Calculation of Potential Green’s Functions for a Planar Metasurface Excited by an Electric Dipole Using Homogenization Method

One of the rapid and efficient methods to calculate the interaction between electromagnetic fields and periodic surfaces with periodicity much less than the wavelength in the surrounding medium is the homogenization method. In this paper, the Hertzian potential Green’s functions corresponding to electric dipoles which excite a homogenized metasurface are presented. The metasurface includes a periodic array of planar scatterers and is replaced by a thin sheet with equivalent electric and magnetic surface polarization density dyads. The magnetic vector potentials are calculated using the generalized sheet transition conditions on the plane of the metasurface. Also the scalar electric potential corresponding to the structure is calculated with the aid of the Lorentz gauge. These potentials together are necessary to use in the mixed potential integral equation formulation of the method of moment in an electromagnetic problem. Two metasurfaces are investigated to calculate the electric fields; a perfect electric conductor square patch array whose surface polarization densities are calculated analytically, and a Jerusalem cross array whose surface polarization dyads are retrieved from reflection and transmission coefficients.