Fringe integral equation method for a truncated grounded dielectric slab

The problem of scattering by a semi-infinite grounded dielectric slab illuminated by an arbitrary incident TM_z polarized electric field is studied by solving a new set of “fringe” integral equations (F-IEs), whose functional unknowns are physically associated to the wave diffraction processes occurring at the truncation. The F-IEs are obtained by subtracting from the surface/surface integral equations pertinent to the truncated slab, an auxiliary set of equations obtained for the canonical problem of an infinite grounded slab illuminated by the same source. The F-IEs are solved by the method of moments by using a set of subdomain basis functions close to the truncation and semi-infinite domain basis functions far from it. These latter functions are properly shaped to reproduce the asymptotic behavior of the diffracted waves, which is obtained by physical inspection. The present solution is applied to the case of an electric line source located at the air-dielectric interface of the slab. Numerical results are compared with those calculated by a physical optics approach and by an alternative solution, in which the integral equation is constructed from the field continuity through an aperture orthogonal to the slab. The applications of the solution to an array of line currents are also presented and discussed