Brownian Thermal Noise in Multilayer Coated Mirrors

Abstract

We analyze the Brownian thermal noise of a multi-layer dielectric coating, used in high-precision optical measurements including interferometric gravitational-wave detectors. We assume the coating material to be isotropic, and therefore study thermal noises arising from shear and bulk losses of the coating materials. We show that coating noise arises not only from layer thickness fluctuations, but also from fluctuations of the interface between the coating and substrate, driven by internal fluctuating stresses of the coating. In addition, the non-zero photoeleastic coefficients of the thin films modifies the influence of the thermal noise on the laser field. The thickness fluctuations of different layers are statistically independent, however, there exists a finite coherence between layers and the substrate-coating interface. Taking into account uncertainties in material parameters, we show that significant uncertainties still exist in estimating coating Brownian noise.

26 pages, 18 figures

References in corpus (7)

• LIGO: The Laser Interferometer Gravitational-Wave Observatory
• Titania-doped tantala/silica coatings for gravitational-wave detection
• Thermo-optic noise in coated mirrors for high-precision optical measurements
• Optical Interferometers with Reduced Sensitivity to Thermal Noise
• Optimal Light Beams and Mirror Shapes for Future LIGO Interferometers
• Effect of interference on thermal noise and coating optimization in dielectric mirrors
• The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers

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