Blueshift of the surface plasmon resonance in silver nanoparticles: substrate effects

Abstract

We study the blueshift of the surface plasmon (SP) resonance energy of isolated Ag nanoparticles with decreasing particle diameter, which we recently measured using electron energy loss spectroscopy (EELS). As the particle diameter decreases from 26 down to 3.5 nm, a large blueshift of 0.5 eV of the SP resonance energy is observed. In this paper, we base our theoretical interpretation of our experimental findings on the nonlocal hydrodynamic model, and compare the effect of the substrate on the SP resonance energy to the approach of an effective homogeneous background permittivity. We derive the nonlocal polarizability of a small metal sphere embedded in a homogeneous dielectric environment, leading to the nonlocal generalization of the classical Clausius-Mossotti factor. We also present an exact formalism based on multipole expansions and scattering matrices to determine the optical response of a metal sphere on a dielectric substrate of finite thickness, taking into account retardation and nonlocal effects. We find that the substrate-based calculations show a similar-sized blueshift as calculations based on a sphere in a homogeneous environment, and that they both agree qualitatively with the EELS measurements.

Invited paper for SPP6 special issue to be published in Opt. Express

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• Extremely confined gap plasmon modes: when nonlocality matters
• How nonlocal damping reduces plasmon-enhanced fluorescence in ultranarrow gaps
• Nonlocal study of ultimate plasmon hybridization
• Two-fluid hydrodynamic model for semiconductors
• Robustness of the far-field response of nonlocal plasmonic ensembles
• Parallel FDTD modelling of nonlocality in plasmonics
• Two-fluid, hydrodynamic model for spherical electrolyte systems
• The influence of a planar metal nanoparticle assembly on the optical response of a quantum emitter