  We propose and model Floquet topological polaritons in semiconductor
microcavities, using the interference of frequency detuned coherent fields to
provide a time periodic potential. For arbitrarily weak field strength, where
the Floquet frequency is larger than the relevant bandwidth of the system, a
Chern insulator is obtained. As the field strength is increased, a topological
phase transition is observed with an unpaired Dirac cone proclaiming the
anomalous Floquet topological insulator. As the relevant bandwidth increases
even further, an exotic Chern insulator with flat band is observed with
unpaired Dirac cone at the second critical point. Considering the polariton
spin degree of freedom, we find that the choice of field polarization allows
oppositely polarized polaritons to either co-propagate or counter-propagate in
chiral edge states.
