Iterative suppression of Kerr-induced instabilities in Bessel beams using on-axis intensity shaping

Abstract

Kerr-induced instabilities in zeroth-order Bessel beams with low focusing angle prevent the formation of longitudinally uniform plasma rods in the filamentation regime. These instabilities lead to the oscillation of the beam on-axis intensity via the generation of new spatial frequencies by a first stage of spectral broadening followed by a second stage of four-wave mixing. Here, we numerically demonstrate an efficient approach to drastically reduce the instabilities due to the second stage. It is based on shaping the longitudinal intensity profile with spatio-spectral components in opposition of phase to the Kerr-generated ones via an iterative approach. Zeroth-order Bessel beams with a longitudinal flat intensity plateau can be generated in a few iterations in the nonlinear regime. This is performed in both monochromatic and pulsed femtosecond regimes.