Resonant enhanced detection of the higher-order modes of a locked cavity

Current gravitational-wave (GW) detectors are limited in the amount of circulating power they can reach. Optical absorption in the test masses leads to thermal effects that shift the eigenmodes of the optical cavities, and cause control issues such as parametric instabilities. Here we experimentally validate a novel technique using optical injection to measure the mode amplitudes within an optical resonator. We use a phase camera, similar to the ones installed at gravitational-wave detectors, in transmission of the cavity, to confirm the mode basis and image modes up to order 10. We showcase as well the capability of the phase camera to determine the optical phase between the carrier fundamental mode and other co-resonating higher-order modes, which can be used for optical suppression of parametric instabilities and automatic mode matching. These results highlight the relevance of implementing a similar scheme in current GW detectors to monitor thermal effects.