Mirror Thermal Noise in Interferometric Gravitational Wave Detectors

The LIGO (Laser Interferometer Gravitational-wave Observatory) project has begun its search for gravitational waves, and efforts are being made to improve its ability to detect these. The LIGO observatories are long, Fabry-Perot-Michelson interferometers, where the interferometer mirrors are also the gravitational wave test masses. LIGO is designed to detect the ripples in spacetime caused by cataclysmic astrophysical events, with a target gravitational wave minimum strain sensitivity of 4 x 10^-22 around 100 Hz. The Advanced LIGO concept calls for an order of magnitude improvement in strain sensitivity, with a better signal to noise ratio to increase the rate of detection of events. Some of Advanced LIGO's major requirements are improvements over the LIGO design for thermal noise in the test mass substrates and reflective coatings. Thermal noise in the interferometer mirrors is a significant challenge in LIGO's development. This thesis reviews the theory of test mass thermal noise and reports on several experiments conducted to understand this theory. Experiments to measure the thermal expansion of mirror substrates and coatings use the photothermal effect in a cross-polarized Fabry-Perot interferometer, with displacement sensitivity of 10^-15 m/rHz. Data are presented from 10 Hz to 4kHz on solid aluminum, and on sapphire, BK7, and fused silica, with and without commercial TiO2/SiO2 dielectric mirror coatings. The substrate contribution to thermal expansion is compared to theories by Cerdonio et al. and Braginsky, Vyatchanin, and Gorodetsky. New theoretical models are presented for estimating the coating contribution to the thermal expansion. These results can also provide insight into how heat flows between coatings and substrates relevant to predicting coating thermoelastic noise. The Thermal Noise Interferometer (TNI) project is a interferometer built specifically to study thermal noise, and this thesis describes its construction and commissioning. Using LIGO-like designs, components, and processes, the TNI has a minimum length noise in each of two arm cavities of 5 x 10^-18 m/rHz around 1 kHz.