In this paper, we present a numerically study of the nanoscale refractive index sensor based on periodically modulated graphene ribbon arrays with finite-difference time-domain method (FDTD). The results show that the resonance wavelengths of the graphene metamaterials structure have an approximate linear correlation with the refractive index of the dielectric substrate, which can be used as the refractive index sensor exhibits a higher sensitive of 3069.1 nm/RIU. Furthermore, the resonant wavelength of the structure tends to exhibit a clearly blue shift with the Fermi-level (Ef) of graphene ribbons increasing. And the shift of the resonant peak ups to 4906.3 nm per unit Fermi level. Besides, the influence of ribbon-width and Fermi level of the graphene on the performance of sensor are investigated in details. We believe that the work is useful for the design and application of the plasmonic refractive index sensors based on a grapheme ribbon array.
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