Analysis of Parametric Oscillatory Instability in Signal Recycled LIGO Interferometer

We present the analysis of undesirable effect of parametric oscillatory instability in signal recycled LIGO interferometer. 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 optical energy stored in the main FP cavity mode, with frequency ${\omega }_0$, exceeds the certain threshold and the frequencies are related as ${\omega }_0\simeq {\omega }_1+{\omega }_m$. We show that possibility of parametric instability in this interferometer is relatively small due to stronger sensitivity to detuning. We propose to ``scan’’ the frequency range where parametric instability may take place varying the position of signal recycling mirror.