The propagation of intense femtosecond laser pulses in air and other transparent media is characterized by the emergence of self-guided structures, named filaments. Laser filamentation, and a fortiori multiple filamentation at high input powers, is characterized by the emergence of long-tailed statistical distributions of filament transverse and longitudinal position, spectral contents, intensity, or pattern within the laser beam. Based on analogue driving equations (Non-linear Schrödinger equation, NLSE), they can offer a model of oceanic rogue waves, i.e., sudden unpredictable waves of up to 25-30 m high over a smoother sea.
We investigate the statistical behaviour of filamentation so as to transfer the acquired knowledge to the description of oceanic rogue waves. We dedicate a special attention to the multifilamentation pattern in terms of phase transition in the same universality class as two-dimensional percolation, so as to offer a novel physical system for such class. These results will be used to assess the predictability and possibility risk assessment of rogue waves, based on the temporal reversibility of the NLSE.