E. Huens et al., NUMERICAL-STUDIES OF THE DYNAMICS OF MULTIPHOTON PROCESSES WITH ARBITRARY FIELD POLARIZATION - METHODOLOGICAL CONSIDERATIONS, Physical review. A, 55(3), 1997, pp. 2132-2143
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.