Method of lines for the analysis of tunable plasmonic devices composed of graphene-dielectric stack arrays

Due to the increasing interest in emerging applications of graphene or other 2D material-based devices in photonics, a powerful, fast and accurate tool for the analysis of such structures is really in need. In this paper, the semi-analytical method of lines (MoL) is generalized for the diffraction analysis of tunable graphene-based plasmonic devices possessing three dimensional periodicity. We employ Floquet's theorem to handle analytically propagation of waves in the periodicity of the graphene-dielectric arrays in the direction of the layers stacking. This makes the method very effective in terms of computational time and memory consumption. To validate its efficiency and accuracy, the method is applied to plasmonic devices formed by alternating patterned graphene sheets and dielectric layers. Direct comparison with results available in literature and those obtained by a commercial software exhibits their full consistency.