Effects of mode degeneracy in the LIGO Livingston Observatory recycling cavity

We analyze the electromagnetic fields in a Pound-Drever-Hall locked, marginally unstable, Fabry-Perot cavity as a function of small changes in the cavity length during resonance. More specifically, we compare the results of a detailed numerical model with the behavior of the recycling cavity of the Laser Interferometer Gravitational-wave Observatory (LIGO) detector that is located in Livingston, Louisiana. In the interferometer's normal mode of operation, the recycling cavity is stabilized by inducing a thermal lens in the cavity mirrors with an external CO2 laser. During the study described here, this thermal compensation system was not operating, causing the cavity to be marginally optically unstable and cavity modes to become degenerate. In contrast to stable optical cavities, the modal content of the resonating beam in the uncompensated recycling cavity is significantly altered by very small cavity length changes. This modifies 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 is it the point where the input beam mode in the cavity is maximized.