Multiple diffraction of a line source field by a three-part thin transmissive slab

Abstract

A uniform asymptotic high-frequency solution is presented for the problem of diffraction of a line source field by a three-part thin transmissive slab. After simulating the slab by a material plane with a set of approximate boundary conditions used recently by RAWLINS et al., the three-part boundary-value problem is transformed into a modified matrix Wiener-Hopf equation. By performing the factorization of the kernel matrix through the DANIELE-KHRAPKOV method, the modified matrix Wiener-Hopf equation is first reduced to a pair of coupled Fredholm integral equations of the second kind and then solved approximately by iterations. An interesting feature of the present solution is that the classical Wiener-Hopf arguments yield unknown constants which may be determined by means of the edge conditions.