Dispersion Theory of Surface Plasmon Polaritons on Bilayer Graphene Metasurfaces

Surface plasmon polaritons (SPPs) on the graphene metasurfaces (GSPs) are crucial to develop a series of novel functional devices that can merge the well-established plasmonics and novel nanomaterials. Dispersion theory on GSPs is an important aspect, which can provide a basic understanding of propagating waves and further guidance for potential applications based on graphene metamaterials. In this paper, the dispersion theory and its modal characteristics of GSPs on double-layer graphene metasurfaces consisting of the same upper and lower graphene micro-ribbon arrays deposited on the dielectric medium are presented. In order to obtain its dispersion expressions of GSP mode on the structure, an analytical approach is provided by directly solving the Maxwell's equations in each region and then applying periodical conductivity boundary onto the double interfaces. The obtained dispersion expressions show that GSPs split into two newly symmetric and antisymmetric modes compared to that on the single graphene metasurface. Further, the resultant dispersion relation and its propagating properties as a function of some important physical parameters, such as spacer, ribbon width, and substrate, are treated and investigated in the Terahertz band, signifying great potentials in constructing various novel graphene-based plasmonic devices, such as deeply sub-wavelength waveguides, lenses, sensors, emitters, etc.