Numerical Approximation of Kramers-Kronig Relations to Transform Discretized Absorption Data
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.
Keywords
Cite
@article{arxiv.2012.02369,
title = {Numerical Approximation of Kramers-Kronig Relations to Transform Discretized Absorption Data},
author = {Patrick D Fitzgerald},
journal= {arXiv preprint arXiv:2012.02369},
year = {2020}
}
Comments
Written during mathematics capstone at Worcester Polytechnic Institute (WPI). Main paper is 15 pages, containing 8 figures, with some experimentally measured data (H2O refractive index, absorption coefficient around 1THz, collected at the Ultrafast THz and Optical Spectroscopy Lab at WPI). Remaining 16 pages contain 10 Matlab source files