  We investigate the effect of a high frequency electromagnetic field with both
of circularly and linearly polarization, on the emergence of quantum phases on
thin topological insulators. Simultaneously, the influence of the system
parameters (such as magnetic impurity, thickness engineering and structural
inversion asymmetry of the potential) on emergence of topological phases is
studied. We take our attention to the high frequency regime in which it is
possible to consider an expansion for the Floquet Hamiltonian in terms of
orders of 1/\Omega. The topological invariants are determined and it is
demonstrated that some phase transitions between quantum anomalous Hall
insulator, quantum pseudospin Hall insulator, quantum spin Hall insulator and
normal insulator can be induced by altering the aforementioned parameters of
the system. To avoid heating process, tuning of the system parameters gives us
the opportunity to observe these phase transitions at small intensities of
light.
