Coating thermal noise for arbitrary shaped beams

Abstract

Advanced LIGO's sensitivity will be limited by coating noise. Though this noise depends on beam shape, and though nongaussian beams are being seriously considered for advanced LIGO, no published analysis exists to compare the quantitative thermal noise improvement alternate beams offer. In this paper, we derive and discuss a simple integral which completely characterizes the dependence of coating thermal noise on shape. The derivation used applies equally well, with minor modifications, to all other forms of thermal noise in the low-frequency limit.

3 pages. Originally performed in August 2004. Submitted to CQG. (v2) : Corrections from referee and others

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• Optimal Light Beams and Mirror Shapes for Future LIGO Interferometers
• The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers
• Numerically modeling Brownian thermal noise in amorphous and crystalline thin coatings
• Perspectives on Beam-Shaping Optimization for Thermal-Noise Reduction in Advanced Gravitational-Wave Interferometric Detectors: Bounds, Profiles, and Critical Parameters
• Finite Mirror Effects in Advanced Interferometric Gravitational Wave Detectors