Mie-scattering controlled all-dielectric resonator-antenna for bright and directional point dipole emission

Designing a deterministic, bright, robust, room temperature stable, on-demand solid-state single photon source has been a major demand in the field of quantum-photonics. For this, various single-photon resonator and antenna schemes are being actively explored. Here, using the Cartesian multi-polar decomposition of the excited Mie-scattering moments, we present the design of a all-dielectric coupled-dipolar antenna comprising of two dielectric (Tin-oxide, TiO$_2$) cylinders sandwiching a nanodiamond based nitrogen-vacancy (NV$^-$) center trapped in a poly-vinyl alcohol (PVA) matrix. The Mie-scattering resonant cavity formed in the middle PVA layer provides more than an order of magnitude decay rate or Purcell enhancement. The balancing of the electric and magnetic dipolar moments (a phenomenon commonly known as the Kerker condition) of the coupled TiO$_2$ cylinders under NV$^-$ dipole excitation, provides significant directionality to the radiation pattern. Using a collection lens with a numerical aperture (NA) of 0.9 the vertical collection efficiency (VCE) was observed to be around 80\% at the NV$^-$ center's zero-phonon line wavelength.