On Singularities of Scattering Amplitudes through a Convex Triangular Obstacle in Scattering Theory

Abstract

A triangular grating is characterized by three parameters like period, groove depth and angle. A smooth convex triangular obstacle, forming a part of the said grating, is considered herewith for finding the Scattering amplitudes through the illuminated faced of the obstacle. Complex Fourier double transforms of the concerning wave functions has been determined for finding the Scattering amplitudes, allowing thereby the wave number to become unlimitedly large. It has been further justified that the singularities of the Scattering amplitudes occur when the concerning surface harmonics behave like distributions. In particular, the Scattering amplitudes have been determined when the Fourier transforms of the concerning wave functions behave like Dirac distributions. Finally, the expressions of relative powers of the groove fields have been determined in terms of the wedge parameters.