A Simple Effective Permittivity Model for Metasurfaces Within Multilayer Stratified Media

A simple and accurate approach for computing the effective permittivity of metasurfaces embedded within arbitrary stratified media is presented. The proposed model provides accurate estimation of the effective permittivity for stackups with several dielectric layers with arbitrary thickness and permittivity. The effect due to the unit cell geometry is also taken into account. The accuracy of the model is rigorously verified by comparing the effective permittivity estimated by the approximate model with the one extracted by using full-wave method of moments (MoM) simulations as a function of the substrate thickness.