  We study the response of topological insulator films to strong magnetic and
electric fields beyond the linear response theory. As a model, we use the
three-dimensional lattice Wilson-Dirac Hamiltonian where we simultaneously
introduce both magnetic field through the Peierls substitution and electric
field as a potential energy depending on lattice coordinate. We compute the
electron energy spectrum by numerically diagonalizing this Hamiltonian and
obtain quantized magnetoelectric polarizability. In addition, we find that the
magnetoelectric effect vanishes as the film width decreases due to the
hybridization of surface wave functions. Furthermore, applying a gate voltage
between the surfaces, we observe several quantized plateaus of $\theta$ term,
which are mainly determined by the Landau level structures on the top and
bottom surfaces.
