Diffraction of a normally incident plane wave by an impedance wedge with its exterior bisected by a semi-infinite impedance sheet

This paper reports an application of a previously proposed procedure to diffraction of a normally incident, arbitrarily polarized plane electromagnetic wave by a canonical structure which consists of a wedge with different face impedances and a semi-infinite impedance sheet bisecting the exterior of the wedge. The use of the Sommerfeld-Malyuzhinets technique converts the original boundary value problem into a system of linear equations for two coupled spectral functions. Eliminating one of them, we get a second-order difference equation for the other spectral function. From this function and the boundary condition on the upper wedge face we construct an even and in the basic strip regular new spectral function. Then we transform the second-order equation into a simpler one by means of a generalized Malyuzhinets function χ_Φ(α), and express the solution to the latter in an integral form with help of the so-called S-integrals. Solving a Fredholm equation of the second kind for points on the imaginary axis of the complex plane, which follows from the integral representation, enables one to compute the sought-for function. The second spectral function is obtained via its dependence upon the first one. We present a first-order uniform asymptotic solution, as well as numerical results.