Yamamoto 2002

Physics Letters A 305 (2002) 18–25 www.elsevier.com/locate/pla Thermal noise caused by an inhomogeneous loss in the mirrors used in the gravitational wave detector Kazuhiro Yamamoto ∗ , Masaki Ando, Keita Kawabe 1 , Kimio Tsubono Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Received 4 September 2002; received in revised form 4 October 2002; accepted 4 October 2002 Communicated by P.R. Holland Abstract We have evaluated the thermal noise of mirrors with inhomogeneous loss in interferometric gravitational wave detectors using a reliable estimation method. Our calculation showed that the traditional estimation by modal expansion is very different from the actual thermal noise. In a typical model case, when the loss is localized on a surface illuminated by a laser beam, the thermal noise is about three times larger than the estimation of the modal expa nsion . When the dissi patio n is concentr ated at points far from the beam spot, the thermal noise is about fifteen times smaller. © 2002 Elsevier Science B.V. All rights reserved. PACS: 05.40.Jc; 04.80.Nn Keywords: Thermal noise of mirror; Interferome tric gravitational wave detector; Inhomogeneous loss; Direct approach; Modal expansion 1. Introduction In precis e measurements, such as gravi tation al ex- periments, the thermal fluctuation of the mechanical components is a fundamental noise source. Since a direct measurement of thermal noise is generally diffi- cult, an estimation of the thermal motion is important in studyin g the noise propertie s. Modal expansion [1] is a frequently employed method to estimate thermal noise. Nevertheless, our recent experiment [2] proved * Corre spon ding auth or. Pres ent address: Gra vit ati onal wa ve group, Institute for Cosmic Ray Research, University of Tokyo, 5- 1-5 Kashiwa-no-Ha, Kashiwa, Chiba 277-8582, Japan. E-mail address: [email protected] (K. Yamamoto). 1 Present address: Max-Planc k-Institut für Gravita tionsphysi k, Albert-Ei nstein-Inst itut, D-85748 Garching, Germany. that this method is invalid in systems with the loss distributed inhomogeneously. Thermal motions must be ev aluate d using other reliabl e methods when dissipation is not uniform. The ther mal nois e of mirr ors in int erfe rome tri c gra vit ati onal wa ve det ect ors [3–7] wa s ev aluate d bas ed on modal expansion [8–10]. However, the dissipation in the mirror is distributed inhomogeneously. For ex- ample, measurements of the Q-values suggest that the loss is localized on the surfaces of the mirror [11–13] and near magnets glued on the mirrors to control thei r positions [14,15]. Since the thermal noise of a mirror derived from the modal expansion is already a limit- ing factor of the sensit ivit y of the interferometer in the observation band, an invalidity of the modal expansion is a serious problem. There have only been a few studies [16–19] for the thermal noise of a mirror with 0375-9601/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0375-9601 (02)013 89-0

Yamamoto 2002

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