Thermal noise in optical cavities revisited

TL;DR

This paper revisits the thermal noise in optical cavities, providing corrected analytical estimates and detailed finite-element analysis to guide low-noise cavity design and material choices for ultra-stable lasers.

Contribution

It corrects previous thermal noise estimates using Levin's formulation and offers detailed finite-element analysis for cavity design optimization.

Findings

Increased dissipation near mirror contact significantly affects thermal noise.

Support structure design can reduce thermal noise contributions.

Thermal expansion can be compensated in mixed-material cavities without increasing noise.

Abstract

Thermal noise of optical reference cavities sets a fundamental limit to the frequency instability of ultra-stable lasers. Using Levin's formulation of the fluctuation-dissipation theorem we correct the analytical estimate for the spacer contribution given by Numata et al.. For detailed analysis finite-element calculations of the thermal noise focusing on the spacer geometry, support structure and the usage of different materials have been carried out. We find that the increased dissipation close to the contact area between spacer and mirrors can contribute significantly to the thermal noise. From an estimate of the support structure contribution we give guidelines for a low-noise mounting of the cavity. For mixed-material cavities we show that the thermal expansion can be compensated without deteriorating the thermal noise.