Thermal noise in optical reference resonators

Thermal noise fundamentally limits the frequency stability of optical resonators used in optical clocks or to generate ultrapure microwaves by optical frequency division. We will give an overview of the relevant noise mechanisms, their calculation and discuss different current developments to reduce the noise. In one approach a cryogenic silicon resonator with very low thermal noise operated at a temperature of 124 K, the point of zero thermal expansion, will be presented. With a laser stabilized to this resonator a fractional laser frequency instability of 10^-16 for averaging times around one second has been reached.