Spectral curve fitting of dielectric constants

M Ruzi,C Ennis,E G Robertson

doi:10.1063/1.4975398

Abstract

Optical constants are important properties governing the response of a material to incident light. It follows that they are often extracted from spectra measured by absorbance, transmittance or reflectance. One convenient method to obtain optical constants is by curve fitting. Here, model curves should satisfy Kramer-Kronig relations, and preferably can be expressed in closed form or easily calculable. In this study we use dielectric constants of three different molecular ices in the infrared region to evaluate four different model curves that are generally used for fitting optical constants: (1) the classical damped harmonic oscillator, (2) Voigt line shape, (3) Fourier series, and (4) the Triangular basis. Among these, only the classical damped harmonic oscillator model strictly satisfies the Kramer-Kronig relation. If considering the trade-off between accuracy and speed, Fourier series fitting is the best option when spectral bands are broad while for narrow peaks the classical damped harmonic oscillator and the Triangular basis fitting model are the best choice.

Highlights

Optical constants are crucial in determining how a substance responds to different frequencies of incident light
The key conclusions are: By neglecting the imaginary component of low frequency bands, the K-K transformation overestimates the real part and the associated error is largest at the lowest available frequency; By neglecting the imaginary component of high frequency bands, the K-K transformation underestimates the real part and the associated error is largest at the highest available frequency
The accuracy of the four curve fitting methods that are commonly employed to extract optical constants from spectral data are evaluated, and in our study applied to model the dielectric constants of water, acetonitrile, and nitric acid dihydrate ices

Summary

Introduction

Optical constants are crucial in determining how a substance responds to different frequencies of incident light. Curve fitting is an alternate method to recover optical constants from spectral data.[16,17] By employing physically meaningful line shape functions that are K-K consistent, it is possible to retrieve optical constants to high accuracy. It is possible to conveniently express these optical constants just using a few parameters, instead of supplementing entire spectral data tables.[14,17,18,19,20,21,22]

Methods

Results

Conclusion