Uniform Ray Description for the PO Scattering by Vertices in Curved Surface With Curvilinear Edges and Relatively General Boundary Conditions

A new high-frequency analysis is presented for the scattering by vertices in a curved surface with curvilinear edges and relatively general boundary conditions, under the physical optics (PO) approximation. Both, impenetrable (e.g., impedance surface, coated conductor) as well as transparent thin sheet materials (e.g., thin dielectric, or frequency selective surface) are treated, via their Fresnel reflection and transmission coefficients. The PO scattered field is cast in a uniform theory of diffraction (UTD) ray format and comprises geometrical optics, edge and vertex diffracted rays. The contribution of this paper is twofold. First, we derive PO-based edge and vertex diffraction coefficients for sufficiently thin but relatively arbitrary materials, while in the literature most of the results (especially for vertex diffraction) are valid only for perfectly conducting objects. Second, the shadow boundary transitional behavior of edge and vertex diffracted fields is rigorously derived for the curved geometry case, as a function of various geometrical parameters such as the local radii of curvature of the surface, of its edges and of the incident ray wavefront. For edge diffracted rays, such a transitional behavior is found to be the same as that obtained heuristically in the original UTD. For vertex diffracted rays, the PO-based transitional behavior is a novel result providing offers clues to generalize a recent UTD solution for a planar vertex to treat the present curved vertex problem. Some numerical examples highlight the accuracy and the effectiveness of the proposed ray description.