Two methods for the exact solution of diffraction problems

$Cover image for Two methods for the exact solution of diffraction problems$

Title:

Personal Author:

Alzofon, Frederick E.

Publication Information:

Bellingham, WA : SPIE Optical Engineering Press, 2004

Physical Description:

xii, 128 p. : ill. ; 26 cm.

ISBN:

9780819451415

Subject Term:

Electromagnetic waves -- Diffraction

Sommerfeld polynomial method

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010178500	QC665.D5 A49 2004	Open Access Book	Book	Searching... Unknown

This text presents two methods of calculating the electromagnetic fields due to radiation scattering by a single scatterer. Both methods yield valid results for all wavelengths of the incident radiation as well as a wide variety of scatterer configurations.

Preface	p. xi
Chapter 1 Introduction	p. 1
1.1 Sommerfeld's Method	p. 2
1.2 Generalizing Boundary Surfaces	p. 3
References	p. 4
Chapter 2 Historical Background of the Sommerfeld Method	p. 7
2.1 The Kelvin Image Method	p. 7
2.2 The Sommerfeld Image Method	p. 9
References	p. 12
Chapter 3 Two-Leaved Generalization of a Spherical Wave: One Branch Line	p. 15
3.1 The Point Radiation Source in Physical Space	p. 15
3.2 Complex Number Notation	p. 16
3.3 Outline of the Construction of a Multiple-Valued Radiation Source	p. 17
3.4 The Analytic Continuation of [phi]'	p. 20
3.5 The Cauchy Integral for a Point Source: Definition of U[subscript 1]	p. 22
3.6 Uniqueness of the Solution	p. 29
3.7 Explicit Expressions for U[subscript 1]	p. 30
3.8 Multiple-Valued Generalization of a Plane Wave	p. 31
References	p. 33
Chapter 4 Fresnel Diffraction by a Semi-Infinite Plane	p. 35
4.1 Scalar Theory	p. 35
4.1.1 Reflection of a spherical wave by a perfectly reflecting semi-infinite plane: scalar theory	p. 36
4.1.2 Diffraction of a spherical wave by a nonperfectly reflecting semi-infinite plane	p. 38
4.2 The Electromagnetic Field Equations	p. 39
4.3 Boundary Conditions	p. 40
4.4 Poincare/Sommerfeld Solution	p. 40
4.5 Solution Using Two Independent Scalar Solutions	p. 43
References	p. 44
Chapter 5 Fresnel Diffraction by a Circular Disk	p. 45
5.1 Coordinate-System Construction	p. 45
5.2 Analytic Continuation of [theta]'	p. 49
5.3 A Multiple-Valued Green's Function with a Circle as a Branch Curve	p. 50
5.3.1 Plane wave approximation	p. 52
5.3.2 Static solution and the harmonic measure of the two-leaved space	p. 52
5.3.3 An alternative method of constructing a multiple-valued spherical wave	p. 53
5.4 Diffraction of a Spherical Wave by a Perfectly Conducting Disk	p. 58
5.5 Diffraction by a Perfectly Conducting Spherical Dome	p. 59
5.6 Comments on the Foregoing Analysis	p. 61
References	p. 61
Chapter 6 Fresnel Diffraction by a Flat Circular Annulus	p. 63
6.1 Outline of the Generalized Sommerfeld Method	p. 65
6.2 The Coordinate System	p. 66
6.3 The Branch Points of D[subscript 2]	p. 70
References	p. 74
Chapter 7 Fresnel Diffraction by a Slit between Perfectly Conducting Half-Planes	p. 75
7.1 Coordinate Systems for Two Branch Lines	p. 75
7.2 Analytic Continuation of [theta]'	p. 79
7.3 Construction of U[subscript 1]	p. 81
7.4 Diffraction of a Spherical Wave by a Slit between Two Perfectly Conducting Half-Planes	p. 82
7.5 Some Remarks on the Sommerfeld Method	p. 83
References	p. 84
Chapter 8 Coordinate Systems	p. 85
8.1 Generalization of the Branch Curves	p. 85
8.2 Cylinders of Arbitrary Shape	p. 87
8.3 Closed Surfaces of Arbitrary Shape	p. 89
8.4 Interpolated Coordinate Systems	p. 89
References	p. 90
Chapter 9 Radiation Scattering by a Hexagonal Ice Cylinder: Coordinate System	p. 91
9.1 Configuration	p. 91
9.2 Unit Vectors	p. 93
9.3 Inscribed Circle	p. 95
References	p. 96
Chapter 10 Radiation Scattering by a Hexagonal Ice Cylinder: Boundary Conditions	p. 97
10.1 Wave Propagation Equation and Elementary Solutions	p. 97
10.2 Boundary Conditions	p. 99
10.3 Field Continuity along the z-Axis	p. 101
10.4 The Boundary Conditions on E[subscript gamma] and H[subscript gamma]	p. 103
10.5 Simplifications by Use of Symmetry	p. 105
10.6 Evaluation of the Fourier Transforms	p. 106
10.6.1 Perturbation method	p. 107
10.6.2 Fourier transforms for small radiation wavelength	p. 108
10.6.3 Trigonometric interpolation	p. 110
References	p. 111
Appendix A Alternative Methods of Exact Diffraction Analyses	p. 113
A.1 General Comments	p. 113
A.2 Historical Development of Some Diffraction Solutions: Post-Sommerfeld	p. 113
A.3 Modern Alternatives to Sommerfeld's Method	p. 114
A.3.1 Finite-element method	p. 114
A.3.2 Integral-equation method	p. 115
A.3.3 The T-matrix	p. 115
References	p. 115
Appendix B Sommerfeld's Original Analyses	p. 117
B.1 Static Fields	p. 117
References	p. 121
Appendix C Analytic Functions of a Complex Variable	p. 123
C.1 Complex Numbers	p. 123
C.2 Differential Properties	p. 123
C.3 Integral Properties of Analytic Functions	p. 124
C.4 Singularities	p. 125
C.5 Contour Integration	p. 125
C.6 Analytic Continuation	p. 126
References	p. 126
Appendix D Uniform Convergence	p. 127
D.1 Definition of Uniform Convergence	p. 127
References	p. 128

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