  The emission of light of an efficient single-photon emitter (SPE) should have
a high-count 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 (Further information is available [F. Ortiz-Huerta et al,
Opt.Express 26, 33245 (2018)]), 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.
