  A hyperbolic metamaterial (HM) resonator is analyzed as a nano-antenna for
enhancing the radiative emission of quantum emitters in its vicinity. It has
been shown that the spontaneous emission rate by an emitter near a hyperbolic
metamaterial substrate is enhanced dramatically due to very large density of
states. However, enhanced coupling to the free-space, which is central to
applications such as solid-state lighting, has not been investigated
significantly. Here, we numerically demonstrate approximately 100 times
enhancement of the free-space radiative emission at 660 nm wavelength by
utilizing a cylindrical HM resonator with a radius of 54 nm and a height of 80
nm on top of an opaque silver-cladded substrate. We also show how the
free-space radiation enhancement factor depends on the dipole orientation and
the location of the emitter near the subwavelength resonator. Furthermore, we
calculate that an array of HM resonators with subwavelength spacings can
maintain most of the enhancement effect of a single resonator.
