Amorphous optical coatings of present gravitational-wave interferometers

We report on the results of an extensive campaign of optical and mechanical characterization of the ion-beam sputtered oxide layers (Ta$_2$O$_5$, TiO$_2$, Ta$_2$O$_5$-TiO$_2$, SiO$_2$) within the high-reflection coatings of the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors: refractive index, thickness, optical absorption, composition, density, internal friction and elastic constants have been measured; the impact of deposition rate and post-deposition annealing on coating internal friction has been assessed. For Ta$_2$O$_5$ and SiO$_2$ layers, coating internal friction increases with the deposition rate, whereas the annealing treatment either erases or largely reduces the gap between samples with different deposition history. For Ta$_2$O$_5$-TiO$_2$ layers, the reduction of internal friction due to TiO$_2$ doping becomes effective only if coupled with annealing. All measured samples showed a weak dependence of internal friction on frequency ($phi_c(f) = af^{b}$, with $-0.208 < b < 0.140$ depending on the coating material considered). SiO$_2$ films showed a mode-dependent loss branching, likely due to spurious losses at the coated edge of the samples. The reference loss values of the Advanced LIGO and Advanced Virgo input (ITM) and end (ETM) mirror HR coatings have been updated by using our estimated value of Youngs modulus of Ta$_2$O$_5$-TiO$_2$ layers (120 GPa) and are about 10% higher than previous estimations.