Thermal noise in half infinite mirrors with non-uniform loss: a slab of excess loss in a half infinite mirror

Abstract

We calculate the thermal noise in half-infinite mirrors containing a layer of arbitrary thickness and depth made of excessively lossy material but with the same elastic material properties as the substrate. For the special case of a thin lossy layer on the surface of the mirror, the excess noise scales as the ratio of the coating loss to the substrate loss and as the ratio of the coating thickness to the laser beam spot size. Assuming a silica substrate with a loss function of 3x10-8 the coating loss must be less than 3x10-5 for a 6 cm spot size and a 7 micrometers thick coating to avoid increasing the spectral density of displacement noise by more than 10%. A similar number is obtained for sapphire test masses.

Passed LSC (internal) review. Submitted to Phys. Rev. D. (5/2001) Replacement: Minor typo in Eq. 17 corrected

References in corpus (2)

• Thermoelastic Noise and Homogeneous Thermal Noise in Finite Sized Gravitational-Wave Test Masses
• Dissipation of mechanical energy in fused silica fibers

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