Kramers-Kronig analysis of infrared reflection spectra with perpendicular polarization.

The application of Kramers-Kronig analysis for reflection spectra from a single interface with perpendicular (s) polarization has been studied theoretically with regard to a phase correction term. The errors in phase shift and complex refractive index obtained by the use of Kramers-Kronig analysis have been examined for such techniques as external, internal, and total internal reflection spectroscopies by the use of spectral simulation and the complex refractive index based on dispersion theory. The advantages and disadvantages of the various measurement techniques used to obtain the complex refractive index of a sample material have been compared. It is concluded that the external reflection technique can be used until the sample thickness becomes too thin to provide the edge shape necessary to avoid the detection of reflection from the back surface. The total internal reflection technique should be used only for a thin-film sample because knowledge of the refractive index at some frequency is required and bcause this technique may yield larger errors than the other techniques in the complex refractive index obtained by the use of Kramers-Kronig analysis.