  Under strong laser illumination, few-layer graphene exhibits both a
transmittance increase due to saturable absorption and a nonlinear phase shift.
Here, we unambiguously distinguish these two nonlinear optical effects and
identify both real and imaginary parts of the complex nonlinear refractive
index of graphene. We show that graphene possesses a giant nonlinear refractive
index n2=10-7cm2W-1, almost nine orders of magnitude larger than bulk
dielectrics. We find that the nonlinear refractive index decreases with
increasing excitation flux but slower than the absorption. This suggests that
graphene may be a very promising nonlinear medium, paving the way for
graphene-based nonlinear photonics.
