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We numerically simulate the compensation of absorption, the near-field enhancement as well as the differential far-field scattering cross section for dye-doped polystyrene spheres (radius 195 nm), which are half-covered by a silver layer of 10-40 nm thickness. Such silver capped spheres are interesting candidates for nanoplasmonic lasers, so-called spasers. We find that spasing requires gain levels less than 3.7 times higher than those in commercially available dye-doped spheres. However, commercially available concentrations are already apt to achieve negative absorption, and to narrow and enhance scattering by higher order modes. Narrowing of the plasmonic modes by gain also makes visible higher order modes, which are normally obscured by the broad spectral features of the lower order modes. We further show that the angular distribution of the far-field scattering of the spasing modes is by no means dipole-like and is very sensitive to the geometry of the structure.

Dye-doped spheres with plasmonic semi-shells: Lasing modes and scattering at realistic gain levels