Calculation of the Nonlinear Optical Tensor Coefficients in Oxygen-Octahedra Ferroelectrics

We show, using the concept of the polarization potential tensor β which relates energy band shifts to the crystal polarization, that the nonlinear optical (NLO) tensor coefficients δ in oxygen-octahedra ferroelectrics are proportional to the quantity βPs where Ps is the crystal spontaneous polarization. Because β is found to be nearly the same in all oxygen-octahedra ferroelectrics, we are able to calculate the δ coefficients from a knowledge of Ps. The polarization-induced energy band shifts are shown to be nearly the same for static polarizations (giving rise to the clamped electro-optic effect) and for optical-frequency electronic polarizations (giving rise to nonlinear optical effects).