Embedding formulae for diffraction by rational wedge and angular geometries

Abstract

Embedding is the process of taking the far-field directivity from a diffraction problem (or problems) involving line sources or multipoles placed at a sharp edge, and then constructing the far field, for the same geometry, for more general incidence using only this canonical problem(s). Thus far, embedding has been limited to planar, parallel scattering surfaces, for instance, collections of parallel cracks or slits; it appeared that there was a fundamental limitation to embedding, disallowing its use for angular structures. In this article, we overcome this limitation and demonstrate the use of embedding upon wedge diffraction problems and upon a simple polygonal shape; a limitation is that the final formulae are for rational wedge angles.