We study the behavior of reduced models for the propagation of intense laser pulses in atomic gases. The models we consider incorporate ionization, blueshifting, and other nonlinear propagation effects in an ab initio manner, by explicitly taking into account the microscopic electron dynamics. Numerical simulations of the propagation of ultrashort linearly-polarized and elliptically-polarized laser pulses over experimentally-relevant propagation distances are presented. We compare the behavior of models where the electrons are treated classically with those where they are treated quantum-mechanically. A classical equivalent to the ground state is found, which maximizes the agreement between the quantum and classical predictions of the single-atom ionization probability as a function of laser intensity. We show that this translates into quantitative agreement between the quantum and classical models for the laser field evolution during propagation through gases of ground-state atoms. This agreement is exploited to provide a classical perspective on low- and high-order harmonic generation in linearly-polarized fields. In addition, we demonstrate the stability of the polarization of a nearly-linearly-polarized pulse using a two-dimensional model.
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