Light propagation in field-ionizing media: Extreme nonlinear optics

A novel equation for light propagation in underdense field-ionizing media i s derived by extending concepts of nonlinear optics into the strong-field d omain. The equation is first order in the propagation coordinate and is val id for arbitrarily short pulse durations. Solutions of the first-order wave equation are found to be in excellent agreement with solutions of the scal ar wave equation. Furthermore, the polarization response of a field-ionizin g medium is derived from semiclassical considerations. The polarization rev eals, in agreement with experiments, a previously unrecognized contribution that is shown to significantly affect the absorption loss in the presence of ionization.