Kramers-Kronig constrained variational analysis of optical spectra

TL;DR

The paper introduces a universal variational method constrained by Kramers-Kronig relations to extract complex dielectric functions from various optical measurements, applicable to diverse sample types without reconfiguration.

Contribution

It presents a novel, flexible approach that generalizes dielectric function extraction, overcoming limitations of traditional KK-based methods and enabling analysis of multiple measurement types simultaneously.

Findings

Consistent dielectric functions obtained from reflectivity data.

Applicable to thin films and anisotropic crystals.

Works with combined optical measurement data.

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.