Quadratic electro-optic Kerr effect in doped graphene

Abstract

We theoretically investigate one of the third-order nonlinear optical (NLO) effects, namely, the quadratic electro-optic Kerr effect (EOKE), in doped graphene. To avoid the screening of an in-plane external dc electric field by the graphene’s electrons, we propose to use ‘low-amplitude’ ( cm−1) terahertz radiation pulses focused onto the graphene sample collinearly with a normally incident optical beam of frequency ω. Using the Dirac cone approximation for the π-electron energy bands of graphene, we calculate the real part of the effective third-order NLO susceptibility , describing the EOKE in doped graphene under the above conditions. The results obtained show that a large electro-optic modulation of the graphene’s refractive index n (up to ) can be achieved by proper tuning the Fermi level of charge carriers in the graphene sample via electrostatic gating. Furthemore, a change of sign of the electro-optic Kerr coefficient of doped graphene can occur in the spectral range below the photon energy threshold value of , corresponding to the onset of the fundamental (single-photon) interband absorption in the graphene. These theoretical findings open up new opportunities for practical exploitation of the EOKE in graphene-based NLO devices.