Bullseye dielectric cavities for photon collection from a surface-mounted quantum-light-emitter

Coupling light from a point source to a propagating mode is an important problem in nano-photonics and is essential for many applications in quantum optics. Circular "bullseye" cavities, consisting of concentric rings of alternating refractive index, are a promising technology that can achieve near-unity coupling into a first lens. Here we design a bullseye structure suitable for enhancing the emission from dye molecules, 2D materials and nano-diamonds positioned on the surface of these cavities. A periodic design of cavity, meeting the Bragg scattering condition, achieves a Purcell factor of 22.5 and collection efficiency of 80 %. We also tackle the more challenging task of designing a cavity for coupling to a low numerical aperture fibre in the near field. Using an iterative procedure, we show that apodized (non-periodic) rings can achieve a collection efficiency that exceeds the periodic Bragg cavity.