The Electromagnetic Field for a PEC Wedge Over a Grounded Dielectric Slab: 1. Formulation and Validation

Complex scattering problems are often made by composite structures where wedges and penetrable substrates may interact at near field. In this paper (Part 1) together with its companion paper (Part 2) we study the canonical problem constituted of a Perfectly Electrically Conducting (PEC) wedge lying on a grounded dielectric slab with a comprehensive mathematical model based on the application of the Generalized Wiener-Hopf Technique (GWHT) with the help of equivalent circuital representations for linear homogenous regions (angular and layered regions). The proposed procedure is valid for the general case, and the papers focus on E-polarization. The solution is obtained using analytical and semianalytical approaches that reduce the Wiener-Hopf factorization to integral equations. Several numerical test cases validate the proposed method. The scope of Part 1 is to present the method and its validation applied to the problem. The companion paper Part 2 focuses on the properties of the solution, and it presents physical and engineering insights as Geometrical Theory of Diffraction (GTD)/Uniform Theory of Diffraction(UTD) coefficients, total far fields, modal fields, and excitation of surface and leaky waves for different kinds of source. The structure is of interest in antenna technologies and electromagnetic compatibility (tip on a substrate with guiding and antenna properties).