Optical torques in the folding Fabry–Perot cavity

Folding the Fabry-Perot cavity allows gravitational wave detectors to enhance their effective arm lengths. However, a different number of mirrors and geometry of the folded cavity will complicate the dynamics of the mirrors under the exertion of radiation pressure forces and torques. This paper gives the framework for analysing the stability of folded cavities in the angular degrees of freedom. In particular, we analyse the optical torques and mirror dynamics of the trifold 12 km cavity, which can serve as a potential upgrade of aLIGO for the kilo-Hertz sensitivity boosting. We explore feasible geometric configurations supporting the target arm cavity power of 1.5 MW and the resulting coating thermal noise. Our analysis suggests that the cavity remains stable by replicating the current arm cavity geometry three times and increasing all mirror masses to 200 kg. It gives thermal noise, 2.94 × 10⁻²⁴ / √Hz at 100 Hz, 8.5% higher than the aLIGO design.