Extensions of the Kramers–Kronig transformation that cover a wide range of practical spectroscopic applications

Abstract

The Kramers–Kronig (KK) transformation has been widely used for the determination of the spectra of the refractive and absorption indices from the normal-incidence reflectivity spectrum of solids. This paper considers the extension of this technique to s-polarized light at nonnormal incidence with a transparent incident medium of arbitrary, constant refractive index. While the KK transformation is known to be inapplicable under certain circumstances, we show that in all cases satisfactory corrections can be applied, and readily applied in most cases. As an example, for the experimentally important case of attenuated total internal reflection from an organic liquid in the infrared, only one additional piece of information is required, namely, the refractive index at a frequency where the absorption is low. The procedures are demonstrated using model systems consisting of sets of damped harmonic oscillators. All the KK transformations were done using the FT software of a commercial Fourier transform infrared spectrometer in order to demonstrate the considerable potential of this approach to the routine determination of optical constants.