Saturation of harmonic generation in one- and three-dimensional atoms

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Abstract
A commonly used numerical technique for calculating the harmonic spectrum emitted by an atom exposed to an intense laser pulse is the direct integration of the Schrödinger equation. We compare the spectra calculated using two different models. The first is in one dimension with an approximate hydrogenic soft-core potential and the second is in three dimensions with a Coulomb potential. We use realistic laser pulse conditions (100 fs,800 nm) and intensities at which there is significant ionization, leading to a saturation of the harmonic-generation process. Although the ionization rates in the two models differ, the harmonic spectra and the positions of the cutoff are remarkably similar. Only a relatively small number of angular momentum states is needed in the three-dimensional calculation to give a reliable estimate of the cutoff, even for intensities at which there is strong ionization.