Caustics, Catastrophes and Wave Fields (inbunden)
Inbunden (Hardback)
Antal sidor
2nd ed. 1993
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
M G Edelev
Edelev, M. G. (ed.)
XII, 216 p.
234 x 156 x 14 mm
504 g
Antal komponenter
1 Hardback
Caustics, Catastrophes and Wave Fields (inbunden)

Caustics, Catastrophes and Wave Fields

Inbunden Engelska, 1998-11-01
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Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 "Geometrical Optics of Inhomogeneous Media" in the present book series, by analysing caustics and their fields on the basis of modern catastrophe theory. This volume covers the key generalisations of geometrical optics related to caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions, Maslov's method of caonical operators, Orlov's method of interference integrals, as well as their modifications for penumbra, space-time, random and other types of caustics. All the methods are amply illustrated by worked problems concerning relevant wave-field applications.
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1 Introduction.- 1.1 Caustic Fields in Physical Problems.- 1.2 The Geometrical Aspect of the Caustic Problem.- 1.3 The Wave Aspect of the Caustic Problem.- 2 Rays and Caustics.- 2.1 Equations of Geometrical Optics.- 2.1.1 The Scalar Problem.- 2.1.2 Electromagnetic Waves in an Isotropic Medium.- 2.1.3 Electromagnetic Waves in an Anisotropic Medium.- 2.2 The Role of Rays in the Method of Geometrical Optics.- 2.2.1 The Locality Principle.- 2.2.2 Rays as Energy and Phase Trajectories.- 2.2.3 Fresnel Volume of a Ray: The Physical Content of the Ray Concept.- 2.2.4 Heuristic Criteria of Applicability for Ray Theory.- 2.2.5 Distinguishability of Rays.- 2.3 Physical Characteristics of Caustics.- 2.3.1 Caustics as Envelopes of Ray Families.- 2.3.2 Caustic Phase Shift.- 2.3.3 Caustic Zone and Caustic Volume.- 2.3.4 Ray Estimates of Fields at Caustics and in Focal Spots.- 2.3.5 Indistinguishability of Rays in a Caustic Zone.- 2.3.6 Reality of Caustics.- 2.3.7 A Remark on Multipath Propagation.- 2.4 Complex Rays.- 2.4.1 Main Properties of Complex Rays.- 2.4.2 Reflection of a Plane Wave from a Linear Slab.- 2.4.3 Nonlocal Nature of Complex Rays.- 2.4.4 Domain of Localization of Complex Rays.- 3 Caustics as Catastrophes.- 3.1 Mappings Induced by Rays.- 3.1.1 The Ray Surface and Lagrange's Manifold.- 3.1.2 Classification of Structurally Stable Caustics.- 3.2 Classification of Typical Caustics.- 3.2.1 Generating Function: Codimension and Corank.- 3.2.2 Caustic Surfaces of Low Codimension.- 3.2.3 Caustics of High Codimension.- 3.2.4 Subordinance Relations.- 4 Typical Integrals of Catastrophe Theory.- 4.1 Standard Caustic Integrals.- 4.1.1 Use of Generating Functions as Phase Functions.- 4.1.2 Reducing Integrals to Normal Form.- 4.1.3 Multiplicity of Standard Integrals.- 4.2 The Airy Integral.- 4.2.1 Basic Properties.- 4.2.2 The Airy Differential Equation.- 4.2.3 An Example of Airy-Integral Solution to the Wave Problem.- 4.2.4 The Airy Integral as a Standard Function for the One-Dimensional Wave Equation.- 4.2.5 Applicability Conditions of the Uniform Airy Asymptotic in One-Dimensional Problems.- 4.3. The Pearcey Integral.- 4.3.1 Properties.- 4.3.2 Focusing in the Presence of Cylindrical Aberration.- 4.3.3 Caustic Indices and Field Structure.- 4.4 Other Typical Integrals.- 4.4.1 Generalized Airy Functions.- 4.4.2 Fresnel Criteria for Transition to Subasymptotics.- 4.4.3 Field Structure in Different Areas of the External Variable Domain.- 4.4.4 Integrals of the Dm+1 Series.- 4.4.5 Caustics with a Large Number of Rays.- 4.4.6 Calculation of Standard Integrals.- 5 Uniform Caustic Asymptotics Derived with Standard Integrals.- 5.1 Uniform Airy Asymptotic of a Scalar Field.- 5.1.1 Heuristic Foundation of the Method of Standard Integrals.- 5.1.2 Guessing at a Form of Solution.- 5.1.3 Equations for Unknown Functions.- 5.1.4 Relation of the Airy Asymptotic to the Ray Fields.- 5.1.5 Field in the Caustic Shadow.- 5.1.6 Local Field Asymptotic near a Caustic.- 5.1.7 Interpolation Formula for a Caustic Field.- 5.1.8 Estimating the Coefficient of the Airy Function Derivative.- 5.1.9 The Geometric Backbone and Wave "Flesh".- 5.1.10 Uniform Airy Asymptotic of an EM Field.- 5.1.11 Local Asymptotic of an EM Field.- 5.1.12 One-Dimensional Problem.- 5.1.13 Applicability Conditions for the Airy Asymptotic.- 5.2 Uniform Caustic Asymptotics Based on General Standard Integrals.- 5.2.1 Structure of a Solution.- 5.2.2 Equations for Phase and Amplitude Functions.- 5.2.3 Relation to Geometrical Optics.- 5.2.4 General Scheme to Compute Caustic Fields.- 5.2.5 Uniform Caustic Asymptotic of an EM Field.- 5.2.6 The Ray Skeleton and Uniform Caustic Asymptotics.- 5.2.7 Some Specific Situations.- 5.2.8 Local Asymptotics.- 5.3 Illustrative Examples.- 5.3.1 The Circular Caustic.- 5.3.2 Point Source in a Linear Slab.- 5.3.3 Swallowtail Caustics in a Linear Layer Bordering upon a Homogeneous Halfspace.- 5.3.4 Butterfly in a Parabolic Plasma Layer.- 5.3.5 Elliptic Umbilic For