A three-dimensional time-dependent Schrödinger equation solver: an application to hydrogen atoms in an elliptical laser field

We extended the two-dimensional generalized pseudo-spectral time-propagator to a three-dimensional time-propagator. With this time-propagator, we theoretically investigated the above-threshold ionization of hydrogen atoms in an elliptical field by solving the time-dependent Schrödinger equation. We found that the total ionization probabilities are suppressed about one order, while the excitation probabilities drop about eight orders from a linearly polarized laser to a circularly polarized one with a given laser intensity. The width of the lateral (perpendicular to the laser polarization plane) momentum distribution increases as the ellipticity increases, which is against our intuition that the large peak laser field results in a broad distribution in the lateral direction. Further analysis shows that the narrow lateral momentum distribution for linearly polarized laser fields originates from Coulomb focusing, which is as less or not important for the circularly polarized field. Such a high precision simulation can be used to calibrate the infrared laser intensity to a high precision. (paper)