Improving Poor Man's Kramers-Kronig analysis and Kramers-Kronig constrained variational analysis.

We report a considerable improvement of Poor Man's Kramers-Kronig analysis and Kramers-Kronig constrained variational analysis. Whereas the first method is an alternative to the well-established conventional Kramers-Kronig analysis, but fully analytical, the second method allows to capture subtle spectral features that might get lost by conventional dispersion analysis using oscillator models. Since both methods share the same physical foundation, an improvement in the Kramers-Kronig conformity will be a benefit for either. The corresponding improvement that we report decreases the average errors and increases conformity by about three orders of magnitude. This puts Poor Man's Kramers-Kronig analysis in the range of Maclaurin's method, which is still one of the numerical benchmarks. Kramers-Kronig constrained variational analysis on the other hand can now unleash its full potential and is able to correctly model even spectra of inorganic materials with their strong absorption bands without being supported by conventional oscillators.