Electromagnetic Scattering

1 Integral Representations for Fields.- 1.1 Preamble.- 1.2 Dyadic Calculus.- 1.3 The Free-space Dyadic Green’s Function in R3.- 1.4 The Franz Representation for an Interior Problem in R3.- 1.5 The Franz Representations for Scattered Fields in R3.- 1.6 The Stratton-Chu Representation in R3.- 1.7 The Helmholtz Representation for Acoustic Fields.- 1.8 Volume Scattering: The Born Approximation.- 1.9 Rellich’s Uniqueness Theorem.- 2 Polarization.- 2.1 Preliminary.- 2.2 Representation of Polarization.- 2.2.1 Classical Method.- 2.2.2 Alternative Method.- 2.2.3 Relationship between (E?, E?) and (Ex, Ey).- 2.3 Stokes Vector for a Monochromatic Electric Field.- 2.4 Change of Polarization Basis.- 2.5 Superposition of Circularly Polarized Waves.- 2.6 Coherency Matrix for Quasi-Monochromatic Waves.- 2.6.1 Spinors, Trace.- 2.6.2 Coherency Matrix.- 2.6.3 Relationship between the Coherency Matrix and the Stokes Vector.- 2.7 Degree of Polarization.- 2.8 Decomposition of Partially Polarized Waves.- 3 Scattering Matrix.- 3.1 Scattering and Polarization Geometries.- 3.2 Equivalent Induced Surface Current Densities.- 3.3 Scattering-and Reflection-Coefficient Matrices.- 3.4 The Reciprocity Relation for $$ /mathop{S}/limits^{ = } (k{{/Omega }_{2}}|k{{/Omega }_{1}}) $$.- 3.5 Backscatter from Large Smooth and Convex Scatterers.- 3.6 The Method of Stationary Phase.- 4 Optimal Polarizations.- 4.1 A Short Historical Sketch.- 4.2 Scattering Geometry and the S-matrix in Backscatter.- 4.3 Optimal Polarizations in Backscatter.- 4.4 Polarizations for Co-Pol Nulls.- 4.5 Polarizations for Cross-Pol Nulls.- 4.6 Optimal Polarization in Bistatic Scattering.- 4.6.1 Bistatic and Reciprocal Scattering Geometries.- 4.6.2 Bistatic Case.- 4.7 A Compact Representation in V4.- 5 Scattering from Moderately Rough Surfaces.- 5.1 Problem Formulation.- 5.2 Gaussian Statistics.- 5.3 ?mn(?x,?y) in Terms of the Correlation Function.- 5.4 Radar Cross Section in Bistatic Scattering.- 6 Scattering from a Stratified Medium.- 6.1 Scattering Geometry.- 6.2 Free-space Dyadic Green’s Function.- 6.3 Dyadic Green’s Functions.- 6.4 Backscattered Field.- 7 Review of Potential Theory.- 7.1 Preliminary.- 7.2 Single-layer Potential.- 7.3 Double-layer Potential.- 7.3.1 Direct Value.- 7.3.2 Boundary Values.- 7.4 Conjugate Double-layer Potential.- 7.5 Normal Derivative of a Double-layer Potential.- 7.6 Tangential Derivatives.- 8 Fredholm Alternative.- 8.1 Algebraic Alternative.- 8.2 Fredholm Alternative.- 8.3 Examples.- 9 Integral Equation Method.- 9.1 Preamble.- 9.2 Basic Concepts.- 9.3 Exterior Dirichlet Problem.- 9.3.1 Double-layer Potential Representation.- 9.3.2 Single-layer Potential Representation.- 9.3.3 Related Interior Eigenvalues.- 9.3.4 The PBW Representation.- 9.4. Exterior Neumann Problem in R2.- 9.4.1 Single-layer Potential Representation.- 9.4.2 The Kussmaul Representation.- 9.5 Electromagnetic Scattering in R2.- 9.5.1 Case of E-Polarization.- 9.5.2 Case of H-Polarization.- 9.6 Summary.- 9.7 Linear Combination Technique.- 9.8 Electromagnetic Scattering in R3.- 9.9 Simple Numerical Examples.- 10 Exterior Resonant Frequencies.- 10.1 Basic Concept.- 10.2 Adaptation of the Gurjuoy-Saxon Approach.- 10.3 Exterior Resonant Frequencies of a Sphere and a Cylinder.- 10.3.1 Sphere.- 10.3.2 Cylinder.- 10.4 Via the Integral Equation Method.- 10.5 Scattering Operator in Electromagnetic Scattering.- 10.5.1 Reciprocity Relation.- 10.5.2 Scattering Operator in Bistatic Scattering.- 10.6 Dyadic Absorption Operator.- 10.7 Forward Scattering Theorem.- A Diagonalization of an S-matrix.- B A Deficient System of Equations.- C Reflection-coefficient Matrix.- D Statistical Averages.- D.1 One-dimensional Case.- D.2 Two-dimensional Case.- D.3 Three-dimensional Case.- E The Cauchy Integral and Potential Functions.- F Decomposition of a Plane Wave.