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