Investigation Of High Order Harmonic Generation Of One-and Two-Dimensional Model Atom

A commonly used numerical technique for investigating the interaction of an atom and an intense laser pulse is the direct integration of Schr(o|¨)dinger equation. The numerical integration of the three-dimensional Schr(o|¨)dinger equation is not an easy task, so one- and or two-dimensional atomic model are often used for predicting the key features of an atom exposed to an intense laser field and avoiding the large computational effort at the same time. Tremendous progress has been made in the work of strong field theory. However, the dimension differences of the models also lead to some interesting questions. In this paper, we discuss qualitatively the reason for the difference of ionization and high harmonic generations between the one-and two-dimensional model atom.Firstly, we investigate the ionization probability of one- and two-dimension atom model in the tunneling and the over-barrier ionization regime. We find that the ratio of ionization probability between one- and two-dimensional atom model I1/I2 decrease with the increase of laser intensity. In order to explain this phenomenon we discuss the reason for the difference of ionization probability of one- and two-dimensional model atom at the same laser intensity in the first place. It is shown that just the different momentum distribution lead to the difference of ionization probability between the two kinds model atom .After that, we find the variation of the I1/I2 with the increase of laser intensity can come down to the following two reasons: first, the change of the barrier of the two-dimensional model atom; second, the depletion of the one-dimension model atom.Secondly, we investigate the mechanism of the high harmonic generations of one- and two-dimensional model H + H~+ system, respectively. By analyzing the reasons for the difference of the high harmonic generation between one- and two-dimensional model atom in I p + 8.0Up cut-off region, contrasting the harmonic spectrum of the I p + 8.0Upand I p + 3.2Up region, and an ideal experiment, we confirm that the escape probability of electron from the direction perpendicular to the laser polarization axis is not the key factor determining the efficiency of the high harmonic generation. To sum up: the mechanism of high harmonic generation of one- and two-dimensional model atom is same; the key factors determining the efficiency of harmonic generation are also same. So even if we consider the electron escape effect in the direction perpendicular to the laser polarization axis, the conclusions on high order harmonic generation (HHG) derived from the one-dimensional model atom can not be overthrown. In other words, my work has shown that it is feasible to study the harmonic generation of single electron atom or molecular ion by one-dimensional model atom.