Silicon Mie resonators for highly directional light emission from monolayer MoS\u3csub\u3e2\u3c/sub\u3e

\u3cp\u3eControlling light emission from quantum emitters has important applications, ranging from solid-state lighting and displays to nanoscale single-photon sources. Optical antennas have emerged as promising tools to achieve such control right at the location of the emitter, without the need for bulky, external optics. Semiconductor nanoantennas are particularly practical for this purpose because simple geometries such as wires and spheres support multiple, degenerate optical resonances. Here, we start by modifying Mie scattering theory developed for plane wave illumination to describe scattering of dipole emission. We then use this theory and experiments to demonstrate several pathways to achieve control over the directionality, polarization state and spectral emission that rely on a coherent coupling of an emitting dipole to optical resonances of a silicon nanowire. A forward-to-backward ratio of 20 was demonstrated for the electric dipole emission at 680 nm from a monolayer MoS\u3csub\u3e2\u3c/sub\u3e by optically coupling it to a silicon nanowire.\u3c/p\u3