Geometrical Optics in Engineering Physics

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9781842651599 | 1842651595
Cover: Hardcover
Copyright: 1/30/2005

Sorry, this item is currently not available.

Geometrical Optics in Engineering Physics provides a concise and clear presentation of modern ray theory without the need of complicated mathematics. Comprehensive coverage is given to wave problems in engineering physics, considering rays and caustics as physical objects.

Implementation of geometrical optics is described to applied optics, to telecommunications, radar and microwave engineering, which are just a few of the fast developing engineering disciplines based on wave physics. This monograph is also relevant to the solution of wave problems that arise in plasma physics, underwater acoustics and seismic exploration.

Preface and Acknowledgements

vii

1. Introduction

(6)

1.1 Two Faces of Geometrical Optics

(1)

1.2 Geometrical Optics as a Powerful Tool in Engineering Physics

(1)

1.3 The Main Goals of the Book

(1)

1.4 Trends in Modern Geometrical Optics

(2)

1.5 The Book's Contents. New Aspects of Geometrical Optics

(2)

2. The Scalar Wave Fields

(96)

2.1 Equations of Geometrical Optics

(7)

2.1.1 Mathematical Background

(1)

2.1.2 Field Expansion in a Dimensionless Parameter

(2)

2.1.3 Field Expansion in Inverse Wave Numbers

(1)

2.1.4 Initial Conditions for the Eikonal and Amplitude Equations

(1)

2.1.5 Asymptotic Nature of the Ray Series

(1)

2.1.6 Divergence of the Geometrical Optics Series in the Region of Its Inapplicability

(2)

2.2 Rays and the Eikonal

(12)

2.2.1 The Method of Characteristics

(2)

2.2.2 Ray Equations and the Eikonal

(1)

2.2.3 Curvature and Torsion of Rays

(2)

2.2.4 Initial Conditions for Rays. Ray Coordinates

(1)

2.2.5 Ray Families and Phase Fronts

(2)

2.2.6 The Fermat Principle

(1)

2.2.7 Ray Equations in Curvilinear Coordinates

(2)

2.2.8 Other Types of Rays

(1)

2.3 Wave Amplitude

(7)

2.3.1 Formal Solution of the Transport Equation

(1)

2.3.2 Rays and the Direction of Energy Flow

(1)

2.3.3 Conservation of Energy Flux in a Ray Tube

(2)

2.3.4 The Field Due to a Point Source in an Inhomogeneous Medium

(1)

2.3.5 The Resultant Field in the Ray-Optics Approximation

(1)

2.3.6 The Field Amplitudes of Higher-Order Approximations

(1)

2.3.7 Accounting for Weak Absorption

(1)

2.4 Caustics

(12)

2.4.1 Fundamental Properties

(2)

2.4.2 Wave-Field Focusing on Caustics

(1)

2.4.3 Types of Caustics

(6)

2.4.4 Structurally Stable and Unstable Caustics in Physical Problems

(1)

2.4.5 Other Types of Caustics

(1)

2.4.6 Singularities of Phase Fronts

(1)

2.4.7 Phase Shifts at Caustics

(2)

2.5 Reflection and Refraction of Waves at Interfaces

(5)

2.5.1 The Locality Principle in Wave Reflection

(1)

2.5.2 Relations for Rays and Eikonals

(2)

2.5.3 Reflection Formulas for Amplitude

(1)

2.5.4 Reflection from Weak Interfaces

(2)

2.5.5 The Geometrical Optics of Surface Waves

(1)

2.6 Reciprocity of Rays and Caustics

(1)

2.6.1 The Reciprocity Theorem

(1)

2.6.2 Reciprocity Relations for Rays and Caustics

(1)

2.7 Space-Time Geometrical Optics

(14)

2.7.1 The Wave Equation for Media with Temporal (Frequency) Dispersion

(2)

2.7.2 Necessary Conditions for the Geometrical-Optics Applicability to Quasi-Monochromatic Wave Packets

(1)

2.7.3 Differential Form of the Constitutive Equation (2.7.2)

(1)

2.7.4 Eikonal and Transport Equations

(1)

2.7.5 Space-Time Rays

(1)

2.7.6 Initial Conditions

(2)

2.7.7 Eikonal and Wave Amplitude

(3)

2.7.8 Space-Time Caustics

(1)

2.7.9 Propagation of Field Discontinuities and pulses in Nondispersive Media

(3)

2.8 Separation of Variables in the Eikonal Equation

(8)

2.8.1 The Complete Integral of the Eikonal Equation

(1)

2.8.2 Separation of Variables in Two Dimensions (Cartesian Coordinates)

(1)

2.8.3 Separation of Variables in Two Dimensions (Curvilinear Orthogonal Coordinates)

(2)

2.8.4 Separation of Variables in Three-Dimensional Space

(1)

2.8.5 Incomplete Separation of Variables

(1)

2.8.6 The Complete Integral of Eikonal and Rays Equations

(2)

2.9 Perturbation Techniques for Geometrical-Optics Equations

(5)

2.9.1 The Perturbation Method for the Eikonal

(1)

2.9.2 The Perturbation Method for Rays

(1)

2.9.3 Perturbations in Homogeneous Media

(1)

2.9.4 Perturbations in Nonhomogeneous Media

(2)

2.10 Applicability of Geometrical Optics

(20)

2.10.1 Existent Estimators of Method's Errors

(1)

2.10.2 Fresnel Zones and Fresnel Volume of Rays in Inhomogeneous Media

(7)

2.10.3 The Physical Meaning of the Ray

(1)

2.10.4 Heuristic Criteria on Geometrical-Optics Applicability

(2)

2.10.5 Applicability Conditions for Space-Time Geometrical Optics

(3)

2.10.6 Heuristic Accuracy Estimates of Geometrical Optics

(1)

2.10.7 Estimating the Width of a Caustic Zone

(2)

2.10.8 Indistinguishability of Rays in the Caustic Zone

(1)

2.10.9 Observability of Caustics

(1)

2.10.10 Field Estimations beyond the Validity Region of Geometrical Optics

(1)

2.10.11 Field-Focusing Indices at Caustics

(1)

2.10.12 Stability with Respect to Small Perturbations

(1)

2.10.13 Wave-Pattern Analysis in General

(1)

2.11 Estimates for Exponentially Small Scattered Wave Fields

(5)

2.11.1 Perturbation Technique for the 1-D Wave Problem

(1)

2.11.2 Perturbative Approach for the 3-D Green Function

(2)

2.11.3 Approximate Solution for the 3-D Wave Field

101

(1)

2.11.4 Scattered Wave Field

101

(2)

3. Applications of the Ray Methods

103

(115)

3.1 Waves in Homogeneous Media

103

(18)

3.1.1 Rays and the Eikonal

103

(1)

3.1.2 The Wave Amplitude

104

(2)

3.1.3 Caustics

106

(1)

3.1.4 The Plane Phase-Amplitude Screen

107

(2)

3.1.5 The Sinusoidal Phase Screen. An Illustrative Example

109

(1)

3.1.6 Applicability Conditions for Geometrical Optics

110

(2)

3.1.7 Geometrical Optics in Far and Near Antenna Fields. Wave Beam Propagation

112

(1)

3.1.8 On the Phase Center of an Antenna or a Scatterer

113

(2)

3.1.9 Field Near a Lens Focus

115

(3)

3.1.10 Field at the Focus of a Lens with Cylindrical (Spherical) Aberration

118

(3)

3.2 Reflection and Refraction at an Interface

121

(11)

3.2.1 Reflection Formulas

121

(1)

3.2.2 Divergence of Reflected and Refracted Rays

122

(3)

3.2.3 Radar Cross Section of a Body in the Geometrical-Optics Approximation

125

(1)

3.2.4 Reflection Far Field of a Directional Point Source

126

(1)

3.2.5 Caustics of Refracted and Reflected Rays

126

(1)

3.2.6 Examples of Catacaustics and Diacaustics

127

(2)

3.2.7 Applicability of Reflection Formulas

129

(2)

3.2.8 The Invalidity Domain in the Vicinity of a Tangent Ray

131

(1)

3.2.9 Wave Diffraction at a Surface of Variable Impedance

131

(1)

3.3 Rays and Caustics in Plane-Stratified Media

132

(14)

3.3.1 Ray Equations

132

(2)

3.3.2 Ray Tracing in a Plane-Stratified Medium

134

(1)

3.3.3 Equations of Caustics, and the Geometry of the Ray Family

135

(3)

3.3.4 Rays and Caustics due to a Point Source in an Inhomogeneous Medium

138

(1)

3.3.5 Rays and Caustics in a Linear Layer

139

(2)

3.3.6 Layers of Other Profiles

141

(1)

3.3.7 Plane Waves in a Parabolic Layer

142

(1)

3.3.8 A Point Source in a Parabolic Layer

143

(3)

3.4 Wave Fields in Plane-Stratified Media

146

(12)

3.4.1 The Field of an Arbitrary Wave

146

(1)

3.4.2 The Field of a Plane Wave

147

(1)

3.4.3 Fields of Point and Line Sources

148

(2)

3.4.4 A Point Source in a Linear Layer

150

(4)

3.4.5 A Point Source in a Parabolic Layer

154

(1)

3.4.6 The Fresnel Volumes in Plane-Stratified Media

155

(2)

3.4.7 Validity Conditions of the Geometrical-Optics Approximation

157

(1)

3.5 Waves in Radially Inhomogeneous Media

158

(10)

3.5.1 Ray Equations for Spherically Stratified Media

158

(3)

3.5.2 The Eikonal Function for Spherically Stratified Media

161

(1)

3.5.3 Cylindrically Stratified Media

161

(2)

3.5.4 Ray Geometry

163

(1)

3.5.5 The Field Due to a Point Source

164

(1)

3.5.6 The Field of a Plane Wave

165

(1)

3.5.7 Caustics

166

(2)

3.6 Tapered and Other Inhomogeneous Media

168

(10)

3.6.1 The Eikonal and Rays in a Tapered Medium

168

(2)

3.6.2 The Field of a Plane Wave

170

(1)

3.6.3 The Field Due to a Line Source

171

(2)

3.6.4 Ray Equations in a Two-Dimensional Medium with a Special Profile

173

(1)

3.6.5 The Field of a Point Source (Axially Symmetric Problem)

174

(2)

3.6.6 A Plane Wave Incident on the 2D Inhomogeneous Medium

176

(1)

3.6.7 Weakly Inhomogeneous, Quasi-Stratified, and Random Media

177

(1)

3.7 Geometrical Optics of Waveguides and Resonators

178

(10)

3.7.1 Geometrical Optics of Waveguides

178

(2)

3.7.2 Ray Description of Modes in Uniform Waveguides

180

(2)

3.7.3 Adiabatic Modes of Smoothly Nonuniform Waveguides

182

(1)

3.7.4 Ionospheric Wave Channels. The Adiabatic Invariant Method

183

(2)

3.7.5 Underwater-Sound Ducts. Summing-Up Incoherent Wave Fields

185

(1)

3.7.6 Optical Fibers

185

(1)

3.7.7 Mode Conversion in Smoothly Nonuniform Waveguides

185

(2)

3.7.8 Normal Modes in Cavity Resonators

187

(1)

3.8 Wave Scattering at Localized Inhomogeneities

188

(11)

3.8.1 Radar Cross Section

188

(3)

3.8.2 Scattering by a Body in an Inhomogeneous Medium

191

(1)

3.8.3 Radar Cross Section of a Spherically Stratified Inhomogeneity

192

(2)

3.8.4 Radar Cross Section of a Perfectly Conducting Sphere in a Spherically Stratified Medium

194

(1)

3.8.5 Radar Cross Section of a Specific Two-Dimensionally Inhomogeneous Formation

195

(1)

3.8.6 Scattering of a Spherical Wave by a Localized Inhomogeneity

196

(2)

3.8.7 Scattering by a Weak Localized Inhomogeneities

198

(1)

3.9 Pulse Propagation

199

(10)

3.9.1 Dispersion Law for a Waveguide and Cold Plasma

199

(1)

3.9.2 A Homogeneous Medium with an Arbitrary Dispersion Law

199

(1)

3.9.3 A Frequency-Modulated Pulse in a Homogeneous Medium

200

(4)

3.9.4 Dispersive Compression of FM Pulses in Homogeneous Media

204

(2)

3.9.5 Plane-Stratified Dispersive Media

206

(1)

3.9.6 Near and Far Fields of a Pulse

207

(2)

3.10 Numerical Methods in the Geometrical Optics of Inhomogeneous Media

209

(5)

3.10.1 The Ray-Tracing Analysis

209

(2)

3.10.2 Computing the Eikonal and Wave Amplitude. Dynamical Ray Tracing

211

(2)

3.10.3 Problems of Numerical Analysis

213

(1)

3.11 Inverse Problems of Geometrical Optics

214

(4)

3.11.1 Reflection and Refraction at Interfaces

215

(1)

3.11.2 Inverse Problems for Given Model of the Inhomogeneous Medium

215

(1)

3.11.3 Multidimensional Inverse Problems

216

(1)

3.11.4 Nonstationary Inverse Problems

217

(1)

4. Electromagnetic Wave Fields

218

(57)

4.1 Transverse Electromagnetic Waves in Isotropic Media

218

(9)

4.1.1 Maxwell Equations for Monochromatic Waves

218

(1)

4.1.2 The Debye Expansion and the Iterative Equations

219

(1)

4.1.3 The Eikonal Equation

219

(1)

4.1.4 Transverse Nature of Zeroth Approximation Waves. Polarization Degeneracy

220

(1)

4.1.5 Consistency of the First-Approximation Equations

221

(1)

4.1.6 Conserving Energy Flow in a Ray Tube

222

(1)

4.1.7 Preserving the Polarization Ellipse

222

(1)

4.1.8 Rotation of Field Vectors (Rytov's Law)

222

(2)

4.1.9 Polarization of Transverse Waves

224

(1)

4.1.10 Longitudinal Components of the Field

225

(1)

4.1.11 Reflection of Transverse Electromagnetic Waves from Interfaces

225

(1)

4.1.12 Polarization Degeneracy in Problems of Quantum Mechanics and Theory of Elasticity

226

(1)

4.1.13 Lifting the Polarization Degeneracy due to the Gradient of Dielectric Permittivity: Circular Birefringence and Optical Magnus Effect

226

(1)

4.2 Independent Normal Waves in an Anisotropic Medium

227

(15)

4.2.1 Equation of the Eikonal

227

(2)

4.2.2 Independent Normal Modes

229

(1)

4.2.3 Ray Equations

229

(2)

4.2.4 Solving the Eikonal Equation

231

(1)

4.2.5 Definition of Mode Polarization Vectors

232

(1)

4.2.6 Consistency of Equations of the First Approximation

232

(1)

4.2.7 The Transport Equation

233

(1)

4.2.8 Equation for the Argument of a Complex Amplitude

234

(1)

4.2.9 Rays and Energy Paths. The Fresnel Volumes in Anisotropic Media

235

(1)

4.2.10 An Account of Weak Absorption

236

(1)

4.2.11 Reflection and Refraction at the Boundaries of Anisotropic Media

236

(2)

4.2.12 Some Specific Results

238

(2)

4.2.13 Divergence of First-Approximation Fields at Polarization Degeneracy

240

(2)

4.2.14 Other Vector Problems

242

(1)

4.3 Interaction of Normal Modes in Inhomogeneous Anisotropic Media

242

(7)

4.3.1 Waves in Weakly Anisotropic Media. The Quasi-Isotropic Approximation

242

(2)

4.3.2 Different Forms of the Equations of the Quasi-Isotropic Approximation

244

(2)

4.3.3 Solution Techniques for the Quasi-Isotropic Approximation

246

(1)

4.3.4 On the Error of the Quasi-Isotropic Approximation

246

(1)

4.3.5 Applications of the Quasi-Isotropic Approximation

247

(1)

4.3.6 The Quasi-Degenerate Approximation of Geometrical Optics

248

(1)

4.4 Equations of Geometrical Optics for Nonharmonic Electromagnetic Waves in the Inhomogeneous and Nonstationary Dispersive Media

249

(11)

4.4.1 The Maxwell Equations in Inhomogeneous and Non-stationary Media of Temporal and Spatial Dispersion

249

(1)

4.4.2 The Constitutive Equation in Differential Form

250

(1)

4.4.3 Equations for the Fields in Zeroth and First Approximations

251

(1)

4.4.4 The Eikonal Equation. Space-Time Rays

252

(1)

4.4.5 The Transport Equation for Independent Normal Modes in an Anisotropic Medium

253

(2)

4.4.6 The Group Velocity Theorem

255

(2)

4.4.7 Integrating the Transport Equation along Space-Time Rays

257

(1)

4.4.8 Transverse Modes in an Isotropic Medium

257

(2)

4.4.9 Longitudinal Waves in an Isotropic Medium

259

(1)

4.4.10 Waves in Weakly Anisotropic Media

260

(1)

4.5 Constitutive Equations for Nonstationary and Inhomogeneous Dispersive Media. Adiabatic Invariance

260

(4)

4.5.1 Corrections to the Quasi-Stationary Permittivity Tensor

260

(1)

4.5.2 Physical Phenomena Due to the Deviation of epsilonαβ from Its Quasi-Stationary Value

261

(1)

4.5.3 Adiabatic Invariant of the Wave Field

262

(1)

4.5.4 Phenomenological Evaluation of the Anti-Hermitian Part of the Correction for the Quasi-Stationary Permittivity Tensor in Transparent Media

263

(1)

4.6 Wave Processes in Nonstationary Media

264

(11)

4.6.1 One-Dimensional Problem. General Relationships

264

(1)

4.6.2 Nonstationary Nondispersive Media

265

(3)

4.6.3 Nonstationary Dispersive Media

268

(2)

4.6.4 Evolution of Short Pulses

270

(1)

4.6.5 Reflection from Moving Interfaces

271

(3)

4.6.6 Perturbation Theory in Nonstationary Problems

274

(1)

5. Complex Geometrical Optics

275

(53)

5.1 Introductory Remarks

275

(3)

5.1.1 Pioneering Works

275

(1)

5.1.2 Character of Wave Fields Described by Complex Geometrical Optics

276

(2)

5.2 Basic Equations of Complex Geometrical Optics

278

(5)

5.2.1 A Ray-Based Form of Complex Geometrical Optics

278

(2)

5.2.2 Eikonal-Based Form of Complex Geometric Optics

280

(1)

5.2.3 Energy Flux in Complex Geometric Optics. Phase and power flux trajectories

281

(2)

5.3 Properties of Complex Rays

283

(9)

5.3.1 Ray Paths in the Complex Space

283

(1)

5.3.2 Fermat's Principle for Complex Rays

284

(1)

5.3.3 Selection Rules for Complex Rays

285

(1)

5.3.4 Complex Rays and the Saddle Point Method

286

(3)

5.3.5 Complex Caustics

289

(1)

5.3.6 Space-Time Complex Rays

289

(1)

5.3.7 Electromagnetic Waves and Complex Rays

290

(1)

5.3.8 Complex Rays and Uniform Asymptotics

291

(1)

5.4 Complex Rays in Physical Problems

292

(13)

5.4.1 Complex Rays Inside a Circular Caustic

292

(2)

5.4.2 Wave Reflection in a Layered Medium

294

(2)

5.4.3 Point Source in a Layered Medium

296

(1)

5.4.4 The Vicinity of a Caustical Cusp in Free Space

297

(1)

5.4.5 Swallow-Tall Caustic: An Example with Four Ray Contributions

297

(1)

5.4.6 Point Source in a Parabolic Layer

298

(2)

5.4.7 Above Barrier Reflection

300

(1)

5.4.8 Complex Rays Behind a Sinusoidal Phase Screen

301

(1)

5.4.9 Surface Waves

301

(1)

5.4.10 Reflection of Inhomogeneous Waves from an Interface

302

(1)

5.4.11 Complex Rays in Weakly Absorbing Media

302

(2)

5.4.12 Complex Geometrical Optics in Other Wave Disciplines

304

(1)

5.5 Gaussian Beams and Complex Rays

305

(9)

5.5.1 Gaussian Beams and Complex Sources

305

(2)

5.5.2 The Gaussian-Beam Diffraction Wave Field in Free Space in a Frame of Ray-Based Complex Geometric Optics

307

(2)

5.5.3 Gaussian-Beam Diffraction Wave Field in Free Space in a Frame of Eikonal-Based Complex Geometrical Optics

309

(2)

5.5.4 Transformation of Gaussian Beams in Optical Systems

311

(2)

5.5.5 Diffraction of Gaussian Beams

313

(1)

5.6 Distinctive Aspects of Complex Geometrical Optics

314

(2)

5.6.1 Nonlocal Properties of Complex Rays

314

(1)

5.6.2 Boundaries of Applicability of Complex Geometrical Optics

315

(1)

5.7 Numerical Algorithms for Complex-Ray Tracing

316

(10)

5.7.1 Initial Conditions for Complex Rays

316

(2)

5.7.2 Numerical Iterative Procedure for the Integration of the Ray Equations

318

(1)

5.7.3 The Shooting Procedure

318

(2)

5.7.4 The Problem of Multirayness

320

(1)

5.7.5 Determination of Amplitude and Phase. The Resulting Wave Field

320

(1)

5.7.6 Exponential Decay of the Wave Field in the Caustic Shadow

321

(1)

5.7.7 Uniform Asymptotic for the Wave Field at a Simple Caustic

322

(1)

5.7.8 Diffraction of a Gaussian Beam in a Homogeneous Medium

323

(2)

5.7.9 Gaussian-Beam Propagation through a Inhomogeneity

325

(1)

5.8 Summary

326

(2)

6. Conclusion

328

(3)

References

331

(20)

Index

351

Please wait while the item is added to your bag...

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Geometrical Optics in Engineering Physics

Summary

Table of Contents

Supplemental Materials