Caustics, Catastrophes and Wave Fields [Hardcover]

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.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.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 Applicablól