  Thermal fluctuations in the coatings used to make high-reflectors are
becoming significant noise sources in precision optical measurements and are
particularly relevant to advanced gravitational wave detectors. There are two
recognized sources of coating thermal noise, mechanical loss and thermal
dissipation. Thermal dissipation causes thermal fluctuations in the coating
which produce noise via the thermo-elastic and thermo-refractive mechanisms. We
treat these mechanisms coherently, give a correction for finite coating
thickness, and evaluate the implications for Advanced LIGO.
