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 ${\sigma }_{\alpha \beta \gamma \delta }^{\left(3\right)}({\omega }_1,{\omega }_2,{\omega }_3)$ 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.

• Received 30 January 2018
• Revised 7 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.165424