  We demonstrate theoretically that a subwavelength spherical dielectric
nanoparticle coated with a gain shell forms a nanolaser. Lasing modes of such a
nanolaser are associated with the Mie resonances of the nanoparticle. We
establish a general condition for the lasing threshold and show that the use of
high refractive index dielectric media allows for lasing with a threshold
significantly lower than that for nanolasers incorporating lossy plasmonic
metals.
