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

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