Surface energy and spatial dispersion in ferroelectrics: the influence on the optical transmission and reflection spectra in the paraelectric state
The description of surface and size effects in ferroelectrics is based on the combined contribution of surface free energy density and gradient dependent terms occurring in the volume free energy density. The dynamics of the polarization waves and, consequently, the optical properties in the infrared range, can be significantly affected in the case of small enough soft mode damping, even in the paraelectric phase at temperatures above those of the ordered ferroelectric state. Reflection and transmission spectra for semi-infinite media and thin films are calculated within this model, using the orders of magnitude generally published in the literature for ferroelectric oxides as regards the values of the physical parameters. It is shown that the tangential and the normal interface extrapolation lengths, as well as the bulk gradient coefficient related to the model studied, could be subjected to a spectroscopical evaluation. The frequencies of the sharp singularities appearing in the transmission and reflection spectra are given with an excellent precision by the frequencies of the surface and of the guided modes calculated in the electrostatic approximation for wavevector equal to zero, thus providing a rather simple way of determining the pertinent physical quantities.