Broadband Measurement of Coating Thermal Noise in Rigid Fabry-Perot Cavities

TL;DR

This study measures coating thermal noise in rigid Fabry-Perot cavities, confirming Brownian noise dominance and estimating coating loss angles, which advances understanding of mirror coating limitations in precision optical systems.

Contribution

It provides the first broadband measurement of coating thermal noise in fixed-spacer cavities and estimates the coating loss angle using Bayesian analysis, improving material characterization.

Findings

Coating thermal noise dominates at 10 Hz to 1 kHz.

Measured coating loss angle is approximately 4×10⁻⁴.

Bayesian analysis estimates individual silica and tantala loss angles.

Abstract

We report on the relative length fluctuation of two fixed-spacer Fabry-Perot cavities with mirrors fabricated from silica/tantala dielectric coatings on fused silica substrates. By locking a laser to each cavity and reading out the beat note $\hat{\nu} = \nu_1 - \nu_2$ of the transmitted beams, we find that, for frequencies from 10 Hz to 1 kHz, the amplitude spectral density of beat note fluctuation is $\sqrt{S_\hat{\nu}(f)} = (0.5\,\mathrm{Hz})/f^{1/2}$. By careful budgeting of noise sources contributing to the beat note, we find that our measurement is consistent with the fluctuation in this band being dominated by the Brownian noise of the mirror coatings. Fitting for the coating loss angle $\phi_\mathrm{c}$, we find it equal to $4\times10^{-4}$. We then use a Bayesian analysis to combine our measurement with previous observations, and thereby extract estimates for the individual loss angles of silica and tantala. It is hoped that the testbed described in this article can be used in the future to measure the length noise of cavities formed with novel mirror materials and geometries.