  Nanostructures can be used for boosting the light outcoupling of color
centers in diamond; however, the fiber coupling performance of these
nanostructures is rarely investigated. Here, we use a finite element method for
computing the emission from color centers in inverted nanocones and the overlap
of this emission with the propagation mode in a single-mode fiber. Using
different figures of merit, the inverted nanocone parameters are optimized to
obtain maximal fiber coupling efficiency, free-space collection efficiency, or
rate enhancement. The optimized inverted nanocone designs show promising
results with 66% fiber coupling or 83% free-space coupling efficiency at the
tin-vacancy center zero-phonon line wavelength of 619 nm. Moreover, when
evaluated for broadband performance, the optimized designs show 55% and 76% for
fiber coupling and free-space efficiencies respectively, for collecting the
full tin-vacancy emission spectrum at room temperature. An analysis of
fabrication insensitivity indicates that these nanostructures are robust
against imperfections. For maximum emission rate into a fiber mode, a design
with a Purcell factor of 2.34 is identified. Finally, possible improvements
offered by a hybrid inverted nanocone, formed by patterning into two different
materials, are investigated, and increases the achievable fiber coupling
efficiency to 71%.
