Fields in the recycling cavity at LIGO Livingston Observatory

We analyze the electromagnetic elds in a Pound-Drever-Hall locked, optically unstable Fabry- Perot cavity as a function of small changes in the cavity length during resonance. The specic cavity under investigation was the recycling cavity of the Laser Interferometer Gravitational Wave Observatory (LIGO) detector that is located in Livingston, Louisiana. In contrast to stable optical cavities, the shape of the resonating beam in the recycling cavity is strongly aected by microscopic cavity length changes during resonance. This modies the error signals used to control the cavity length in such a way that the zero crossing point is no longer the point of maximum power in the cavity nor the point where the input beam mode in the cavity is maximized . An FFT based optical simulation program has generated numerical results that agree well with the experimental observations. A less sophisticated but meaningful analytical model, that takes into account the transverse distribution of the observed eld reected from the cavity provides our explanation of the fundamental mechanism by which the observed eects are generated. The eects described are signican t for LIGO and other ground-based power recycled gravitational wave interferometers that use heterodyne signal extraction.