Nonlinear propagation of self-guided ultra-short pulses in ionized gases

The nonlinear propagation regimes of femtosecond pulses in noble gases and air are analyzed from an extended nonlinear Schrödinger equation coupled with the inertial response of an electron plasma created by multiphoton process and avalanche ionization. By means of integral relations supplemented by two variational approaches, it is shown that the electron density produced by photo-ionization defocuses the beam and arrests the self-focusing promoted by the Kerr response of the gas, so that a balance between both these effects can be realized for incident pulses with sufficiently high input power. Theoretical descriptions of self-guided beams emphasize the distortions caused by multiphoton sources in the temporal pulse profiles and they are confronted with direct numerical simulations. Dissipative effects as multiphoton absorption and the delayed Kerr response induced by air are finally discussed.