NUMERICAL-STUDIES OF THE DYNAMICS OF MULTIPHOTON PROCESSES WITH ARBITRARY FIELD POLARIZATION - METHODOLOGICAL CONSIDERATIONS

We describe an approach of spectral type for numerically integrating t he time-dependent Schrodinger equation associated to the interaction o f a one active electron atom with an electromagnetic pulsed field whos e polarization may be arbitrary. The wave function is represented on a Coulomb-Sturmian basis. The time propagation method is based on a par allel-iterated Runge-Kutta method of predictor-corrector type. This me thod is in fact fully implicit and of very high order, ensuring a high stability of the time propagation. Moreover, it has the following adv antages: it provides a scheme for an adaptive time step and it is part icularly well suited to parallel computing. Wt discuss the performance of the present approach and compare it to already existing ones. In t he case of linearly polarized fields, most of our results are in good agreement with those obtained with other approaches, In the case of ci rcularly polarized fields, we compare our results with those obtained by, so far, the only existing method which is based on the single stat e Floquet approximation. Finally, and for the sake of illustration, we treat the case of the interaction of atomic hydrogen with a strong pu lsed electromagnetic field whose polarization depends on time.