Homogenized Dyadic Potential Green’s Function for Planar Metasurface Placed at Two Half Spaces Interface Excited by Vertical and Horizontal Ideal Electric Dipole

Abstract

In this article, dyadic magnetic vector potential Green’s functions corresponding to electric dipole which illuminates homogenized metasurface have been presented. Metasurface is constructed by a periodic arrangement of planar metallic scatterers and located at the interface of two different dielectric half spaces. The metasurface is replaced by a thin sheet with the dyadic equivalent surface distribution of electric and magnetic susceptibilities. These vector potentials have been derived employing generalized sheet transition condition (GSTC) on the plane of the metasurface. The retrieval relations to obtain equivalent surface susceptibilities of such a surface are calculated by means of the calculated reflection and transmission coefficients due to TE polarized plane waves. Also, the transverse and longitudinal scalar electric potentials relative to the problem have been calculated with the aid of the Lorentz gauge. These vector and scalar potentials together are necessary to use in the mixed potential integral equation (MPIE) formulation of the method of moment (MoM) in an electromagnetic problem.