Diffraction of a skew incident plane electromagnetic wave by a wedge with axially anisotropic impedance faces

This paper presents, as an extension of the authors' recent work, an exact solution to diffraction of a skew incident plane electromagnetic wave by a wedge with axially anisotropic impedance faces. Applying the Sommerfeld-Malyuzhinets technique to the boundary-value problem yields a coupled system of difference equations for the spectra; on elimination, a functional difference (FD) equation of higher order for one spectrum arises; after simplification in terms of a generalized Malyuzhinets function and accounting for the Meixner's edge condition as well as the poles and residues of the spectrum in the basic strip of the complex plane, the FD equation is converted, via the so-called S integrals, to an integral equivalent; for points on the imaginary axis which belong to the basic strip the integral equivalent becomes a Fredholm equation of the second kind with a nonsingular, wave number-free and exponentially decreasing kernel; solving this integral equation by the quadrature method the spectrum can be determined by integral extrapolation and by analytical continuation; a first-order uniform asymptotic solution follows from evaluating the Sommerfeld integrals with the saddle-point method. Comparison with available exact solutions in several special cases shows that this approach leads to a fast and accurate solution of the problem under study.