  We study the photon-dressed electronic band structure of topological
insulator thin films which could be also doped doped by magnetic impurities in
response to an off-resonance time-periodic electromagnetic field. The thin
films irradiated by a circularly polarized light undergo phase transition, in a
driven system made by and a fascinating feature of distinct phases emerges in
the phase diagram depending on the parameters such as frequency, intensity and
polarization of the light. As a particular case, quantum anomalous Hall
insulator phase is induced purely by the light-induced mass term with no need
to any external magnetic field or even magnetization arising from the
doped-doping magnetic impurities. Moreover, a novel phase, quantum pseudo-spin
Hall insulator, emerges in the phase diagram leading to anisotropic helical
edge states with zero total Chern number. We verify these achievements in the
phase diagrams are supported by numerical calculations for a nanoribbon of the
thin film for which the edge mode behavior is observed at several points on the
phase diagram. The emergence of the mentioned topological phases and the edge
modes are further confirmed by both calculating the Hall conductivity by means
of the Kubo formula and the Chern number of each band. The effect of light
parameters on the Landau level fan diagram in the presence of a perpendicular
magnetic field indicates various topological phases occurring at higher Chern
numbers.
