Properties of self-focusing of elliptic beams

Stationary self-focusing of collimated elliptic Gaussian beams is studied numerically. It is shown that the critical self-focusing power increases with increasing the axial ratio of the initial elliptic cross section. Self-focusing is accompanied by oscillations of the beam transverse size caused by the competition between the diffraction-limited divergence and nonlinear compression. As the power of the beam with the axial ratio a/b≥3 increases, aberration self-focusing occurs, at which, after the formation and competition of several intensity maxima in the beam cross section, a global maximum appears at the beam centre, which forms a nonlinear focus. The approximation formula for the self-focusing distance is generalised to elliptic beams.