Simple model for the nonlinear optical response of gases in the transparency region

We present a simple model for the nonlinear optical response of atomic gases for pulses with center wavelengths in the transparency region and peak fields for which ionization is not prevalent. By comparing with simulations based on the Schrödinger equation for a hydrogen atom we demonstrate that the model accurately captures the dispersion of the nonlinear polarization as well as noninstantaneous effects for a variety of photon energies and also a two-color pulse. Our approach should be of utility in simulating near- and mid-infrared pulse propagation in dielectric media for which extreme nonlinear effects can arise.