Analysis of the strong field approximation for harmonic generation and multiphoton ionization in intense ultrashort laser pulses

We apply the strong field approximation (SFA) to the study of harmonic generation (HG) and above threshold ionization (ATI) in intense low-frequency laser fields. We review in a systematic way the SFA model from the literature to date, and fill in some gaps regarding its analytical and computational aspects. Special attention is devoted to the analysis of the saddle point method, which is widely used to calculate the highly oscillatory integrals describing the physical processes. Its accuracy is compared against the results from numerical integration; for the latter task, we propose two methods, which prove to be fast and reliable for all practical purposes. In the context of HG, we discuss non-dipole effects, using a non-dipole non-relativistic method. The use of a second, weaker laser pulse is shown to allow the emission enhancement of selected harmonics. We briefly discuss the importance of relativistic effects using the results of a fully relativistic calculation of Miloˇsevi´c et al.. In the context of ATI, quantitative comparisons are made with results obtained by integrating the exact static ionization rates over the pulse or, where possible, with ab initio results. Direct ionization in short pulses is extensively presented in the framework of a Coulomb-corrected version of the SFA, due to Krainov; interesting interference effects are shown to take place, in particular modulations in the angle-resolved ATI spectra depending strongly on the phase of the carrier. These modulations happen for pulses that are not too long, typically fewer than (9-10) optical cycles. As a consequence, the ATI peaks in the 2 angle-integrated spectra have a good resolution or are undistinguishable from the background, if the electric field component of the pulse is symmetrical or anti-symmetrical with respect to the pulse half duration, respectively. Partial conclusions are drawn regarding the applicability of the SFA to the study of the ionization process and possible ways to further improve the model are suggested.