Brownian thermal birefringent noise due to non-diagonal anisotropic photoelastic effect in multilayer coated mirrors

TL;DR

This paper investigates how Brownian motion-induced anisotropic photoelastic effects in multilayer mirror coatings can generate birefringent thermal noise, potentially limiting the sensitivity of high-precision optical experiments.

Contribution

It introduces a model for non-diagonal anisotropic photoelastic noise in mirror coatings and calculates its spectrum, highlighting its significance in precision measurements.

Findings

Calculated the spectrum of non-diagonal anisotropic Brownian photoelastic noise.

Identified this noise as a potential limiting factor in optical cavity experiments.

Suggested further experiments to validate and mitigate this noise source.

Abstract

Thermal noise in the mirror coatings limits the accuracy of today's most optical precision measurement experiments. Unlike the more commonly discussed thermal phase noise, the crystalline coating can generate thermal birefringent noise due to its anisotropic nature. In this study, we propose that the non-diagonal anisotropic photoelastic effect induced by the Brownian motion of mirror coating layers may contribute to this noise. Employing a standard model for the coating surface, we calculate the spectrum of the non-diagonal anisotropic Brownian photoelastic(NABP) noise to be $1.2 \times 10^{-11} p_{63} f^{-1/2}/\rm{Hz}^{1/2}$. Further experiments are warranted to validate the influence of this effect and reduce its uncertainty. Our findings highlight that for high-precision experiments involving optical resonant cavities targeting signals imprinted in optical polarizations, this noise could emerge as a limiting factor for experimental sensitivity.