Thermo-optic noise in coated mirrors for high-precision optical measurements

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 thermoelastic and thermorefractive mechanisms. We treat these mechanisms coherently, give a correction for finite coating thickness, and evaluate the implications for Advanced LIGO.

Figure 1

Thermo-optic noises and Brownian noise for an Advanced LIGO input mirror.

Figure 2

Thermo-optic noises and Brownian noise for an Advanced LIGO end mirror.

Figure 3

An Advanced LIGO sensitivity curve. The thermo-optic curve labeled “NEW” uses Eq. (47), while the “OLD” curve uses a conservative estimate of TO noise: the sum of TR and TE, with the TE correction factor of 1.56 from 8.

Figure 4

A high-reflection coating made of $1/4$-wave doublets with a $1/2$-wave cap layer.