Here, the authors calculate the fields due to the electric dipole that excites a homogenized metasurface which is printed on a finite thickness dielectric slab. The problem is solved by replacing the total parts below the periodic array which contain the dielectric slab and the half-space under it, with an effective homogenous half-space. Furthermore, the static interaction constants between dipoles which are located at two different materials' interface are calculated. Then, with the help of the Lorentz method, the analytical formulae are presented to calculate the surface susceptibility densities of the homogenized metasurface located at two materials' interface. These analytical formulae can be applied to arrays with both square and rectangular periodicity. An array of circular patches printed on dielectric slabs with different thicknesses is considered to verify the results. The results show good agreement compared to the fields calculated by commercial numerical software FEKO. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
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