Tuning of resonant doublets in coupled optical cavities

The mode profile of a coupled optical cavity often exhibits a resonant doublet, which arises from the strong coupling between its sub-cavities. Traditional readout methods rely on setting fields of different frequencies to be resonant in either sub-cavity, which is challenging in the case of strong coupling. In this regime, the coupled cavity behaves as a single resonator, and a field must be resonant in all its parts. Consequently, specialized sensing schemes are necessary to control strongly coupled cavities. To address this issue, we propose a novel technique for the relative measurement of the degrees of freedom of a strongly coupled cavity. Our approach enables simultaneous frequency stabilization and fine-tuning of frequency splitting in the resonant doublet. Overall, our proposed technique offers a promising solution to control the properties of coupled cavities, facilitating advanced applications in the fields of gravitational-wave detection, quantum cavity optomechanics, and other related areas.