Strategies to reduce the thermoelastic loss of multimaterial coated finite substrates

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 (GW) 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 GW detectors and for other experiments sensitive to energy dissipation mechanisms when different materials are in contact.

Automated summary

Thermoelastic loss is an important energy dissipation mechanism in resonant systems that needs careful analysis. This paper provides analytical solutions to thermoelastic loss between different materials in contact, focusing on finite substrates with multimaterial coatings. The results show that reducing operating mirror temperature, using thinner layers and more interfaces in the coating, and choosing the first layer that minimizes thermal expansion mismatch can effectively reduce thermoelastic loss and improve resolution in sensing applications. The findings are valuable for the development of low-noise gravitational-wave detectors and experiments where different materials are in contact for energy dissipation.