Numerical modelling of the coupling efficiency of single quantum emitters in photonic-crystal waveguides

Planar photonic nanostructures have recently attracted a great deal of attention for quantum optics applications. In this article, we carry out full 3D numerical simulations to fully account for all radiation channels and thereby quantify the coupling efficiency of a quantum emitter embedded in a photonic-crystal waveguide. We utilize mixed boundary conditions by combining active Dirichlet boundary conditions for the guided mode and perfectly-matched layers for the radiation modes. In this way, the leakage from the quantum emitter to the surrounding environment can be determined and the spectral and spatial dependence of the coupling to the radiation modes can be quantified. The spatial maps of the coupling efficiency, the $\beta$-factor, reveal that even for moderately slow light, near-unity $\beta$ is achievable that is remarkably robust to the position of the emitter in the waveguide. Our results show that photonic-crystal waveguides constitute a suitable platform to achieve deterministic interfacing of a single photon and a single quantum emitter, which has a range of applications for photonic quantum technology.