……Page 514
16.6 Inverse Problems and Abel’s Integral Equation Applied to Probing of the Ionosphere ……Page 516
16.7 Radar Polarimetry and Radar Equation ……Page 518
16.8 Optimization of Polarization ……Page 521
16.9 Stokes Vector Radar Equation and Polarization Signature ……Page 522
16.10 Measurement of Stokes Parameter ……Page 525
Problems ……Page 526
17.1 Radiometry ……Page 527
17.2 Brightness and Flux Density ……Page 528
17.3 Blackbody Radiation and Antenna Temperature ……Page 529
17.4 Equation of Radiative Transfer ……Page 532
17.5 Scattering Cross Sections and Absorptivity and Emissivity of a Surface ……Page 534
17.6 System Temperature ……Page 537
17.7 Minimum Detectable Temperature ……Page 539
17.9 Aperture Illumination and Brightness Distributions ……Page 540
17.10 Two-Antenna Interferometer ……Page 543
Problems ……Page 545
18.1 Moment Method ……Page 547
18.2 Choice of Basis Functions and Weighting Functions ……Page 551
18.3 Weak Formulation and Examples ……Page 554
18.4 Variational Expressions and the Rayleigh-Ritz Method ……Page 559
18.5 Finite-Element Method ……Page 561
18.6 Finite-Difference Method ……Page 568
Problems ……Page 571
A. Mathematical Formulas ……Page 572
A. The Field near the Turning Point ……Page 575
B. Stokes Differential Equation and Airy Integral ……Page 577
A. Green’s Identities and Theorem ……Page 580
B. Bessel Functions $Z_v(x)$ ……Page 581
A. Delta Function ……Page 583
A. Stratton-Chu Formula ……Page 586
A. Periodic Green’s Function ……Page 591
C. Edge Conditions ……Page 592
A. Matrix Algebra ……Page 595
A. Forward Scattering Theorem (Optical Theorem) ……Page 598
A. Branch Points and Riemann Surfaces ……Page 601
B. Choice of the Contour of Integration and the Branch Cut ……Page 604
C. Saddle-Point Technique and Method of Stationary Phase ……Page 609
D. Complex Integrals and Residues ……Page 614
A. Improper Integrals ……Page 617
B. Integral Equations ……Page 619
A. Stationary Phase Evaluation of a Multiple Integral $I$ ……Page 621
A. Sommerfeld’s Solution ……Page 624
B. Riemann Surfaces for the Sommerfeld Problem ……Page 625
C. Modified Saddle-Point Technique ……Page 630
A. Hilbert Transform ……Page 636
B. Rytov Approximation ……Page 638
C. Abel’s Integral Equation ……Page 639
REFERENCES ……Page 641
INDEX ……Page 648