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A graphene/Si system, which is composed of a two-dimensional subwavelength silicon gratings and a graphene sheet, is designed to realize the complete band gap in infrared region for graphene surface plasmons (GSPs) theoretically. The complete band gap originates from the strong scatterings, which is caused by the periodical distribution of effective refractive index. The band structure has been calculated using the plane wave expansion method, and full wave numerical simulations are conducted by finite element method. Thanks to the tunable permittivity of graphene, the band structure can be easily tuned, which provides a way to manipulate in-plane GSPs’ propagation

Graphene surface plasmon bandgap based on two dimensional Si gratings