It is shown that Floquet states follow adiabatic changes of laser puls
es unless quasi-energies meet avoided crossings. At these avoided cros
sings quantum systems jump from one Floquet state to another with sign
ificant probability rates. These transitions, which we call the optica
l Landau-Zener transitions, lead to modifications of the power spectru
m of scattered radiation, increasing its background significantly. It
is shown, on the basis of numerical model calculations, that there is
a connection between the chaotic behaviour of scattered radiation, mea
sured by the autocorrelation function of its power spectrum, and the s
pectrum of quasi-energies for different light intensities. Namely, it
appears that the more avoided crossings a quantum system passes during
the switching on and off of the laser pulse the more chaotic is the p
ower spectrum of scattered radiation. Resonant scattering of electrons
by quantum wells is also considered.