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

Abstract

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).

The Electromagnetic Field for a PEC Wedge Over a Grounded Dielectric Slab: 2. Diffraction, Modal Field, Surface Waves, and Leaky Waves

“…In this companion paper we have described from a practical physical/engineering point of view the application of the generalized Wiener‐Hopf technique (GWHT) to complex scattering problems (Daniele, ; Daniele & Lombardi, ; Daniele et al, ) constituted of wedges and layers that may interact at near field. The mathematical formulation and its validation is fully described in paper Part 1 (Daniele et al, ). The generalized Wiener‐Hopf technique (GWHT) (Daniele, ; Daniele & Lombardi, ) has been introduced to extend the classical Wiener‐Hopf technique (CWHT) to problems involving angular regions (see Lawrie & Abrahams, , and references therein).…”

“…Alternative approaches applied to similar structures are reported in (Angulo & Chang, 1959;Bates & Mittra, 1968;Kobayashi, 1984;Noble, 1958;Yee & Felsen, 1969). For what concerns alternative approaches to wedge problems and the application of the Wiener-Hopf technique to similar context, we make references to the bibliography of Part 1 (Daniele et al, 2017).…”

“…In Part 1 (Daniele et al, ) the problem is formulated first in terms of generalized Wiener‐Hopf equations (GWHEs) for each region and then the solution is obtained through the reduction of the factorization problem to Fredholm integral equations (FIEs) (Daniele & Lombardi, ; Daniele & Zich, ). In particular, we obtain integral representations for each region in terms of the axial spectral unknowns V + ( η ), I + ( η ) that can be easily and practically interpreted as a circuital constitutive relation, that is, Norton circuital representation of the GWHE for each region.…”

“…In particular, we obtain integral representations for each region in terms of the axial spectral unknowns V + ( η ), I + ( η ) that can be easily and practically interpreted as a circuital constitutive relation, that is, Norton circuital representation of the GWHE for each region. We recall that the axial spectral unknowns are the Laplace transform of field components on the aperture ( x > 0, y = 0, i.e., φ = 0) and with reference to the definitions reported in (6)–(9) of Part 1 (Daniele et al, ), we have …”

“…In the companion paper Part 1 (Daniele et al, ), we formulate, validate, and solve in terms of analytical elements of the spectral unknowns the canonical problem reported in Figure , where a perfectly electrically conducting (PEC) wedge is lying on a grounded dielectric slab bounded by a PEC plane. The proposed procedure is valid for the general case although the papers focus on E polarization.…”