Robustness of the far-field response of nonlocal plasmonic ensembles

Abstract

Contrary to classical predictions, the optical response of few-nm plasmonic particles depends on particle size due to effects such as nonlocality and electron spill-out. Ensembles of such nanoparticles are therefore expected to exhibit a nonclassical inhomogeneous spectral broadening due to size distribution. For a normal distribution of free-electron nanoparticles, and within the simple nonlocal hydrodynamic Drude model, both the nonlocal blueshift and the plasmon linewidth are shown to be considerably affected by ensemble averaging. Size-variance effects tend however to conceal nonlocality to a lesser extent when the homogeneous size-dependent broadening of individual nanoparticles is taken into account, either through a local size-dependent damping model or through the Generalized Nonlocal Optical Response theory. The role of ensemble averaging is further explored in realistic distributions of isolated or weakly-interacting noble-metal nanoparticles, as encountered in experiments, while an analytical expression to evaluate the importance of inhomogeneous broadening through measurable quantities is developed. Our findings are independent of the specific nonclassical theory used, thus providing important insight into a large range of experiments on nanoscale and quantum plasmonics.

How nonlocal damping reduces plasmon-enhanced fluorescence in ultranarrow gaps

“…The hydrodynamic parameter β is taken equal to 3/5v F , where v F = 1.39 × 10 6 m s −1 is the Fermi velocity of silver [41], while for the diffusion constant D we use D = 2.684 × 10 4 m 2 s −1 [61]. As can be seen from Eqs.…”

On the origin of nonlocal damping in plasmonic monomers and dimers

“…A more detailed description of the differences between the four models and their application to different types of metals and statistical ensembles of small, weakly interacting nanoparticles can be found in Ref. 46.…”

“…46. The two spheres, of radius R = 5 nm, are separated by a 2-nm gap, and illuminated by a plane wave polarized along the dimer axis (taken to be the x axis), as shown in the schematics.…”

Inhomogeneous broadening in non-interacting nonlocal plasmonic ensembles

“…Extensive simulations for more realistic size distributions of non-or weakly-interacting noble-metal NPs show that in these situations inhomogeneous broadening tends to be almost totally concealed by single NP damping, as long as the distribution function is not too wide [7]. A simple analytical formula, which relates plasmon linewidths to the statistical properties of the distribution function, can be immediately applied in every occasion to conclude whether inhomogeneous broadening will be observable or not [7]. …”

“…More importantly, it is now well known that, for few-nm NPs, LRA also fails to predict the frequency position of plasmon resonances, because nonclassical effects such as nonlocality and electron spill-out become relevant [5,6]. It is therefore expected that in ensembles of such plasmonic NPs inhomogeneous broadening due to size distribution, which has been so far overlooked, will become important [7]. This effect is studied here theoretically, through simulations based on either the more common hydrodynamic Drude model (HDM) or the recently developed Generalized Nonlocal Optical Response (GNOR) [8] theory.…”