Signal extraction and optica design for an advanced gravitational wave interferometer

The LIGO project is two 4 km baseline interferometers which are currently being constructed in the quest to directly detect gravitational radiation. Concurrent with this effort is research aimed at increasing the strain sensitivity of the initial interferometers to 2.5 × 10−23/$Hz$. The optical configuration, which defines the detector gain and bandwidth, is one such area of research. Resonant sideband extraction (RSE) is the configuration which is proposed for advanced LIGO. RSE allows for much more freedom in the optimization of the detector response compared to the initial configuration.; The principle of RSE is examined in the context of a three mirror coupled cavity. The effect of optical losses on the design of an RSE interferometer is discussed. Two model optimizations of the interferometer design are done: one for binary inspiral sources and one for periodic sources at 1 kHz.; An optical heterodyne signal extraction scheme is proposed to sense the deviation of the mirrors away from their nominal positions, and to read out the gravitational wave signal. The scheme is applied to the two model interferometers previously designed, and its performance is analyzed for each case. Allowable residual deviations of the common mode degrees of freedom are also derived.; A tabletop prototype of an RSE interferometer has been constructed to demonstrate both the viability of the proposed signal extraction scheme and the tunability of the RSE interferometer. Good agreement on both counts is found between the measured experimental data and the modeled predictions.; The coupling of laser frequency and amplitude noise into the gravitational wave readout port is analyzed for the RSE configuration assuming the proposed gravitational wave signal readout scheme. Specifications for the allowable laser frequency and amplitude noise, as well as allowable residual deviations of the differential mode degrees of freedom, are derived for the two model interferometers.