  Starting from a three dimensional Hamiltonian, we study the optical
properties of ultra-thin topological insulator slabs for which the coupling
between Dirac fermions on opposite surfaces results in two degenerated gapped
hyperbolic bands. The gap is a threshold for the optical absorption and
translates in a peak in the imaginary part of the optical conductivity. An
exchange field applied perpendicular to the slab splits the degenerated
hyperbolic bands and a double step structure come out in the optical
absorption, whereas a double peak structure appears in the imaginary part of
the longitudinal optical conductivity. The exchange field breaks time-reversal
symmetry and for exchange fields larger than the surfaces coupling gap, the
zero frequency Hall conductivity is quantized to $e^2/h$. This result implies
large values of the Kerr and Faraday rotation angles. In ultra-thin slabs, the
absence of light multiple scattering and bulk conductivity, makes the Kerr and
Faradays angles to remain rather large in a wide range of frequencies.
