Electromagnetic Radiation, Scattering, and Diffraction

Cover
Title Page
Copyright
Contents
About the Authors
Preface
Acknowledgments
1 Maxwell's Equations, Constitutive Relations, Wave Equation, and Polarization
1.1 Introductory Comments
1.2 Maxwell's Equations
1.3 Constitutive Relations
1.4 Frequency Domain Fields
1.5 Kramers-Kronig Relationship
1.6 Vector and Scalar Wave Equations
1.6.1 Vector Wave Equations for EM Fields
1.6.2 Scalar Wave Equations for EM Fields
1.7 Separable Solutions of the Source-Free Wave Equation in Rectangular Coordinates and for Isotropic Homogeneous Media. Plane Waves
1.8 Polarization of Plane Waves, Poincar•e Sphere, and Stokes Parameters
1.8.1 Polarization States
1.8.2 General Elliptical Polarization
1.8.3 Decomposition of a Polarization State into Circularly Polarized Components
1.8.4 Poincare Sphere for Describing Polarization States
1.9 Phase and Group Velocity
1.10 Separable Solutions of the Source-Free Wave Equation in Cylindrical and Spherical Coordinates and for Isotropic Homogeneous Media
1.10.1 Source-Free Cylindrical Wave Solutions
1.10.2 Source-Free Spherical Wave Solutions
References
2 EM Boundary and Radiation Conditions
2.1 EM Field Behavior Across a Boundary Surface
2.2 Radiation Boundary Condition
2.3 Boundary Conditions at a Moving Interface
2.3.1 Nonrelativistic Moving Boundary Conditions
2.3.2 Derivation of the Nonrelativistic Field Transformations
2.3.3 EM Field Transformations Based on the Special Theory of Relativity
2.4 Constitutive Relations for a Moving Medium
References
3 Plane Wave Propagation in Planar Layered Media
3.1 Introduction
3.2 Plane Wave Reection from a Planar Boundary Between Two Di erent Media
3.2.1 Perpendicular Polarization Case
3.2.2 Parallel Polarization Case
3.2.3 Brewster Angle θb
3.2.4 Critical Angle θc
3.2.5 Plane Wave Incident on a Lossy Half Space
3.2.6 Doppler Shift for Wave Reection from a Moving Mirror
3.3 Reection and Transmission of a Plane Wave Incident on a Planar Stratified Isotropic Medium Using a Transmission Matrix Approach
3.4 Plane Waves in Anisotropic Homogeneous Media
3.5 State Space Formulation for Waves in Planar Anisotropic Layered Media
3.5.1 Development of State Space Based Field Equations
3.5.2 Reection and Transmission of Plane Waves at the Interface Between Two Anisotropic Half Spaces
3.5.3 Transmission Type Matrix Analysis of Plane Waves in Multilayered Anisotropic Media
References
4 Plane Wave Spectral Representation for EM Fields
4.1 Introduction
4.2 PWS Development
References
5 Electromagnetic Potentials and Fields of Sources in Unbounded Regions
5.1 Introduction to Vector and Scalar Potentials
5.2 Construction of the Solution for Ā
5.3 Calculation of Fields from Potentials
5.4 Time Dependent Potentials for Sources and Fields in Unbounded Regions
5.5 Potentials and Fields of a Moving Point Charge
5.6 Cerenkov Radiation
5.7 Direct Calculation of Fields of Sources in Unbounded Regions Using a Dyadic Green's Function
5.7.1 Fields of Sources in Unbounded, Isotropic, Homogeneous Media in Terms of a Closed Form Representation of Green's Dyadic, G0
5.7.2 On the Singular Nature of G0(rr) for Observation Points Within the Source Region
5.7.3 Representation of the Green's Dyadic G0 in Terms of an Integral in the Wavenumber (k) Space
5.7.4 Electromagnetic Radiation by a Source in a General Bianisotropic Medium Using a Green's Dyadic Ga in k-Space
References
6 Electromagnetic Field Theorems and Related Topics
6.1 Conservation of Charge
6.2 Conservation of Power
6.3 Conservation of Momentum
6.4 Radiation Pressure
6.5 Duality Theorem
6.6 Reciprocity Theorems and Conservation of Reactions
6.6.1 The Lorentz Reciprocity Theorem
6.6.2 Reciprocity Theorem for Bianisotropic Media
6.7 Uniqueness Theorem
6.8 Image Theorems
6.9 Equivalence Theorems
6.9.1 Volume Equivalence Theorem for EM Scattering
6.9.2 A Surface Equivalence Theorem for EM Scattering
6.9.3 A Surface Equivalence Theorem for Antennas
6.10 Antenna Impedance
6.11 Antenna Equivalent Circuit
6.12 The Receiving Antenna Problem
6.13 Expressions for Antenna Mutual Coupling Based on Generalized Reciprocity Theorems
6.13.1 Circuit Form of the Reciprocity Theorem for Antenna Mutual Coupling
6.13.2 A Mixed Circuit Field Form of a Generalized Reciprocity Theorem for Antenna Mutual Coupling
6.13.3 A Mutual Admittance Expression for Slot Antennas
6.13.4 Antenna Mutual Coupling, Reaction Concept, and Antenna Measurements
6.14 Relation Between Antenna and Scattering Problems
6.14.1 Exterior Radiation by a Slot Aperture Antenna Configuration
6.14.2 Exterior Radiation by a Monopole Antenna Configuration
6.15 Radar Cross Section
6.16 Antenna Directive Gain
6.17 Field Decomposition Theorem
References
7 Modal Techniques for the Analysis of Guided Waves, Resonant Cavities, and Periodic Structures
7.1 On Modal Analysis of Some Guided Wave Problems
7.2 Classification of Modal Fields in Uniform Guiding Structures
7.2.1 TEMz Guided waves
7.3 TMz Guided Waves
7.4 TEz Guided Waves
7.5 Modal Expansions in Closed Uniform Waveguides
7.5.1 TMz Modes
7.5.2 TEz Modes
7.5.3 Orthogonality of Modes in Closed Perfectly Conducting Uniform Waveguides
7.6 Eect of Losses in Closed Guided Wave Structures
7.7 Source Excited Uniform Closed Perfectly Conducting Waveguides
7.8 An Analysis of Some Closed Metallic Waveguides
7.8.1 Modes in a Parallel Plate Waveguide
7.8.2 Modes in a Rectangular Waveguide
7.8.3 Modes in a Circular Waveguide
7.8.4 Coaxial Waveguide
7.8.5 Obstacles and Discontinuities in Waveguides
7.8.6 Modal Propagation Past a Slot in a Waveguide
7.9 Closed and Open Waveguides Containing Penetrable Materials and Coatings
7.9.1 Material-Loaded Closed PEC Waveguide
7.9.2 Material Slab Waveguide
7.9.3 Grounded Material Slab Waveguide
7.9.4 The Goubau Line
7.9.5 Circular Cylindrical Optical Fiber Waveguides
7.10 Modal Analysis of Resonators
7.10.1 Rectangular Waveguide Cavity Resonator
7.10.2 Circular Waveguide Cavity Resonator
7.10.3 Dielectric Resonators
7.11 Excitation of Resonant Cavities
7.12 Modal Analysis of Periodic Arrays
7.12.1 Floquet Modal Analysis of an Infinite Planar Periodic Array of Electric Current Sources
7.12.2 Floquet Modal Analysis of an Infinite Planar Periodic Array of Current Sources Configured in a Skewed Grid
7.13 Higher-Order Floquet Modes and Associated Grating Lobe Circle Diagrams for Infinite Planar Periodic Arrays
7.13.1 Grating Lobe Circle Diagrams
7.14 On Waves Guided and Radiated by Periodic Structures
7.15 Scattering by a Planar Periodic Array
7.15.1 Analysis of the EM Plane Wave Scattering by an Infinite Periodic Slot Array in a Planar PEC Screen
7.16 Finite 1-D and 2-D Periodic Array of Sources
7.16.1 Analysis of Finite 1-D Periodic Arrays for the Case of Uniform Source Distribution and Far Zone Observation
7.16.2 Analysis of Finite 2-D Periodic Arrays for the Case of Uniform Distribution and Far Zone Observation
7.16.3 Floquet Modal Representation for Near and Far Fields of 1-D Nonuniform Finite Periodic Array Distributions
7.16.4 Floquet Modal Representation for Near and Far Fields of 2-D Nonuniform Planar Periodic Finite Array Distributions
References
8 Green's Functions for the Analysis of One-Dimensional Source-Excited Wave Problems
8.1 Introduction to the Sturm-Liouville Form of Di erential Equation for 1-D Wave Problems
8.2 Formulation of the Solution to the Sturm-Liouville Problem via the 1-D Green's Function Approach
8.3 Conditions Under Which the Green's Function Is Symmetric
8.4 Construction of the Green's Function G(x|x')
8.4.1 General Procedure to Obtain G(x|x')
8.5 Alternative Simplified Construction of G(x|x') Valid for the SymmetricCase
8.6 On the Existence and Uniqueness of G(x|x')
8.7 Eigenfunction Expansion Representation for G(x|x')
8.8 Delta Function Completeness Relation and the Construction of Eigenfunctions from G(x|x') = U(x<)T(x)/W
8.9 Explicit Representation of G(x|x') Using Step Functions
References
9 Applications of One-Dimensional Green's Function Approach for the Analysis of Single and Coupled Set of EM Source Excited Transmission Lines
9.1 Introduction
9.2 Analytical Formulation for a Single Transmission Line Made Up of Two Conductors
9.3 Wave Solution for the Two Conductor Lines When There Are No Impressed Sources Distributed Anywhere Within the Line
9.4 Wave Solution for the Case of Impressed Sources Placed Anywhere on a Two Conductor Line
9.5 Excitation of a Two Conductor Transmission Line by an Externally Incident lectromagnetic Wave
9.6 A Matrix Green's Function Approach for Analyzing a Set of Coupled Transmission Lines
9.7 Solution to the Special Case of Two Coupled Lines (N = 2) with Homogeneous Dirichlet or Neumann End Conditions
9.8 Development of the Multiport Impedance Matrix for a Set of Coupled Transmission Lines
9.9 Coupled Transmission Line Problems with Voltage Sources and Load Impedances at the End Terminals
References
10 Green's Functions for the Analysis of Two- and Three-Dimensional Source-Excited Scalar and EM Vector Wave Problems
10.1 Introduction
10.2 General Formulation for Source-Excited 3-D Separable Scalar Wave Problems Using Green's Functions
10.3 General Procedure for Construction of Scalar 2-D and 3-D Green’s Function in Rectangular Coordinates
10.4 General Procedure for Construction of Scalar 2-D and 3-D Green's Functions in Cylindrical Coordinates
10.5 General Procedure for Construction of Scalar 3-D Green's Functions in Spherical Coordinates
10.6 General Formulation for Source-Excited 3-D Separable EM Vector Wave Problems Using Dyadic Green's Functions
10.7 Some Specific Green's Functions for 2-D Problems
10.7.1 Fields of a Uniform Electric Line Source
10.7.2 Fields of an Infinite Periodic Array of Electric Line Sources
10.7.3 Line Source-Excited PEC Circular Cylinder Green's Function
10.7.4 A Cylindrical Wave Series Expansion for Ho(2)(k|p-p|)
10.7.5 Line Source Excitation of a PEC Wedge
10.7.6 Line Source Excitation of a PEC Parallel Plate Waveguide
10.7.7 The Fields of a Line Dipole Source
10.7.8 Fields of a Magnetic Line Source on an Infinite Planar Impedance Surface
10.7.9 Fields of a Magnetic Line Dipole Source on an Infinite Planar Impedance Surface
10.7.10 Circumferentially Propagating Surface Fields of a Line Source Excited Impedance Circular Cylinder
10.7.11 Analysis of Circumferentially Propagating Waves for a Line Dipole Source-Excited Impedance Circular Cylinder
10.7.12 Fields of a Traveling Wave Line Source
10.7.13 Traveling Wave Line Source Excitation of a PEC Wedge and a PEC Cylinder
10.8 Examples of Some Alternative Representations of Green's Functions for Scalar 3-D Point Source-Excited Cylinders, Wedges and Spheres
10.8.1 3-D Scalar Point Source-Excited Circular Cylinder Green's Function
10.8.2 3-D Scalar Point Source Excitation of a Wedge
10.8.3 Angularly and Radially Propagating 3-D Scalar Point Source Green's Function for a Sphere
10.8.4 Kontorovich{Lebedev Transform and MacDonald Based Approaches for Constructing an Angularly Propagating 3-D Point Source Scalar Wedge Green's Function
10.8.5 Analysis of the Fields of a Vertical Electric or Magnetic Current Point Source on a PEC Sphere
10.9 General Procedure for Construction of EM Dyadic Green's Functions for Source-Excited Separable Canonical Problems via Scalar Green's Functions
10.9.1 Summary of Procedure to Obtain the EM Fields of Arbitrarily Oriented Point Sources Exciting Canonical Separable Configurations
10.10 Completeness of the Eigenfunction Expansion of the Dyadic Green's Function at the Source Point
References
11 Method of Factorization and the Wiener{Hopf Technique for Analyzing Two-Part EM Wave Problems
11.1 The Wiener{Hopf Procedure
11.2 The Dual Integral Equation Approach
11.3 The Jones Method
References
12 Integral Equation-Based Methods for the Numerical Solution of Nonseparable EM Radiation and Scattering Problems
12.1 Introduction
12.2 Boundary Integral Equations
12.2.1 The Electric Field Integral Equation (EFIE)
12.2.2 The Magnetic Field Integral Equation (MFIE)
12.2.3 Combined Field and Combined Source Integral Equations
12.2.4 Impedance Boundary Condition
12.2.5 Boundary Integral Equation for a Homogeneous Material Volume
12.3 Volume Integral Equations
12.4 The Numerical Solution of Integral Equations
12.4.1 The Minimum Square-Error Method
12.4.2 The Method of Moments (MoM)
12.4.3 Simplification of the MoM Impedance Matrix Integrals
12.4.4 Expansion and Testing Functions
12.4.5 Low-Frequency Break-Down
12.5 Iterative Solution of Large MoM Matrices
12.5.1 Fast Iterative Solution of MoM Matrix Equations
12.5.2 The Fast Multipole Method (FMM)
12.5.3 Multilevel FMM and Fast Fourier Transform FMM
12.6 Antenna Modeling with the Method of Moments
12.7 Aperture Coupling with the Method of Moments
12.8 Physical Optics Methods
12.8.1 Physical Optics for a PEC Surface
12.8.2 Iterative Physical Optics
References
13 Introduction to Characteristic Modes
13.1 Introduction
13.2 Characteristic Modes from the EFIE for a Conducting Surface
13.2.1 Electric Field Integral Equation and Radiation Operator
13.2.2 Eigenfunctions of the Electric Field Radiation Operator
13.2.3 Characteristic Modes from the EFIE Impedance Matrix
13.3 Computation of Characteristic Modes
13.4 Solution of the EFIE Using Characteristic Modes
13.5 Tracking Characteristic Modes with Frequency
13.6 Antenna Excitation Using Characteristic Modes
References
14 Asymptotic Evaluation of Radiation and Di raction Type Integrals for High Frequencies
14.1 Introduction
14.2 Steepest Descent Techniques for the Asymptotic Evaluation of Radiation Integrals
14.2.1 Topology of the Exponent in the Integrand Containing a First-Order Saddle Point
14.2.2 Asymptotic Evaluation of Integrals Containing a First-Order Saddle Point in Its Integrand Which Is Free of Singularities
14.2.3 Asymptotic Evaluation of Integrals Containing a Higher-Order Saddle Point in Its Integrand Which Is Free of Singularities
14.2.4 Pauli-Clemmow Method (PCM) for the Asymptotic Evaluation of Integrals Containing a First-Order Saddle Point Near a Simple Pole Singularity
14.2.5 Van der Waerden Method (VWM) for the Asymptotic Evaluation of Integrals Containing a First-Order Saddle Point Near a Simple Pole Singularity
14.2.6 Relationship Between PCM and VWM Leading to a Generalized PCM (or GPC) Solution
14.2.7 An Extension of PCM for Asymptotic Evaluation of an Integral Containing a First-Order Saddle Point and a Nearby Double Pole
14.2.8 An Extension of PCM for Asymptotic Evaluation of an Integral Containing a First-Order Saddle Point and Two Nearby First-Order Poles
14.2.9 An Extension of VWM for Asymptotic Evaluation of an Integral Containing a First-Order Saddle Point and a Nearby Double Pole
14.2.10 Nonuniform Asymptotic Evaluation of an Integral Containing a Saddle Point and a Branch Point
14.2.11 Uniform Asymptotic Evaluation of an Integral Containing a Saddle Point and a Nearby Branch Point
14.3 Asymptotic Evaluation of Integrals with End Points
14.3.1 Watson's Lemma for Integrals
14.3.2 Generalized Watson's Lemma for Integrals
14.3.3 Integration by Parts for Asymptotic Evaluation of a Class of Integrals
14.4 Asymptotic Evaluation of Radiation Integrals Based on the Stationary Phase Method
14.4.1 Stationary Phase Evaluation of 1-D Infinite Integrals
14.4.2 Nonuniform Stationary Phase Evaluation of 1-D Integrals with End Points
14.4.3 Uniform Stationary Phase Evaluation of 1-D Integrals with a Nearby End Point
14.4.4 Nonuniform Stationary Phase Evaluation of 2-D Infinite Integrals
References
15 Physical and Geometrical Optics
15.1 The Physical Optics (PO) Approximation for PEC Surfaces
15.2 The Geometrical Optics (GO) Ray Field
15.3 GO Transport Singularities
15.4 Wavefronts, Stationary Phase, and GO
15.5 GO Incident and Reected Ray Fields
15.6 Uniform GO Valid at Smooth Caustics
References
16 Geometrical and Integral Theories of Diraction
16.1 Geometrical Theory of Di raction and Its Uniform Version (UTD)
16.2 UTD for an Edge in an Otherwise Smooth PEC Surface
16.3 UTD Slope Diraction for an Edge
16.4 An Alternative Uniform Solution (the UAT) for Edge Di raction
16.5 UTD Solutions for Fields of Sources in the Presence of Smooth PEC Convex Surfaces
16.5.1 UTD Analysis of the Scattering by a Smooth, Convex Surface
16.5.2 UTD for the Radiation by Antennas on a Smooth, Convex Surface
16.5.3 UTD Analysis of the Surface Fields of Antennas on a Smooth, Convex Surface
16.6 UTD for a Vertex
16.7 UTD for Edge-Excited Surface Rays
16.8 The Equivalent Line Current Method (ECM)
16.8.1 Line Type ECM for Edge-Diracted Ray Caustic Field Analysis
16.9 Equivalent Line Current Method for Interior PEC Waveguide Problems
16.9.1 TEy Case
16.9.2 TMy Case
16.10 The Physical Theory of Di raction (PTD)
16.10.1 PTD for Edged Bodies - A Canonical Edge Di raction Problem in the PTD Development
16.10.2 Details of PTD for 3-D Edged Bodies
16.10.3 Reduction of PTD to 2-D Edged Bodies
16.11 On the PTD for Aperture Problems
16.12 Time-Domain Uniform Geometrical Theory of Di raction (TD-UTD)
16.12.1 Introductory Comments
16.12.2 Analytic Time Transform (ATT)
16.12.3 TD-UTD for a General PEC Curved Wedge
References
17 Development of Asymptotic High-Frequency Solutions to Some Canonical Problems
17.1 Introduction
17.2 Development of UTD Solutions for Some Canonical Wedge Di raction Problems
17.2.1 Scalar 2-D Line Source Excitation of a Wedge
17.2.2 Scalar Plane Wave Excitation of a Wedge
17.2.3 Scalar Spherical Wave Excitation of a Wedge
17.2.4 EM Plane Wave Excitation of a PEC Wedge
17.2.5 EM Conical Wave Excitation of a PEC Wedge
17.2.6 EM Spherical Wave Excitation of a PEC Wedge
17.3 Canonical Problem of Slope Diraction by a PEC Wedge
17.4 Development of a UTD Solution for Scattering by a Canonical 2-D PEC Circular Cylinder and Its Generalization to a Convex Cylinder
17.4.1 Field Analysis for the Shadowed Part of the Transition Region
17.4.2 Field Analysis for the Illuminated Part of the Transition Region
17.5 A Collective UTD for an Ecient Ray Analysis of the Radiation by Finite Conformal Phased Arrays on Infinite PEC Circular Cylinders
17.5.1 Finite Axial Array on a Circular PEC Cylinder
17.5.2 Finite Circumferential Array on a Circular PEC Cylinder
17.6 Surface, Leaky, and Lateral Waves Associated with Planar Material Boundaries
17.6.1 Introduction
17.6.2 The EM Fields of a Magnetic Line Source on a Uniform Planar Impedance Surface
17.6.3 EM Surface and Leaky Wave Fields of a Uniform Line Source over a Planar Grounded Material Slab
17.6.4 An Analysis of the Lateral Wave Phenomena Arising in the Problem of a Vertical Electric Point Current Source over a Dielectric Half Space
17.7 Surface Wave Di raction by a Planar, Two-Part Impedance Surface: Development of a Ray Solution
17.7.1 TEz Case
17.7.2 TMz Case
17.8 Ray Solutions for Special Cases of Discontinuities in Nonconducting or Penetrable Boundaries
References
18 EM Beams and Some Applications
18.1 Introduction
18.2 Astigmatic Gaussian Beams
18.2.1 Paraxial Wave Equation Solutions
18.2.2 2-D Beams
18.2.3 3-D Astigmatic Gaussian Beams
18.2.4 3-D Gaussian Beam from a Gaussian Aperture Distribution
18.2.5 Reection of Astigmatic Gaussian Beams (GBs)
18.3 Complex Source Beams and Relation to GBs
18.3.1 Introduction to Complex Source Beams (GBs)
18.3.2 Complex Source Beam from Scalar Green's Function
18.3.3 Representation of Arbitrary EM Fields by a CSB Expansion
18.3.4 Edge Di raction of an Incident CSB by a Curved Conducting Wedge
18.4 Pulsed Complex Source Beams in the Time Domain
References
A Coordinate Systems, Vectors, and Dyadics
B The Total Time Derivative of a Time Varying Flux Density Integrated Over a Moving Surface
C The Delta Function
D Transverse Fields in Terms of Axial Field Components for TMz and TEz Waves Guided Along z
E Two Di erent Representations for Partial Poisson Sum Formulas and Their Equivalence
F Derivation of 1-D Green's Second Identity
G Green's Second Identity for 3-D Scalar, Vector, and Vector-Dyadic Wave Fields
H Formal Decomposition and Factorization Formulas
I On the Transition Function F(+ka)
J On the Branch Cuts Commonly Encountered in the Evaluation of Spectral Wave Integrals
K On the Steepest Descent Path (SDP) for Spectral Wave Integrals
L Parameters Used in the Uniform GO Solution for the Lit and Shadow Sides of a Smooth Caustic
M Asymptotic Approximations of Hankel Functions for Large Argument and Various Orders
Index
Series Page
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