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

The determination of natural frequencies for graphene scatterers is attained in the present work using a finite-difference (FD) scheme. The frequency-dispersive, 2-D material is treated as an equivalent surface current density, while an appropriately derived auxiliary differential equation (ADE) is introduced to acquire a linear eigenvalue problem. Then, FD 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 (SPP) waves of the 2-D material are supported. The numerically extracted eigenstates are compared with the absorption cross section (ACS) analysis of full-wave simulations, with respect to the resonance frequencies. The obtained results substantiate precise modeling, while also retrieving the quality factor of the supported modes.