Fig. 3. Plasmon-mediated Purcell enhancement at the nanoscale.

Normalized LDOS, ${\rho }^{\mathrm{E}}∕{\rho }_0^{\mathrm{E}}$, of a normally-oriented emitter near a–b a planar metal surface and c–e a metal sphere. a Normalized LDOS as a function of the emitterʼs frequency and separation from the jellium surface. The horizontal line marks ${\omega }_{\mathrm{p}}∕\sqrt{2}$. b LDOS enhancement at different emitter–surface separations. The vertical line marks ${\omega }_{\mathrm{p}}∕\sqrt{2}$. c Normalized LDOS near an $R=\mathrm{5}\mathrm{nm}$ jellium sphere as a function of the emitterʼs frequency and $h∕R$ ratio. Horizontal lines mark the nonretarded classical LSP frequencies ${\omega }_{\mathrm{p}}∕\sqrt{1+\left(l+1\right)∕l}$ for $l\in \left\{1,2\right\}$. d LDOS enhancement near an $R=\mathrm{5}\mathrm{nm}$ sphere for different emitter–surface distances. Vertical lines mark the $l=1$, $l=2$, and $l=\infty$ nonretarded classical LSPs. e Normalized LDOS for plasmonic spheres of differing radii at a fixed $h=10\mathrm{nm}$ emitter–surface separation. Material parameters as in Fig. 2.