  We describe the gated bilayer graphene system when it is subjected to intense
terahertz frequency electromagnetic radiation. We examine the electron band
structure and density of states via exact diagonalization methods within
Floquet theory. We find that dynamical states are induced which lead to
modification of the band structure. We first examine the situation where there
is no external magnetic field. In the unbiased case, dynamical gaps appear in
the spectrum which manifest as dips in the density of states. For finite
interlayer bias (where a static gap is present in the band structure of
unirradiated bilayer graphene), dynamical states may be induced in the static
gap. These states can show a high degree of valley polarization. When the
system is placed in a strong magnetic field, the radiation induces coupling
between the Landau levels which allows dynamical levels to exist. For strong
fields, this means the Landau levels are smeared to form a near-continuum of
states.
