  We model the broadband enhancement of single-photon emission from color
centres in silicon carbide nanocrystals coupled to a planar hyperbolic
metamaterial, HMM resonator. The design is based on positioning the single
photon emitters within the HMM resonator, made of a dielectric index-matched
with silicon-carbide material. The broadband response results from the
successive resonance peaks of the lossy Fabry Perot structure modes arising
within the high-index HMM cavity. To capture this broadband enhancement in the
single photon emitters spontaneous emission, we placed a simple gold based
cylindrical antenna on top of the HMM resonator. We analyzed the performance of
this HMM coupled antenna structure in terms of the Purcell enhancement, quantum
efficiency, collection efficiency and overall collected photon rate. For
perpendicular dipole orientation relative to the interface, the HMM coupled
antenna resonator leads to a significantly large spontaneous emission
enhancement with Purcell factor of the order of 250 along with a very high
average total collected photon rate, CPR of about 30 over a broad emission
spectrum, 700 nm to 1000 nm. The peak CPR increases to about 80 at 900 nm,
corresponding to the emission of silicon-carbide quantum emitters. This is a
state of the art improvement considering the previous computational designs
have reported a maximum average CPR of 25 across the nitrogen-vacancy centre
emission spectrum, 600 nm to 800 nm with the highest value being about 40 at
650 nm.
