ON DIFFRACTION BY A HALF-PLANE IN AN ARBITRARY ANISOTROPIC MEDIUM

Abstract

A method of uncoupling simultaneous Wiener–Hopf equations is developed. If the kernel-matrix G of the equations has the form G = Γ1(A + Γ1B), where Γ1, Γ2 are scalars and A and B are polynomial matrices, then the method works if the elements of A and B satisfy a certain equation called the "criterion".The method is applied to the diffraction of an arbitrary plane wave by a conducting half-plane in a medium with arbitrary tensor permittivity. It is found that in certain circumstances, G has the correct form Γ1(A + Γ2B). Application of the criterion then yields in principle a catalogue of solvable problems. In practice a complete listing has not been obtained because of the amount of algebra involved. However, a partial catalogue has been prepared. It includes most of the previously solved problems plus one or two which have not yet been considered. An example is briefly considered.