Experimental Characterization of Ultrafast, Tunable and Broadband Optical Kerr Nonlinearity in Graphene

In this study we systematically measure the near-infrared spectral dependence, the sub-picosecond temporal evolution and pulse-width dependence of the effective Kerr coefficient ($n_{2,eff}$) of graphene in hundreds of femtosecond regime. The spectral dependence measured using the Z-scan technique is corroborated by quantum theory to extract a $n_{2,eff} \propto \lambda^2$ dependence. The temporal evolution extracted using the time-resolved Z-scan measurement shows the nonlinear response peaking at zero delay time and relaxing on a time scale of carrier relaxation. Since the Kerr-type response originated from the optically induced carrier population difference, the time-scale of the evolution of the nonlinear response is apt. The $n_{2,eff}$ shows a dependence on the pulse-width attributed to the relative heating and cooling times of the carriers. This dependence is strong when the pulse-duration is on the same time-scale as the decay constant. Throughout our study the $n_{2,eff}$ remains positive.