Modeling the filamentation of ultra-short pulses in ionizing media

The filamentation of ultra-short pulses is investigated for plane waves propagating in gases ionized by multiphoton sources. The spatial growth rate of the filamentary modulational instability is computed as a function of the transverse wavenumber and frequency of periodic perturbations. Classical results for optical filamentation in Kerr media are recovered when the density of the electron plasma produced by ionization is close to zero. However, when the electron density is high enough, a beam with an input power above the Kerr self-focusing threshold is shown to stop forming filaments. Stability domains are expressed in terms of the electron density and pulse peak power, both for stationary perturbations and when the inertial plasma response together with the group-velocity dispersion of the wave are taken into account. These theoretical results are supported by numerical simulations and the influence of a delayed Kerr response on filament formation is finally discussed.