Strategies to reduce the thermoelastic loss of multimaterial coated finite substrates

TL;DR

This paper provides analytical solutions for thermoelastic loss in multimaterial coatings on finite substrates, identifying design strategies like temperature reduction and interface optimization to minimize thermal noise in high-precision resonant systems.

Contribution

It introduces new analytical expressions for thermoelastic loss in multimaterial coatings, considering material properties, design, and operating conditions, aiding low-noise device development.

Findings

Lower temperature reduces thermoelastic loss.

Thinner layers and more interfaces decrease loss.

Choosing the first layer to match thermal expansion minimizes mismatch.

Abstract

Thermoelastic loss is an important energy dissipation mechanisms in resonant systems. A careful analysis of the thermoelastic loss is critical to the design of low-noise devices for high-precision applications, such as the mirrors used for gravitational-wave detectors. In this paper, we present analytical solutions to the thermoelastic loss due to thermoelasticity between different materials that are in contact. We find expressions for the thermoelastic loss of multimaterial coatings of finite substrates, and analyze its dependencies on material properties, mirror design and operating experimental conditions. Our results show that lower operating mirror temperature, thinner layers and higher number of interfaces in the coating, and the choice of the first layer of the coating that minimizes the thermal expansion mismatch with the substrate are strategies that reduce the thermoelastic loss and, therefore, diminish the thermal noise that limits the resolution in sensing applications. The results presented in this paper are relevant for the development of low-noise gravitational-wave detectors and for other experiments sensitive to energy dissipation mechanisms when different materials are in contact.