Broadband Optical Characterization of Tetragonal Barium Titanate by Mueller-Matrix Spectroscopic Ellipsometry

Abstract

Barium titanate (BTO), one of the earliest reported ferroelectric materials, exhibits strong second-order nonlinearity and an ultrafast Pockels effect, making it highly attractive for photonics. However, its optical constants remain uncertain largely due to the ubiquitous ferroelectric–ferroelastic multidomain microstructure, which depolarizes and averages out the anisotropic optical response, thereby complicating conventional ellipsometric approaches. Here, we report a Kramers–Kronig-consistent complex refractive-index tensor of tetragonal BTO from the ultraviolet (190 nm) to the far-infrared (40 μm) derived from multimodal Mueller-matrix spectroscopic ellipsometry. We further quantify optical loss by incorporating transmission intensity measured over the 2–10 μm transparency window, resolving the extinction coefficient down to ∼10–5. To verify the underlying domain configuration, we performed independent structural analyses, including electron backscatter diffraction, confocal Raman microscopy, and Kelvin probe force microscopy. We then reconstruct an effective optical model for our multidomain BTO sample, formulated as a mixture of three tetragonal variants with the determined intrinsic refractive indices, to link microscopic domains to the macroscopic optical response. Our work presents a unified, experimentally cross-validated data set, enabling accurate modeling for electro-optic modulators and high-Q nanophotonic resonators without ad hoc approximations, and provides a general strategy for optical metrology of complex ferroic crystals.