Diffraction of an obliquely incident plane wave by a two‐face impedance half plane: Wiener‐Hopf approach

Abstract

The problem of diffraction of plane electromagnetic waves at an imperfectly conducting half plane with different impedances on upper and lower faces for oblique (skew) incidence either leads to a Wiener‐Hopf equation with a 4×4 Fourier symbol matrix for the tangential field components or to two formally decoupled Wiener‐Hopf equations with 2×2 symbol matrices of the Daniele‐Khrapkov form for the electric and magnetic field components perpendicular to the diffracting edge. The higher‐order edge singularity of the normal field components leads to undetermined constants in the classical Wiener‐Hopf solution that are used to eliminate “unphysical” leaky wave poles that appear in the final solution by the residue calculus technique. The interrelation between both formulations involves an analytic family of polynomial transformation matrices. Consideration of the range restriction of this mapping is shown to be equivalent to the pole elimination procedure.