Highly directional emission from a quantum emitter embedded in a hemispherical cavity.

We report the design of a solid-state, micron-sized hemispherical cavity that yields significantly enhanced extraction efficiency with modest Purcell enhancement from embedded quantum emitters. A simple analytical model provides a guideline for the design and optimization of the structure, while finite-difference time-domain simulations are used for full analysis of the optimum structure. Cavity modes with up to 90% extraction efficiency, a Purcell enhancement factor >2, and a quality factor of ≈50 are achieved. In addition, Gaussian-like far-field beam profiles with low divergence are exhibited for several modes. These monolithic cavities are promising for solid-state emitters buried in a high dielectric environment, such as self-assembled quantum dots and optically active defects in diamond.