Diffraction by dielectric wedge

The scattering of a plane monochromatic wave by a infinite dielectric wedge is discussed for arbitrary direction of incidence. The wave velocities in the interior and exterior of the wedge are distinct. At the boundary of the wedge there is a pair of transmissions conditions. We also impose Meixner´s condition at the edge. The wave field should also satisfy the radiation condition at infinity. Here we follow the approach based on Sommerfeld transforms and first applied in scalar problem by Maliuzhinets (1955, 1957, 1958) in his study of diffraction by wedge with impedance boundary conditions. Maliuzhinets reformulated the diffraction problem in the form of functional equations for Sommerfeld transform. Budaev (1995) reduced the diffraction problem for an elastic wedge to two decoupled systems of two functional equations and then to two singular integral equations. The Sommerfeld-Maliuzhinets method is used to represent the field in the interior and exterior regions of the wedge by means of two spectral functions. The original problem is decoupled into two, symmetric and antisymmetric. A pair of functional equations are obtained for these unknown spectral functions