# The Influence of Dual-Recycling on Parametric Instabilities at Advanced LIGO

## TL;DR

This paper models the dual-recycled Advanced LIGO interferometer, revealing how its design influences parametric instabilities and identifying factors affecting mode suppression.

## Contribution

It provides a comprehensive model of the full dual-recycled Advanced LIGO, highlighting the impact of recycling cavities on parametric instability behavior.

## Key findings

- Recycling cavities increase the number of mechanical mode peaks by up to four times.
- Phase adjustments in the signal-recycling cavity significantly affect parametric gain.
- Modeling includes inherent imperfections for realistic predictions.

## Abstract

Laser interferometers with high circulating power and suspended optics, such as the LIGO gravitational wave detectors, experience an optomechanical coupling effect known as a parametric instability: the runaway excitation of a mechanical resonance in a mirror driven by the optical field. This can saturate the interferometer sensing and control systems and limit the observation time of the detector. Current mitigation techniques at the LIGO sites are successfully suppressing all observed parametric instabilities, and focus on the behaviour of the instabilities in the Fabry-Perot arm cavities of the interferometer, where the instabilities are first generated. In this paper we model the full dual-recycled Advanced LIGO design with inherent imperfections. We find that the addition of the power- and signal-recycling cavities shapes the interferometer response to mechanical modes, resulting in up to four times as many peaks. Changes to the accumulated phase or Gouy phase in the signal-recycling cavity have a significant impact on the parametric gain, and therefore which modes require suppression.