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Defect centers in diamond are promising building blocks for quantum networksthanks to a long-lived spin state and bright spin-photon interface. However,their low fraction of emission into a desired optical mode limits theentangling success probability. The key to overcoming this is through Purcellenhancement of the emission. Open Fabry-Perot cavities with an embedded diamondmembrane allow for such enhancement while retaining good emitter properties. Toguide the focus for design improvements it is essential to understand theinfluence of different types of losses and geometry choices. In particular, inthe design of these cavities a high Purcell factor has to be weighed againstcavity stability and efficient outcoupling. To be able to make these trade-offswe develop analytic descriptions of such hybrid diamond-and-air cavities as anextension to previous numeric methods. The insights provided by this analysisyield an effective tool to find the optimal design parameters for a diamond-aircavity.

Optimal design of diamond-air microcavities for quantum networks using an analytical approach