▎ 摘　　要

We theoretically study the effective third-order nonlinear response and optical bistability of the 3D graphene based composite consisting of graphene wrapped dielectric nanoparticles embedded in dielectric host at terahertz frequencies. Taking into account the nonlinear conductivity of graphene, we derive the analytical expressions for the effective third-order nonlinear coefficient chi((3))(e) in weakly nonlinear limit. Moreover, for strong applied fields, the criterion for achieving optical bistability in such a graphene coated sphere, as well as the switching thresholds of optical bistability are discussed. We find that both chi((3))(e) and optical bistability are strongly dependent on the Fermi energy of graphene and it is possible to achieve very low switching thresholds under the normal graphene dissipation. We further propose a scheme to study the transmittance of this nonlinear composite slab. These results reveal novel regime of the optical bistability of the transmittance of light. We show that this kind of graphene-wrapped composite, which has tunable and low threshold optical bistability, can be the best candidate for unique nonlinear optical materials.