Second Harmonic Generation in Graphene

We report on theoretical study of second harmonic generation in graphene. Phenomenological analysis based on symmetry arguments is carried out. It is demontrated, that in ideal graphene samples second harmonic generation is possible only if the radiation wave vector or its magnetic field is taken into account. Microscopic theory is developed for the classical regime of radiation interaction with electrons, where photon energy is much smaller than the charge carriers characteristic energy. It is demonstrated, that the emitted radiation can be strongly circularly polarized for the linearly polarized incident wave.