We discuss the influence of the laser pulse turn-on on the radiation s
pectrum emitted by an atom strongly driven by an intense laser field.
For this purpose we use the results obtained from the direct numerical
solution of the time-dependent Schrodinger equation and from a Floque
t analysis of the wave function. We observe a strong dependence of the
intensities of the harmonics and of the hyper-Raman lines on the dura
tion of the turn-on, with differences that can reach several orders of
magnitude. This dependence can be explained in terms of population tr
ansfers between Floquet states at avoided crossings. We support our an
alysis with numerical simulations for a two-level system and also with
the help of a more realistic model, the one-dimensional soft Coulomb
potential, obtaining similar results.