The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers

Abstract

In second-generation, ground-based interferometric gravitational-wave detectors such as Advanced LIGO, the dominant noise at frequencies $f\sim 40$ Hz to $\sim 200$ Hz is expected to be due to thermal fluctuations in the mirrors' substrates and coatings which induce random fluctuations in the shape of the mirror face. The laser-light beam averages over these fluctuations; the larger the beam and the flatter its light-power distribution, the better the averaging and the lower the resulting thermal noise. In semi-infinite mirrors, scaling laws for the influence of beam shape on the four dominant types of thermal noise (coating Brownian, coating thermoelastic, substrate Brownian, and substrate thermoelastic) have been suggested by various researchers and derived with varying degrees of rigour. Because these scaling laws are important tools for current research on optimizing the beam shape, it is important to firm up our understanding of them. This paper (1) gives a summary of the prior work and of gaps in the prior analyses, (2) gives a unified and rigorous derivation of all four scaling laws, and (3) explores, relying on work by J. Agresti, deviations from the scaling laws due to finite mirror size.

arXiv comment25 pages, 10 figures, submitted to Class. Quantum Grav

References in corpus (6)

• Internal thermal noise in the LIGO test masses : a direct approach
• Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings
• Thermoelastic Noise and Homogeneous Thermal Noise in Finite Sized Gravitational-Wave Test Masses
• Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors
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• Perspectives on Beam-Shaping Optimization for Thermal-Noise Reduction in Advanced Gravitational-Wave Interferometric Detectors: Bounds, Profiles, and Critical Parameters
• A New Class of Optical Beams for Large Baseline Interferometric Gravitational Wave Detectors
• Finite Mirror Effects in Advanced Interferometric Gravitational Wave Detectors