Computation and optimization of the Purcell factor of an open tunable Fabry-Perot microcavity

The spontaneous emission of atoms can be controlled by placing them between two mirrors that form an optical cavity. Rapid advances in material processing techniques in the last 10 years have made it possible to fabricate microscopic optical cavities that can be finely tuned into resonance with the emitter. This has enabled progress in single-photon sources, nano-lasers and spectroscopy of new nano-emitters such as semiconductor quantum dots and Nitrogen-vacancy centres in diamond. Here we introduce a step-by-step method for computing the Purcell factor of the latest generation of open tunable Fabry-Perot microcavities used in micro-photoluminescence studies. We discuss how the Purcell factor can be optimised as a function of the cavity's geometry and find the conditions for resonance with the emitter. Subtleties such as the optical properties of the emitter and penetration depth of the electric field into the cavity mirrors are also considered.