Determination of the damping co-efficient of electrons in optically transparent glasses at the true resonance frequency in the ultraviolet from an analysis of the Lorentz-Maxwell model of dispersion

TL;DR

This paper analyzes the Lorentz-Maxwell dispersion model to accurately determine the true resonance frequency and damping coefficient of electrons in optically transparent glasses in the ultraviolet, aligning theoretical predictions with experimental data.

Contribution

It introduces a method to find the true resonance frequency and damping coefficient by solving maximum absorption and energy conditions simultaneously.

Findings

The true resonance frequency in UV matches experimental data.

The damping coefficient is estimated at the resonance frequency.

The model accurately predicts optical properties like extinction and reflectance.

Abstract

The Lorentz-Maxwell model of dispersion of light has been analyzed in this paper to determine the true resonance frequency in the ultraviolet for the electrons in optically transparent glasses and the damping coefficient at this frequency. For this we needed the refractive indices of glass in the optical frequency range. We argue that the true resonance condition in the absorption region prevails when the frequency at which the absorption coefficient is maximum is the same as the frequency at which the average energy per cycle of the electrons is also a maximum. We have simultaneously solved the two equations obtained from the two maxima conditions numerically to arrive at a unique solution for the true resonance frequency and the damping coefficient at this frequency. Assuming the damping coefficient to be constant over a small frequency range in the absorption region, we have determined the frequencies at which the extinction coefficient and the reflectance are maxima. These frequencies match very well with the published data for silica glasses available from the literature.