New analytic estimate of thermal noise in spindle optical cavities

Thermal noise in optical reference cavities sets a severe limit to the frequency instability of ultra-stable lasers. We, for the first time, give an analytic expression of the contribution of the spindle spacer based on Levin´s formulation of the fluctuation-dissipation-theorem (FDT). The analysis indicates that the thermal noise of spindle cavity has a few different features from cylindrical cavities with similar geometry. The analytic estimate for the spindle spacer by our equation fits better with finite element analysis (FEA) results compared with previous equations.