Analysis of parametric oscillatory instability in Fabry–Perot cavity with Gauss and Laguerre–Gauss main mode profile

We calculate the parametric instabilities in Fabry–Perot cavities of advanced VIRGO and LIGO interferometers with different main mode profiles. All unstable combinations of elastic and Stokes modes both for the case with TEM00 and LG33 as a carriers are deduced.