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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.

 

The sensitivity of gravitational-wave detectors is limited by the mechanical loss associated with the amorphous coatings of the detectors’ mirrors. Amorphous silicon has higher refraction index and lower mechanical loss than current high-index coatings, but its optical absorption at the wavelength used for the detectors is at present large. The addition of hydrogen to the amorphous silicon network reduces both optical absorption and mechanical loss for films prepared under a range of conditions at all measured wavelengths and temperatures, with a particularly large effect on films grown at room temperature. The uptake of hydrogen is greatest in the films grown at room temperature, but still below 1.5 at.% H, which show an ultralow optical absorption (below 10 ppm) measured at 2000 nm for 500-nm-thick films. These results show that hydrogenation is a promising strategy to reduce both optical absorption and mechanical loss in amorphous silicon, and may enable fabrication of mirror coatings for gravitational-wave detectors with improved sensitivity.