Non-linear Control for Stabilisation of Optical Experiments

Optical resonators are a crucial component in many experimental setups involving lasers. In these setups, the lasers or resonators usually need to be actively stabilised, because the resonance frequency of the cavities changes relative to the laser's frequency due to various disturbances. The changes in transmission or reflection themselves reveal nothing about the sign of the detuning, so it is necessary to generate a suitable error signal that reveals the sign and magnitude of the mismatch. There are various schemes that achieve this, but they usually require additional optical elements, increasing the complexity of the setup. There is one approach that does not require additional components, it is colloquially called "dither locking", and relies on harmonic perturbations of the cavity resonance to gain information about the detuning and its sign. However, the performance of this method is usually worse than the more complex ones, and it requires more careful tuning to achieve good performance. In this work I present a new approach called "quadratic dither locking" that extends the conventional dither locking approach to a higher order approximation that should allow for more efficient estimation of the cavity detuning. The new control scheme is based on a physically motivated model of the cavity, enabling rule-based optimal controller design, as opposed to ad-hoc expert-based tuning. The new scheme is demonstrated to work by stabilising a triangular cavity with the custom controller implemented on a Red Pitaya. While the new control system does not yet surpass the performance of a conventional dither lock in the investigated application, it is shown to be very bandwidth efficient, which could prove to be beneficial for slow temperature-based actuators. The new approach is also generalisable to systems that require stabilisation of multiple degrees of freedom from a single measurement channel.