Whispering-gallery exciton polaritons in submicron spheres

We show that a semiconductor sphere with a radius comparable with the wavelength of light at the exciton resonance frequency can behave as a high-quality three-dimensional microcavity or "polariton dot." We obtain numerical results for gallium arsenide submicron spheres and demonstrate that, in contrast to a larger sphere or planar microcavity, they can simultaneously possess both large quality factor and high finesse. In the strong-coupling regime the Rabi splitting approaches the bulk polariton splitting.