  We investigated the Dirac electrons transmission through a potential barrier
in the presence of circularly polarized light. An anomalous photon-assisted
enhanced transmission is predicted and explained in a comparison with the
well-known Klein paradox. It is demonstrated that the perfect transmission for
nearly-head-on collision in an infinite graphene is suppressed in gapped
dressed states of electrons, which is further accompanied by shift of peaks as
a function of the incident angle away from the head-on collision. In addition,
the perfect transmission in the absence of potential barrier is partially
suppressed by a photon-induced gap in illuminated graphene. After the effect of
rough edges of the potential barrier or impurity scattering is included, the
perfect transmission with no potential barrier becomes completely suppressed
and the energy range for the photon-assisted perfect transmission is reduced at
the same time.
