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 × 10 −4 for coatings deposited on commercially polished slides and 1.0 ± 0.3 × 10 −4 for a coating deposited on a superpolished disk. 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.

No abstract

We calculate the thermal noise in half-infinite mirrors containing a layer of arbitrary thickness and depth made of excessively lossy material but with the same elastic material properties as the substrate. For the special case of a thin lossy layer on the surface of the mirror, the excess noise scales as the ratio of the coating loss to the substrate loss and as the ratio of the coating thickness to the laser beam spot size. Assuming a silica substrate with a loss function of 3x10 -8 the coating loss must be less than 3x10 -5 for a 6 cm spot size and a 7 µm thick coating to avoid increasing the spectral density of displacement noise by more than 10%. A similar number is obtained for sapphire test masses. IntroductionThe second generation LIGO gravitational wave detector will require large core optics with low internal dissipation. The baseline design for LIGO II will use 30 kg sapphire mirrors; a fall back design would use silica mirrors. (1) A loss function less than 3.3x10 -9 has been measured at high frequencies in small samples of sapphire (2, 3). Substrate loss functions for silica have been measured to be around or below 3x10 -8 in several different sample geometries (4,5,6,7). However, to achieve this low loss in a full size coated and suspended LIGO II mirror the attachments for the fused silica suspension and the multilayer mirror high reflector coating and the antireflection optical coating must not increase the displacement noise of the mirror in the frequency range of interest.Until recently the approach used to calculate mirror thermal noise i nvolved a normal mode expansion of the mirror acoustic modes (8). Direct approaches to the problem have been developed by Levin (9), Nakagawa et al. (10,11), Bondu et al. (12) and Liu and Thorne (13). Moreover, Levin has used this approach to point out that non-uniform loss in a mirror can lead to higher than otherwise expected thermal noise.(9) In this paper we use the general formalism developed in (10) and (11) to derive expressions for the phase noise imposed on a Gaussian light beam when it is reflected from a half-infinite lossless mirror with a lossy layer of arbitrary thickness placed at an arbitrary depth from the surface from which the light beam is reflected. To compute the noise for the case where the mirror has both loss and an extra layer with a different loss we take the incoherent sum of the noises from the uniform lossy mirror and the lossless mirror with a lossy layer. This procedure is legitimate for low-loss cases where the loss can be estimated accurately by up to linear terms in the loss functions. Finally, we discuss the experimentally important special case where the lossy layer is at the surface of the mirror and is thin compared to the spot size of the light beam. Mathematical Formalism and ReviewIn our previous paper (11) we used the fluctuation dissipation theorem to compute the cross spectral density of the mirror surface displacements resulting from the off-resonance thermal noise in the test masses. The loss was parameterized t...

Interferometric gravitational wave detectors use mirrors whose substrates are formed from materials of low intrinsic mechanical dissipation. The two most likely choices for the test masses in future advanced detectors are fused silica or sapphire [1]. These test masses must be coated to form mirrors, highly reflecting at 1064nm. We have measured the excess mechanical losses associated with adding dielectric coatings to substrates of fused silica and calculate the effect of the excess loss on the thermal noise in an advanced interferometer.

All current gravitational wave detectors use test masses coated with alternating layers of two different dielectric materials to form highly reflective mirrors. The thermal noise from mechanical dissipation associated with such coatings may be significant for future detectors such as advanced LIGO. We have measured the mechanical dissipation of a number of types of coatings formed from SiO2 (silica) and Ta2O5 (tantala). The frequency dependence of the dissipation has been determined, taking into account the contribution of thermoelastic loss.