Wiener-Hopf analysis of the EM diffraction by an impedance discontinuity in a planar surface and by an impedance half-plane

The Wiener-Hopf technique is used to solve two canonical problems. The first problem considered is the electromagnetic (EM) diffraction, by a planar surface with an impedance discontinuity (two-part surface), of an arbitrarily polarized plane wave obliquely incident to the axis of the two-dimensional objects. The second problem considers the EM diffraction by a half-plane with equal impedances on both sides. The solutions obtained are cast in a matrix notation which is useful for diffraction problems. The exact formal solutions are expressed in terms of integrals which can be asymptotically evaluated. Uniform asymptotic expressions are obtained where the presence of the geometrical optics (GO) poles as well as the surface-wave poles near the saddle point are fully taken into account. Several numerical examples are presented and it is shown that the solutions are continuous across the shadow boundaries of the GO and surface-wave fields