Unraveling absorptive and refractive optical nonlinearities in CVD grown graphene layers transferred onto a foreign quartz substrate

•Z-scan technique has been employed to examine the optical nonlinearities of graphene layers.•Combination of saturation absorption and reverse saturation absorption was observed from open aperture Z-scan.•Self-defocusing effect and hence negative nonlinear refraction was observed from closed aperture Z-scan.•Optical nonlinearity is found to reduce upon annealing of graphene layers.•Annealing paves a way to manipulate sp2/sp3 fractions.