  Three-mode opto-acoustic interactions in advanced laser interferometer
gravitational wave detectors have high sensitivity to thermally excited
ultrasonic modes in their test masses. Three mode interaction signal gain can
change by 100% for thermally induced radius of curvature variations ~ 10-5,
allowing the monitoring of thermal distortions corresponding to wavefront
changes ~2 x 10-13m. We show that the three-mode gain for single cavity
interactions can be monitored by observing beat signals in the transmitted or
reflected light due to the thermal excitation of the many hundreds of
detectable acoustic modes. We show that three mode interaction signals can be
used at low optical power to predict parametric instabilities that could occur
at higher power. In addition, at any power, the observed mode amplitudes can be
used to control the interferometer operating point against slow environmental
perturbations. We summarize data on an 80m cavity that demonstrates these
effects and propose testing on full scale interferometer cavities to evaluate
whether the technique has practical benefits that can be extended from single
cavities to dual recycling interferometers.
