Optical response of a metallic nanoparticle immersed in a medium with optical gain

We study theoretically the polarizability of a single metallic nanoparticle immersed into an externally pumped, active gain medium able to couple to the plasmon resonance. Within the frame of a simple long-wavelength, macroscopic description, and under steady-state conditions, we show that localized plasmons can be strongly amplified, until becoming singular for a specific amount of surrounding gain; however, we find that such gain-assisted singular plasmons exhibit spectrally spread imaginary responses and are therefore intrinsically different from singular plasmons in idealized, lossless metals. More generally, we carry a systematic study of how the plasmonic response transforms under changes in the amount of gain, and show that the coupled particle and active medium act as a self-tuned Fano resonant system. The resulting plasmons exhibit strongly distorted line shapes with unusual but interesting features. One particularly attractive situation is that of "conjugate plasmons," which, at resonance, display a strong real response in association with minimal losses. These findings could have some applications in plasmonics, nanoantennas, nanosensing, and optical metamaterials.