Computation of high frequency fields near caustics

Theodoros Katsaounis*, G. T. Kossioris, G. N. Makrakis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

It is well known that although the usual harmonic ansatz of geometrical optics fails near a caustic, uniform expansions can be found which remain valid in the neighborhood of the caustic, and reduce asymptotically to the usual geometric field far enough from it. Such expansions can be constructed by several methods which make essentially use of the symplectic structure of the phase space. In this paper we efficiently apply the Kravtsov-Ludwig method of relevant functions, in conjunction with Hamiltonian ray tracing to define the topology of the caustics and compute high-frequency scalar wave fields near smooth and cusp caustics. We use an adaptive Runge-Kutta method to successfully retrieve the complete ray field in the case of piecewise smooth refraction indices. We efficiently match the geometric and modified amplitudes of the multi-valued field to obtain numerically the correct asymptotic behavior of the solution. Comparisons of the numerical results with analytical calculations in model problems show excellent accuracy in calculating the modified amplitudes using the Kravtsov-Ludwig formulas.

Original languageEnglish (US)
Pages (from-to)199-228
Number of pages30
JournalMathematical Models and Methods in Applied Sciences
Volume11
Issue number2
DOIs
StatePublished - Mar 1 2001

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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