Estimation of thermal noise for spindle optical reference cavities

Thermal noise in optical reference cavities sets a severe limit to the frequency stability of ultra-stable lasers of the order of a few parts of 10−16 at 1 s. Various reference cavity designs have been developed to attempt to attain ultimate performance. Numata derived three equations based on strain energy and the fluctuation-dissipation-theorem (FDT) to estimate the noise contributions of the spacer, substrates and coatings, and these equations work well for cylindrical cavities. However, only axial strain energy has been calculated previously. Extending from that, we derive the thermal noise for a spindle spacer, including the contribution of shearing strain energy, based on FDT, and focusing on the spacer geometry and materials. We compare our new approach with finite element analysis (FEA) of the strain energy in spindle cavities, and conclude that the new analytic estimate for the spindle spacer contributions fits better with FEA.