  Topological insulators (TIs) are characterized by the quantum anomalous Hall
effect (QAHE) on the topological surface states under time-reversal symmetry
breaking. Motivated by recent experiments on the magneto-optical effects
induced by the QAHE, we develop a theory for the dynamical Hall conductivity
for subgap optical frequency and intense optical fields using the
Keldysh-Floquet Green's function formalism. Our theory reveals a nonlinear
regime in which the Hall conductivity remains close to $e^2/2h$ at low
frequencies. At higher optical fields, we find that the subsequent collapse of
the half quantization is accompanied by coherent oscillations of the dynamical
Hall conductivity as a function of field strength, triggered by the formation
of Floquet subbands and the concomitant inter-subband transitions.
