[Truncated abstract] Advanced laser interferometer gravitational wave detectors require an extremely high optical power in order to improve the coupling between the gravitational wave signal and the optical field. This high power requirement leads to new physical phenomena arising from nonlinear interactions associated with radiation pressure. In particular, detectors with multi-kilometer-long arm cavities containing high density optical fields suffer the possibility of 3-mode opto-acoustic interactions. This involves the process where ultrasonic vibrations of the test mass cause the steady state optical modes to scatter. These 3-mode interactions induce transverse optical modes in the arm cavities, which then can provide positive feedback to the acoustic vibrations in the test masses. This may result in the exponential growth of many acoustic mode amplitudes, known as Parametric Instability (PI). This thesis describes research on 3-mode opto-acoustic interactions in advanced interferometric gravitational wave detectors through numerical investigations of these interactions for various interferometer configurations. Detailed analysis reveals the properties of opto-acoustic interactions, and their dependence on the interferometer configuration. This thesis is designed to provide a pathway towards a tool for the analysis of the parametric instabilities in the next generation interferometers. Possible techniques which could be helpful in the design of control schemes to mitigate this undesirable phenomenon are also discussed. The first predictions of parametric instability considered only single interactions involving one transverse mode and one acoustic mode in a simple optical cavity. ... In Chapter 6, I was able to make use of a new analytical model due to Strigin et al., which describes parametric instability in dual recycling interferometers. To make the solution tractable, it was necessary to consider two extreme cases. In the worst case, recycling cavities are assumed to be resonant for all transverse modes, whereas in the best cases, both recycling cavities are anti-resonant for the transverse modes. Results show that, for the worst case, parametric gain values as high as ~1000 can be expected, while in the best case the gain can be as low as ~ 3. The gain is shown to be very sensitive to the precise conditions of the interferometer, emphasising the importance of understanding the behaviour of the detectors when the cavity locking deviates from ideal conditions. Chapter 7 of this thesis contains work on the observation of 3-mode interactions in an optical cavity at Gingin, which confirms the analysis presented here, and also a paper which shows how the problem of 3-mode interactions can be harnessed to create new devices called opto-acoustic parametric amplifiers. In the conclusions in Chapter 8, I discuss the next important steps in understanding parametric interactions in real interferometers – including the need for more automated codes relevant to the design requirements for recycling cavities. In particular, it is pointed out how the modal structure of power and signal recycling cavities must be understood in detail, including the Gouy phase for each transverse mode, to be able to obtain precise predictions of parametric gain. This thesis is organised as a series of papers which are published or have been submitted for publication. Such writing style fills the condition for Ph.D. thesis at the University of Western Australia.

Virgo est un interféromètre de Michelson dont les bras contiennent des cavités Fabry-Perot. Il a été construit pour détecter directement les ondes gravitationnelles. Le projet Advanced Virgo est une amélioration majeure de Virgo pour atteindre une sensibilité encore plus élevée avec laquelle la détection des ondes gravitationnelles deviendra probable. On prévoit un système laser mono-fréquence de 175 Watts de puissance optique présentant des stabilités accrues pour le bruit relatif de puissance et pour le bruit de fréquence. Ce travail de thèse a pour objet la réalisation de ce système laser de haute-puissance et de haute-stabilité basée sur l'utilisation d'amplificateurs à fibre combinés de façon cohérente. Des amplificateurs à fibre disponibles dans le commerce sont caractérisés en termes de qualité de faisceau, de bruit de puissance, de bruit de fréquence, de stabilité de pointé du faisceau, et également en terme de stabilité à long terme sur quelques milliers d'heures. On implémente l'interférométrie de Mach-Zehnder pour la combinaison cohérente de faisceaux. Les techniques de caractérisation de faisceaux laser sont aussi développées en considérant leurs limites ultimes. Hormis un déficit de puissance optique, le système laser développé dans cette étude sur la base de la combinaison cohérente de Master Oscillator Fiber Power Amplifiers, remplit les conditions posées par Advanced Virgo. / Virgo is a cavity-enhanced Michelson interferometer built for the direct detection of gravitational waves. The Advanced Virgo project consists of major upgrades to the Virgo gravitational wave detector for an order of magnitude improvement in differential strain sensitivity, one of which is the tenfold increase in injected laser power to 175 Watts. The use of fiber laser amplifiers and their coherent combination are foreseen to deliver the required high-power low-noise beam. In this thesis work, we review the laser requirements for gravitational wave detectors, introduce the design of the laser system for Advanced Virgo, and develop the means for laser characterization in accordance with the stringent noise specifications. We then present the results to date, notably the quasi-continuous long-term operation of two 40-Watt fiber laser amplifiers over thousands of hours and their coherent combination with Mach-Zehnder interferometry. Although the targeted power for Advanced Virgo is not yet attained, the developed system shows decent noise performance and is promising for further power-scaling efforts.