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 Schrödinger 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.
The results of studies of the femtosecond laser pulses propagation in air in the mode of self-focusing and filamentation are presented. The analysis of the numerical simulation results is carried out based on the method of diffraction-ray tubes. This approach made it possible to evaluate the characteristics of the energy-replenishing diffraction-ray tube, which forms a nonlinear focus, contains energy sufficient for compensation of the beam energy loss throughout the entire life cycle of the filament, and after its completion determines the boundaries of the postfilamentation channel (PFC). It is found that the average power in PFC formed by beams of sub- and millimeter radius is about 0.6-0.9 critical power for self-focusing, and it weakly depends on the initial parameters of the femtosecond laser pulse. In general, the energy consumption of radiation on filamentation decreases with increasing the initial beam radius. The angular divergence of PFC decreases by an order when the initial radius of the laser beam increases from submillimeter to millimeter values. For the last class of beams, the angular divergence of PFC remains approximately constant (20-25 microradians). Dependence of the angular divergence of post-filamentation light channels on the peak pulse power is less pronounced.
The results of natural experiments of the propagation of powerful femtosecond laser radiation in glass and water, accompanied by multiple filamentation, and the results of numerical simulation of the process are presented. Based on the diffusive equations for density of the number of filament estimates of the positions of maxima in the number of filaments were obtained. Sufficient criterion of macroscopic refocusing for density of the number of filaments was established.