Thermal noise in optical cavities revisited

Thermal noise of optical reference cavities sets a fundamental limit to the frequency instability of ultra-stable lasers. Using Levin's formulation of the fluctuation-dissipation theorem we correct the analytical estimate for the spacer contribution given by Numata et al.. For detailed analysis finite-element calculations of the thermal noise focusing on the spacer geometry, support structure and the usage of different materials have been carried out. We find that the increased dissipation close to the contact area between spacer and mirrors can contribute significantly to the thermal noise. From an estimate of the support structure contribution we give guidelines for a low-noise mounting of the cavity. For mixed-material cavities we show that the thermal expansion can be compensated without deteriorating the thermal noise.