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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 (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 ability to observe astronomical events through the detection of gravitational waves relies on the quality of multilayer coatings used on the optical mirrors of interferometers. Amorphous Ta2O5 (including TiO2:Ta2O5) currently limits detector sensitivity due to high mechanical loss. In this paper, mechanical loss measured at both cryogenic and room temperatures of amorphous Ta2O5 films grown by magnetron sputtering and annealed in air at 500 ◦C is shown to decrease for elevated growth temperature. Films grown at 310 ◦C and annealed yield a mechanical loss of 3.1×10−4 at room temperature, the lowest value reported for pure amorphous Ta2O5 grown by magnetron sputtering to date, and comparable to the lowest values obtained for films grown by ion beam sputtering. Additionally, the refractive index n increases 6% for elevated growth temperature, which could lead to improved sensitivity of gravitational-wave detectors by allowing a thickness reduction in the mirrors’ coatings. Structural characterization suggests that the observed mechanical loss reduction in amorphous Ta2O5 films with increasing growth temperature correlates with a reduction in the coordination number between oxygen and tantalum atoms, consistent with TaOx polyhedra with increased corner-sharing and reduced edge- and facesharing structures. 

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.