Window functions for self-consistency evaluation of optical constants

Optical-constant data of a material typically come from various sources, which may result in inconsistent data. Sum rules are tests to evaluate the self-consistency of optical constant data sets. Standard sum rules provide collective self-consistency evaluation of an optical-constant set in the full electromagnetic spectrum, but they give no information on the specific spectral range originating the inconsistency. Spectrally-resolved self-consistency information can be obtained with the use of window functions (WFs). Window functions can give more weight to the desired spectral range in the calculation of the sum rule. A previously developed WF was successfully used to evaluate self-consistency over the spectrum, but since it involves steep transition at the window edges and center, it has a trend to turn unstable in the calculation of sum-rule integrals for a fast decaying WF outside the window band. Two new WFs have been developed to reduce such instability. They use weight functions that smoothly cancel at the two window edges and center. The two new WFs use a weight function with three straight lines or with two 4-degree polynomials. The new WFs have been tested on exact optical constants with a coarse sampling, and they provide a strong instability reduction in self-consistency evaluation compared with the old WF. The new WFs have been also tested on experimental data sets of Al and Au reported in the literature, which unveils ranges of inconsistency. The large stability of the new WFs compared with the old one helps decide that the inconsistency calculated with the new WFs on experimental data must be attributed to inconsistency of the data sets, and not to poor sampling rate. A WF that has been used in the literature in the calculations of the dielectric function at imaginary energies for the thermal Casimir effect is also analyzed in terms of self-consistency when it is applied to sum rules involving optical constant at real (not imaginary) energies.