Brownian Thermal Noise in Multilayer Coated Mirrors

TL;DR

This paper investigates the sources and characteristics of Brownian thermal noise in multilayer dielectric coatings used in high-precision optical systems, highlighting the impact of interface fluctuations and photoelastic effects.

Contribution

It introduces a comprehensive model accounting for interface fluctuations, photoelastic effects, and uncertainties in material parameters affecting coating thermal noise estimation.

Findings

Coating noise arises from layer thickness and interface fluctuations.

Finite coherence exists between layers and substrate-coating interface.

Significant uncertainties remain in estimating Brownian noise due to material parameter variations.

Abstract

We analyze the Brownian thermal noise of a multi-layer dielectric coating, used in high-precision optical measurements including interferometric gravitational-wave detectors. We assume the coating material to be isotropic, and therefore study thermal noises arising from shear and bulk losses of the coating materials. We show that coating noise arises not only from layer thickness fluctuations, but also from fluctuations of the interface between the coating and substrate, driven by internal fluctuating stresses of the coating. In addition, the non-zero photoeleastic coefficients of the thin films modifies the influence of the thermal noise on the laser field. The thickness fluctuations of different layers are statistically independent, however, there exists a finite coherence between layers and the substrate-coating interface. Taking into account uncertainties in material parameters, we show that significant uncertainties still exist in estimating coating Brownian noise.