Enhancement and suppression of opto-acoustic parametric interactions using optical feedback

A three mode opto-acoustic parametric amplifier (OAPA) is created when two orthogonal optical modes in a high finesse optical cavity are coupled via an acoustic mode of the cavity mirror. Such interactions are predicted to occur in advanced long baseline gravitational wave detectors. They can have high positive gain, which leads to strong parametric instability. Here we show that an optical feedback scheme can enhance or suppress the parametric gain of an OAPA, allowing exploration of three-mode parametric interactions, especially in cavity systems that have insufficient optical power to achieve spontaneous instability. We derive analytical equations and show that optical feedback is capable of controlling predicted instabilities in advanced gravitational wave detectors within a time scale of 1 similar to 10 s.