Embedding formulae for diffraction by non-parallel slits

Embedding formulae for diffraction theory encode the diffraction coefficients for some given wave incidence on a scatterer in terms of the directivity from a single or reduced number of scattering problems. If one deduces the relation between these directivities, then the resulting formulae enable rapid computations and allow one to concentrate computational resources accordingly. Unfortunately, the range of applicability of embedding formulae is currently rather restricted. In this article, we demonstrate how embedding is applied to plane-wave scattering by non-parallel strips or slits. Primarily, we concentrate upon the problem of a line crack, or strip, inclined to a flat infinite surface and we derive and implement the embedding formula. Various other generalizations are possible given these formulae and we outline them.