Edge Functions and Their Application to Solution of Canonical Problems of Scattering in Wedge-shaped Domains

Abstract

This paper presents a promising semi-analytical method for solving canonical problems of electromagnetic scattering by non-metallic wedges (dielectric or impedance). The edge functions are introduced as partial solutions of Maxwell's equations, which satisfy the edge conditions at the edge of a wedge and continuity conditions for the tangential field components across each material interface. The eigenvalues are found from the condition of solvability of the problem. Since the edge functions do not meet the radiation conditions, the total field diffracted by a wedge is constructed by superposing the edge functions in such a way so as to get the radiation conditions satisfied. The paper illustrates usability of the technique by considering the canonical problem of scattering of an obliquely incident plane electromagnetic wave by a wedge with impedance faces.