0.1 Introduction The present volume is about the physics of electromagnetic scattering, not mathematics, and is intended as a reference book for engineering and physics students as well as researchers in electromagnetic scattering. Although the subject is on electromagnetic scattering, acoustic or scalar scattering will be discussed occasionally when it is deemed helpful and advantageous. In the current decade we are witnessing an emergence of inverse scattering theory. Before we embark on this exciting journey, perhaps this is an appropriate time to summarize and assess in one volume some of…mehr
0.1 Introduction The present volume is about the physics of electromagnetic scattering, not mathematics, and is intended as a reference book for engineering and physics students as well as researchers in electromagnetic scattering. Although the subject is on electromagnetic scattering, acoustic or scalar scattering will be discussed occasionally when it is deemed helpful and advantageous. In the current decade we are witnessing an emergence of inverse scattering theory. Before we embark on this exciting journey, perhaps this is an appropriate time to summarize and assess in one volume some of the important re sults of electromagnetic scattering which have been found in recent decades. Since the end of WW II two significant physical phenomena in electromag netic scattering, optimal polarization and exterior resonant frequencies, have been discovered and a powerful mathematical technique, called the integral equation method, has been incorporated. These physical quantities, which characterize the scattered field for a given scatterer, are not directly observ able but can only be extracted by mathematical means from the measured scattering data. They are given special attention.
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.
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.
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