(Almost-)blind locking algorithm for high finesse suspended optical cavities

Suspended resonant optical cavities are basic building blocks for several experimental devices. An important issue is the control strategy required to bring them in the resonant or slightly detuned configuration needed for their operation, the so-called \textit{ locking} procedure. This can be obtained with a feedback strategy, but the error signal needed is tipically available only when the cavity is near the resonance with a precision of the order $\Delta L\simeq\lambda_{\ell}{\cal F}^{-1}$, where ${\cal F}$ is the cavity finesse and $\lambda_{\ell}$ is the laser's wavelength. When the mirrors are freely swinging the locking can be attempted only in the short time windows when this condition is verifyed. Tipically this means that the procedure must be repeated several times, and that large forces must be applied. In this paper we describe a different strategy, which tries to take advantage by the fact that the dynamics of the mirrors is known at least in an approximate way. We argue that the locking procedure considered can be more efficient compared with the naive one, with a reduced needed maximal feedback. Finally we discuss possible generalizations and we point to future investigations.