Analysis of Parametric Oscillatory Instability in Signal Recycled LIGO Interferometer

TL;DR

This paper analyzes the potential for parametric oscillatory instability in signal recycled LIGO interferometers, showing it is unlikely due to detuning sensitivity and proposing a method to scan for instability conditions.

Contribution

The study provides a detailed analysis of parametric instability in LIGO, highlighting its low likelihood and introducing a frequency scanning approach to detect potential instabilities.

Findings

Parametric instability likelihood is low due to detuning sensitivity.

Adjusting the signal recycling mirror can scan for instability regions.

The analysis identifies specific frequency conditions for potential instability.

Abstract

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.