Theory of far infrared spectroscopy for ferroelectric size effects

We propose that far-infrared reflection and transmission measurements would be a sensitive probe of possible variations in the polarization P of a ferroelectric near a surface. We present a general formulation based on the Landau-Devonshire model, including both linear and nonlinear processes. Surface effects are described by parameters D, giving the free-energy cost of spatial variations in P, and delta, governing the boundary condition on P. Detailed calculations for linear reflection in normal incidence from a semi-infinite medium are presented. If delta(-1) = 0 the calculations are analytic and the results for this case serve as a check on the numerical calculations that are applied for general delta. Altogether, the results suggest that the effects of D and delta should be distinct and measurable.