Suppression of the Effect of Parametric Instability in the LIGO Voyager Gravitational Wave Detector

The number of unstable combinations of elastic and Stokes optical modes of the LIGO Voyager gravitational wave detector, frequencies and spatial distributions of displacement vectors of elastic modes of the mirrors were calculated. The values of overlap factors for unstable modes up to ninth-order optical modes were calculated, taking into account the azimuthal condition of parametric instability. An analysis of the influence of the temperature dependence of the Young’s modulus of the mirror material on the number of unstable modes in the Fabry–Perot cavity was performed.