Generalization of UTD Double Diffraction to the Case of Impenetrable Wedges With Relatively General Boundary Conditions

Abstract

In the framework of the uniform geometrical theory of diffraction (UTD), a novel high-frequency solution is provided which allows the description of the rays doubly diffracted by a pair of impenetrable straight wedges, with relatively general boundary conditions, under a spherical wave illumination. Such a UTD solution is heuristically derived by imposing the continuity of the total field at the shadow boundaries of the first order (i.e., geometrical optics + UTD wedge single diffracted ray field) UTD solution. It is the extension, to the case of double diffraction, of the first order solutions proposed by Luebbers and by Burnside and Burgener; it allows a uniform description of the field at any observation point, including those aspects where transition regions overlap and the cascading of UTD single wedge diffraction coefficients fails. The proposed solution does not consider surface wave effects and, for the special case of two perfectly conducting wedges, it reduces to the formulation present in the literature, of which it can be considered a generalization. Indeed, it requires the same special functions involved in UTD double diffraction by two perfectly conducting wedges. The double diffracted ray field is expressed in analytical closed form, providing a deeper understanding of the physics involved in double diffraction, and a new powerful tool to be employed in any modern ray-based code.