Revised transmission line model for electromagnetic characterization of metasurfaces

We have revised the transmission line model with the purpose of simplifying the electromagnetic characterization of metasurfaces with both electric and magnetic responses. The revised model is an efficient tool for the case when a metasurface is located on top of a finite-thickness substrate or inside a finite-thickness slab. We have derived analytical expressions for the grid series impedance and shunt admittance of a substrated metasurface. The presented theory is illustrated by a numerical example of an array consisting of Mie-resonant silicon nanospheres. We have retrieved individual polarizabilities of a single sphere in a uniform host medium and compared them with the predictions of classical Mie theory. Further, we have studied a more practical case when the array of Si spheres is located on top of a finite-thickness glass substrate.