Ray-based methods in multidimensional linear wave conversion

Abstract

A tutorial introduction to the topic of linear wave conversion in multiple spatial dimensions is provided. The emphasis is on physical concepts, particularly those features of multidimensional conversion that are new and different from the more familiar “mode conversion” problem in one spatial dimension. After introductory comments, a brief review of WKB theory for vector wave equations in the absence of conversion is provided in order to introduce notation, terminology, and geometrical ideas. A primary theme of the discussion is that, although WKB (ray-based) methods break down in conversion regions, the ray geometry in the conversion region can be used to develop local wave equations that govern the two coupled wave channels undergoing conversion. These methods can be incorporated into ray-tracing algorithms providing, for the first time, the ability to follow the “ray splitting” associated with linear conversion in multidimensions, including the amplitude and phase changes associated with the conversion.