Thermal tuning of optical cavities for parametric instability control

Thermal tuning of optical Fabry-Perot cavities has been proposed to reduce the parametric gain of high-frequency parametric instabilities in gravitational wave detectors. We investigate the performance achievable for such tuning obtained by thermal actuation of the mirrors (also called test masses) of the arm cavities. We show that for test mass dimensions used in advanced detectors, when circularly symmetric heating is applied to the rear side of the mirror, the steady-state tuning performance is almost independent of the heating pattern and depends only on the heating power. We derived the optimal time-dependent heating required to achieve the fastest possible actuation in sapphire and fused-silica substrates. Our simulations show that sapphire mechanical deformation response to heating is 15 times faster than that of fused silica, although sapphire requires three times more heating power to obtain the same radius of curvature change. (C) 2007 Optical Society of America