Flux density and caustics for sound multiply reflected or refracted in variable index media

Abstract

A formula is given for the flux density along a ray path when sound or light is propagated in variable index media. The sound may be reflected or refracted by an arbitrary interface between media of different indices of refraction. Results are applicable in the geometrical optics limit, that is, the wavelength must be small relative to other dimensions. The only requirement is that the equation for the geodesics in the media be solvable so that an explicit expression is available for the ray path. Results are applicable to multiple reflection of sound from underwater objects and in assessing the performance of variable index lenses. Equations are also given for the associated caustics.