  This paper analyzes Floquet topological insulators resulting from the
time-harmonic irradiation of electromagnetic waves on two dimensional materials
such as graphene. We analyze the bulk and edge topologies of approximations to
the evolution of the light-matter interaction. Topologically protected
interface states are created by spatial modulations of the drive polarization
across an interface. In the high-frequency modulation regime, we obtain a
sequence of topologies that apply to different time scales. Bulk-difference
invariants are computed in detail and a bulk-interface correspondence is shown
to apply. We also analyze a high-frequency high-amplitude modulation resulting
in a large-gap effective topology topologically that remains valid only for
moderately long times.
