Propagation of high-power phase-modulated femtosecond laser pulses in air in the self-channeling and filamentation modes

Propagation of high-power phase-modulated femtosecond laser pulses in air is simulated numerically. Spatial modulation of the initial wavefront of the pulse was implemented using a programmable phase mask consisting of checkered zones with a varied phase jump of the wave. Within the framework of the numerical solution of the nonlinear Schrödinger equation for the time-averaged amplitude of the electric field, modes of self-focusing, filamentation, and postfilamentation channeling of radiation for phase-modulating masks with different phase shifts at boundaries of adjacent segments are studied. It is shown that for certain types of phase modulation of the pulse the filamentation domain in air can be significantly shifted (in the coordinate) and elongated as compared with a nonmodulated pulse. In addition, it is established that using phase modulation makes it possible to decrease angular divergence of high-intensity light channels forming at the stage of postfilamentation propagation. This provides the possibility of radiation self-channeling at distances multiple exceeding the Rayleigh length