Contribution of spontaneous polarization and its fluctuations to refraction of light in ferroelectrics

The expressions for the spontaneous polar contribution $\delta n_{i}^{S}$ to the principal values of the refractive index due to the quadratic electro-optic effect in ferroelectrics have been considered within the phenomenological approach taking into account the polarization fluctuations. A method has been proposed for calculating the magnitude and temperature dependence of the root-mean-square fluctuations of the polarization (short-range local polar order) $P_{\operatorname{sh}}=\langle P^{2}_{\operatorname{fl}}\rangle^{1/2}$ below the ferroelectric transition temperature $T_{c}$ from temperature changes in the spontaneous polar contribution $\delta n_{i}^{S}(T)$ if the average spontaneous polarization $P_{\operatorname{s}}=\langle P\rangle$ characterizing the long-range order is determined from independent measurements (for example, from dielectric hysteresis loops). For the case of isotropic fluctuations, the proposed method has made it possible to calculate $P_{\operatorname{sh}}$ and $P_{\operatorname{s}}$ only from refractometric measurements. It has been shown that, upon interferometric measurements, the method developed in this work allows calculating $P_{\operatorname{sh}}$ and $P_{\operatorname{s}}$ directly from the measured temperature and electric-field changes in the relative optical path (the specific optical retardation) of the light.