Nonlocal inhomogeneous broadening in plasmonic nanoparticle ensembles

Nonclassical effects are increasingly more relevant in plasmonics as modern nanofabrication techniques rapidly approach the extreme nanoscale limits, for which departing from classical electrodynamics becomes important. One of the largest-scale necessary corrections towards this direction is to abandon the local response approximation (LRA) and take the nonlocal response of the metal into account, typically through the simple hydrodynamic Drude model (HDM), which predicts a sizedependent deviation of plasmon modes from the quasistatic (QS) limit. While this behaviour has been explored for simple metallic nanoparticles (NPs) or NP dimers, the possibility of inhomogeneous resonance broadening due to size variation in a large NP collection and the resulting spectral overlap of modes (as depicted in Fig. 1), has been so far overlooked. Here we study theoretically the effect of nonlocality on ensemble averaging through both HDM and the recent Generalized Nonlocal Optical Response (GNOR) theory, which apart from the resonance frequency shifts accounts successfully for size-dependent damping as well. We examine NPs made of either ideal Drude-like metals [of plasmon frequency (wavelength) ωp (λp)] or realistic noble metals, following sharp or smooth size distribution functions around an ensemble mean value, and identify examples where inhomogeneous broadening can be significant. We also explain how its role becomes less important in most experimentally accessible situations, provided that all homogeneous broadening mechanisms are taken into account. We further develop an analytical tool to determine the strength of inhomogeneous broadening in any NP collection, simply through knowledge of the ensemble size-distribution function [1].