## Abstract

Temporally broadened ultrashort laser pulses impart thermal effects in the system under study even with nJ energies at high repetition rates (HRRs). The absorption induced accumulated thermal effects are prominent in materials with higher absorption. A numerical and experimental study with the help of a Z-scan has been carried out to estimate the nonlinear thermo-optic parameters of graphene by varying the input pulse duration ranging from sub-ps (100 fs) to a few ps (2.3 ps) at 780 nm. It is well known that for longer input pulses (in ns range), the thermal effects are high. In this study, we have found that the thermal effects in the sub-ps to few ps regime also result in a higher value of the thermo-optic nonlinear refractive index. Finite difference method calculations have been used to simulate the effect on the nonlinear phase shift under HRR fs pulses. The study has been found to be consistent with experiments. The experimental results along with the numerical simulation provide the importance of the contribution of the thermally induced refractive index change under HRRs within a few ms after excitation.

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