Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states

The filamentation of optical beams in focusing Kerr media is investigated. First, the creation of filamentary structures is shown to strongly depend on the radial distribution of the incident beam in the diffraction plane. With a cubic nonlinearity, broadening an input beam from Gaussian to super-Gaussian (SG) shapes relaxes the self-focusing (SF) attractor and triggers the formation of independent filaments. Analytical criteria for the mutual coalescence of filaments in the context of collapsing and saturating nonlinearities are proposed. Second, the influence of the polarization state on the filamentation instability is investigated. Rigorous conditions for the SF of beams with different polarizations are derived, which prove that the power threshold for collapse noticeably increases for circularly-polarized beams. The growth rate for modulational instability decreases accordingly and the minimal separation distance for coalescence becomes larger, which slows down the production of uncorrelated filaments. Implications of these results in atmospheric propagation are finally discussed.