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.