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 the Fabry-Perot (FP) cavities in the arms. The basis for this effect is the excitation of the additional (Stokes) optical mode with frequency omega(1) and the mirror elastic mode with frequency omega(m), when the optical energy stored in the main FP cavity mode with frequency omega(0) exceeds the certain threshold and the frequencies are related as omega(0) similar or equal to omega(1) + omega(m). The presence of anti-Stokes modes (with frequency omega(1a) similar or equal to omega(0) + omega(m)) can depress parametric instability. However, it is very likely that the anti-Stokes modes will not compensate the parametric instability completely. (C) 2002 Elsevier Science B.V. All rights reserved.