Intensity limitation for a self-focusing femtosecond laser pulse propagating in a medium with cubic nonlinearity

The self-focusing of an axisymmetric beam propagating in a cubically nonlinear medium has been studied by computer simulation with allowance for the temporal dispersion of the nonlinear response, which is manifested for femtosecond laser pulses. It shown that, depending on the ratio of the medium length and the diffraction length, the dispersion of the nonlinear response can lead either to limitation of the intensity growth rate in the nonlinear focus or its absence (for weakly diffracting beams), to an increase in the range of the nonlinear focus formation (for beams with a diffraction length 2.5-25 times the medium length), or to a decrease in this range (for beams with a diffraction length approximately equal to or shorter than the medium length). These phenomena are related to the dependence of the group velocity of pulse propagation on its intensity.