Ray-based diffraction calculations using stable aggregates of flexible elements

Diffraction effects are incorporated into a ray-based method for wave propagation, referred to as stable aggregates of flexible elements (SAFE). SAFE is based on the assignment of a Gaussian field contribution to each ray, where these contributions are not independent beam solutions of the wave equation. The effects of diffraction by planar opaque obstacles (within the Kirchhoff approximation) are accounted for by introducing rays emanating from the obstacle's edges. The two leading asymptotic terms to the complex amplitudes for these contributions are derived. It is shown that this scheme leads to field estimates that remain valid and accurate at caustics and shadow boundaries, as illustrated by two examples, corresponding to a focused wave in free space and a field propagating in a layered inhomogeneous medium. For simplicity, two-dimensional propagation is considered.