  Lowering of the thickness of a thin-film three-dimensional topological
insulator down to a few nanometers results in the gap opening in the spectrum
of topologically protected two-dimensional surface states. This phenomenon,
which is referred to as the anomalous finite-size effect, originates from
hybridization between the states propagating along the opposite boundaries. In
this work, we consider a bismuth-based topological insulator and show how the
coupling to an intense high-frequency linearly polarized pumping can further be
used to manipulate the value of a gap. We address this effect within recently
proposed Brillouin-Wigner perturbation theory that allows us to map a
time-dependent problem into a stationary one. Our analysis reveals that both
the gap and the components of the group velocity of the surface states can be
tuned in a controllable fashion by adjusting the intensity of the driving field
within an experimentally accessible range and demonstrate the effect of
light-induced band inversion in the spectrum of the surface states for high
enough values of the pump.
