Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings

We report on thermal noise from the internal friction of dielectric coatings made from alternating layers of Ta₂O₅ and SiO₂ deposited on fused silica substrates. We present calculations of the thermal noise in gravitational wave interferometers due to optical coatings, when the material properties of the coating are different from those of the substrate and the mechanical loss angle in the coating is anisotropic. The loss angle in the coatings for strains parallel to the substrate surface was determined from ringdown experiments. We measured the mechanical quality factor of three fused silica samples with coatings deposited on them. The loss angle, φ∥(f), of the coating material for strains parallel to the coated surface was found to be 4.2 ± 0.3 × 10⁴ for coatings deposited on commercially polished slides, and 1.0 ± 0.3 × 10⁴ for a coating deposited on a superpolished disc. Using these numbers, we estimate the effect of coatings on thermal noise in the initial LIGO and Advanced LIGO interferometers. We also find that the corresponding prediction for thermal noise in the 40 m LIGO prototype at Caltech is consistent with the noise data. These results are complemented by results for a different type of coating, presented in a companion paper.