Parametric Instability in Long Optical Cavities and Suppression by Dynamic Transverse Mode Frequency Modulation

TL;DR

This paper reports the first observation of three-mode parametric instability in a large optical cavity, revealing that transverse mode frequency modulation caused by mirror errors and motion can suppress instability, with potential mitigation techniques.

Contribution

It demonstrates that transverse mode frequency modulation due to mirror errors and motion can suppress parametric instability in large optical cavities, challenging previous stability assumptions.

Findings

Parametric instability observed in a large-scale suspended optical cavity.

Mirror figure errors cause transverse mode frequency dependence on spot position.

Frequency modulation can suppress parametric gain by factors of 10-20.

Abstract

Three mode parametric instability has been predicted in Advanced gravitational wave detectors. Here we present the first observation of this phenomenon in a large scale suspended optical cavity designed to be comparable to those of advanced gravitational wave detectors. Our results show that previous modelling assumptions that transverse optical modes are stable in frequency except for frequency drifts on a thermal deformation time scale is unlikely to be valid for suspended mass optical cavities. We demonstrate that mirror figure errors cause a dependence of transverse mode offset frequency on spot position. Combined with low frequency residual motion of suspended mirrors, this leads to transverse mode frequency modulation which suppresses the effective parametric gain. We show that this gain suppression mechanism can be enhanced by laser spot dithering or fast thermal modulation. Using Advanced LIGO test mass data and thermal modelling we show that gain suppression factors of 10-20 could be achieved for individual modes, sufficient to greatly ameliorate the parametric instability problem.