| As a result of the rapid development of ultra-short and ultra-intense laser technology, the peak electric field strength of lasers has reached or exceeded the coulomb field strength seen by the electron in the ground state of atomic hydrogen. The application of such intense laser fields to the atoms leaded to the discovery of a number of novel strong-field phenomena such as above-threshold ionization (ATI), tunneling ionization (Tl), high-order harmonic generation (HHG), dynamic stabilization (DS) of atoms, etc. Because of the failure of the traditional perturbative theories in this field region, it is necessary to establish and develop non-perturbative approaches for the treatment of these phenomena.Non-perturbative theoretical investigations of atomic systems interacting with intense laser fields generally require the time-dependent solution of the corresponding Schro'dinger equation. The Floquet theory and pure numerical integral method are accepted as the most generally used approaches of solving the time-dependent Schrodinger equation. In addition, the field-free eigenstate expansion approach (FFEEA), which naturally gives the time-dependent population on each eigenstate, provides a powerful tool to gain more insights into the essence of the physical processes. However, for the reasons givenblow, the approach is of low computational efficiency. When the electrons are ionized under the action of the strong laser fields, their population on continuum states in low energy domain is much more complex than that in high energy domain. Accordingly, very small energy step-length is indispensable to guarantee computational convergence. On the other hand, the approach will have to involve the integrals of large numbers of matrix elements in every step of the evolution, which is really time-consuming.To overcome these shortcomings, we improved the field-free eigenstate expansion approach by performing a representation transform from energy E Xoq = 2E . It is shown that the improved method works well in promoting the efficiency of computation since it results in increased state density in low energy domain. The reliability of the improved method is examined by two comparisons of the high-order harmonic generation (HHG) spectra: one is that obtained in the length and acceleration forms, respectively; the other is that obtained by itself and the purely numerical integral approach, respectively, in the same acceleration form. (We programmed the Crank-Nicloson approach independently in order to investigate physical phenomena from different standpoints and testify the improved approach.)With the improved field-free eigenstate expansion approach (IFFEEA) and the Crank-Nicholson approach we studied the DS of the one-dimensional (ID) model atoms and the HHG of the ID united-atoms (single-electron molecular ions with large inter-nuclear distances)driven by intense laser fields.The DS of atoms is defined as the phenomenon that the ionization probability at the end of the laser pulse of fixed shape and duration does not approach unity as the peak intensity isincreased, but either start decreasing with the intensity(possibly in a oscillatory manner), or flattens out at a value smaller than unity. The phenomenon has been reinforced by many theoretical and experimental works since its first discovery by Gersten and Gavrila. Up to now, the physical interpretation of the DS mainly comes from the high frequency Floquet theory; however, the related calculations are obtained from the direct solutions of the time-dependent Schrodinger equations (TDSE). Why shouldn't one explain the phenomenon from the viewpoint of wave-packets obtained by TDSE? For this purpose, we calculated the DS of a ID model atom in the super-intense and high-frequency laser pulses with the two methods mentioned above, respectively. The excellent agreement of the two results corroborates the physical reality of the DS, about which the dispute is still underway heretofore. And then... |
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