Caustics, Catastrophes and Wave Fields by Yu.A. Kravtsov

By Yu.A. Kravtsov

Caustics, Catastrophes and Wave Fields in a feeling maintains the therapy of the sooner quantity 6 "Geometrical Optics of Inhomogeneous Media" through analysing caustics and their fields at the foundation of recent disaster thought. the current quantity covers neighborhood and uniform caustic asymptotic expansions: The Lewis-Kravtsov approach to normal features, Maslov's approach to canonical operators , Orlov's approach to interference integrals, in addition to their adjustments for penumbra, space-time, random and different kinds of caustics. the entire equipment are amply illustrated through labored difficulties referring to suitable wave-field functions.

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Has recently received a proof to the opposite. 16] found a positive phase shift of Sc = nl2 corresponding to a negative Maslov index. This topic will be revisited in Chap. 10. 3 Caustic Zone and Caustic Volume Because the ampitude U 0 becomes infinite at a caustic, the geometrical optics solution at a caustic and in the close neighborhood is inapplicable as actual wave fields are always finite. Available exact and approximate solutions for some wave problems involving caustics indicate that a substantial concentration of the field takes place near a caustic.

The boundary r of a caustic inapplicability zone may be derived on other grounds. We recognize that in the vicinity of a caustic every point of observation r is hit by a few rays belonging to the same initial wave front. Consider the simplest situation of two rays with reference to Fig. 3. When the observation point is at a sufficient distance from the caustic, Fig. 3a, the Fresnel zones of these rays do not overlap in any intermediate surface Q. When r is moved closer to the caustic, at some time instant there will occur an overlap of the Fresnel zones, Fig.

It is integer-valued since the signature of matrix fj varies in even-numbered increments. The Maslov index occurs in many problems, specifically in the evaluation of eigenmodes in open resonators. , has recently received a proof to the opposite. 16] found a positive phase shift of Sc = nl2 corresponding to a negative Maslov index. This topic will be revisited in Chap. 10. 3 Caustic Zone and Caustic Volume Because the ampitude U 0 becomes infinite at a caustic, the geometrical optics solution at a caustic and in the close neighborhood is inapplicable as actual wave fields are always finite.

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