Equivalent circuit of the double-fishnet metamaterial

In this paper, an equivalent circuit for the fishnet metamaterial of two stacked holey metallic layers it is shown. All lumped elements of the circuit are extracted from a full physical interpretation of its electrodynamics when the structure is excited with a normally incident plane wave. Besides the well known LC parallel tank that accounts for the transmission through a single subwavelength hole array, the coupling between the layers is modeled as another LC series tank which is also related with the non-propagating higher order modes. The effective index of refraction and the scattering parameters retrieved from the proposed circuit matches remarkably the one obtained from full-wave numerical calculations. The importance of the extraordinary transmission (ET) phenomenon in the electromagnetic behavior of the fishnet metamaterial is shown as well.