Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams

We have studied the spontaneous breakup of highly elliptical laser beams into one- and two-dimensional arrays of light filaments in fused silica. Although the multiple filamentation process is initiated by random intensity modulation across the beam (amplitude noise), the output patterns exhibit a certain periodicity and high shot-to-shot reproducibility. The experimentally observed periodicity of the multiple filament arrays depends on the input beam intensity and this behavior is reproduced in detail by the numerical simulations. With the help of a simple analytical model we propose that the formation of periodic multiple filament structures could be understood within a simple framework of multistep phase-matched four-wave optical parametric amplification.