Dynamics of laser interferometric gravitational wave detectors

Dynamics of fields and mirrors in the new laser interferometric gravitational wave detectors is described. The dynamics of fields is formulated in terms of difference equations, which take into account the large delay due to the light transit time in the interferometer arm cavities. Solutions of these field equations are found in both transient and steady-state regimes. The solutions for fields in the transient regime can be used for the measurement of the parameters of Fabry-Perot cavities. The solutions for fields in the steady-state regime can be used for the analysis of noise performance of Fabry-Perot cavities. The dynamics of the mirrors is described in terms of two normal coordinates: the cavity length and its center of mass. Such dynamics is strongly affected by the radiation pressure of light circulating in the cavity. The forces of radiation pressure are nonlinear and nonconservative. These two effects introduce instabilities and give rise to a violation of conservation of energy for the motion of the suspended mirrors. Analytical calculations and numerical simulations of the dynamics are done with applications to the Laser Interferometer Gravitational-Wave Observatory (LIGO).; The dynamics of signal recycling and power recycling interferometers is analyzed using the field equations. The response of the interferometers to the input laser field and motion of its mirrors is calculated. Several basic transfer functions are found. These correspond to either a single or a nested cavity. A nested cavity appears either in the dynamics of the differential mode in signal recycling interferometers or in the dynamics of the common mode of power recycling interferometers. The poles of transfer functions of these nested cavities are found.; The response of the interferometers to gravitational waves is described: the analysis is done in the rest frame of a local observer which is a natural coordinate system of the detector. This response is given by the interferometer transfer function which takes into account both acceleration of the mirrors and changes of the laser wavelength due to the gravitational wave. Finally, a resonant detection of gravitational waves based on radiation pressure instabilities is proposed. Such a resonant detection can significantly increase the sensitivity of the interferometers in a narrow band, and can be used for searches of periodic sources of gravitational waves.