Time evolution of parametric instability in large-scale   gravitational-wave interferometers
  We present a study of three-mode parametric instability in large-scale gravitational-wave detectors. Previous work used a linearised model to study the onset of instability. This paper presents a non-linear study of this phenomenon, which shows that the initial stage of exponential rise of the amplitudes of a higher order optical mode and the mechanical internal mode of the mirror is followed by a saturation phase, in which all three participating modes reach a new equilibrium state with constant oscillation amplitudes. Results suggest that stable operation of interferometers may be possible in the presence of such instabilities, thereby simplifying the task of suppression. 
Stefan L. Danilishin, Sergey P. Vyatchanin, David G. Blair, Ju Li,   Chunnong Zhao
gr-qc astro-ph.IM physics.ins-det physics.optics