Thermal noise of whispering-gallery resonators

By direct application of the fluctuation-dissipation theorem, we numerically\ncalculate the fundamental dimensional fluctuations of crystalline CaF2\nwhispering gallery resonators in the case of structural damping, and the limit\nthat this noise imposes on the frequency stability of such resonators at both\nroom and cryogenic temperatures. We analyze elasto-optic noise - the effect of\nBrownian dimensional fluctuation on frequency via the strain-dependence of the\nrefractive index - a noise term that has so far not been considered for\nwhispering-gallery resonators. We find that dimensional fluctuation sets a\nlower limit of 1E-16 to the Allan deviation for a 10-millimeter-radius sphere\nat 5 K, predominantly via induced fluctuation of the refractive index.\n