Electromagnetic Wave Propagation, Radiation, and Scattering

Akira Ishimaru, PhD, has served as a member-at-large of the U.S. National Committee (USNC) and was chairman of Commission B of the USNC/International Union of Radio Science. He is a Fellow of the IEEE, the Optical Society of America, the Acoustical Society of America and the Institute of Physics, U.K. He is also the recipient of numerous awards in his field. He is a member of the National Academy of Engineering.

• About The Author XixPreface XxiPreface To The First Edition XxvAcknowledgments XxviiPart I Fundamentals 11 Introduction 32 Fundamental Field Equations 72.1 Maxwell’s Equations / 72.2 Time-Harmonic Case / 102.3 Constitutive Relations / 112.4 Boundary Conditions / 152.5 Energy Relations and Poynting’s Theorem / 182.6 Vector and Scalar Potentials / 222.7 Electric Hertz Vector / 242.8 Duality Principle and Symmetry of Maxwell’s Equations / 252.9 Magnetic Hertz Vector / 262.10 Uniqueness Theorem / 272.11 Reciprocity Theorem / 282.12 Acoustic Waves / 30Problems / 333 Waves In Inhomogeneous And Layered Media 353.1 Wave Equation for a Time-Harmonic Case / 353.2 Time-Harmonic Plane-Wave Propagation in Homogeneous Media / 363.3 Polarization / 373.4 Plane-Wave Incidence on a Plane Boundary: Perpendicular Polarization (s Polarization) / 393.5 Electric Field Parallel to a Plane of Incidence: Parallel Polarization (p Polarization) / 433.6 Fresnel Formula, Brewster’s Angle, and Total Reflection / 443.7 Waves in Layered Media / 473.8 Acoustic Reflection and Transmission from a Boundary / 503.9 Complex Waves / 513.10 Trapped Surface Wave (Slow Wave) and Leaky Wave / 543.11 Surface Waves Along a Dielectric Slab / 573.12 Zenneck Waves and Plasmons / 633.13 Waves in Inhomogeneous Media / 663.14 WKB Method / 683.15 Bremmer Series / 723.16 WKB Solution for the Turning Point / 763.17 Trapped Surface-Wave Modes in an Inhomogeneous Slab / 773.18 Medium With Prescribed Profile / 80Problems / 814 Waveguides And Cavities 854.1 Uniform Electromagnetic Waveguides / 854.2 TM Modes or E Modes / 864.3 TE Modes or H Modes / 874.4 Eigenfunctions and Eigenvalues / 894.5 General Properties of Eigenfunctions for Closed Regions / 914.6 k–β Diagram and Phase and Group Velocities / 954.7 Rectangular Waveguides / 984.8 Cylindrical Waveguides / 1004.9 TEM Modes / 1044.10 Dispersion of a Pulse in a Waveguide / 1064.11 Step-Index Optical Fibers / 1094.12 Dispersion of Graded-Index Fibers / 1164.13 Radial and Azimuthal Waveguides / 1174.14 Cavity Resonators / 1204.15 Waves in Spherical Structures / 1234.16 Spherical Waveguides and Cavities / 128Problems / 1335 Green’s Functions 1375.1 Electric and Magnetic Dipoles in Homogeneous Media / 1375.2 Electromagnetic Fields Excited by an Electric Dipole in a Homogeneous Medium / 1395.3 Electromagnetic Fields Excited by a Magnetic Dipole in a Homogeneous Medium / 1445.4 Scalar Green’s Function for Closed Regions and Expansion of Green’s Function in a Series of Eigenfunctions / 1455.5 Green’s Function in Terms of Solutions of the Homogeneous Equation / 1505.6 Fourier Transform Method / 1555.7 Excitation of a Rectangular Waveguide / 1575.8 Excitation of a Conducting Cylinder / 1595.9 Excitation of a Conducting Sphere / 163Problems / 1666 Radiation From Apertures And Beam Waves 1696.1 Huygens’ Principle and Extinction Theorem / 1696.2 Fields Due to the Surface Field Distribution / 1736.3 Kirchhoff Approximation / 1766.4 Fresnel and Fraunhofer Diffraction / 1786.5 Fourier Transform (Spectral) Representation / 1826.6 Beam Waves / 1836.7 Goos–Hanchen Effect / 1876.8 Higher-Order Beam-Wave Modes / 1916.9 Vector Green’s Theorem, Stratton–Chu Formula, and Franz Formula / 1946.10 Equivalence Theorem / 1976.11 Kirchhoff Approximation for Electromagnetic Waves / 198Problems / 1997 Periodic Structures And Coupled-Mode Theory 2017.1 Floquet’s Theorem / 2027.2 Guided Waves Along Periodic Structures / 2037.3 Periodic Layers / 2097.4 Plane Wave Incidence on a Periodic Structure / 2137.5 Scattering from Periodic Surfaces Based on the Rayleigh Hypothesis / 2197.6 Coupled-Mode Theory / 224Problems / 2298 Dispersion And Anisotropic Media 2338.1 Dielectric Material and Polarizability / 2338.2 Dispersion of Dielectric Material / 2358.3 Dispersion of Conductor and Isotropic Plasma / 2378.4 Debye Relaxation Equation and Dielectric Constant of Water / 2408.5 Interfacial Polarization / 2408.6 Mixing Formula / 2418.7 Dielectric Constant and Permeability for Anisotropic Media / 2448.8 Magnetoionic Theory for Anisotropic Plasma / 2448.9 Plane-Wave Propagation in Anisotropic Media / 2478.10 Plane-Wave Propagation in Magnetoplasma / 2488.11 Propagation Along the DC Magnetic Field / 2498.12 Faraday Rotation / 2538.13 Propagation Perpendicular to the DC Magnetic Field / 2558.14 The Height of the Ionosphere / 2568.15 Group Velocity in Anisotropic Medium / 2578.16 Warm Plasma / 2598.17 Wave Equations for Warm Plasma / 2618.18 Ferrite and the Derivation of Its Permeability Tensor / 2638.19 Plane-Wave Propagation in Ferrite / 2668.20 Microwave Devices Using Ferrites / 2678.21 Lorentz Reciprocity Theorem for Anisotropic Media / 2708.22 Bi-Anisotropic Media and Chiral Media / 2728.23 Superconductors, London Equation, and the Meissner Effects / 2768.24 Two-Fluid Model of Superconductors at High Frequencies / 278Problems / 2809 Antennas, Apertures, And Arrays 2859.1 Antenna Fundamentals / 2859.2 Radiation Fields of Given Electric and Magnetic Current Distributions / 2899.3 Radiation Fields of Dipoles, Slots, and Loops / 2929.4 Antenna Arrays with Equal and Unequal Spacings / 2969.5 Radiation Fields from a Given Aperture Field Distribution / 3019.6 Radiation from Microstrip Antennas / 3059.7 Self- and Mutual Impedances of Wire Antennas with Given Current Distributions / 3089.8 Current Distribution of a Wire Antenna / 313Problems / 31410 Scattering Of Waves By Conducting And Dielectric Objects 31710.1 Cross Sections and Scattering Amplitude / 31810.2 Radar Equations / 32110.3 General Properties of Cross Sections / 32210.4 Integral Representations of Scattering Amplitude and Absorption Cross Sections / 32510.5 Rayleigh Scattering for a Spherical Object / 32810.6 Rayleigh Scattering for a Small Ellipsoidal Object / 33010.7 Rayleigh–Debye Scattering (Born Approximation) / 33410.8 Elliptic Polarization and Stokes Parameters / 33810.9 Partial Polarization and Natural Light / 34110.10 Scattering Amplitude Functions f11, f12, f21, and f22 and the Stokes Matrix / 34210.11 Acoustic Scattering / 34410.12 Scattering Cross Section of a Conducting Body / 34610.13 Physical Optics Approximation / 34710.14 Moment Method: Computer Applications / 350Problems / 35411 Waves In Cylindrical Structures, Spheres, And Wedges 35711.1 Plane Wave Incident on a Conducting Cylinder / 35711.2 Plane Wave Incident on a Dielectric Cylinder / 36111.3 Axial Dipole Near a Conducting Cylinder / 36411.4 Radiation Field / 36611.5 Saddle-Point Technique / 36811.6 Radiation from a Dipole and Parseval’s Theorem / 37111.7 Large Cylinders and the Watson Transform / 37311.8 Residue Series Representation and Creeping Waves / 37611.9 Poisson’s Sum Formula, Geometric Optical Region, and FockRepresentation / 37911.10 Mie Scattering by a Dielectric Sphere / 38211.11 Axial Dipole in the Vicinity of a Conducting Wedge / 39011.12 Line Source and Plane Wave Incident on a Wedge / 39211.13 Half-Plane Excited by a Plane Wave / 394Problems / 39512 Scattering By Complex Objects 40112.1 Scalar Surface Integral Equations for Soft and Hard Surfaces / 40212.2 Scalar Surface Integral Equations for a Penetrable Homogeneous Body / 40412.3 EFIE and MFIE / 40612.4 T-Matrix Method (Extended Boundary Condition Method) / 40812.5 Symmetry and Unitarity of the T-Matrix and the Scattering Matrix / 41412.6 T-Matrix Solution for Scattering from Periodic Sinusoidal Surfaces / 41612.7 Volume Integral Equations for Inhomogeneous Bodies: TM Case / 41812.8 Volume Integral Equations for Inhomogeneous Bodies: TE Case / 42312.9 Three-Dimensional Dielectric Bodies / 42612.10 Electromagnetic Aperture Integral Equations for a Conducting Screen / 42712.11 Small Apertures / 43012.12 Babinet’s Principle and Slot and Wire Antennas / 43312.13 Electromagnetic Diffraction by Slits and Ribbons / 43912.14 Related Problems / 441Problems / 44113 Geometric Theory Of Diffraction And Lowfrequency Techniques 44313.1 Geometric Theory of Diffraction / 44413.2 Diffraction by a Slit for Dirichlet’s Problem / 44713.3 Diffraction by a Slit for Neumann’s Problem and Slope Diffraction / 45213.4 Uniform Geometric Theory of Diffraction for an Edge / 45513.5 Edge Diffraction for a Point Source / 45713.6 Wedge Diffraction for a Point Source / 46113.7 Slope Diffraction and Grazing Incidence / 46313.8 Curved Wedge / 46313.9 Other High-Frequency Techniques / 46513.10 Vertex and Surface Diffraction / 46613.11 Low-Frequency Scattering / 467Problems / 47014 Planar Layers, Strip Lines, Patches, And Apertures 47314.1 Excitation of Waves in a Dielectric Slab / 47314.2 Excitation of Waves in a Vertically Inhomogeneous Medium / 48114.3 Strip Lines / 48514.4 Waves Excited by Electric and Magnetic Currents Perpendicular to Dielectric Layers / 49214.5 Waves Excited by Transverse Electric and Magnetic Currents in Dielectric Layers / 49614.6 Strip Lines Embedded in Dielectric Layers / 50014.7 Periodic Patches and Apertures Embedded in Dielectric Layers / 502Problems / 50615 Radiation From A Dipole On The Conducting Earth 50915.1 Sommerfeld Dipole Problem / 50915.2 Vertical Electric Dipole Located Above the Earth / 51015.3 Reflected Waves in Air / 51415.4 Radiation Field: Saddle-Point Technique / 51715.5 Field Along the Surface and the Singularities of the Integrand / 51915.6 Sommerfeld Pole and Zenneck Wave / 52115.7 Solution to the Sommerfeld Problem / 52415.8 Lateral Waves: Branch Cut Integration / 52815.9 Refracted Wave / 53615.10 Radiation from a Horizontal Dipole / 53815.11 Radiation in Layered Media / 54115.12 Geometric Optical Representation / 54515.13 Mode and Lateral Wave Representation / 549Problems / 550Part II Applications 55316 Inverse Scattering 55516.1 Radon Transform and Tomography / 55516.2 Alternative Inverse Radon Transform in Terms of the Hilbert Transform / 55916.3 Diffraction Tomography / 56116.4 Physical Optics Inverse Scattering / 56716.5 Holographic Inverse Source Problem / 57016.6 Inverse Problems and Abel’s Integral Equation Applied to Probing of the Ionosphere / 57216.7 Radar Polarimetry and Radar Equation / 57516.8 Optimization of Polarization / 57816.9 Stokes Vector Radar Equation and Polarization Signature / 58016.10 Measurement of Stokes Parameter / 582Problems / 58417 Radiometry, Noise Temperature, And Interferometry 58717.1 Radiometry / 58717.2 Brightness and Flux Density / 58817.3 Blackbody Radiation and Antenna Temperature / 58917.4 Equation of Radiative Transfer / 59217.5 Scattering Cross Sections and Absorptivity and Emissivity of a Surface / 59417.6 System Temperature / 59817.7 Minimum Detectable Temperature / 60017.8 Radar Range Equation / 60117.9 Aperture Illumination and Brightness Distributions / 60217.10 Two-Antenna Interferometer / 604Problems / 60718 Stochastic Wave Theories 61118.1 Stochastic Wave Equations and Statistical Wave Theories / 61218.2 Scattering in Troposphere, Ionosphere, and Atmospheric Optics / 61218.3 Turbid Medium, Radiative Transfer, and Reciprocity / 61218.4 Stochastic Sommerfeld Problem, Seismic Coda, and Subsurface Imaging / 61318.5 Stochastic Green’s Function and Stochastic Boundary Problems / 61518.6 Channel Capacity of Communication Systems with Random Media Mutual Coherence Function / 61918.7 Integration of Statistical Waves with Other Disciplines / 62118.8 Some Accounts of Historical Development of Statistical Wave Theories / 62219 Geophysical Remote Sensing And Imaging 62519.1 Polarimetric Radar / 62619.2 Scattering Models for Geophysical Medium and Decomposition Theorem / 63019.3 Polarimetric Weather Radar / 63219.4 Nonspherical Raindrops and Differential Reflectivity / 63419.5 Propagation Constant in Randomly Distributed Nonspherical Particles / 63619.6 Vector Radiative Transfer Theory / 63819.7 Space–Time Radiative Transfer / 63919.8 Wigner Distribution Function and Specific Intensity / 64119.9 Stokes Vector Emissivity from Passive Surface and Ocean Wind Directions / 64419.10 Van Cittert–Zernike Theorem Applied to Aperture Synthesis Radiometers Including Antenna Temperature / 64619.11 Ionospheric Effects on SAR Image / 65020 Biomedical Em, Optics, And Ultrasound 65720.1 Bioelectromagnetics / 65820.2 Bio-EM and Heat Diffusion in Tissues / 65920.3 Bio-Optics, Optical Absorption and Scattering in Blood / 66320.4 Optical Diffusion in Tissues / 66620.5 Photon Density Waves / 67020.6 Optical Coherence Tomography and Low Coherence Interferometry / 67220.7 Ultrasound Scattering and Imaging of Tissues / 67720.8 Ultrasound in Blood / 68021 Waves In Metamaterials And Plasmon 68521.1 Refractive Index n and μ–ε Diagram / 68621.2 Plane Waves, Energy Relations, and Group Velocity / 68821.3 Split-Ring Resonators / 68921.4 Generalized Constitutive Relations for Metamaterials / 69221.5 Space–Time Wave Packet Incident on Dispersive Metamaterial and Negative Refraction / 69721.6 Backward Lateral Waves and Backward Surface Waves / 70121.7 Negative Goos–Hanchen Shift / 70421.8 Perfect Lens, Subwavelength Focusing, and Evanescent Waves / 70821.9 Brewster’s Angle in NIM and Acoustic Brewster’s Angle / 71221.10 Transformation Electromagnetics and Invisible Cloak / 71621.11 Surface Flattening Coordinate Transform / 72022 Time-Reversal Imaging 72322.1 Time-Reversal Mirror in Free Space / 72422.2 Super Resolution of Time-Reversed Pulse in MultipleScattering Medium / 72922.3 Time-Reversal Imaging of Single and Multiple Targets and DORT (Decomposition of Time- eversal Operator) / 73122.4 Time-Reversal Imaging of Targets in Free Space / 73522.5 Time-Reversal Imaging and SVD (Singular Value Decomposition) / 73922.6 Time-Reversal Imaging with MUSIC (Multiple Signal Classification) / 73922.7 Optimum Power Transfer by Time-Reversal Technique / 74023 Scattering By Turbulence, Particles, Diffuse Medium, And Rough Surfaces 74323.1 Scattering by Atmospheric and Ionospheric Turbulence / 74323.2 Scattering Cross Section per Unit Volume of Turbulence / 74623.3 Scattering for a Narrow Beam Case / 74823.4 Scattering Cross Section Per Unit Volume of Rain and Fog / 75023.5 Gaussian and Henyey–Greenstein Scattering Formulas / 75123.6 Scattering Cross Section Per Unit Volume of Turbulence,Particles, and Biological Media / 75223.7 Line-of-Sight Propagation, Born and Rytov Approximation / 75323.8 Modified Rytov Solution with Power Conservation, and Mutual Coherence Function / 75423.9 MCF for Line-of-Sight Wave Propagation in Turbulence / 75623.10 Correlation Distance and Angular Spectrum / 75923.11 Coherence Time and Spectral Broadening / 76023.12 Pulse Propagation, Coherence Bandwidth, and Pulse Broadening / 76123.13 Weak and Strong Fluctuations and Scintillation Index / 76223.14 Rough Surface Scattering, Perturbation Solution, Transition Operator / 76523.15 Scattering by Rough Interfaces Between Two Media / 77123.16 Kirchhoff Approximation of Rough Surface Scattering / 77423.17 Frequency and Angular Correlation of Scattered Waves from Rough Surfaces and Memory Effects / 77924 Coherence In Multiple Scattering And Diagram Method 78524.1 Enhanced Radar Cross Section in Turbulence / 78624.2 Enhanced Backscattering from Rough Surfaces / 78724.3 Enhanced Backscattering from Particles and PhotonLocalization / 78924.4 Multiple Scattering Formulations, the Dyson and Bethe–Salpeter Equations / 79124.5 First-Order Smoothing Approximation / 79324.6 First- and Second-Order Scattering and Backscattering Enhancement / 79424.7 Memory Effects / 79525 Solitons And Optical Fibers 79725.1 History / 79725.2 KDV (Korteweg–De Vries) Equation for Shallow Water / 79925.3 Optical Solitons in Fibers / 80226 Porous Media, Permittivity, Fluid Permeability Of Shales And Seismic Coda 80726.1 Porous Medium and Shale, Superfracking / 80826.2 Permittivity and Conductivity of Porous Media, Archie’s Law, and Percolation and Fractal / 80926.3 Fluid Permeability and Darcy’s Law / 81126.4 Seismic Coda, P-Wave, S-Wave, and Rayleigh Surface Wave / 81226.5 Earthquake Magnitude Scales / 81326.6 Waveform Envelope Broadening and Coda / 81426.7 Coda in Heterogeneous Earth Excited by an Impulse Source / 81526.8 S-wave Coda and Rayleigh Surface Wave / 819Appendices 821References 913Index 929