  We study the topology of the Floquet states and time-averaged optical
conductivity of the lattice model of a thin topological insulator subject to a
circularly polarized light using the extended Kubo formalism. Two driving
regimes, the off-resonant and on-resonant, and two models for the occupation of
the Floquet states, the ideal and mean-energy occupation, are considered. In
the ideal occupation, the real part of DC optical Hall conductivity is shown to
be quantized while it is not quantized for the mean energy distribution. The
optical transitions in the Floquet band structure depend strongly on the
occupation and also the optical weight which consequently affect all components
of optical conductivity. At high frequency regime, we present an analytical
calculation of the effective Hamiltonian and also its phase diagram which
depends on the tunneling energy between two surfaces. The topology of the
system shows rich phases when it is irradiated by a weak on-resonant drive
giving rise to emergence of anomalous edge states.
