  We report on the effects of laser illumination on the electronic properties
of bilayer graphene. By using Floquet theory combined with Green's functions we
unveil the appeareance of laser-induced gaps not only at integer multiples of
$\hbar \Omega /2$ but also at the Dirac point with features which are shown to
depend strongly on the laser polarization. Trigonal warping corrections are
shown to lead to important corrections for radiation in the THz range, reducing
the size of the dynamical gaps. Furthermore, our analysis of the topological
properties at low energies reveals that when irradiated with linearly polarized
light, ideal bilayer graphene behaves as a trivial insulator, whereas circular
polarization leads to a non-trivial insulator per valley.

Mesoscale and Nanoscale Physics