Recently, an approximate boundary condition [Opt. Lett. 38, 3009 (2013)] was proposed for fast analysis of one-dimensional periodic arrays of graphene ribbons by using the Fourier modal method (FMM). Correct factorization rules are applicable to this approximate boundary condition where graphene is modeled as surface conductivity. We extend this approach to obtain the optical properties of two-dimensional periodic arrays of graphene. In this work, optical absorption of graphene squares in a checkerboard pattern and graphene nanodisks in a hexagonal lattice are calculated by the proposed formalism. The achieved results are compared with the conventional FMM, in which graphene is modeled as a finite thickness dielectric layer. We show that for the same truncation order, computation time can be reduced to one-ninth by the proposed formulation in comparison with the conventional FMM. Furthermore, the convergence rate is increased. Therefore, thanks to the improved convergence rate and reduced computational cost for a given truncation order, the computational time is saved more than 100 times for relative error of less than 1%. This is crucially important in analyzing two-dimensional periodic structures of graphene by the FMM.
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