Hallam, Jonathan Mark (2011)
Ph.D. thesis, University of Birmingham.
Einstein’s Theory of General Relativity describes gravity as the curvature of space-time and predicts gravitational waves. Laser interferometric gravitational wave detectors attempt to observe the strain gravitational waves exert on space-time, which is obscured by seismic, thermal and quantum among other noises. Diffraction gratings have been proposed in all reflective configurations as core optical elements in future detectors. In this thesis phase changes are shown to occur due to lateral displacement of diffractive optics. These couple noise from interferometer alignment into the gravitational wave phase signal. For the end-mirror tilt of a 3 km Fabry-Perot arm cavity as used in gravitational wave detectors, this was found to set quite severe isolation requirements. This result was supported by a bench-top experiment, and by collaborative work on the Joint Interferometer Facility (JIF) diffractive cavity. Using a steady-state technique to derive the coupling relations, a signal to noise ratio between lateral grating displacement and a notional gravitational wave signal was determined for each output port of the three-port coupled diffractive Fabry-Perot cavity. The forward-reflecting output port offers the highest SNR at low frequencies due to cancellation of the phase noise. The JIF cavity result confirmed this calculation.
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