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We present a three-dimensional finite element (FEM) field-flux eigenmode formulation, able to provide accurate modeling of the propagation characteristics of periodic structures featuring graphene. The proposed formulation leads to a linear eigenmode problem, where the effective refractive index is a unknown eigenvalue; the electric field intensity and magnetic flux density are the state variables; and graphene’s contribution is efficiently incorporated via a finite conductivity boundary condition. The FEM formulation is spurious-mode free and capable of providing accurate dispersion diagrams and field distributions for arbitrary propagation directions, as opposed to other analytical or numerical approaches, while also efficiently dealing with graphene’s dispersive nature. The novelty of the presented approximation is substantiated by computational results for structures incorporating graphene of random periodicity, both within passbands and bandgap frequencies.

COMPUTATIONAL ANALYSIS OF GRAPHENE-BASED PERIODIC STRUCTURES VIA A THREE-DIMENSIONAL FIELD-FLUX EIGENMODE FINITE ELEMENT FORMULATION