Kramers–Kronig constrained variational analysis of optical spectra

TLDR

The method generalizes multi‑oscillator fitting by treating the number of oscillators as comparable to the number of data points. The study develops a universal method to extract the complex dielectric function from measurable optical data. ε₂(ω) is independently parameterized at anchor frequencies while ε₁(ω) is linked through the Kramers‑Kronig transformation. The method reproduces conventional KK results for normal‑incidence reflectivity and, unlike traditional approaches, applies without readaptation to any linear‑response optical measurement—including reflectivity, transmission, ellipsometry—on thin films, anisotropic crystals, and other sample types.

Abstract

A universal method of extraction of the complex dielectric function $\epsilon(\omega)=\epsilon_{1}(\omega)+i\epsilon_{2}(\omega)$ from experimentally accessible optical quantities is developed. The central idea is that $\epsilon_{2}(\omega)$ is parameterized independently at each node of a properly chosen anchor frequency mesh, while $\epsilon_{1}(\omega)$ is dynamically coupled to $\epsilon_{2}(\omega)$ by the Kramers-Kronig (KK) transformation. This approach can be regarded as a limiting case of the multi-oscillator fitting of spectra, when the number of oscillators is of the order of the number of experimental points. In the case of the normal-incidence reflectivity from a semi-infinite isotropic sample the new method gives essentially the same result as the conventional KK transformation of reflectivity. In contrast to the conventional approaches, the proposed technique is applicable, without readaptation, to virtually all types of linear-response optical measurements, or arbitrary combinations of measurements, such as reflectivity, transmission, ellipsometry {\it etc. }, done on different types of samples, including thin films and anisotropic crystals.