# Light scattering in the medium with fluctuating gyrotropy: application to spin noise spectroscopy

## TL;DR

This paper provides a rigorous theoretical description of spin noise signals in media with fluctuating gyrotropy, exploring both single-beam and two-beam configurations to enhance signal detection and study spin correlations.

## Contribution

It introduces a detailed model of spin noise signal formation, including the impact of two-beam setups and wave vector overlap on signal strength and information content.

## Key findings

- Signal arises only from scattered fields with wave vectors matching the probe
- Two-beam configuration enhances signal by increasing field overlap in momentum space
- Fourier transform of gyrotropy relief relates to auxiliary beam contribution

## Abstract

The spin noise signal in the Faraday-rotation-based detection technique can be considered equally correctly either as a manifestation of the spin-flip Raman effect or as a result of light scattering in the medium with fluctuating gyrotropy. In this paper, we present rigorous description of the signal formation process upon heterodyning of the field scattered due to fluctuating gyrotropy. Along with conventional single-beam experimental arrangement, we consider here a more complicated, but more informative, two-beam configuration that implies the use of an auxiliary light beam passing through the same scattering volume and delivering additional scattered field to the detector. We show that the signal in the spin noise spectroscopy arising due to heterodyning of the scattered field is formed only by the scattered field components whose wave vectors coincide with those of the probe beam. Therefore, in principle, the detected signal in spin noise spectroscopy can be increased by increasing overlap of the two fields in the momentum space. We also show that, in the two-beam geometry, contribution of the auxiliary (tilted) beam to the detected signal is represented by Fourier transform of the gyrotropy relief at the difference of two wave vectors. This effect can be used to study spin correlations by means of noise spectroscopy.