Uniform high-frequency description of singly, doubly, and vertex diffracted rays for a plane angular sector

Abstract

A high-frequency analysis of the scattered field at a plane angular sector is presented, for the scalar case in which hard boundary conditions are imposed on the two faces. In this formulation, the ordinary UTD field is augmented by uniform vertex diffraction contributions that provide the compensation of the UTD ray field when the first order diffraction points disappear from the tip. Furthermore, an expression of the doubly diffracted rays from the two edges is derived, that provides a uniform description of the total field at the ordinary double diffraction transition regions, including their possible overlapping. Moreover, a new transition function is introduced, which uniformly describes the transition field between doubly diffracted and vertex rays, that occurs when the double diffraction points merge in the tip. In spite of the complication of the physical mechanism, the final solution is simple and easy to implement.