The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers
- Creators
- Lovelace, Geoffrey
Abstract
In second-generation, ground-based interferometric gravitational-wave detectors such as Advanced LIGO, the dominant noise at frequencies f ~ 40 Hz to ~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.
Additional Information
Copyright © Institute of Physics and IOP Publishing Limited 2007. Received 22 April 2007, in final form 27 July 2007. Published 21 August 2007. Print publication: Issue 17 (7 September 2007) I would like to thank Kip Thorne for suggesting this problem and for his advice and encouragement. I would also like to thank Juri Agresti for helpful discussions as well as for providing for comparison the data that will be published in [10]. This work was supported in part by NSF grants PHY-0099568 and PHY-0601459. The numerical computations described in this paper were performed using Mathematica version 5.2. The figures, including best fit lines, were prepared using Grace 5.1.18.Files
Name | Size | Download all |
---|---|---|
md5:19322449cee792e39563730528a732e8
|
309.1 kB | Preview Download |
Additional details
- Eprint ID
- 8646
- Resolver ID
- CaltechAUTHORS:LOVcqg07
- Created
-
2007-09-02Created from EPrint's datestamp field
- Updated
-
2022-07-12Created from EPrint's last_modified field