Optical Kerr effect in graphene: Theoretical analysis of the optical heterodyne detection technique

Graphene is an atomically thin two-dimensional material demonstrating strong optical nonlinearities, including harmonics generation, four-wave mixing, Kerr, and other nonlinear effects. In this paper we theoretically analyze the optical heterodyne detection (OHD) technique of measuring the optical Kerr effect (OKE) in two-dimensional crystals and show how to relate the quantities measured in such experiments with components of the third-order conductivity tensor sigma((3))(alpha beta gamma delta)(omega(1)omega(2)omega(3)) of the two-dimensional crystal. Using results of a recently developed quantum theory of the third-order nonlinear electrodynamic response of graphene, we analyze the frequency, charge carrier density, temperature, and other dependencies of the OHD-OKE response of this material. We compare our results with a recent OHD-OKE experiment in graphene and find good agreement between the theory and experiment.