High-order-harmonic spectra from atoms in intense laser fields: Exact versus approximate methods

Abstract

We compare harmonic spectra from hydrogen based on the numerical solution of the time-dependent Schrödinger equation and three approximate models: (i) the strong field approximation (SFA), (ii) the Coulomb-Volkov modified strong field approximation (CVA), and (iii) the strong field approximation with the stationary phase approximation applied to the momentum integrals (SPSFA). At laser intensities in the range of (1-3)×1014W/cm2 we find good agreement when comparing the SFA and CVA with exact results. In general the CVA displays an overall better agreement with ab initio results, which reflects the role of the Coulomb field in the ionization as well as in the recombination process. Furthermore, it is found that the widely used SPSFA breaks down for low-order harmonic generation; i.e., the approximation turns out to be accurate only in the outer part of the harmonic plateau region as well as in the cutoff region. We trace this deficiency to the singularity of the SPSFA associated with short trajectories, i.e., short return times. When removing these, we obtain a version of the SPSFA which works rather well for the entire harmonic spectrum.