Fundamental thermal fluctuations in microspheres

The development of modern technology in many fields has led to further miniaturization of components. This makes it necessary to take into account certain fundamental physical limitations. An example of such limitations is the thermodynamical fluctuation of temperature in a small volume. Such fluctuations are transformed into wideband noise in output channels because of the temperature dependence of device parameters. The same limitations also appear frequently in experimental physics in macroscopic high-precision measurements. As was recently shown, fundamental fluctuations with the same origin limit the sensitivity of gravitational wave antennas [such as at the international Laser Interferometer Gravitational Wave Observatory1 (LIGO)], where thermal expansion, the thermal dependence of refractive indices, and Young’s modulus give rise to different types of noise.2–5 Thermorefractive fluctuations lead to phase noise in long fibers,6,7 which were used in observation of the effect for the first reported time.8 Microspheres9 are a relatively novel type of optical resonator that uniquely combine small size (from tens to thousands of micrometers) and high quality factor, as much as Q . 1010 for the so-called whispering-gallery modes10 (WGMs). The small size of the effective volume occupied by the electromagnetic (e.m.) field of the mode makes for low thresholds of nonlinear effects such as bistability and oscillatory instability,11 which are preconditioned by Kerr’s and thermal effects. The small volume makes it possible for such resonators to be used as tools for detection and measurement of thermorefractive noise.12 Apart from its importance in the LIGO project, the measurement of thermorefractive noise can serve as an innovative experimental examination of the theory of microscopic fluctuations of temperature. Thermorefractive noise should also be taken into account in possible applications of WGM resonators such as in diode-laser stabilization.