Surface scattering contribution to the plasmon width in embedded Ag nanospheres.

R Carmina Monreal,S Peter Apell,Tomasz J Antosiewicz

doi:10.1364/oe.22.024994

Abstract

Nanometer-sized metal particles exhibit broadening of the localized surface plasmon resonance (LSPR) in comparison to its value predicted by the classical Mie theory. Using our model for the LSPR dependence on non-local surface screening and size quantization, we quantitatively relate the observed plasmon width to the nanoparticle radius R and the permittivity of the surrounding medium ε(m). For Ag nanospheres larger than 8 nm only the non-local dynamical effects occurring at the surface are important and, up to a diameter of 25 nm, dominate over the bulk scattering mechanism. Qualitatively, the LSPR width is inversely proportional to the particle size and has a nonmonotonic dependence on the permittivity of the host medium, exhibiting for Ag a maximum at ε(m) ≈ 2.5. Our calculated LSPR width is compared with recent experimental data.

Highlights

Since the early 1980s calculations and measurements on the optical properties of ultra-small particles have seen important progress [1, 2]
The surface scattering mechanism for the damping of the surface plasmons is introduced in the theory using the framework presented in [15], which includes non-local surface screening and size quantization effects, and was used to reproduce the localized surface plasmon resonance (LSPR) shift in frequency
We will see that they are able to account for the experimental magnitude of the surface plasmon width of Ag nanospheres in SiO2, reinforcing the importance of an appropriate treatment of the surface electronic density. ε(ω) and 1 are taken from the experimental data of Johnson and Christy [33] from where h =

Summary

Introduction

Since the early 1980s calculations and measurements on the optical properties of ultra-small particles have seen important progress [1, 2]. In a recent paper [15] we presented a theoretical model for analyzing the size dependence of the surface plasmon resonance of metallic nanospheres in a range of sizes down to a few nanometers Within this model, we explicitly showed how different microscopic mechanisms affect the energy of the surface plasmon in quantitative agreement with recent published experimental results for Ag and Au. In this article we address a question related to the one considered in [15]. For metal spheres less than 25 nm in diameter, the wavelengths of interest are typically much larger than the size so that a quasi-static dipolar approximation is valid to calculate the optical properties Within this approximation, the surface scattering mechanism for the damping of the surface plasmons is introduced in the theory using the framework presented in [15], which includes non-local surface screening and size quantization effects, and was used to reproduce the LSPR shift in frequency. The remarkable agreement we find between the experimental and our calculated plasmon widths affirms our approach

Theory

Results

Conclusions