Analysis of Kramers-Kronig relations in modulation spectroscopy

A new method of extrapolation in the analysis of Kramers-Kronig relations, applying to the case of the modulation spectroscopy, is presented. The extrapolation of the differential reflectance, Delta R/R, is avoided, since this quantity is not theoretically the simplest, and it depends on unmodulated optical constants in an essential way. Rather, the extrapolation is made directly in the quantity of greatest theoretical simplicity, the real part of the (differential) optical conductivity itself. A formula is found which gives the differential optical conductivity in terms of the measured differential reflectivity and the extrapolated conductivity. The results are discussed and illustrated by the example of the optical conductivity of tungsten, modulated by a chemisorbed hydrogen layer.