Effective Finite-Difference Modeling of Graphene Micro-Resonators for the Accurate Natural Frequency Extraction

The determination of the natural frequencies for graphene scatterers is attained in the present work using a finite-difference scheme. The frequency-dispersive, two-dimensional material is treated as an equivalent surface current density, while an appropriately derived auxiliary differential equation is introduced to acquire a linear eigenvalue problem. Then, the finite-difference discretization is performed in a Yee-cell manner to straightforwardly implement all the required curl operations. The proposed scheme is validated using a rectangular graphene patch at the THz regime, where the surface plasmon polariton waves of the two-dimensional material are supported. The numerically extracted eigenstates are compared with the absorption cross-section analysis of full-wave simulations, with respect to the resonance frequencies. The obtained results substantiate the precise modeling, while, also, retrieving the quality factor of the supported modes.