Suppressing filamentation instability due to laser beam self-filtering

The development of small-scale self-focusing in a nonlinear Kerr medium after preliminary self-filtering of a laser beam propagating in free space is studied numerically.It is shown that,under definite conditions,due to self-filtering,filamentation instability(beam splitting into filaments)either occurs at significantly larger values of the B-integral,or does not occur at all.In the latter case,there develops the honeycomb instability revealed in this work.This instability is the formation of a random honeycomb structure in the beam cross-section.It is shown that self-filtering can significantly increase the permissible values of the B-integral,at which the beam quality remains acceptable.