Abstract
Use of flat instead of Gaussian beams in the long cavities of the next generation of gravitational wave interferometers has been proposed in order to reduce, by an averaging process, the readout noise caused by mirror surface fluctuations. It is thus expected to reduce the thermoelastic noise, and the conventional thermal noise (or Brownian noise in the substrate) as well. But a direct calculation was still missing. We present here a model of a mirror coupled to a flat beam and give the spectral density of conventional thermal noise first in the case of an infinite substrate, then for a finite cylindrical substrate.
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