Deriving a Lumped Element Surface Impedance Model for Periodic Arrays of Graphene Micro-Rings

In this paper, a lumped element circuit model for a periodic array of Graphene rings is derived using analytical procedures. The computations are in the subwavelength regime and under normal incidence. It is shown that the model is also valuable for a single Graphene ring. The methodology includes solving the surface current integral equation for the rings by designing an eigenvalue problem. The absorption spectrum of proposed model is compared with full-wave simulations to verify the model accuracy. Furthermore, inspection of the simulation results for different Fermi energies and unit cell dimensions, helped us examine the validity of analytical formulas. This model opens up the way to control the structure performance and refine it in favor of our requirements for different applications.