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We have measured the temperature dependence of the direct band gap, $E_g$, inSrTi$^{16}$O$_3$ and BaTiO$_3$ and related materials with quantum-paraelectricand ferroelectric properties using optical spectroscopy. We show that $E_g$exhibits an anomalous temperature dependence with pronounced changes in thevicinity of the ferroelectric transition that can be accounted for in terms ofthe Fr\"ohlich electron-phonon interaction with an optical phonon mode, theso-called soft mode. We demonstrate that these characteristic changes of $E_g$can be readily detected even in very thin films of SrTi$^{16}$O$_3$ with astrain-induced ferroelectric order. Optical spectroscopy thus can be used as arelatively simple but sensitive probe of ferroelectric order in very thin filmsof these titanates and probably also in subsequent multilayers and devices.

Optical probe of ferroelectric order in bulk and thin film perovskite titanates