Nonlinear optics of graphene in a strong magnetic field

Graphene placed in a magnetic field possesses an extremely high mid/far-infrared optical nonlinearity originating from its unusual band structure and selection rules for the optical transitions near the Dirac point. Here we study the linear and nonlinear optical response of graphene in strong magnetic and optical fields using quantum- mechanical density-matrix formalism. We calculate the power of coherent terahertz radiation generated as a result of four-wave mixing in graphene. We show that even one monolayer of graphene gives rise to appreciable nonlinear frequency conversion efficiency and Raman gain for modest intensities of incident infrared radiation.