Microscopic model for the higher-order nonlinearity in optical filaments

Using an exactly soluble one-dimensional atomic model we explore the idea that the recently observed high-order nonlinearity in optical filaments is due to virtual transitions involving the continuum states. We show that the model's behavior is qualitatively comparable with the experimentally observed cross-over from self-focusing to de-focusing at high intensities, and only occurs at intensities which result in significant ionization. Based on these observations, we conjecture that this continuum electron nonlinear refraction exhibits strong memory effects, and most importantly, the change of its sign is effectively masked by the de-focusing due to free electrons.