Numerical simulations of self-channeling and filamentation of spatially pre-modulated high-power femtosecond laser pulse in air

The numerical simulations of propagation of high-power femtosecond laser pulses in air under conditions of superposed spatial phase modulation are carried out on the basis of the reduced form of nonlinear Schrцdinger equation for time-averaged electric field envelope. Initial spatial modulations are applied to pulse wavefront profiling by a staggered phase mask with variable phase jumps between adjacent elements. It is shown that with specific phase modulations, the pulse filamentation region in air can be markedly shifted further and elongated compared to a non-modulated pulse