Abstract
We study nonlinear optical response of graphene in the quantum Hall regime to an intense laser pulse. In particular, we consider harmonic generation process. We demonstrate that the generalized magneto-optical conductivity of graphene on the harmonics of a strong pump laser radiation has a characteristic Hall plateaus feature. The plateaus heights depend on the laser intensity and broadening of Landau levels, so that are not quantized exactly. This nonlinear effect remains robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and nonlinear Faraday effect, which are within the experimental feasibility.