Effective dispersion length during the propagation of powerful femtosecond laser pulses in air

The effect of the group velocity dispersion of a pulse on the propagation of pulses of a titanium-sapphire laser in air is considered. Numerical simulation is performed for powerful femtosecond laser pulses with a duration of 100 and 20 fs, while laser beams with different initial radius and peak powers is considered. The study is based on the analysis of the results of numerical solutions of the nonlinear Schrodinger equation in a Kerr-plasma dissipative dispersion medium, carried out in the framework of the diffraction-ray tube method. The manifestation of dispersion is detected in the case when the dispersion length is not the smallest scale of all the characteristic longitudinal scales of the problem. The relation for the effective dispersion length is obtained in order to evaluate the effect of normal dispersion on the propagation of powerful femtosecond laser pulses. It has been established that in a nonlinear focusing medium, an increase in the initial radius of the laser beam can cause a disruption of filamentation even at high levels of supercritical power.