Radius dependent shift of surface plasmon frequency in large metallic nanospheres: theory and experiment

TL;DR

This paper develops a theoretical model for surface and volume plasmons in large metallic nanospheres, demonstrating how the surface plasmon resonance frequency shifts with sphere size, and confirms predictions with experimental measurements.

Contribution

It provides a comprehensive semiclassical theory including Lorentz friction effects and experimentally verifies the radius-dependent plasmon frequency shift in metallic nanospheres.

Findings

Resonance frequency shift is highly sensitive to sphere radius.

Surface plasmons of dipole type are primarily excited by homogeneous fields.

Experimental data for Au and Ag nanospheres agree with theoretical predictions.

Abstract

Theoretical description of oscillations of electron liquid in large metallic nanospheres (with radius of few tens nm) is formulated within random-phase-approximation semiclassical scheme. Spectrum of plasmons is determined including both surface and volume type excitations. It is demonstrated that only surface plasmons of dipole type can be excited by homogeneous dynamical electric field. The Lorentz friction due to irradiation of electro-magnetic wave by plasmon oscillations is analyzed with respect to the sphere dimension. The resulting shift of resonance frequency turns out to be strongly sensitive to the sphere radius. The form of e-m response of the system of metallic nanospheres embedded in the dielectric medium is found. The theoretical predictions are verified by a measurement of extinction of light due to plasmon excitations in nanosphere colloidal water solutions, for Au and Ag metallic components with radius from 10 to 75 nm. Theoretical predictions and experiments clearly agree in the positions of surface plasmon resonances and in an emergence of the first volume plasmon resonance in the e-m response of the system for limiting big nanosphere radii, when dipole approximation is not exact.