Coating thermal noise of a finite-size cylindrical mirror

TL;DR

This paper derives the coating thermal noise for finite-size cylindrical mirrors using the fluctuation-dissipation theorem, improving accuracy in gravitational-wave detectors and quantum measurement experiments.

Contribution

It provides a new derivation for finite-size mirrors that aligns with previous models for large or thin mirrors, enhancing thermal noise estimation accuracy.

Findings

Results agree with infinite-size mirror models in the large-thickness limit.

Matches mode expansion results with thin-mirror approximation.

Facilitates better thermal noise analysis in gravitational-wave detection.

Abstract

Thermal noise of a mirror is one of the limiting noise sources in the high precision measurement such as gravitational-wave detection, and the modeling of thermal noise has been developed and refined over a decade. In this paper, we present a derivation of coating thermal noise of a finite-size cylindrical mirror based on the fluctuation-dissipation theorem. The result agrees to a previous result with an infinite-size mirror in the limit of large thickness, and also agrees to an independent result based on the mode expansion with a thin-mirror approximation. Our study will play an important role not only to accurately estimate the thermal-noise level of gravitational-wave detectors but also to help analyzing thermal noise in quantum-measurement experiments with lighter mirrors.