A Laplace transform technique for wedge shaped isorefractive regions

Many techniques have been proposed for studying wedge shaped regions: among them it is important to mention the Malyuzhinets (1958) approach, which is based on the Sommerfeld representation. This technique yields an elegant formal procedure for solving difficult problems, like the diffraction by wedges with given surface impedances. However, even if the Sommerfeld integral is a valid ansatz for representing the solutions of the wave equation in angular regions, the Laplace transform appears to be a more valid representation, because of its solid mathematical foundation. Other authors have shown that the Laplace transform technique may be an alternative with respect to the Malyuzhinets approach, even if in some cases it is not so simple and elegant. In this paper we propose a new technique, based on the Laplace representations of the electromagnetic field, for solving isorefractive angular regions excited by an incident E-polarized plane wave in the z-direction.