▎ 摘　　要

We theoretically investigate the optical bistability in compound systems composed of one-dimensional graphene arrays and dielectrics. Graphene sheets are periodically assembled in the dielectric substrate to form the arrays of graphene and a bulk dielectric contacts on the right of the structure. The standing wave resonances can enhance the nonlinearity of graphene arrays and consequently multiple optical bistabilities are achieved with appropriate red-detunings in incident wavelengths. The realization of multiple bistabilities and the bistable thresholds depend on the thickness of the bulk dielectric. Otherwise, the multiple bistabilities could be modulated by impurity-doping in graphene or an external gate voltage on graphene arrays as well. This investigation has potentials applied in multivalued all-optical switches and optical memory.