Temperature dependence and dispersion of electro-optic and elasto-optic effect in perovskite crystals

We relate the linear electro-optic coefficients to the quadratic polarization-optic and the elasto-optic tensors by analyzing the dielectric phenomena driven by the spontaneous and induced polarization as well as the mechanical effects given by the deformation of the crystals. We determine the temperature dependence and the wavelength dispersion of the electro-optic tensor in all the ferroelectric phases from a smaller set of data: the quadratic polarization-optic tensor of the cubic phase, the dielectric permittivity, and the spontaneous polarization. Under the assumption that the elasto-optic tensor at constant polarization is constant, the elasto-optic coefficients at constant electric field in the ferroelectric phases are derived. Numerical evaluations of these coefficients for two perovskite crystals KNbO3 and BaTiO3 are presented. Modifications of the electro-optic properties in doped crystals, mainly due to a change of the dielectric permittivity, are discussed as well.