Atmospheric propagation of gradient-shaped and spinning femtosecond light pulses

The multiple filamentation of high power, ultrashort laser pulses is investigated for special waveforms exhibiting either sharp intensity gradients or vortex shapes having an angular orbital momentum. First, theoretical estimates are established on the basis of a (2+1)-dimensional model discarding temporal dependences, in order to evaluate the number of filaments and their onset distance with respect to the peak beam power or with the topological charge of optical vortices. Numerical simulations are next performed from this model and they confirm the theoretical expectations, at least qualitatively. These are shown to hold in (3+1)-dimensional geometry involving time variations, through direct numerical integrations of the propagation equations.