A Semi-Analytical Solution of the Impedance-Wedge Problem

Abstract

Diffraction of a plane electromagnetic wave by a wedge with infinite planar faces is a key canonical problem of high-frequency diffraction and scattering theories, including Geometrical, Uniform and Physical Theories of Diffraction (GTD, UTD and PTD). This paper presents a new solution of the problem, in the framework of which the spectra of the Sommerfeld-Maliuzhinets plane-wave expansion are constructed as meromorphic functions on the complex plane of the spectral variable. Retaining a finite number of poles in the approximation results in a finite system of equations that can be easily solved. Already the inclusion of several poles ensures accuracy acceptable in most practical applications.