Titolo: Geometrical Optics of Inhomogeneous Media (Springer Series on Wave Phenomena)
Editore: Springer
Data di pubblicazione: 2011
Lingua: Inglese
ISBN 10: 3642840337
ISBN 13: 9783642840333
Rilegatura: Brossura
Condizione: New

Descrizione articolo

Riassunto

Geometrical Optics of Inhomogeneous Media presents a systematic treatment of geometrical optics, the most effective and widely used method of wave theory. The treatment includes the major developments of recent decades, among them the space-time geometrical optics of dispersive media, the quasi-isotropic approximation, new perturbation techniques for rays, and universally valid limits of applicability.

Contenuti

1. Introduction.- 2. The Scalar Wave Field.- 2.1 Equations of Geometrical Optics.- 2.1.1 Mathematical Background.- 2.1.2 Field Expansion in a Dimensionless Parameter.- 2.1.3 Field Expansion in Inverse Wave Numbers.- 2.1.4 Initial Conditions for the Eikonal and Amplitude Equations.- 2.1.5 Asymptotic Nature of the Ray Series.- 2.2 Rays and the Eikonal.- 2.2.1 The Method of Characteristics.- 2.2.2 Ray Equations and the Eikonal.- 2.2.3 Curvature and Torsion of Rays.- 2.2.4 Initial Conditions for Rays. Ray Coordinates.- 2.2.5 Ray Families and Phase Fronts.- 2.2.6 The Fermat Principle.- 2.2.7 Ray Equations in Curvilinear Coordinates.- 2.2.8 Other Types of Ray.- 2.3 Wave Amplitude.- 2.3.1 Formal Solution of the Transport Equation.- 2.3.2 Rays and the Direction of Energy Flow.- 2.3.3 Conservation of Energy Flux in a Ray Tube.- 2.3.4 The Field due to a Point Source in an Inhomogeneous Medium.- 2.3.5 The Resultant Field in the Ray-Optics Approximation.- 2.3.6 The Field Amplitudes of Higher-Order Approximations.- 2.3.7 Accounting for Weak Absorption.- 2.4 Caustics.- 2.4.1 Fundamental Properties.- 2.4.2 Wave-Field Focusing on Caustics.- 2.4.3 Types of Caustics.- 2.4.4 Structurally Stable and Unstable Caustics in Physical Problems.- 2.4.5 Other Types of Caustics.- 2.4.6 Singularities of Phase Fronts.- 2.4.7 Phase Shifts at Caustics.- 2.5 Reflection and Refraction of Waves at Interfaces.- 2.5.1 The Locality Principle in Wave Reflection.- 2.5.2 Relations for Rays and Eikonals.- 2.5.3 Reflection Formulas for Amplitude.- 2.5.4 Reflection from Weak Interfaces.- 2.5.5 The Geometrical Optics of Surface Waves.- 2.6 Reciprocity of Rays and Caustics.- 2.6.1 The Reciprocity Theorem.- 2.6.2 Reciprocity Relations for Rays and Caustics.- 2.7 Space-Time Geometrical Optics.- 2.7.1 The Wave Equation for Media with Temporal (Frequency) Dispersion.- 2.7.2 Necessary Conditions for the Geometrical-Optics Applied to Quasi-Monochromatic Wave Packets.- 2.7.3 Differential Form of the Constitutive Equation (2.7.2).- 2.7.4 Eikonal and Transport Equations.- 2.7.5 Space-Time Rays.- 2.7.6 Initial Conditions.- 2.7.7 Eikonal and Wave Amplitude.- 2.7.8 Space-Time Caustics.- 2.7.9 Propagation of Field Discontinuities in Nondispersive Media.- 2.8 Separation of Variables in the Eikonal Equation.- 2.8.1 The Complete Integral of the Eikonal Equation.- 2.8.2 Separation of Variables in Two Dimensions (Cartesian Coordinates).- 2.8.3 Separation of Variables in Two Dimensions (Curvilinear Orthogonal Coordinates).- 2.8.4 Separation of Variables in Three-Dimensional Space.- 2.8.5 Incomplete Separation of Variables.- 2.8.6 The Complete Integral of Eikonal and Ray Equations.- 2.9 Perturbation Techniques for Geometrical-Optics Equations.- 2.9.1 The Perturbation Method for the Eikonal.- 2.9.2 The Perturbation Method for Rays.- 2.9.3 Perturbations in Homogeneous Media.- 2.9.4 Perturbations in Nonhomogeneous Media.- 2.10 Applicability of Geometrical Optics.- 2.10.1 Existent Estimators of Method’s Errors.- 2.10.2 Fresnel Zones and Fresnel Volume of Rays in Inhomogeneous Media.- 2.10.3 The Physical Meaning of the Ray.- 2.10.4 Heuristic Criteria on Geometrical-Optics Applicability.- 2.10.5 Applicability Conditions for Space-Time Geometrical Optics.- 2.10.6 Heuristic Accuracy Estimates of Geometrical Optics.- 2.10.7 Estimating the Width of a Caustic Zone.- 2.10.8 Indistinguishability of Rays in the Caustic Zone.- 2.10.9 Observability of Caustics.- 2.10.10 Field Estimations Beyond the Validity Region of Geometrical Optics.- 2.10.11 Field-Focusing Indices at Caustics.- 2.10.12 Stability with Respect to Small Perturbations.- 2.10.13 Wave-Pattern Analysis in General.- 3. Applications of the Ray Methods.- 3.1 Waves in Homogeneous Media.- 3.1.1 Rays and the Eikonal.- 3.1.2 The Wave Amplitude.- 3.1.3 Caustics.- 3.1.4 The Plane Phase-Amplitude Screen.- 3.1.5 The Sinusoidal Phase Screen. An Illustrative Example.- 3.1.6 Applicability Conditions for Geometrical Optics.- 3.1.7 Geometrical Optics in Far and Near Antenna Fields. Wave Beam Propagation.- 3.1.8 On the Phase Center of an Antenna or a Scatterer.- 3.1.9 Field Near a Lens Focus.- 3.1.10 Field at the Focus of a Lens with Cylindrical (Spherical) Aberration.- 3.2 Reflection and Refraction at an Interface Between Homogeneous Media.- 3.2.1 Reflection Formulas.- 3.2.2 Divergence of Reflected and Refracted Rays.- 3.2.3 Effective Scattering Surface of a Body in the Geometrical-Optics Approximation.- 3.2.4 Reflection Far Field of a Directional Point Source.- 3.2.5 Caustics of Refracted and Reflected Rays.- 3.2.6 Examples of Catacaustics and Diacaustics.- 3.2.7 Applicability of Reflection Formulas.- 3.2.8 The Invalidity Domain in the Vicinity of a Tangent Ray.- 3.2.9 Wave Diffraction at a Surface of Variable Impedance.- 3.3 Rays and Caustics in Plane-Stratified Media.- 3.3.1 Ray Equations.- 3.3.2 Ray Tracing in a Plane-Stratified Medium.- 3.3.3 Equations of Caustics, and the Geometry of the Ray Family.- 3.3.4 Rays and Caustics due to a Point Source in an Inhomogeneous Medium.- 3.3.5 Rays and Caustics in a Linear Layer.- 3.3.6 Layers of Other Profiles.- 3.3.7 Plane Waves in a Parabolic Layer.- 3.3.8 A Point Source in a Parabolic Layer.- 3.4 Wave Fields in Plane-Stratified Media.- 3.4.1 The Field of an Arbitrary Wave.- 3.4.2 The Field of a Plane Wave.- 3.4.3 Fields of Point and Linear Sources.- 3.4.4 A Point Source in a Linear Layer.- 3.4.5 A Point Source in a Parabolic Layer.- 3.4.6 The Fresnel Volumes in Plane-Stratified Media.- 3.4.7 Validity Conditions of the Geometrical-Optics Approximation.- 3.5 Waves in Radially Inhomogeneous Media.- 3.5.1 Ray Equations for Spherically Stratified Media.- 3.5.2 The Eikonal Function for Spherically Stratified Media.- 3.5.3 Cylindrically Stratified Media.- 3.5.4 Ray Geometry.- 3.5.5 The Field due to a Point Source.- 3.5.6 The Field of a Plane Wave.- 3.5.7 Caustics.- 3.6 Tapered and Other Inhomogeneous Media.- 3.6.1 The Eikonal and Rays in a Tapered Medium.- 3.6.2 The Field of a Plane Wave.- 3.6.3 The Field due to a Linear Source.- 3.6.4 Ray Equations in a Two-Dimensional Medium with a Special Profile.- 3.6.5 The Field of a Point Source (Axially Symmetric Problem).- 3.6.6 A Plane Wave Incident on the Two-Dimensionally Inhomogeneous Medium.- 3.6.7 Weakly Inhomogeneous, Quasi-Stratified, and Random Media.- 3.7 Geometrical Optics of Waveguides and Resonators.- 3.7.1 Geometrical Optics of Waveguides.- 3.7.2 Ray Description of Modes in Uniform Waveguides.- 3.7.3 Adiabatic Modes of Smoothly Nonuniform Waveguides.- 3.7.4 Ionospheric Wave Channels. The Adiabatic Invariant Method.- 3.7.5 Underwater-Sound Ducts. Summing-Up Incoherent Wave Fields.- 3.7.6 Optical Fibers.- 3.7.7 Mode Conversion in Smoothly Nonuniform Waveguides.- 3.7.8 Normal Modes in Cavity Resonators.- 3.8 Wave Scattering at Localized Inhomogeneities.- 3.8.1 Effective Scattering Surface.- 3.8.2 Scattering by a Body in an Inhomogeneous Medium.- 3.8.3 Effective Scattering Surface of a Spherically Stratified Inhomogeneity.- 3.8.4 Effective Scattering Surface of a Perfectly Conducting Sphere in a Spherically Stratified Medium.- 3.8.5 Effective Scattering Surface of a Specific Two-Dimensionally Inhomogeneous Formation.- 3.8.6 Scattering of a Spherical Wave by a Localized Inhomogeneity.- 3.8.7 Scattering by Weak Localized Inhomogeneities.- 3.9 Pulse Propagation.- 3.9.1 General Relations for the Plasma (Guided) Dispersion Law.- 3.9.2 A Homogeneous Medium with an Arbitrary Dispersion Law.- 3.9.3 A Plane, Frequency-Modulated Pulse in a Homogeneous Medium.- 3.9.4 Dispersive Compression of FM Pulses in Homogeneous Media.- 3.9.5 Plane-Stratified Dispersive Media.- 3.9.6 Near and Far Fields of a Pulse.- 3.10 Numerical Methods in the Geometrical Optics of Inhomogeneous Media.- 3.10.1 The Ray-Tracing Analysis.- 3.10.2 Computing the Eikonal and Wave Amplitude.- 3.10.3 Problems of Numerical Analysis.- 3.11 Inverse Problems of Geometrical Optics.- 3.11.1 Reflection and Refraction at Interfaces.- 3.11.2 Inverse Problems for Given Models of the Inhomogeneous Medium.- 3.11.3 Multidimensional Inverse Problems.- 3.11.4 Nonstationary Inverse Problems.- 4. Vector Wave Fields.- 4.1 Transverse Electromagnetic Waves in Isotropic Media.- 4.1.1 Maxwell Equations for Monochromatic Waves.- 4.1.2 The Debye Expansion and the Iterative Equations.- 4.1.3 The Eikonal Equation.- 4.1.4 Transverse Nature of Zero Approximation Waves. Polarization Degeneracy.- 4.1.5 Consistency of the First-Approximation Equations.- 4.1.6 Conserving Energy Flow in a Ray Tube.- 4.1.7 Preserving the Polarization Ellipse.- 4.1.8 Rotation of Field Vectors (Rytov’s Law).- 4.1.9 Polarization of Transverse Waves.- 4.1.10 Longitudinal Components of the Field.- 4.1.11 Reflection of Transverse Electromagnetic Waves from Interfaces.- 4.1.12 Polarization Degeneracy in Problems of Quantum Mechanics and Theory of Elasticity.- 4.2 Independent Normal Waves in an Anisotropic Medium.- 4.2.1 Equation of the Eikonal.- 4.2.2 Independent Normal Mode.- 4.2.3 Ray Equations.- 4.2.4 Solving the Eikonal Equation.- 4.2.5 Definition of Mode Polarization Vectors.- 4.2.6 Consistency of Equations of the First Approximation.- 4.2.7 The Transfer Equation.- 4.2.8 Equation for the Argument of a Complex Amplitude.- 4.2.9 Rays and Energy Paths. The Fresnel Volumes in Anisotropic Media.- 4.2.10 An Account of Weak Absorption.- 4.2.11 Reflection and Refraction at the Boundaries of Anisotropic Media.- 4.2.12 Some Specific Results.- a) The Field of a Point Source in an Anisotropic Medium.- b) Waves in Plane-Stratified Anisotropic Media.- c) Separation of Variables in the Equation of Eikonal in the General Case.- d) Perturbation Theory.- 4.2.13 Divergence of First-Approximation Fields at Polarization Degeneracy.- 4.2.14 Other Vector Problems.- 4.3 Interaction of Normal Modes in Inhomogeneous Anisotropic Media.- 4.3.1 Waves in Weakly Anisotropic Media. The Quasi-Isotropic Approximation.- 4.3.2 Different Forms of the Equations of the Quasi-Isotropic Approximation.- 4.3.3 Solution Techniques for the Quasi-Isotropic Approximation.- 4.3.4 On the Error of the Quasi-Isotropic Approximation.- 4.3.5 Applications of the Quasi-Isotropic Approximation.- 4.3.6 The Quasi-Degenerate Approximation...

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