Theory of the nonlinear optical frequency mixing effect in graphene

A quantum theory of the frequency mixing effect in graphene is developed. A graphene layer is assumed to be irradiated by two monochromatic waves with the frequencies ω1 and ω2 and the nonlinear third order electromagnetic response at the mixed frequency ωe=2ω1−ω2 is calculated. The corresponding third order nonlinear conductivity of graphene is calculated as a function of frequency, charge carrier density, as well as the intensity and the polarization of the incident waves. The intensity of the nonlinear optical signal is also calculated as a function of the number N of graphene layers in a multi-layered system and it is shown that the best performance of the graphene/graphite based nonlinear optical mixer or frequency multiplier can be achieved in thin graphite layers with N≃25−30.