A uniform geometrical theory of diffraction for vertices formed by truncated curved wedges

A uniform geometrical theory of diffraction (UTD) ray analysis is developed for analyzing the problem of electromagnetic (EM) scattering by vertices at the tip of a pyramid formed by curved surfaces with curvilinear edges when illuminated by an arbitrarily polarized astigmatic wavefront. The UTD vertex diffraction coefficient involves various geometrical parameters such as the local radii of curvature of the faces of the pyramid, of its edges, and of the incident ray wavefront, and it is able to compensate for those discontinuities of the field predicted by the UTD for edges (i.e., geometrical optics (GO) combined with the UTD edge diffracted rays) occurring when an edge diffraction point lies at the tip or vertex. This provides an effective engineering tool able to describe the field scattered by truncated edges in curved surfaces within a UTD framework, as required in modern ray-based codes. Some numerical examples highlight the accuracy and the effectiveness of the proposed UTD ray solution for vertex diffraction.