DIFFRACTION BY AN ELLIPTIC CONE AND THE SOLUTION OF THE WEDGE DIFFRACTION PROBLEM

Contents: The paper deals with scalar diffraction by an elliptic cone in the limit case of ellipticity parameter k = 0. In this case the elliptic cone degenerates into a wedge with exterior opening angle 290. We solve the two-parameter eigenvalue problem for two coupled Lame differential equations for k = 0 and obtain the eigenvalues and the eigenfunctions for the wedge problem by a completely analytical calculation. We utilize a precise transformation of the sphero-conal coordinates into spherical coordinates with the edge of the wedge as polar axis and determine, by substitution of the transformed Lame products into Green's functions for the elliptic cone, the solution of the scalar diffraction problem for the wedge. The results obtained are in full agreement with those reported in [2]. In the special case of half-plane diffraction (theta0 = pi) the solution reduces to that in [1].