On a Uniform Geometrical Optics Analysis Valid Across Smooth Caustics of Rays Reflected by Smoothly Indented Boundaries

Abstract

Abstract : It is well known that the geometrical optics solution fails at and near ray caustics. It therefore becomes necessary to analyze the fields within ray caustic regions via uniform asymptotic procedures. Uniform asymptotic high frequency expressions are presented here for the fields reflected from both two and three dimensional smoothly curved boundaries, respectively, which are concave, or contain inflection points. These expressions remain uniformly valid across the transition regions adjacent to the smooth caustics of rays reflected in these configurations. While the subject of caustic field analysis is not new, and relatively sophisticated mathematical treatments for evaluating the fields uniformly in caustic regions have become available recently, those solutions do not appear to be readily ammendable for use in practical applications. Other uniform solutions, which also recover the geometrical optics field outside the caustic transition regions on the lit side of the caustic, mostly contain parameters that require a detailed knowledge of the caustic geometry and its location, especially for evaluating the field of dark side of the caustic.