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.
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