Retroreflective surface optimization for optical cavities with custom mirror profiles

Coupling an emitter to a Fabry-Pérot 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 optimizing the mirror shape is numerically challenging as the multidimensional parameter space features many local optima. Here we develop a two-step method to optimize mirror surface profiles while avoiding these issues. First, we optimize the target cavity eigenmode for the chosen application directly, and, second, we construct the mirror surfaces to retroreflect this optimized 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.