On a uniform asymptotic solution valid across smooth caustics of rays reflected by smoothly indented boundaries

Abstract

An asymptotic high-frequency solution is described which remains uniformly valid across smooth caustics of geometrical optics rays reflected from two- and three-dimensional boundaries that are concave or exhibit points of inflection. In particular, outside the caustic transition region this solution not only reduces uniformly to the reflected geometrical optics real ray field on the lit side of the caustic, but it also uniformly recovers the reflected geometrical optics complex ray field on the dark side of the caustic. Furthermore, it is expressed in terms of parameters that can be calculated relatively easily. This analysis is used to calculate the electromagnetic field scattered from a concave-convex shaped boundary with an edge, as well as by a smoothly indented cavity, each of which contains points of inflection thereby giving rise to caustics of reflected rays. The accuracy of the numerical results presented for the edged concave-convex boundary is established with results obtained via an independent moment method analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>