In this paper Hertzian vector potential Green's function as well as the electric scalar potential Green's function is calculated for metfilm located on two half-spaces interface to use in the mixed potential integral equation. However, in practical applications, metafilm is located on a finite thickness dielectric layer such as dielectric slab. This practical problem is solved by replacing all the parts beneath the periodic array, with an effective homogenous half-space. Therefore the finite thickness dielectric slab problem changes into the half-space problem. When metafilm is located at two different materials interface, the induced bound charges in the dielectric result in different surface susceptibility densities. This paper attempts to derive analytical formulae to calculate the surface susceptibility densities. To this aim, the interaction constant between dipole elements which are arranged in a rectangular periodic array and embedded at two materials interface are calculated. Furthermore, the retrieval formulae are presented to obtain the susceptibility parameters of metafilms constructed by arbitrary shaped elements. Two metafilms are considered as examples to verify the formulation. The results show good agreements with numerical method ASM-MoM and commercial numerical software FEKO.
