Cavity QED treatment of scattering-induced efficient free-space excitation and collection in high-Q whispering-gallery microcavities

Whispering-gallery microcavity laser possesses ultralow threshold, whereas convenient free-space optical excitation and collection suffer from low efficiencies due to its rotational symmetry. Here we analytically study a three-dimensional microsphere coupled to a nano-sized scatterer in the framework of quantum optics. It is found that the scatterer is capable of coupling light in and out of the whispering-gallery modes (WGMs) without seriously degrading their high-Q properties, while the microsphere itself plays the role of a lens to focus the input beam on the scatterer and vice versa. Our analytical results show that (1) the high-Q WGMs can be excited in free space, and (2) over 50% of the microcavity laser emission can be collected within less than ${1}^{\circ}$. This coupling system holds great potential for low threshold microlasers free of external couplers.