  We carry out first-principles calculations of the nonlinear dielectric
response of short-period ferroelectric superlattices. We compute and store not
only the total polarization, but also the Wannier-based polarizations of
individual atomic layers, as a function of electric displacement field, and use
this information to construct a model capable of predicting the nonlinear
dielectric response of an arbitrary superlattice sequence. We demonstrate the
successful application of our approach to superlattices composed of SrTiO$_3$,
CaTiO$_3$, and BaTiO$_3$ layers.
