Mitigating parametric instability in optical gravitational wave detectors

Abstract

Fundamental sensitivity of an optical interferometric gravitational wave detector increases with increase of the optical power which, in turn, limited because of the opto-mechanical parametric instabilities of the interferometer. We propose to optimize geometrical shape of the mirrors of the detector to reduce the diffraction-limited finesse of unessential optical modes of the interferometer resulting in increase of the threshold of the opto-mechanical instabilities and subsequent increase of the measurement sensitivity. Utilizing parameters of the LIGO interferometer we found that the proposed technique allows constructing a Fabry-Perot interferometer with round trip diffraction loss of the fundamental mode not exceeding $5$~ppm, whereas the loss of the first dipole as well as the other high order modes exceed $1,000$~ppm and $8,000$~ppm, respectively. The optimization comes at the price of tighter tolerances on the mirror tilt stability, but does not result in a significant modification of the optical beam profile and does not require changes in the the gravity detector read-out system. The cavity with proposed mirrors is also stable with respect to the slight modification of the mirror shape.