Diffraction of a plane wave by a transparent wedge. Calculation of the diffraction coefficients of wave scattered by vertex of the wedge

Two dimensional scalar diffraction of a plane wave by a transparent wedge is considered. The wave process is described by the classical Helmholtz equations with wave velocities different inside and outside the wedge, with conjugation boundary condition on its sides. The solution satisfies radiation conditions at infinity and Meixner condition in the neighborhood of the vertex. Incident plane wave is assumed to illuminate both sides of the wedge. We seek the solution as a sum of layer potentials with densities belonging to a special class. This problem reduces to obtaining Fourier transforms of the densities from a certain system of integral equations, which is solved numerically using collocation method. Diffraction coefficients of the wave scattered by the vertex is presented via Fourier transforms of the densities. Calculation of diffraction coefficients requires an analytical extension, which is done using the functional equation. The calculation of diffraction coefficients is similar to that by J.-P. Croisille and G. Lebeau [1].