Analytical Circuit Model for Periodic Arrays of Graphene Disks

In this paper, an analytical circuit model is proposed for 2-D arrays of graphene disks. First, we derive an analytical expression for the surface current density on a single graphene disk in the subwavelength regime, induced by a normally incident plane wave. The solution is then extended to 2-D arrays of graphene disks using perturbation theory. Finally, by applying appropriate boundary conditions, an R-L-C equivalent circuit of the structure is obtained. It is shown that both a single graphene disk and periodic array of graphene disks have dual capacitive-inductive nature. The results of the proposed model are in excellent agreement with those obtained by full-wave simulations.