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

• Received 10 June 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.2930