Gate-Tunable Nonlinear Refraction and Absorption in Graphene-Covered Silicon Nitride Waveguides

The nonlinear optical properties of graphene have received significant interest in the past years. Especially third-order nonlinear effects have been demonstrated to be large. Recently several groups have shown, through four-wave mixing (FWM) and third harmonic generation (THG) experiments, that the optical nonlinearity of graphene can be tuned through electrostatic gating. These effects are quantified by a strongly tunable vertical bar sigma((3))(s)vertical bar, with sigma((3))(s) the complex third-order conductivity. Here, by simultaneously observing cross-phase and cross-amplitude modulation on a silicon nitride waveguide covered with gated graphene, we are able to confirm such strong tunability for these nonlinear effects as well. Moreover, we can separately quantify the real and imaginary parts of sigma((3))(s), which respectively represent nonlinear absorption and refraction. This unveils a tunability that is far more drastic than what could be observed through FWM or THG, including sign changes in both the nonlinear absorption and refraction. Our results are confirmed by a theoretical model for the optical nonlinearity of graphene. The ability to tailor the nonlinearity of graphene to this extent can lead to new opportunities, such as nanophotonic devices with electrically tunable nonlinear properties.