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Modern electromagnetic scattering theory with applications / Andrey V. Osipov, Microwave and Radar Institute, German Aerospace Center (DLR), Germany, Sergei A. Tretyakov, School of Electrical Engineering, Aalto University, Finland.

By: Osipov, Andrey (Andrey V.) [author.].
Contributor(s): Tretyakov, Sergei | IEEE Xplore (Online Service) [distributor.] | Wiley [publisher.].
Material type: materialTypeLabelBookPublisher: Chichester, West Sussex : Wiley, 2017Distributor: [Piscataqay, New Jersey] : IEEE Xplore, [2017]Description: 1 PDF (xviii, 806 pages) : illustrations.Content type: text Media type: electronic Carrier type: online resourceISBN: 9781119004639.Subject(s): Electromagnetic waves -- Scattering | Electromagnetic fields | Radar cross sectionsGenre/Form: Electronic books.DDC classification: 539.2 Online resources: Abstract with links to resource Also available in print.
Contents:
Preface xi -- Acknowledgements xiii -- List of Abbreviations xv -- 1 Introduction 1 -- 1.1 Scattering and Diffraction Theory 1 -- 1.2 Books on Related Subjects 3 -- 1.3 Concept and Outline of the Book 5 -- References 8 -- 2 Fundamentals of Electromagnetic Scattering 11 -- 2.1 Introduction 11 -- 2.2 Fundamental Equations and Conditions 11 -- 2.2.1 Maxwell's Equations 12 -- 2.2.2 Constitutive Relations 12 -- 2.2.3 Time-harmonic Scattering Problems 19 -- 2.3 Approximate Boundary Conditions 26 -- 2.3.1 Impedance Boundary Conditions 26 -- 2.3.2 Generalized (Higher-order) Impedance Boundary Conditions 31 -- 2.3.3 Sheet Transition Conditions 32 -- 2.4 Fundamental Properties of Time-harmonic Electromagnetic Fields 35 -- 2.4.1 Energy Conservation and Uniqueness 35 -- 2.4.2 Reciprocity 39 -- 2.5 Basic Solutions of Maxwell's Equations in Homogeneous Isotropic Media 42 -- 2.5.1 Plane, Spherical, and Cylindrical Waves 43 -- 2.5.2 Electromagnetic Potentials and Fields of External Currents 46 -- 2.5.3 Tensor Green's Function 50 -- 2.5.4 E and H Modes 54 -- 2.5.5 Fields with Translational Symmetry 58 -- 2.6 Electromagnetic Formulation of Huygens' Principle 61 -- 2.6.1 Compact Scatterers 62 -- 2.6.2 Cylindrical Scatterers 67 -- 2.7 Problems 70 -- References 84 -- 3 Far-field Scattering 87 -- 3.1 Introduction 87 -- 3.2 Scattering Cross Section 87 -- 3.2.1 Monostatic and Bistatic, Backscattering and Forward-scattering Cross Sections, Differential, Total, Absorption, and Extinction Cross Sections 87 -- 3.2.2 Scattering Width 91 -- 3.2.3 Backscattering from Impedance-matched Bodies 93 -- 3.3 Scattering Matrix 95 -- 3.3.1 Definition 95 -- 3.3.2 Scattering Matrix in Spherical Coordinates 97 -- 3.3.3 Scattering Matrix in the Plane of Scattering Coordinates 99 -- 3.4 Far-field Coefficient 101 -- 3.4.1 Integral Representations and Far-field Conditions 102 -- 3.4.2 Reciprocity of Scattered Fields 106 -- 3.4.3 Forward Scattering 108 -- 3.4.4 Cylindrical Bodies 113 -- 3.5 Scattering Regimes 120.
3.5.1 Resonant-size Scatterers 120 -- 3.5.2 Electrically Large Scatterers 121 -- 3.6 Electrically Small Scatterers 125 -- 3.6.1 Physics of Dipole Scattering 126 -- 3.6.2 Dipole Scattering in Terms of Polarizability Tensors 129 -- 3.6.3 Magneto-dielectric Ellipsoid 131 -- 3.6.4 Rotationally Symmetric Particles 137 -- 3.7 Problems 148 -- References 162 -- 4 Planar Interfaces 165 -- 4.1 Introduction 165 -- 4.2 Interface of Two Homogeneous Semi-infinite Media 167 -- 4.2.1 Reflection and Transmission Coefficients 167 -- 4.2.2 Brewster's Angle 173 -- 4.2.3 Total Internal Reflection 173 -- 4.2.4 Interfaces with Double-negative Materials 176 -- 4.2.5 Surface Waves 177 -- 4.2.6 Vector Solution of Reflection and Transmission Problems 179 -- 4.3 Arbitrary Number of Planar Layers 182 -- 4.3.1 Solution by the Method of Characteristic Matrices 182 -- 4.3.2 Discussion and Limiting Cases 189 -- 4.4 Reflection and Transmission of Cylindrical and Spherical Waves 195 -- 4.4.1 Excitation by a Linear Electric Current 195 -- 4.4.2 Excitation by an Electric Dipole 202 -- 4.5 A Layer between Homogeneous Half-spaces 207 -- 4.5.1 Different Half-spaces 207 -- 4.5.2 A PEC-backed Layer 213 -- 4.5.3 Layer Immersed in a Homogeneous Space 215 -- 4.6 Modeling with Approximate Boundary Conditions 224 -- 4.6.1 Accuracy of Impedance Boundary Conditions 225 -- 4.6.2 Accuracy of Transition Boundary Conditions 229 -- 4.6.3 Impedance-matched Surface 232 -- 4.7 Problems 235 -- References 249 -- 5 Wedges 251 -- 5.1 Introduction 251 -- 5.2 The Perfectly Conducting Wedge 253 -- 5.2.1 Formulation of Boundary Value Problem 254 -- 5.2.2 Solution by Separation of Variables 256 -- 5.2.3 Fields and Currents at the Edge 258 -- 5.2.4 Reduction to an Integral Form 260 -- 5.2.5 Special Cases 262 -- 5.2.6 Edge-diffracted and GO Components. Diffraction Coefficient 266 -- 5.3 Scattering from a Half-plane (Solution by Factorization Method) 271 -- 5.3.1 Statement of the Problem 271 -- 5.3.2 Functional Equation 273 -- 5.3.3 Factorization and Solution 274.
5.3.4 Scattered Field Far from the Edge 276 -- 5.4 The Impedance Wedge 279 -- 5.4.1 Boundary Value Problem, Sommerfeld's Integrals, and Functional Equations 279 -- 5.4.2 Normal Incidence (Maliuzhinets' Solution) 288 -- 5.4.3 Unit Surface Impedance 297 -- 5.4.4 Further Exactly Solvable Cases 300 -- 5.5 High-frequency Scattering from Impenetrable Wedges 306 -- 5.5.1 GO Components and Surface Waves 307 -- 5.5.2 Edge-diffracted Field, Diffraction Coefficient, and Scattering Widths 310 -- 5.5.3 Uniform Asymptotic Approximations 316 -- 5.5.4 GTD/UTD Formulation 319 -- 5.6 Behavior of Electromagnetic Fields at Edges 322 -- 5.6.1 Determining the Degree of Singularity 322 -- 5.6.2 Analytical Structure of Meixner's Series 328 -- 5.7 Problems 329 -- References 336 -- 6 Circular Cylinders and Convex Bodies 339 -- 6.1 Introduction 339 -- 6.2 Perfectly Conducting Cylinders: Separation of Variables and Series Solution 340 -- 6.2.1 Separation of Variables 342 -- 6.2.2 Satisfying the Boundary Conditions 342 -- 6.2.3 Scattered Fields 343 -- 6.2.4 Numerical Examples 345 -- 6.3 Homogeneous Cylinders under Normal Illumination 350 -- 6.3.1 Field Equations and Boundary Conditions 350 -- 6.3.2 Rayleigh Series Solution 351 -- 6.3.3 Numerical Examples 352 -- 6.4 Watson's Transformation and High-frequency Approximations 354 -- 6.4.1 Watson's Transformation 355 -- 6.4.2 Alternative Solution by Separation of Variables 358 -- 6.4.3 High-frequency Approximations 360 -- 6.4.4 Surface Currents in the Penumbra Region. Fock's Functions 369 -- 6.5 Coated and Impedance Cylinders under Oblique Illumination 375 -- 6.5.1 PEC Cylinder with Magneto-dielectric Coating 376 -- 6.5.2 Impedance Cylinder 383 -- 6.6 Extension to Generally Shaped Convex Impedance Bodies 392 -- 6.6.1 Fock's Principle of the Local Field in the Penumbra Region 393 -- 6.6.2 Asymptotic Solution for the Field on the Surface of Circular Impedance Cylinders under Oblique Illumination 396 -- 6.6.3 Fock- and GTD-type Solutions for Electrically Large Convex Impedance Bodies 398.
6.7 Problems 403 -- References 411 -- 7 Spheres 412 -- 7.1 Introduction 412 -- 7.2 Exact Solution for a Multilayered Sphere 414 -- 7.2.1 Formulation of the Problem in Terms of Debye's Potentials 415 -- 7.2.2 Derivation of the Series Solution 417 -- 7.2.3 Solution for Impedance Boundary Conditions 427 -- 7.3 Physics of Scattering from Spheres 429 -- 7.3.1 Classification of Scattering 430 -- 7.3.2 Spiral Waves 436 -- 7.3.3 Debye's Expansions for Homogeneous Spheres 438 -- 7.3.4 Waves in Electrically Large Homogeneous Low-absorption Spheres 442 -- 7.4 Scattered Field in the Far Zone 463 -- 7.4.1 Far-field Coefficient, Scattering Cross Sections, and Polarization Structure. Approximations for Electrically Large Spheres 463 -- 7.4.2 Electrically Small Spheres: Dipole, Quasi-static, and Resonance Approximations 471 -- 7.4.3 PEC Spheres 479 -- 7.4.4 Core-shell Spheres 483 -- 7.4.5 Impedance Spheres 488 -- 7.5 Far-field Scattering from Homogeneous Spheres 493 -- 7.5.1 Exact Solution and Limiting Cases 494 -- 7.5.2 Electrically Small Lossy Spheres 495 -- 7.5.3 Electrically Small Low-absorption Spheres 499 -- 7.5.4 Electrically Large Lossy Spheres: Relation to the Impedance Sphere and the Role of Absorption 506 -- 7.5.5 Electrically Large Low-absorption Spheres: Light Scattering from Water Droplets 513 -- 7.6 Metamaterial Effects in Scattering from Spheres 542 -- 7.6.1 Small Spheres 542 -- 7.6.2 Invisibility Cloak 546 -- 7.7 Problems 552 -- References 562 -- 8 Method of Physical Optics 565 -- 8.1 Introduction 565 -- 8.1.1 On Numerical Techniques for Studying Scattering from Arbitrary-shaped Bodies 565 -- 8.1.2 PO as one of the Approximate Analytical Techniques 566 -- 8.1.3 Structure of the Chapter 567 -- 8.2 Principles and General Solution 567 -- 8.2.1 Principles of PO 567 -- 8.2.2 Derivation of PO Solutions 569 -- 8.2.3 PO for Cylindrical Bodies 573 -- 8.3 Transmission through Apertures 575 -- 8.3.1 PO Solution 575 -- 8.3.2 GO Rays and Fresnel Zones 576 -- 8.3.3 Contribution from the Rim of the Aperture: Edge-diffracted Rays 582.
8.4 Scattering from Curved Surfaces 594 -- 8.4.1 Fock's Reflection Formula 594 -- 8.4.2 Application to a Spherical Segment 600 -- 8.4.3 Reflection Formula in the Far-field Region 605 -- 8.4.4 Diffraction by an Edge in a Non-metallic Surface 609 -- 8.5 Advantages and Limitations of Physical Optics 615 -- 8.6 Problems 616 -- References 632 -- 9 Physical Optics Solutions of Canonical Problems 634 -- 9.1 Introduction 634 -- 9.2 Vertices 635 -- 9.2.1 Vertex on an Edge of a Thin Plate 637 -- 9.2.2 Apex of a Pyramid 641 -- 9.2.3 Tip of an Elliptic Cone 643 -- 9.3 Electrically Large Plates 652 -- 9.3.1 Arbitrarily Shaped Plates 653 -- 9.3.2 Circular Disc 658 -- 9.3.3 Polygonal Plates 663 -- 9.3.4 Far-field Patterns of Polygonal Plates and Apertures 667 -- 9.4 Bodies of Revolution 671 -- 9.4.1 PO Solution for Bodies of Revolution 672 -- 9.4.2 Imperfectly Reflecting Bodies under Axial Illumination 675 -- 9.4.3 PEC Bodies under Oblique Illumination 677 -- 9.4.4 Axial Backscattering 678 -- 9.4.5 Examples 684 -- 9.5 Problems 689 -- References 712 -- A Definitions and Useful Relations of Vector Analysis and Differential Geometry 714 -- A.1 Vector Algebra 714 -- A.2 Vector Analysis 716 -- A.3 Vectors and Vector Differential Operators in Orthogonal Curvilinear Coordinates 717 -- A.3.1 General Orthogonal Curvilinear Coordinates 717 -- A.3.2 Spherical Coordinates 718 -- A.4 Curves and Surfaces in Space 720 -- A.4.1 Curves 720 -- A.4.2 Surfaces 720 -- A.5 Problems 722 -- References 724 -- B Fresnel Integral and Related Functions 725 -- B.1 Fresnel Integral 725 -- B.2 Relation to the Error Function 728 -- B.3 Transition Functions of Uniform Theories of Diffraction 730 -- B.4 Problems 731 -- References 732 -- C Principles of Complex Integration 733 -- C.1 Introduction 733 -- C.2 Deforming the Integration Contour 734 -- C.2.1 Basic Facts about Functions of a Complex Variable 734 -- C.2.2 Integrals over Infinite Contours 736 -- C.3 Steepest Descent Method 737 -- C.3.1 Steepest Descent Path 738.
C.3.2 Saddle Point Contribution 739 -- C.3.3 Pole Singularity near the Saddle Point 741 -- C.3.4 Further Cases 742 -- C.4 Problems 743 -- References 745 -- D The Stationary Phase Method 746 -- D.1 Introduction 746 -- D.2 One-dimensional Integrals 746 -- D.2.1 No Stationary Points on the Integration Interval 747 -- D.2.2 Isolated Stationary Points 748 -- D.2.3 Two Coalescing Stationary Points 751 -- D.3 Two-dimensional Integrals 756 -- D.3.1 Stationary Point in the Integration Domain 756 -- D.3.2 Stationary Point near the Boundary of the Integration Domain 758 -- D.3.3 Contribution from the Boundary of the Integration Domain 760 -- D.3.4 Kontorovich's Formula 763 -- D.3.5 Integrand Vanishing on the Boundary 765 -- D.3.6 Summary of the Two-dimensional Stationary-phase Method 766 -- D.4 Problems 766 -- References 768 -- E Asymptotic Approximations of Bessel Functions of Large Argument and Arbitrary Order 770 -- E.1 Introduction 770 -- E.1.1 Basic Definitions and Properties 770 -- E.1.2 Large-argument Approximations (|z| ?a 1) 772 -- E.1.3 Content of the Appendix 775 -- E.2 Debye's Asymptotic Approximations 776 -- E.2.1 Debye's Method 776 -- E.2.2 WKB Approximation 778 -- E.2.3 Bessel Functions on the Complex � Plane 791 -- E.3 Almost Equal Argument and Order 795 -- E.3.1 Approximations in Terms of Airy Functions 796 -- E.3.2 Approximations in Terms of Normalized Airy Functions 797 -- E.3.3 Zeros in the Neighborhood of the Points � = <<z 798 -- References 799 -- Index 801.
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Includes bibliographical references and index.

Preface xi -- Acknowledgements xiii -- List of Abbreviations xv -- 1 Introduction 1 -- 1.1 Scattering and Diffraction Theory 1 -- 1.2 Books on Related Subjects 3 -- 1.3 Concept and Outline of the Book 5 -- References 8 -- 2 Fundamentals of Electromagnetic Scattering 11 -- 2.1 Introduction 11 -- 2.2 Fundamental Equations and Conditions 11 -- 2.2.1 Maxwell's Equations 12 -- 2.2.2 Constitutive Relations 12 -- 2.2.3 Time-harmonic Scattering Problems 19 -- 2.3 Approximate Boundary Conditions 26 -- 2.3.1 Impedance Boundary Conditions 26 -- 2.3.2 Generalized (Higher-order) Impedance Boundary Conditions 31 -- 2.3.3 Sheet Transition Conditions 32 -- 2.4 Fundamental Properties of Time-harmonic Electromagnetic Fields 35 -- 2.4.1 Energy Conservation and Uniqueness 35 -- 2.4.2 Reciprocity 39 -- 2.5 Basic Solutions of Maxwell's Equations in Homogeneous Isotropic Media 42 -- 2.5.1 Plane, Spherical, and Cylindrical Waves 43 -- 2.5.2 Electromagnetic Potentials and Fields of External Currents 46 -- 2.5.3 Tensor Green's Function 50 -- 2.5.4 E and H Modes 54 -- 2.5.5 Fields with Translational Symmetry 58 -- 2.6 Electromagnetic Formulation of Huygens' Principle 61 -- 2.6.1 Compact Scatterers 62 -- 2.6.2 Cylindrical Scatterers 67 -- 2.7 Problems 70 -- References 84 -- 3 Far-field Scattering 87 -- 3.1 Introduction 87 -- 3.2 Scattering Cross Section 87 -- 3.2.1 Monostatic and Bistatic, Backscattering and Forward-scattering Cross Sections, Differential, Total, Absorption, and Extinction Cross Sections 87 -- 3.2.2 Scattering Width 91 -- 3.2.3 Backscattering from Impedance-matched Bodies 93 -- 3.3 Scattering Matrix 95 -- 3.3.1 Definition 95 -- 3.3.2 Scattering Matrix in Spherical Coordinates 97 -- 3.3.3 Scattering Matrix in the Plane of Scattering Coordinates 99 -- 3.4 Far-field Coefficient 101 -- 3.4.1 Integral Representations and Far-field Conditions 102 -- 3.4.2 Reciprocity of Scattered Fields 106 -- 3.4.3 Forward Scattering 108 -- 3.4.4 Cylindrical Bodies 113 -- 3.5 Scattering Regimes 120.

3.5.1 Resonant-size Scatterers 120 -- 3.5.2 Electrically Large Scatterers 121 -- 3.6 Electrically Small Scatterers 125 -- 3.6.1 Physics of Dipole Scattering 126 -- 3.6.2 Dipole Scattering in Terms of Polarizability Tensors 129 -- 3.6.3 Magneto-dielectric Ellipsoid 131 -- 3.6.4 Rotationally Symmetric Particles 137 -- 3.7 Problems 148 -- References 162 -- 4 Planar Interfaces 165 -- 4.1 Introduction 165 -- 4.2 Interface of Two Homogeneous Semi-infinite Media 167 -- 4.2.1 Reflection and Transmission Coefficients 167 -- 4.2.2 Brewster's Angle 173 -- 4.2.3 Total Internal Reflection 173 -- 4.2.4 Interfaces with Double-negative Materials 176 -- 4.2.5 Surface Waves 177 -- 4.2.6 Vector Solution of Reflection and Transmission Problems 179 -- 4.3 Arbitrary Number of Planar Layers 182 -- 4.3.1 Solution by the Method of Characteristic Matrices 182 -- 4.3.2 Discussion and Limiting Cases 189 -- 4.4 Reflection and Transmission of Cylindrical and Spherical Waves 195 -- 4.4.1 Excitation by a Linear Electric Current 195 -- 4.4.2 Excitation by an Electric Dipole 202 -- 4.5 A Layer between Homogeneous Half-spaces 207 -- 4.5.1 Different Half-spaces 207 -- 4.5.2 A PEC-backed Layer 213 -- 4.5.3 Layer Immersed in a Homogeneous Space 215 -- 4.6 Modeling with Approximate Boundary Conditions 224 -- 4.6.1 Accuracy of Impedance Boundary Conditions 225 -- 4.6.2 Accuracy of Transition Boundary Conditions 229 -- 4.6.3 Impedance-matched Surface 232 -- 4.7 Problems 235 -- References 249 -- 5 Wedges 251 -- 5.1 Introduction 251 -- 5.2 The Perfectly Conducting Wedge 253 -- 5.2.1 Formulation of Boundary Value Problem 254 -- 5.2.2 Solution by Separation of Variables 256 -- 5.2.3 Fields and Currents at the Edge 258 -- 5.2.4 Reduction to an Integral Form 260 -- 5.2.5 Special Cases 262 -- 5.2.6 Edge-diffracted and GO Components. Diffraction Coefficient 266 -- 5.3 Scattering from a Half-plane (Solution by Factorization Method) 271 -- 5.3.1 Statement of the Problem 271 -- 5.3.2 Functional Equation 273 -- 5.3.3 Factorization and Solution 274.

5.3.4 Scattered Field Far from the Edge 276 -- 5.4 The Impedance Wedge 279 -- 5.4.1 Boundary Value Problem, Sommerfeld's Integrals, and Functional Equations 279 -- 5.4.2 Normal Incidence (Maliuzhinets' Solution) 288 -- 5.4.3 Unit Surface Impedance 297 -- 5.4.4 Further Exactly Solvable Cases 300 -- 5.5 High-frequency Scattering from Impenetrable Wedges 306 -- 5.5.1 GO Components and Surface Waves 307 -- 5.5.2 Edge-diffracted Field, Diffraction Coefficient, and Scattering Widths 310 -- 5.5.3 Uniform Asymptotic Approximations 316 -- 5.5.4 GTD/UTD Formulation 319 -- 5.6 Behavior of Electromagnetic Fields at Edges 322 -- 5.6.1 Determining the Degree of Singularity 322 -- 5.6.2 Analytical Structure of Meixner's Series 328 -- 5.7 Problems 329 -- References 336 -- 6 Circular Cylinders and Convex Bodies 339 -- 6.1 Introduction 339 -- 6.2 Perfectly Conducting Cylinders: Separation of Variables and Series Solution 340 -- 6.2.1 Separation of Variables 342 -- 6.2.2 Satisfying the Boundary Conditions 342 -- 6.2.3 Scattered Fields 343 -- 6.2.4 Numerical Examples 345 -- 6.3 Homogeneous Cylinders under Normal Illumination 350 -- 6.3.1 Field Equations and Boundary Conditions 350 -- 6.3.2 Rayleigh Series Solution 351 -- 6.3.3 Numerical Examples 352 -- 6.4 Watson's Transformation and High-frequency Approximations 354 -- 6.4.1 Watson's Transformation 355 -- 6.4.2 Alternative Solution by Separation of Variables 358 -- 6.4.3 High-frequency Approximations 360 -- 6.4.4 Surface Currents in the Penumbra Region. Fock's Functions 369 -- 6.5 Coated and Impedance Cylinders under Oblique Illumination 375 -- 6.5.1 PEC Cylinder with Magneto-dielectric Coating 376 -- 6.5.2 Impedance Cylinder 383 -- 6.6 Extension to Generally Shaped Convex Impedance Bodies 392 -- 6.6.1 Fock's Principle of the Local Field in the Penumbra Region 393 -- 6.6.2 Asymptotic Solution for the Field on the Surface of Circular Impedance Cylinders under Oblique Illumination 396 -- 6.6.3 Fock- and GTD-type Solutions for Electrically Large Convex Impedance Bodies 398.

6.7 Problems 403 -- References 411 -- 7 Spheres 412 -- 7.1 Introduction 412 -- 7.2 Exact Solution for a Multilayered Sphere 414 -- 7.2.1 Formulation of the Problem in Terms of Debye's Potentials 415 -- 7.2.2 Derivation of the Series Solution 417 -- 7.2.3 Solution for Impedance Boundary Conditions 427 -- 7.3 Physics of Scattering from Spheres 429 -- 7.3.1 Classification of Scattering 430 -- 7.3.2 Spiral Waves 436 -- 7.3.3 Debye's Expansions for Homogeneous Spheres 438 -- 7.3.4 Waves in Electrically Large Homogeneous Low-absorption Spheres 442 -- 7.4 Scattered Field in the Far Zone 463 -- 7.4.1 Far-field Coefficient, Scattering Cross Sections, and Polarization Structure. Approximations for Electrically Large Spheres 463 -- 7.4.2 Electrically Small Spheres: Dipole, Quasi-static, and Resonance Approximations 471 -- 7.4.3 PEC Spheres 479 -- 7.4.4 Core-shell Spheres 483 -- 7.4.5 Impedance Spheres 488 -- 7.5 Far-field Scattering from Homogeneous Spheres 493 -- 7.5.1 Exact Solution and Limiting Cases 494 -- 7.5.2 Electrically Small Lossy Spheres 495 -- 7.5.3 Electrically Small Low-absorption Spheres 499 -- 7.5.4 Electrically Large Lossy Spheres: Relation to the Impedance Sphere and the Role of Absorption 506 -- 7.5.5 Electrically Large Low-absorption Spheres: Light Scattering from Water Droplets 513 -- 7.6 Metamaterial Effects in Scattering from Spheres 542 -- 7.6.1 Small Spheres 542 -- 7.6.2 Invisibility Cloak 546 -- 7.7 Problems 552 -- References 562 -- 8 Method of Physical Optics 565 -- 8.1 Introduction 565 -- 8.1.1 On Numerical Techniques for Studying Scattering from Arbitrary-shaped Bodies 565 -- 8.1.2 PO as one of the Approximate Analytical Techniques 566 -- 8.1.3 Structure of the Chapter 567 -- 8.2 Principles and General Solution 567 -- 8.2.1 Principles of PO 567 -- 8.2.2 Derivation of PO Solutions 569 -- 8.2.3 PO for Cylindrical Bodies 573 -- 8.3 Transmission through Apertures 575 -- 8.3.1 PO Solution 575 -- 8.3.2 GO Rays and Fresnel Zones 576 -- 8.3.3 Contribution from the Rim of the Aperture: Edge-diffracted Rays 582.

8.4 Scattering from Curved Surfaces 594 -- 8.4.1 Fock's Reflection Formula 594 -- 8.4.2 Application to a Spherical Segment 600 -- 8.4.3 Reflection Formula in the Far-field Region 605 -- 8.4.4 Diffraction by an Edge in a Non-metallic Surface 609 -- 8.5 Advantages and Limitations of Physical Optics 615 -- 8.6 Problems 616 -- References 632 -- 9 Physical Optics Solutions of Canonical Problems 634 -- 9.1 Introduction 634 -- 9.2 Vertices 635 -- 9.2.1 Vertex on an Edge of a Thin Plate 637 -- 9.2.2 Apex of a Pyramid 641 -- 9.2.3 Tip of an Elliptic Cone 643 -- 9.3 Electrically Large Plates 652 -- 9.3.1 Arbitrarily Shaped Plates 653 -- 9.3.2 Circular Disc 658 -- 9.3.3 Polygonal Plates 663 -- 9.3.4 Far-field Patterns of Polygonal Plates and Apertures 667 -- 9.4 Bodies of Revolution 671 -- 9.4.1 PO Solution for Bodies of Revolution 672 -- 9.4.2 Imperfectly Reflecting Bodies under Axial Illumination 675 -- 9.4.3 PEC Bodies under Oblique Illumination 677 -- 9.4.4 Axial Backscattering 678 -- 9.4.5 Examples 684 -- 9.5 Problems 689 -- References 712 -- A Definitions and Useful Relations of Vector Analysis and Differential Geometry 714 -- A.1 Vector Algebra 714 -- A.2 Vector Analysis 716 -- A.3 Vectors and Vector Differential Operators in Orthogonal Curvilinear Coordinates 717 -- A.3.1 General Orthogonal Curvilinear Coordinates 717 -- A.3.2 Spherical Coordinates 718 -- A.4 Curves and Surfaces in Space 720 -- A.4.1 Curves 720 -- A.4.2 Surfaces 720 -- A.5 Problems 722 -- References 724 -- B Fresnel Integral and Related Functions 725 -- B.1 Fresnel Integral 725 -- B.2 Relation to the Error Function 728 -- B.3 Transition Functions of Uniform Theories of Diffraction 730 -- B.4 Problems 731 -- References 732 -- C Principles of Complex Integration 733 -- C.1 Introduction 733 -- C.2 Deforming the Integration Contour 734 -- C.2.1 Basic Facts about Functions of a Complex Variable 734 -- C.2.2 Integrals over Infinite Contours 736 -- C.3 Steepest Descent Method 737 -- C.3.1 Steepest Descent Path 738.

C.3.2 Saddle Point Contribution 739 -- C.3.3 Pole Singularity near the Saddle Point 741 -- C.3.4 Further Cases 742 -- C.4 Problems 743 -- References 745 -- D The Stationary Phase Method 746 -- D.1 Introduction 746 -- D.2 One-dimensional Integrals 746 -- D.2.1 No Stationary Points on the Integration Interval 747 -- D.2.2 Isolated Stationary Points 748 -- D.2.3 Two Coalescing Stationary Points 751 -- D.3 Two-dimensional Integrals 756 -- D.3.1 Stationary Point in the Integration Domain 756 -- D.3.2 Stationary Point near the Boundary of the Integration Domain 758 -- D.3.3 Contribution from the Boundary of the Integration Domain 760 -- D.3.4 Kontorovich's Formula 763 -- D.3.5 Integrand Vanishing on the Boundary 765 -- D.3.6 Summary of the Two-dimensional Stationary-phase Method 766 -- D.4 Problems 766 -- References 768 -- E Asymptotic Approximations of Bessel Functions of Large Argument and Arbitrary Order 770 -- E.1 Introduction 770 -- E.1.1 Basic Definitions and Properties 770 -- E.1.2 Large-argument Approximations (|z| ?a 1) 772 -- E.1.3 Content of the Appendix 775 -- E.2 Debye's Asymptotic Approximations 776 -- E.2.1 Debye's Method 776 -- E.2.2 WKB Approximation 778 -- E.2.3 Bessel Functions on the Complex � Plane 791 -- E.3 Almost Equal Argument and Order 795 -- E.3.1 Approximations in Terms of Airy Functions 796 -- E.3.2 Approximations in Terms of Normalized Airy Functions 797 -- E.3.3 Zeros in the Neighborhood of the Points � = <

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