LIGO Publication Abstract
Dynamics of Laser Interferometric Gravitational Wave Detectors
Rakhmanov, M.
PhD Thesis, CIT (2000)

This thesis is a study of dynamics of the new laser gravitational-wave detectors. The analysis in the thesis is developed primarily for LIGO (Laser Interferometer Gravitational-Wave Observatory) but can be used for other interferometers such as VIRGO and TAMA. The dynamics of fields in the interferometers are described in terms of difference equations which take into account the light transit time in the arm cavities. Solutions for these equations are found in the transient and steady-state regimes. In particular, a matrix technique is introduced to analyze the dynamics of fields in a three-mirror coupled cavity. The dynamics of mirrors in the interferometer are described in terms of nonlinear differential equations with delays. The mirrors interact with each other through the light circulating in the interferometer. This interaction gives rise to instabilities which lead to violations of the energy conservation. The instabilities and the associated energy transfers are studied using both analytical methods and numerical simulations. The dynamics of interferometers are described in terms of the time-domain difference equations. Linear transfer functions representing the basic interferometer responses are found by solving the time-domain equations for different special cases. The main parameters for these transfer functions, the poles and zeros, are found as functions of the mirror reflectivities. Finally, the dynamic response of the interferometers to gravitational waves is described. The response function includes the forces acting on the mirrors, the delays in the interferometer arm cavities, and the gravitational red-shift of light. Optimization of this response suggests a possibility of resonant detection of gravitational waves which can significantly increase the sensitivity of the interferometers in a narrow band.


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