Mie-scattering controlled all-dielectric cavity coupled antenna for bright and directional single-photon emission

A deterministic, bright, room-temperature stable single-photon-source (SPS) has been a major demand in the field of quantum-photonics. Here, using computational and analytical techniques, we showed that the Mie-scattering moments of an all-dielectric cavity-cum-antenna helps in shaping the spontaneous emission process of a point-dipole emitter, the nanodiamond NV$^-$ center here. Our cavity-cum-antenna design comprises of two top and bottom TiO$_2$ cylinders with a sandwiched poly-vinyl-alcohol (PVA) layer enclosing the nanodiamond crystal. The Cartesian multi-polar decomposition (CMD) of the Mie-scattering moments of the sandwiched PVA layer with subwavelength scale thickness showed strong electric-dipole (ED) resonance which resulted in significant field confinement, making the PVA layer to act as a cavity, providing a Purcell enhancement of more than an order-of-magnitude for all dipole orientations. Further, the Mie-scattering moments of the top and bottom TiO$_2$ cylinders were observed to control the radiation pattern of the embedded dipole-emitter. The radiation directionality along the vertical directions was found to be maximum at the Kerker point (electric dipole moment, ED = magnetic dipole moment, MD), the collection efficiency (CE) being about 80\%. This will result in photon collection rates of a few 100 MHz, unachievable till now. Our results are therefore substantial to accelerate the research for generating on-demand SPS for quantum-photonic applications.