Refractive index of air 2 Group index

TLDR

Earlier work introduced equations for the phase refractive index of air and an inaccurate method for computing the group refractive index. This study rigorously derives the group refractive index using the Lorentz‑Lorenz formula. The authors derive and evaluate a simplified equation for exploratory calculations. The derivation shows that deviations from the Lorentz‑Lorenz formula are negligible for atmospheric dispersion measurements, and the study clarifies the validity limits of the standard group index equation while correcting minor errors from the earlier paper.

Abstract

In a previous paper [Appl. Opt. 35, 1566 (1996)] one of us presented new equations for evaluation of the phase refractive index of air over a range of wavelengths and atmospheric parameters. That paper also gave an incorrect, although sufficiently accurate, procedure for calculating the group refractive index. Here we describe the results of a more rigorous derivation of the group index that takes proper account of the Lorentz-Lorenz formula, and we demonstrate that deviations from the Lorentz-Lorenz formula are insignificant to within a foreseeable precision of dispersion measurements for atmospheric conditions. We also derive and evaluate a simplification of the resultant equation that is useful for exploratory calculations. We clarify the limits of validity of the standard equation for the group refractive index and correct some minor errors in the previous paper.