Robustness of the far-field response of nonlocal plasmonic ensembles

TL;DR

This paper investigates how nonlocal effects and size distribution influence the optical response of plasmonic nanoparticle ensembles, revealing that ensemble averaging can mask nonlocality effects and providing analytical tools for experimental evaluation.

Contribution

It demonstrates that ensemble averaging effects depend on size-dependent broadening models and offers an analytical expression to quantify inhomogeneous broadening in realistic nanoparticle distributions.

Findings

Nonlocal blueshift and linewidth are affected by ensemble averaging.

Size-variance effects can conceal nonlocality depending on broadening models.

An analytical expression for inhomogeneous broadening is developed.

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 (NPs) are therefore expected to exhibit a nonclassical inhomogeneous spectral broadening due to size distribution. For a normal distribution of free-electron NPs, and within the simple nonlocal Hydrodynamic Drude Model (HDM), 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 NPs is taken into account, either through a local size-dependent damping (SDD) model or through the Generalized Nonlocal Optical Response (GNOR) theory. The role of ensemble averaging is further explored in realistic distributions of noble-metal NPs, 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.