Uniform diffraction coefficients at a plane angular sector

A high-frequency description of the scattering from complex structures that exhibits surface discontinuities such as edges and vertices is of importance in a wide variety of practical applications. To this end, the geometrical theory of diffraction (GTD) and its uniform extension (UTD) provided very effective tools for most engineering purposes. Within this framework, an important canonical problem is that of a corner at the interconnection of two straight edges, joined by a plane angular sector. Corner diffraction coefficients have been derived in the plane wave-far field regime by using the induction theorem. These non-uniform coefficients, that account for second order interactions between the two edges, exhibit the expected singularities at the caustics of single and doubly diffracted rays. The above solution is used to weight the plane wave spectrum representation of a source, located at a finite distance from the vertex. Via a suitable asymptotic evaluation of the spectral integrals, a high-frequency uniform solution is obtained. For the sake of simplicity, the scalar case is treated and the formulation for hard boundary conditions is given explicitly.<>