  We study quasiparticle dynamics in graphene exposed to a linearly-polarized
electromagnetic wave of very large intensity. Low-energy transport in such
system can be described by an effective time-independent Hamiltonian,
characterized by multiple Dirac points in the first Brillouin zone. Around each
Dirac point the spectrum is anisotropic: the velocity along the polarization of
the radiation significantly exceeds the velocity in the perpendicular
direction. Moreover, in some of the points the transverse velocity oscillates
as a function of the radiation intensity. We find that the conductance of a
graphene p-n junction in the regime of strong irradiation depends on the
polarization as $G(\theta)\propto|\sin\theta|^{3/2}$, where $\theta$ is the
angle between the polarization and the p-n interface, and oscillates as a
function of the radiation intensity.
