Diffraction Coefficients for Higher Order Edges and Vertices

Diffraction coefficients are determined for diffraction of a scalar field by a jth order edge or jth order vertex on a boundary surface or on an interface for $j\geqq 2$. By a jth order edge or vertex, we mean a curve or isolated point on a surface at which some jth derivative of the surface has a jump discontinuity, or at which some $( j - 1 )$st derivative of a coefficient in the boundary or interface condition has a jump. Previously, diffraction coefficients had been found only for first order edges and vertices. The method used here to find these coefficients consists in obtaining two asymptotic expansions of the field, both valid for large values of the wavenumber k. One is an outer expansion given by the geometrical theory of diffraction, and the other is a boundary layer expansion obtained by stretching coordinates and then expanding the field. The far field behavior of the boundary layer expansion is found by asymptotic evaluation of certain integrals. Matching the two expansions yields the diffra...