Parametric instability in gravitational wave detectors

In 2000 Vladimir Braginsky and co-workers predicted that high power laser light in very long baseline gravitational wave detectors could give rise to parametric instability consisting of uncontrolled laser powered amplification of acoustic vibrations of the mirrors. In 2005 Chunnong Zhao and co-workers published a detailed simulation which predicted that the planned Advanced LIGO gravitational wave detectors would experience such instabilities and that these would occur at a small fraction of design power. This would prevent full sensitivity from being achieved. This thesis describes experimental studies of parametric instability. The first experiments took place at Gingin, where the author made the first observations of free running parametric instability using an 80m high power cavity. The second set of experiments took place at LIGO Livingston after parametric instability was first observed there, these experiments focused on refining thermal detuning, a technique that had been proposed and tested at Gingin. Thermal detuning enabled the laser power to be raised sufficiently for the first detection of gravitational waves on Sept 14, 2015. The third set of experiments demonstrated the electrostatic damping technique in preparation for increased laser power: the initial demonstration was performed at LIGO Livingston, further work was carried out at LIGO Hanford. The control of parametric instability was crucial to the first detection of gravitational wave signals from the coalescence of a binary black hole system. It will be of increasing importance in the new era of gravitational wave astronomy as detector sensitivity is increased. There is a realistic prospect of being able to detect gravitational waves from the very edge of the observable universe but this will require higher optical power and improved parametric instability control. The first three chapters of this thesis provide introductions to gravitational waves, optomechanics and parametric instability respectively. They aim to engage an audience that includes postgraduate students. Chapter 1 includes; a brief history of the field, fundamentals of gravitational wave detection, laser interferometer physics, an introduction to the research center at Gingin and a brief discussion about future gravitational wave detectors. Gravitational wave detectors are high power optomechanical devices in which mechanical motion and resonances interact with optical resonances. Chapter 2 reviews some of the optical and mechanical resonances and discusses optomechanics in gravitational wave detectors. This introduction to optomechanics provides a foundation for the remainder of the thesis which focuses on the three-mode optomechanical interactions that lead to parametric instability. These interactions couple one elastic eigenmode of the mirror to two optical eigenmodes. Chapter 3 reviews the theory of parametric instability and the history of experimental studies, followed by a review of proposed mitigation strategies. Chapters 4 and 5 focus on experimental confirmation of the theory of parametric instability. Chapter 4 describes an experiment in the low power regime at Gingin, which confirmed the optical drive mechanism. It provided a method for measuring parametric gains well below the instability threshold. Chapter 5 describes the characterisation of parametric instability at LIGO Livingston immediately prior to Observation Run 1, and the method used for avoiding instability. Instability was observed in LIGO in November 2014 when the laser power first exceeded the instability threshold. I was invited on the LIGO visitor program to assist in optimising the thermal detuning technique. Thermal detuning allowed the optical power to be increased by 150%, which soon afterwards resulted in the momentous discovery of the first two gravitational wave signals. Chapter 5 also discusses the requirements of parametric instability control at full design optical power, which is eight times higher than the power used in the first obser-