Analytical and numerical design of a hybrid Fabry-Perot plano-concave microcavity for hexagonal boron nitride

An efficient single-photon emitter (SPE) should emit photons at a high rate into a well-defined spatio-temporal mode along with an accessible numerical aperture (NA) to increase the light extraction efficiency that is required for effective coupling into optical waveguides. Based on a previously developed experimental approach to fabricate hybrid Fabry-Perot microcavities (Ortiz-Huerta et al. Opt. Express 2018, 26, 33245), we managed to find analytical and finite-difference time-domain (FDTD) values for the, experimentally achievable, geometrical parameters of a hybrid plano-concave microcavity that enhances the spontaneous emission (i.e., Purcell enhancement) of color centers in two-dimensional (2D) hexagonal boron nitride (hBN) while simultaneously limiting the NA of the emitter. Paraxial approximation and a transfer matrix model are used to find the spotsize of the fundamental Gaussian mode and the resonant modes of our microcavity, respectively. A Purcell enhancement of 6 is found for a SPE (i.e., in-plane dipole) hosted by a 2D hBN layer inside the hybrid plano-concave microcavity.