Numerical studies of the dynamics of multiphoton processes with arbitrary field polarization: Methodological considerations

We describe an approach of spectral type for numerically integrating the time-dependent Schrödinger equation associated to the interaction of a one active electron atom with an electromagnetic pulsed field whose polarization may be arbitrary. The wave function is represented on a Coulomb-Sturmian basis. The time propagation method is based on a parallel-iterated Runge-Kutta method of predictor-corrector type. This method is in fact fully implicit and of very high order, ensuring a high stability of the time propagation. Moreover, it has the following advantages: it provides a scheme for an adaptive time step and it is particularly well suited to parallel computing. We discuss the performance of the present approach and compare it to already existing ones. In the case of linearly polarized fields, most of our results are in good agreement with those obtained with other approaches. In the case of circularly polarized fields, we compare our results with those obtained by, so far, the only existing method which is based on the single state Floquet approximation. Finally, and for the sake of illustration, we treat the case of the interaction of atomic hydrogen with a strong pulsed electromagnetic field whose polarization depends on time. @S1050-2947~97!02902-8#