Numerical Approximation of Kramers-Kronig Relations to Transform Discretized Absorption Data

TL;DR

This paper presents a numerical method for applying Kramers-Kronig relations to discretized absorption data, improving the accuracy of refractive index extraction from indirect measurements using a Matlab implementation.

Contribution

It introduces a novel numerical approximation technique for Kramers-Kronig relations tailored for discretized data, with a focus on precision and practical implementation.

Findings

Enhanced accuracy in transforming absorption data to refractive index.

A Matlab implementation demonstrating the method's effectiveness.

Potential for improved optical material characterization.

Abstract

The Kramers-Kronig relations describe a pair of integral transforms relating the real and imaginary components of an analytic function in the complex plane. These relations are particularly useful in extracting refractive index characteristics of a given physical test species, wherein more direct measurements are not terribly reliable. In this report, a method of performing this integral transformation is derived and discussed. Special attention is given to the precision of these methodologies, and a specific implementation of this in Matlab is presented.