Controlling advanced gravitational wave detector output mode cleaners acting on the laser frequency

Advanced gravitational wave interferometers are the second generation of high sensitivity detectors aiming at the direct observation of gravitational waves of astrophysical origin. To improve the sensitivity tenfold around the most sensitive frequency region at 100 Hz with respect to first generation instruments, several new techniques are being implemented. This paper focuses on the output mode cleaner (OMC), which is a resonant cavity, placed at the main output port of the interferometer. The OMC plays the role of a passive spatial and frequency filter for the beam carrying the gravitational wave signal. Such a cavity is crucial to reach the design sensitivity of advanced detectors. So far, the proper resonance condition of the laser beam was ensured by actively controlling the optical length of the OMC. We propose a new scheme: in order to keep the OMC at resonance, the laser frequency is controlled instead of the OMC length. This approach no longer requires actuators on the OMC, allowing an improvement of the OMC in terms of filtering capabilities, noise performances and simplicity. We show how to implement this technique in the control acquisition sequence, and the sensing and control strategy of advanced detectors.