On a uniform asymptotic solution valid across smooth caustics of rays reflected by smoothly indented boundaries
Abstract
An asymptotic highfrequency solution is described which remains uniformly valid across smooth caustics of geometrical optics rays reflected from two and threedimensional 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 concaveconvex 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 concaveconvex boundary is established with results obtained via an independent moment method analysis.
 Publication:

IEEE Transactions on Antennas and Propagation
 Pub Date:
 August 1990
 DOI:
 10.1109/8.56955
 Bibcode:
 1990ITAP...38.1192P
 Keywords:

 Asymptotic Methods;
 Electromagnetic Scattering;
 Geometrical Optics;
 Surface Geometry;
 Wave Reflection;
 Caustics (Optics);
 Electromagnetic Fields;
 Communications and Radar