A Dynamical Phase-Field Model for the Optical Properties of Ferroelectrics

Ferroelectric materials are promising platforms for controllable photonic devices because of the strong coupling between their spontaneous polarization and optical properties. Yet, these materials remain challenging to design because of the close connection between the ferroelectric domain structure and optical response, which no existing theoretical approach can capture. Here, we develop a dynamical phase-field model that directly couples the ferroelectric order to the local optical response by introducing an electronic polarization field. This approach enables the prediction of the spatially resolved temperature- and wavelength-dependent optical properties in complex ferroelectric microstructures. Applying this method to BaTiO3 thin films, we investigate the evolution of the local refractive index and electro-optic response under varying electric fields and temperatures. We show that the ferroelectric domain structure strongly modifies the local electro-optic response, exceeding 4000 pm/V near domain walls, several times larger than the bulk single crystal value (r_51=1300 pm/V). Our simulations quantitatively reproduce the electro-optic coefficient measured in BaTiO3 on silicon films and capture the temperature-dependent behavior across multiple ferroelectric phase transitions, revealing the role of phase competition and coexistence in determining the electro-optic response. More broadly, this work establishes a general approach for predicting light-matter interactions in complex ferroelectric microstructures, enabling the computational design of ferroelectric materials for photonics.