Thermal noise caused by an inhomogeneous loss in the mirrors used in the gravitational wave detector

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 expansion. When the dissipation is concentrated at points far from the beam spot, the thermal noise is about fifteen times smaller. (C) 2002 Elsevier Science B.V. All rights reserved.