Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors

TL;DR

This paper analyzes thermoelastic damping in coated test masses for gravitational wave detectors, providing formulas to interpret loss measurements and displacement noise, which are crucial for improving detector sensitivity.

Contribution

It introduces new expressions for thermoelastic dissipation and displacement noise in inhomogeneous coated media relevant to gravitational wave detectors.

Findings

Thermoelastic damping significantly affects mirror noise.

Formulas enable better interpretation of loss measurements.

Design implications for advanced detectors.

Abstract

The displacement noise in the test mass mirrors of interferometric gravitational wave detectors is proportional to their elastic dissipation at the observation frequencies. In this paper, we analyze one fundamental source of dissipation in thin coatings, thermoelastic damping associated with the dissimilar thermal and elastic properties of the film and the substrate. We obtain expressions for the thermoelastic dissipation factor necessary to interpret resonant loss measurements, and for the spectral density of displacement noise imposed on a Gaussian beam reflected from the face of a coated mass. The predicted size of these effects is large enough to affect the interpretation of loss measurements, and to influence design choices in advanced gravitational wave detectors.