We study numerically the interaction between an intense circularly polarize
d laser field and an electron moving in a potential that has a discrete cyl
indrical symmetry with respect to the laser-pulse propagation direction. Th
is setup serves as a simple model, e.g., for benzene and other aromatic com
pounds. From general symmetry considerations, within a Floquet approach, se
lection rules for the harmonic generation [O. Alon er al., Phys. Rev. Lett.
80, 3743 (1998)] have been derived recently. Instead, the results we prese
nt in this paper have been obtained solving the time-dependent Schrodinger
equation ab initio for realistic pulse shapes. We find a rich structure tha
t is not always dominated by the laser harmonics.