  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.
