Analytical Circuit-based Model for Low Thickness Tunable Metasurfaces Design

An analytical model of metasurfaces made of a rectangular array deposited on a low thickness (10-150 µm) grounded dielectric layer is presented. The surface impedance and the equivalent circuit are extracted from full wave simulations. Contrary to previous works on higher thickness metasurfaces, the absorption corresponds to the first resonance under the patch. The equivalent circuit is made of a parallel resonant RLC circuit in series with an inductance Ls. The analytical expressions of the RLC components and of the quality factors are established from the study of the influence of the different parameters. The inductance Ls is attributed to the non-metallized part of the mesh. The impedance of the resonant circuit expresses as the product of a proportionality factor, the impedance of a single patch and a periodicity factor. The model is validated on different examples. Specific properties are evidenced like the quasi-independence of the equivalent circuit resistance versus the length of the patch, the total absorption condition and the extension of the model to a two patches metasurfaces. Giving a better understanding of the role of the different parameters, the model is useful in view of new applications development notably electrically driven tunable metasurfaces.