Combined Spectral Methods to Study Complex Scattering Problems Formulated with the Wiener-Hopf Technique: the Semi-infinite Grounded Dielectric Slab problem

In this work we present a new combination of spectral methods that allows to study complex scattering problem in spectral domain containing abrupt discontinuities of materials. The method is applied to a formulation of problem given in terms of incomplete Wiener-Hopf (WH) equations, where, for incompleteness, we intend that some of the physical boundary conditions arising from abrupt discontinuities provide terms in the WH equations not directly related to the plus and minus unknowns of the problem. This is the case of the semi-infinite grounded dielectric slab problem where the semi-infiniteness geometry of the material provide such situation. This problem is of great interest in antennas and propagation community and studies are proposed in different papers with different methods; see references in [1]. The WH incomplete equations are obtained as in [1] starting from the application of unilateral Laplace transform to wave equations defined in three different sub-regions, see Fig. 1.