  Laser interferometers with high circulating power and suspended optics, such
as the LIGO gravitational wave detectors, experience an optomechanical coupling
effect known as a parametric instability: the runaway excitation of a
mechanical resonance in a mirror driven by the optical field. This can saturate
the interferometer sensing and control systems and limit the observation time
of the detector. Current mitigation techniques at the LIGO sites are
successfully suppressing all observed parametric instabilities, and focus on
the behaviour of the instabilities in the Fabry-Perot arm cavities of the
interferometer, where the instabilities are first generated. In this paper we
model the full dual-recycled Advanced LIGO design with inherent imperfections.
We find that the addition of the power- and signal-recycling cavities shapes
the interferometer response to mechanical modes, resulting in up to four times
as many peaks. Changes to the accumulated phase or Gouy phase in the
signal-recycling cavity have a significant impact on the parametric gain, and
therefore which modes require suppression.
