Theory of far-infrared reflection and transmission by ferroelectric thin films

We present a detailed formulation to describe far-infrared reflection and transmission from a ferroelectric film at normal incidence. The formalism begins with the Gibbs free energy per unit area and the Landau-Khalatnikov equations of motion. To take size and surface effects in the film into account, boundary values and possible spatial variation in polarization are included in the free-energy expression, which leads to the existence of two additional parameters, D and delta. The inclusion of D leads to the presence of another spin-wave type of optical mode in addition to the normal polariton type of waves in the dispersion curves and the appearance of the spin-wave mode fringes in the reflectivity curves. Reflection curves for various values of delta are illustrated, and the results show that the effects of these two parameters are distinctively different in reflectivity. Far-infrared reflectivity measurements are proposed here as a tool to determine surface and size effects in ferroelectric thin films. (C) 2001 Optical Society of America.