Electromagnetic Energy Surface Modes in Metamaterial-Filled Bi-layer Graphene Structures

This paper presents a theoretical study on the propagation of electromagnetic surface waves supported by the metamaterial-filled bi-layered graphene structure. The effective surface conductivity approach based upon the Kubo’s formalism is used to model the atomically thick graphene layer, while the analytical modeling of the metamaterials used the framework of causality principle-based Kramers-Kroing relations. With respect to the index of refraction, the two configurations of metamaterials have been considered—i.e., double positive (DPS) and double negative (DNG). The impedance boundary conditions (IBCs) have been employed at the interface for the computation of characteristics equations of odd and even surface modes under DPS and DNG configurations. The numerical results regarding the dispersion relations, effective mode index, and phase speed for the odd and even modes of electromagnetic surface waves supported by each configuration of structure have been presented. Further, the influence of chemical potential and thickness of metamaterial filling in parallel graphene layers on the wave propagation characteristics has been analyzed. To check the accuracy of the numerical results, special conditions were employed, which converge to the published results. The proposed work may have potential applications in plasmonic based logic designs, renewable energy devices, THz surface wave guides, and near-field communication devices.