Retroreflective surface optimisation for optical cavities with custom mirror profiles

TL;DR

This paper presents a novel two-step method for optimizing mirror surface profiles in optical cavities, significantly enhancing emitter-photon coupling strength and cooperativity, with broad applicability across different geometries.

Contribution

The authors develop a new two-step optimization approach for custom mirror profiles that improves coupling efficiency in optical cavities, overcoming numerical challenges of traditional methods.

Findings

Mirror shaping can increase coupling cooperativity by about 3 times.

The method achieves over tenfold improvements for multi-emitter coupling.

Optimized mirror profiles enhance cavity performance across various geometries.

Abstract

Coupling an emitter to a Fabry-P\'{e}rot optical cavity can provide a coherent and strong light-matter interface whose performance in a variety of applications depends critically on the emitter-photon coupling strength. Altering the typically spherical profiles of the cavity mirrors can improve this coupling strength, but directly optimising the mirror shape is numerically challenging as the multidimensional parameter space features many local optima. Here, we develop a two-step method to optimise mirror surface profiles while avoiding these issues. First, we optimise the target cavity eigenmode for the chosen application directly, and second, we construct the mirror surfaces to retroreflect this optimised target mode at both ends of the cavity. We apply our procedure to different emitter-cavity coupling scenarios. We show that mirror shaping can increase the cooperativity of coupling to a central emitter by a factor of approximately 3 across a wide range of geometries, and that, for coupling two or more emitters to a single cavity mode, the improvement factors can far exceed an order of magnitude.