Analysis of parametric oscillatory instability in signal recycled LIGO interferometer with different arms

The basis of undesirable effect of parametric oscillatory instability in signal recycled LIGO interferometer is the excitation of the additional (Stokes) optical mode, with frequency ω1ω1, and the mirror elastic mode, with frequency ωmωm, when optical energy stored in the main mode, with frequency ω0ω0, exceeds the certain threshold and the frequencies are related as ω0≃ω1+ωmω0≃ω1+ωm. We analyze parametric instability in the general case when eigen frequencies of Fabry–Perot (FP) cavities in arms of interferometer are detuned from each other and show that parametric instability in this interferometer is relatively small due to small bandwidth of interferometer. We propose to “scan” the frequency range where parametric instability may take place by varying the position of signal recycling mirror.