Polarization Fluctuations and the Optical-Absorption Edge in BaTi<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Results of optical absorption and electroabsorption (EA) measurements in the vicinity of the interband absorption edge are reported for top-seeded solution-grown crystals of BaTi${\mathrm{O}}_{3}$. In common with other perovskite oxides, the absorption edge in BaTi${\mathrm{O}}_{3}$ is found to display Urbach-rule behavior. The exponential absorption tail can be described between 20 and 450 \ifmmode^\circ\else\textdegree\fi{}C by an effective temperature ${T}^{*}=T+{T}_{0}$, where ${T}_{0}=140$ K, i.e., $\ensuremath{\alpha}\ensuremath{\propto}{e}^{\frac{\ensuremath{\hbar}\ensuremath{\omega}}{k{T}^{*}}}$. Although no uniquely defined band gap can be extracted from an exponential edge, we propose, on the basis of indirect arguments, that the room-temperature band gaps are 3.38 and 3.27 eV, respectively, for light polarized parallel and perpendicular to the ferroelectric $c$ axis. At high temperatures in the cubic phase, the band gap decreases at the rate -4.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ eV/\ifmmode^\circ\else\textdegree\fi{}C. EA measurements in the tetragonal phase show that an applied electric field along the $c$ axis shifts the entire Urbach edge rigidly upward in energy by an amount $\ensuremath{\Delta}\mathcal{E}$, which is proportional to the square of the total polarization $P$, spontaneous plus field-induced, i.e., $\ensuremath{\Delta}\mathcal{E}=\ensuremath{\beta}{P}^{2}$. The effect can be described by a temperature-independent band-edge polarization potential $\ensuremath{\beta}$ having the value ${\ensuremath{\beta}}_{11}=1.16$ eV ${\mathrm{m}}^{4}$/${\mathrm{C}}^{2}$. The smaller ${\ensuremath{\beta}}_{12}$ coefficient could not be measured, because of photoconductivity and carrier-trapping effects. An anomalous increase in the band gap with decreasing temperature within 150\ifmmode^\circ\else\textdegree\fi{}C of the Curie point is attributed to coupling between polarization fluctuations and the band edge. A simple thermodynamic model is shown to describe the temperature dependence of this fluctuation contribution with reasonable accuracy. The results suggest that the correlation volume ${V}_{c}$ is at most a weak function of temperature and that ${V}_{c}$ does not display critical behavior. This conclusion is consistent with several recent experiments in displacive ferroelectrics. The magnitude of the observed mean square polarization fluctuation contribution to the band-edge position ($\ensuremath{\approx}15$ meV at $T={T}_{C}$) can be understood using the simple fluctuation theory with the value ${V}_{c}\ensuremath{\approx}4.5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ ${\mathrm{\AA{}}}^{3}$ deduced previously from photoelastic constant measurements. It is also suggested that a mean square polarization fluctuation contribution to the band-edge position is present in the tetragonal phase below approximately 100 \ifmmode^\circ\else\textdegree\fi{}C owing to the proximity of the tetragonal-orthorhombic transition. A fluctuation contribution of about 40 meV is indicated at room temperature.