Automatic coupling of high-finesse Fabry-Pérot cavities with a mode convergence algorithm

The high-finesse Fabry-Pérot cavity is the most critical component of an ultra-stable laser. The coupling efficiency of the intra-cavity beam directly influences the frequency stability of ultra-stable lasers. For transportable or space-borne ultra-stable lasers, an automatic coupling procedure is typically required to address the reduction in coupling efficiency caused by environmental changes. We propose an automatic coupling method based on coupling efficiency feedback, which can achieve a fundamental mode coupling efficiency of 94% within a cavity displacement of 1.6 mm. Compared to conventional image recognition-based methods, our approach eliminates the need for bulky and expensive charge-coupled devices and complex image recognition algorithms. Most importantly, the maximum coupling range and coupling efficiency are no longer limited by the algorithm but are determined by hardware performance. This makes our automatic coupling method highly suitable for transportable and space-borne ultra-stable lasers.