Thermodynamic theory of linear optical and electro-optical properties of ferroelectrics

Ferroelectric materials underlie key optical technologies in optical communications, integrated optics, and quantum computing. Yet, there is a lack of a consistent thermodynamic framework to predict the optical properties of ferroelectrics and the mutual connections among ferroelectric polarization, optical properties, and optical dispersion. For example, there is no existing thermodynamic model for establishing the relationship between the ferroelectric polarization and the optical properties in the visible spectrum. Here we present a thermodynamic theory of the linear optical and electro-optic properties of ferroelectrics by separating the lattice and electronic contributions to the total polarization. We introduce a biquadratic coupling between the lattice and electronic contributions validated by both first-principles calculations and experimental measurements. As an example, we derive the temperature and wavelength-dependent anisotropic optical properties of $\mathrm{BaTi}{\mathrm{O}}_{3}$, including the full linear optical dielectric tensor and the linear electro-optic (Pockels) effect through multiple ferroelectric phase transitions, which are in excellent agreement with existing experimental data and first- principles calculations. We further demonstrate the validity by comparing our predictions to the experimental temperature- and wavelength-dependent optical properties of $\mathrm{LiNb}{\mathrm{O}}_{3}$. This general framework incorporates essentially all optical properties of materials, including coupling between the ionic and electronic order parameters, as well as their dispersion and temperature dependence, and thus offers a powerful theoretical tool for analyzing light-matter interactions in ferroelectrics-based optical devices.