▎ 摘　　要

Based on the tight-binding model we construct a nonlinear Hamiltonian to describe the effective electric system around the M point for the single layer graphene. The local energy spectrum at the M point is approximated by the perfect hyperbolic geometry, and the modification by the screening effect from the substrate is taken into account. With the method based on the concept of the Floquet states and quasienergies (FSQ) we investigate the third order nonlinear conductivity sigma(3)(omega), sigma(3)(3 omega) for the different frequency ranges, respectively, in which only the pi - pi* bands are involved. A positive cusplike peak arises at h omega=epsilon(gap)(M)/3 for sigma(3)(3 omega) which originates from the three-photon processes. Also, there is a peak at epsilon(gap)(M)/2 for sigma(3)(omega) resulting from two-photon-resonant processes. The analysis of the pole processes indicates that a self-energy-like term transition process plays a role in the nonlinear optical response, and the different transition processes interact with each other during the response to the external field. These interactions can be influenced by the polarization of the external field.