Sorry for the delay in posts. The beginning of the new academic year is a hectic time.
This paper is a very exciting new result. Unfortunately there does not appear to be a publicly accessible version available. Ordinarily, lasing (that is, light amplification by the stimulated emission of radiation) requires a few things. One needs a "gain medium", some kind of optically active system that has (at least one) radiative transition. In this paper, the medium is a dielectric oxide containing dye molecules known to fluoresce at a wavelength of 520 nm. This medium needs to be pumped somehow, so that there are more optically active systems in the excited state than in the ground state. This is called "population inversion". (It is possible to get lasing without inversion, but that's a very special case....) Finally, one generally needs a cavity - an optical resonator of high enough quality that an emitted photon stays around long enough to stimulate the emission of many more photons. The cavity has to be somewhat leaky, so that the laser light can get out. However, if the cavity is too leaky, the optical gain from stimulated emission in the pumped medium can't outpace the cavity losses. The usual approach is to have a rather high quality cavity, made using either dielectric mirrors, total internal reflection, or some other conventional reflectors.
In this paper, however, the authors take a different tactic. They use the near-field from the plasmon resonance of the gold core (not coincidentally, at around 520 nm wavelength) of Au-core-dielectric-shell nanoparticles. Plasmon resonances are often quite lossy, and this is no exception - the Q of the plasmon resonance is around 14. However, the enhanced near field is so large, and the effective mode volume (confinement) is so small, that gain still outpaces loss. When the dye is optically pumped, it is possible to make these nanoparticles lase. This paper is likely to spawn a great deal of further work! It's cool, and there are many clear directions to pursue now that this has been demonstrated.