An analytical model of Faraday rotation in hot alkali metal vapours

TL;DR

This paper develops an analytical model for Faraday rotation in hot alkali vapours, accurately predicting rotation and absorption spectra, and identifies regimes where hyperfine pumping effects are negligible.

Contribution

It introduces a simple analytical model for off-resonant Faraday rotation applicable to all hot alkali vapours, validated against experimental data.

Findings

Model predicts Faraday rotation within 1% accuracy at high temperatures.

Identifies a weak probe intensity limit where hyperfine pumping is negligible.

Computer code accurately predicts Doppler-broadened spectra within 0.5% rms deviation.

Abstract

We report a thorough investigation into the absorptive and dispersive properties of hot caesium vapour, culminating in the development of a simple analytical model for off-resonant Faraday rotation. The model, applicable to all hot alkali metal vapours, is seen to predict the rotation observed in caesium, at temperatures as high as 115 $^{\circ}$C, to within 1% accuracy for probe light detuned by greater than 2 GHz from the $D_{2}$ lines. We also demonstrate the existence of a weak probe intensity limit, below which the effect of hyperfine pumping is negligible. Following the identification of this regime we validate a more comprehensive model for the absorption and dispersion in the vicinity of the $D_{2}$ lines, implemented in the form of a computer code. We demonstrate the ability of this model to predict Doppler-broadened spectra to within 0.5% rms deviation for temperatures up to 50 $^{\circ}$C.