Tabletop investigation of parametric instability and light scattering phenomena in gravitational wave detectors

[Truncated] Parametric instability is a potential threat to the operation of advanced gravitational wave detectors. It arises from three-mode parametric interactions between the test mass acoustic modes and the optical modes, mediated by the radiation pressure force.

This thesis describes experiments to observe and characterise three-mode parametric instability on a table-top setup. The setup consists of a 50 nm thick silicon nitride membrane, with a high Q factor (106 at 1.7 MHz), placed in the middle of a 10 cm Fabry-P´erot optical cavity. This configuration allows tuning of the cavity to achieve parametric interactions. The cavity was tuned until the injected optical mode and the scattered optical mode were resonant in the cavity, and were thus enhanced by cavity resonance. High circulating power per unit mass was achieved by using mirrors with highly reflective coatings and a low mass resonator.

I observed the mechanical mode ring-up when the input power is above the instability threshold. The ring-up rate agrees with previous model predictions. Contrary to expectations, I observed power saturation of the mechanical amplitude, and parametric instability does not lead to loss of cavity lock. This facilitates the implementation of control techniques in advanced gravitational wave detectors. This is the first observation of three-mode parametric instability in a free-space Fabry-P´erot cavity.

Because previous models do not describe the power saturation of the mechanical amplitude, a large amplitude model was developed to describe three-mode parametric instability. The experimental results are consistent with this model, which predicts exponential growth of the mechanical oscillation, followed by saturation.

A scheme of acoustic feedback is designed for controlling the parametric interaction. Theoretical analysis shows that this feedback is able to introduce damping in the mechanical mode. Heating and cooling of the mechanical mode was demonstrated by applying feedback with appropriate phase.