  We theoretically study the role of nonlinear surface plasmoms on the optical
bistability of graphene-wrapped dielectric cylinders, within the framework of
both full-wave scattering theory and the quasistatic limit. Typical hysteresis
curves are observed in both near-field and far-field spectra. Moreover, we
demonstrate that introducing the full wave theory results in another bistable
behavior with a high applied electromagnetic field, suggesting a more explicit
way in analyzing the unstable behavior of the graphene-wrapped dielectric
cylinder. Furthermore, optical stable region and the switching threshold values
are proved to be tunable by changing either the size, permittivity of the
nanocylinder or the chemical potential of graphene, promising the
graphene-wrapped dielectric cylinder a candidate for all-optical switching and
nano-memories.
