How nonlocal damping reduces plasmon-enhanced fluorescence in ultranarrow gaps

The nonclassical modification of plasmon-assisted fluorescence enhancement is theoretically explored by placing two-level dipole emitters at the narrow gaps encountered in canonical plasmonic architectures, namely, dimers and trimers of different metallic nanoparticles. Through detailed simulations, in comparison with appropriate analytical modeling, it is shown that within classical electrodynamics and for the reduced separations explored here, fluorescence enhancement factors of the order of ${10}^5$ can be achieved, with a divergent behavior as the particle touching regime is approached. This remarkable prediction is mainly governed by the dramatic increase in excitation rate triggered by the corresponding field enhancement inside the gaps. Nevertheless, once nonclassical corrections are included, the amplification factors decrease by up to two orders of magnitude, and a saturation regime for narrower gaps is reached. These nonclassical limitations are demonstrated by simulations based on the generalized nonlocal optical response theory, which accounts in an efficient way not only for nonlocal screening but also for the enhanced Landau damping near the metal surface. A simple strategy to introduce nonlocal corrections to the analytic solutions is also proposed. It is therefore shown that the nonlocal optical response of the metal imposes more realistic, finite upper bounds to the enhancement feasible with ultrasmall plasmonic cavities, thus providing a theoretical description closer to state-of-the-art experiments.

Figure 1

(a) Normalized extinction cross section ${\sigma }_{\mathrm{ext}}$ of the Ag nanosphere dimer shown schematically in the inset in the absence of an emitter. The two spheres (of equal radius $R=$ 20 nm) are separated by a gap of width $d$ and are excited by a plane wave with its electric field ${\mathbf{E}}_0$ parallel to the dimer axis. (b) Fluorescence enhancement ${\gamma }_{\mathrm{em}}/{\gamma }_{\mathrm{em}}^0$ spectra for a dipole emitter placed in the middle of the interparticle gap of the dimers in (a), with its dipole moment oscillating parallel to the dimer axis. (c) Normalized quantum yield $q/q^0$ and (d) excitation rate enhancement ${\gamma }_{\mathrm{exc}}/{\gamma }_{\mathrm{exc}}^0$ spectra for the emitter in (b). The insets in (c) and (d) show electric-field contours on resonance (saturated at a maximum enhancement of 200) around the dimer within LRA (right-hand insets) and GNOR (left-hand insets) upon (c) dipole emission and (d) excitation. In all cases blue, green, and red lines correspond to $d=$ 5, 2, and 0.9 nm, respectively. Solid and dashed lines represent calculations with the GNOR and LRA models, respectively.

Figure 2

(a) Fluorescence enhancement spectra for a dipole emitter placed in the middle of a bow-tie antenna gap, with its dipole moment oscillating parallel to the antenna axis, as shown in the schematics. The bow-tie antenna consists of two Ag triangles with a height of 40 nm and a thickness of 10 nm. (b) Fluorescence enhancement spectra for a dipole emitter placed in the middle of the gap formed by two ${\mathrm{SiO}}_2$/Ag nanoshells ($R_1=$ 18 nm, $R=$ 20 nm), with its dipole moment oscillating parallel to the dimer axis, as shown in the schematics. In all cases blue, green, and red lines correspond to $d=$ 5, 2, and 0.9 nm, respectively. Solid and dashed lines represent calculations with the GNOR and LRA models, respectively.

Figure 3

Fluorescence enhancement spectra for dipole emitters placed in the middle of gaps formed by Ag nanosphere trimers, with their dipole moments oscillating parallel to the trimer axis, as shown in the schematics. (a) A single emitter placed in one of the gaps in a trimer of $R=20$ nm spheres. Two emitters placed in the two gaps of the trimer in (a), oscillating (b) in phase and (c) with opposite phases. In all cases blue, green, and red lines correspond to $d=$ 5, 2, and 0.9 nm, respectively. Solid and dashed lines represent calculations with the GNOR and LRA models, respectively. (d) A self-similar nanolens consisting of three Ag nanospheres with decreasing radii equal to 20, 8, and 3.2 nm and, accordingly, decreasing gaps equal to 2 and 0.8 nm (following a geometric progression with a common ratio of 2.5). Black lines denote a single emitter at the smallest gap, while gray lines denote emitters placed in both gaps and oscillating in phase, as shown in the schematics.

Figure 4

Analytic calculations of fluorescence enhancement spectra for a dipole emitter placed in the middle of the gap between (a) two Ag nanospheres ($R=$ 20nm) and (b) two ${\mathrm{SiO}}_2$/Ag nanoshells ($R_1$ = 18 nm, $R=$ 20 nm), with its dipole moment oscillating parallel to the dimer axis, as shown in the schematics. Blue, green, and red lines correspond to $d=$ 5, 2, and 0.9 nm, respectively. Solid and dashed lines represent calculations within the nonlocal and standard (local) coupled-mode models, respectively.