Analysis of parametric oscillatory instability in power recycled LIGO interferometer

We present the analysis of a nonlinear effect of parametric oscillatory instability in power recycled LIGO interferometer with Fabry-Perot cavities in the arms. The basis for this effect is the excitation of the additional Stokes optical mode and the mirror elastic mode when the optical energy stored in the main Fabry-Perot cavity mode exceeds the certain threshold. We demonstrate that in the resonance case the parametric oscillatory instability will take place at the energy stored in the cavity of about five orders smaller than one planned for LIGO-II interferometer. The presence of anti-Stokes modes can depress parametric oscillatory instability. However, it is very likely that the anti-Stokes modes will not compensate the parametric instability completely because of the existence of the mode combinations which interact with each other quite strongly.