# Parametric Oscillatory Instability in a Fabry-Perot Cavity of the Einstein Telescope with different mirror's materials

## TL;DR

This paper investigates the parametric oscillatory instability in the Einstein Telescope's Fabry-Perot cavity, analyzing different mirror materials and configurations, and compares these findings with existing gravitational wave detectors like LIGO.

## Contribution

It identifies unstable mode combinations in the Einstein Telescope and compares their behavior with those in LIGO and LIGO Voyager, providing insights for detector design.

## Key findings

- Unstable elastic and optical mode combinations are identified for different configurations.
- Comparison shows similarities and differences with LIGO and LIGO Voyager.
- Results inform mirror material choices to mitigate instabilities.

## Abstract

We discuss the parametric oscillatory instability in a Fabry-Perot cavity of the Einstein Telescope. Unstable combinations of elastic and optical modes for two possible configurations of gravitational wave third-generation detector are deduced. The results are compared with the results for gravita- tional wave interferometers LIGO and LIGO Voyager.