  We demonstrated a large enhancement of Kerr electro-optic nonlinearity
through cascaded Pockels effects in a domain inversion ferroelectric crystal.
We designed a structure that can implement the cascaded Pockels effects and
second-harmonic generation simultaneously. The energy coupling between the
fundamental lights of different polarizations led to a large nonlinear phase
shift, and thus an effective electro-optic nonlinear refractive index. The
effective nonlinearity can be either positive or negative, causing the
second-harmonic spectra to move towards the coupling center, which in turn,
offered us a way to measure the effective electro-optic nonlinear refractive
index. The corresponding enhanced Kerr electro-optic nonlinearity is more than
three orders of magnitude higher than the intrinsic value. These results open a
door to manipulate the nonlinear phase by applying external electric field
instead of light intensity in noncentrosymmetric crystals.
