Control of instabilities in high optical power cavities

[Truncated abstract] The gravitational waves (GWs) that come to us from astrophysical sources carry interesting and important information, such as information about the collisions and explosions of stellar cores, or possibly on events in the early universe. Directly observing GWs therefore would o er us an innovative tool with which to explore our Universe. So far, several laser interferometric GW detectors are being constructed, and are now operating around the world. The proposed second generation GW detectors are designed to signi cantly improve strain sensitivities, down to 1024/pHz in a reasonably broad band around 100 Hz. In order to reduce the effect of shot noise, which limits the detector performance in the high frequency range, very high optical power ( 1 MW) will circulate in the detector arm cavities. However, such a high level of laser power can result in a wide variety of nonlinear e ects, including: thermal lensing arising from the residual optical absorptions inside the substrate and coatings of the optical components; parametric instability (PI) due to resonant interactions between the optical cavity modes and the high Q-factor acoustic modes of the mirrors; and Sidles-Sigg instability (angular instability) created by relatively large radiation pressure forces exerting torques on the suspended mirrors. These nonlinear e ects will induce wavefront distortions in the cavity beams, and instabilities in the interferometers, and they consequently constrain the improvement in detector sensitivities, or even disrupt the detector operation entirely. This thesis is a collection of published (or soon to be submitted) papers, which report on the experimental research results related to these nonlinear problems.