Analysis of Parametric Oscillatory Instability in Power Recycled LIGO Interferometer

TL;DR

This paper analyzes the nonlinear parametric oscillatory instability in LIGO interferometers, focusing on the excitation of optical and elastic modes and the potential mitigating role of anti-Stokes modes.

Contribution

It provides a detailed analysis of the conditions leading to parametric instability in power recycled LIGO with Fabry-Perot cavities, highlighting the likelihood of incomplete suppression by anti-Stokes modes.

Findings

Parametric instability occurs when optical and elastic mode frequencies satisfy specific relations.

Anti-Stokes modes can partially suppress the instability but are unlikely to eliminate it entirely.

Threshold energy levels for the onset of instability are identified.

Abstract

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 and the mirror elastic mode, when the optical energy stored in the main FP cavity main mode exceeds the certain threshold and the frequencies are related so that sum of frequencies of Stokes and elastic modes are approximately equal to frequencyof main mode. The presence of anti-Stokes modes (with frequency approximately equal to sum of frequencies of main and elastic modes) can depress parametric instability. However, it is very likely that the anti-Stokes modes will not compensate the parametric instability completely.