Pulse repetition-rate effect on the critical power for self-focusing of femtosecond laser in air

The femtosecond laser filamentation is of significant interest due to its remarkable characteristics, and determining the critical power of self-focusing is essential for the process of filamentation. In this work, the critical power for self-focusing of intense femtosecond laser pulses at different repetition rates is experimentally measured according to the focus-shift method. A bimodal fitting method is proposed to more accurately determine the self-focusing critical power. It is found that the self-focusing critical power decreases as the laser repetition rate increases. A numerical simulation of the filamentation process based on the modified nonlinear Schr & ouml;dinger equation effectively explains the experimental results obtained. This work provides valuable insights for the generation and application of high repetition rate femtosecond laser filamentation.