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

Søren Raza,Wei Yan,Martijn Wubs,N Asger Mortensen,Nicolas Stenger

doi:10.1364/oe.21.027344

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) [1]. 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.

Highlights

The use of metal nanoparticles to create astonishing colors in stained glass dates back to ancient Roman times
While in most cases a classical treatment based on the dielectric function is justified, important effects due to surface structure [4,5,6,7,8], nonlocal response [9,10,11,12,13,14,15,16] and quantum size effects [17,18,19,20] manifest themselves in the response of metal nanoparticles, when the particle sizes are below ∼ 10 nm
We have studied the experimentally observed blueshift of the surface plasmon (SP) resonance energy of Ag nanoparticles, when the particle diameters decrease from 26 nm to 3.5 nm

Summary

Introduction

The use of metal nanoparticles to create astonishing colors in stained glass dates back to ancient Roman times. Many experiments on tiny nanoparticles using both optical measurements [21,22,23,24,25] and electron energy-loss studies [1, 26, 27] have shown that the classical approach is insufficient to describe the experimental observations. The interpretation of these results has been based on semi-classical models, such as the nonlocal hydrodynamic [28] and semi-classical infinite barrier (SCIB) [29] approaches, or more complicated quantum calculations using density functional theory [4]

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