Surface plasmon dispersion and modes on the graphene metasurface with periodical ribbon arrays

Graphene plasmonics on the structured metasurface demonstrate many exotic properties which can combine novel nanomaterials and well-established plasmonics, providing unique opportunities to develop a series of novel photonic, plasmonic and optoelectronic devices across a wideband spectrum. Dispersion theory and its propagating characteristics of surface plasmon polaritons (SSPs) mode along the graphene metasurface can provide a powerful guidance to design related devices and systems. In this paper, the fundamental dispersion theory and the numerical studies of graphene SSPs (GSPs) on a graphene metasurface i.e. periodical ribbon arrays which are bounded by a superstrate and substrate dielectric are presented. The dispersion expression of GSPs is deduced and revealed by a modal expansion method combined with periodical boundary conditions on the structure. According to this fully analytical dispersion expression of SSPs mode on the graphene metasurface, the dispersion characteristics, propagation loss and field profiles of SSPs mode with different graphene material parameters (e.g. graphene ribbon width and chemical potential) and bounded dielectric mediums are studied and analyzed in detail in terahertz (THz) band. Moreover, the dynamical tunable dispersion characteristics of SSPs mode on the graphene metasurface via electrostatic gating of a ground metal plate can be readily obtained by applying a graphene biased voltage model to this analytical dispersion theory. The presented studies on the dispersion theory of the graphene metasurface provide an analytical method to understand the propagation characteristics of SSPs mode on the structure. Besides, the calculation results on the structure can also be used to design some novel graphene-based optoelectronic and plasmonic devices with planar gradient-index distributions such as couplers, tunable focused lens and enhanced radiation sources in THz band.