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Introduction to the Uniform Geometrical Theory of Diffraction : Antennas & Propagation Library - D.A. McNamara

Introduction to the Uniform Geometrical Theory of Diffraction

Antennas & Propagation Library


Published: 19th January 1990
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A text for senior undergraduate or beginning graduate students, as well as practicing engineers, that bridges the gap between specialist papers and the use of GTD in practical problems. It introduces the principal results and concepts, their various parameters, and applications to a wide variety of

Prefacep. xiii
The Nature of High-Frequency Methodsp. 1
Introductionp. 1
A Brief Historical Overviewp. 2
High-Frequency Phenomenap. 5
Referencesp. 6
Geometrical Optics Fieldsp. 7
Introductionp. 7
Ray Optical Construction of the High-Frequency Fieldp. 8
Preliminary Remarksp. 8
Some Conventional Electromagnetic Theoryp. 8
The Luneberg-Kline Anticipated Solution (Ansatz)p. 10
The Eikonal Equationp. 11
The Transport Equationsp. 15
The Geometrical Optics Terms and Their Interpretationp. 17
Ray Paths, Amplitude Functions, and Phase Functionsp. 19
Sign Conventions and Caustics of the Geometrical Optics Fieldsp. 28
The Geometrical Optics Field and Fermat's Principlep. 33
Summary of the Properties of a High-Frequency Field and Some Special Casesp. 34
Specific Examples of Geometrical Optics Fieldsp. 37
Initial Comments and Some Definitionsp. 37
Uniform Plane Wave Fieldsp. 37
The Fields of Electric and Magnetic Line Sourcesp. 40
The Fields of a Hertzian Dipolep. 42
The Far-Zone Fields of Horn Antennasp. 43
The Fields of a Piecewise-Sinusoidal Dipolep. 46
Sources with Fields That Are Not Geometrical Optics or Ray-Optic Fieldsp. 48
Further Commentp. 48
Reduction of Results to Two-Dimensional Ray Tubesp. 48
Rays in Lossy Mediap. 52
Concluding Remarksp. 52
A Taste of Things to Comep. 53
Problemsp. 57
Referencesp. 58
Geometrical Optics Reflected Fieldsp. 61
Introductionp. 61
Initial Remarksp. 61
A Stroll in the Sunp. 61
A Strategy for This Chapterp. 63
The Law of Reflection, Polarization Properties, and Phase Functionsp. 66
The Definition of Certain Geometrical Terms and Coordinate Systemsp. 66
The Law of Reflectionp. 70
Trajectories of Reflected Raysp. 74
Polarization of Reflected Raysp. 75
Phase Continuation along Reflected Raysp. 77
Invocation of the Locality Principlep. 78
More about Shadowingp. 78
Geometrical Optics Surface Currentsp. 81
An Alternative Interpretation of the Form of R and the Law of Reflectionp. 82
What More Do We Need?p. 83
The Expressions for the Geometrical Optics Field Reflected from Smooth Conducting Surfaces: Two-Dimensional Problemsp. 84
When Is a Problem of a Two-Dimensional Nature?p. 84
Description of the Two-Dimensional Reflecting Surface Geometryp. 86
Simplifications for Two-Dimensional Problemsp. 86
Simplification of the Polarization Description of Reflected GO Fields for Two-Dimensional Problemsp. 86
Amplitude Continuation along Two-Dimensional Reflected Ray Tubesp. 88
The Classical Geometrical Optics Interpretationp. 91
Summary of Reflected Field Expressions for Two-Dimensional Problemsp. 93
On the Specular Point Q[subscript r] and Its Locationp. 96
Initial Two-Dimensional Problem Examplesp. 97
Interpretation in Terms of Fundamental Electromagnetic Theoryp. 116
Relationship to Physical Opticsp. 117
Comments on GO Reflected Fields about Shadow Boundariesp. 120
Further Examples of Two-Dimensional Reflected Field Problemsp. 121
General Expressions for the Reflected Fields from Three-Dimensional Smooth Conducting Surfacesp. 131
Introductionp. 131
Principal Radii of Curvature of Reflected Ray Tube at Q[subscript r]--First Formatp. 134
Principal Radii of Curvature of Reflected Ray Tube at Q[subscript r]--Second Formatp. 135
Important Special Casesp. 136
Principal Directions of the Reflected Wavefrontp. 138
Alternative Form for the Reflected GO Field at the Specular Point Q[subscript r]p. 140
Comments on the Expressions for the Reflected GO Fieldp. 142
Alternative Determination of Principal Radii of Curvature of the Reflected Wavefrontp. 144
Examples of Three-Dimensional Reflected Field Problemsp. 145
Concluding Remarksp. 154
Problemsp. 156
Referencesp. 157
Two-Dimensional Wedge Diffractionp. 159
Introductionp. 159
Diffraction by Huygens' Principlep. 163
Keller's Original GTDp. 165
The Uniform Theory of Diffractionp. 174
Shadow Boundariesp. 175
Two-Dimensional UTD Diffraction Coefficientsp. 179
Enforcing Continuity across the Shadow Boundariesp. 191
Transition Regionsp. 197
Grazing Incidencep. 203
Half-Plane and Curved Screenp. 205
Continuity across the Shadow Boundary: Grazing Incidencep. 206
Full-Planep. 218
Slope Diffractionp. 220
General Two-Dimensional Edge Diffracted Fieldsp. 225
Dielectric and Impedance Wedgesp. 227
Problemsp. 228
Referencesp. 231
Applications of Two-Dimensional Wedge Diffractionp. 235
Radiation from a Parallel Plate Waveguide with TEM Mode Propagation, Terminated in an Infinite Ground Planep. 235
Antenna Gainp. 238
Radiation from an E-Plane Horn Antennap. 240
Radiation from an H-Plane Horn Antennap. 244
Radar Width of a Two-Dimensional Structurep. 248
Problemsp. 257
Referencesp. 260
Three-Dimensional Wedge Diffraction and Corner Diffractionp. 263
Introductionp. 263
Edge-Fixed Coordinate Systemp. 265
Three-Dimensional UTD Diffraction Coefficientsp. 268
Examples of Three-Dimensional Wedge Diffractionp. 274
Corner Diffractionp. 288
Corner Diffraction from a Flat Platep. 288
Corner Diffraction from a Vertex in Which Wedges with Arbitrary Wedge Angles Are Terminatedp. 298
Alternative Forms of the Diffraction Coefficientsp. 300
Problemsp. 301
Referencesp. 304
Equivalent Currentsp. 305
Introductionp. 305
Equivalent Currents for Edge Diffractionp. 306
Radiation From Equivalent Currentsp. 312
Reflected Fields Using Equivalent Currentsp. 322
Problemsp. 327
Referencesp. 328
Diffraction at a Smooth Convex Conducting Surfacep. 331
The Phenomenon of Creeping Waves, or Curved Surface Diffractionp. 331
Introductionp. 331
Asymptotic Evaluation of Eigenfunction Solutions for Line Source Illumination of a Conducting Circular Cylinderp. 332
Interpretation of the Asymptotic Solution in Terms of Surface Raysp. 335
Invocation of Locality and the Generalized Fermat Principlep. 336
The Significance of the UTD Results for Diffraction by Smooth Convex Surfacesp. 341
Problem Classes for Curved-Surface Diffractionp. 343
Differential Geometry for 2D Curved-Surface Diffractionp. 344
The Two-Dimensional Scattering Formulationp. 344
The Scattering Problem Geometryp. 344
UTD Scattering Solution in the Lit Regionp. 345
UTD Scattering Solution in the Shadow Regionp. 350
Field Continuity at the SSBp. 356
UTD Scattering Solution in the Surface-Based Ray Coordinate Systemp. 370
The Radiation Problem for a Source Mounted on a Smooth Convex Conducting Surfacep. 374
The Radiation Problem Geometryp. 374
Sources of the Radiated Fieldsp. 375
UTD Solution for the Radiation Problem: Observation Point in the Lit Zonep. 377
UTD Solution for the Radiation Problem: Observation Point in the Shadow Zonep. 381
Noninfinitesimal Sourcesp. 385
Deep Shadow Zone Field Expressions and Their Interpretationp. 387
The Two-Dimensional Convex Conducting Surface Coupling Problemp. 401
Detailed Geometry for the Coupling Problemp. 401
Preliminariesp. 401
UTD Coupling Solution for Magnetic Current Sourcesp. 402
UTD Coupling Solution for Electric Current Sourcesp. 403
Special Geometriesp. 403
A Form of the Coupling Solution in the Deep Shadow Region and Its Interpretationp. 405
Bibliographic Remarksp. 408
Problemsp. 409
Referencesp. 410
Unit Vectorsp. 413
Cartesian Coordinate Systemp. 413
Spherical Coordinate Systemp. 413
Cylindrical Coordinate Systemp. 414
Special Functions for the Uniform Geometrical Theory of Diffractionp. 417
Introductionp. 417
The Fresnel Integrals and Transition Functionp. 418
Bessel and Hankel Functionsp. 420
The Airy Functionsp. 422
The Fock Scattering Functionsp. 424
The Fock Radiation Functionsp. 428
The Fock Coupling Functionsp. 430
Concluding Remarksp. 432
Referencesp. 432
Differential Geometryp. 435
Curvesp. 435
Surfacesp. 440
Unit Vector Normal to a Surfacep. 440
Radius of Curvature of a Surfacep. 442
Referencesp. 449
The Method of Stationary Phasep. 451
Introductionp. 451
The Method of Stationary Phasep. 452
Bibliographical Remarksp. 456
Referencesp. 457
Additional Referencesp. 459
Computer Subroutine Listingsp. 465
Fresnel Integralsp. 465
Transition Functionp. 465
Wedge-Diffraction Coefficientp. 466
Wedge-Slope-Diffraction Coefficientp. 466
Fock Scattering Functionsp. 467
Universal Fock Radiation Functionsp. 467
Fock Coupling Functionsp. 467
Referencesp. 467
Indexp. 469
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ISBN: 9780890063019
ISBN-10: 089006301X
Series: Antennas & Propagation Library
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 488
Published: 19th January 1990
Publisher: Artech House Publishers
Country of Publication: US
Dimensions (cm): 22.9 x 15.2  x 3.1
Weight (kg): 0.93