Forced Damped Harmonic Oscillator Model of the Dipole Mode of Localized Surface Plasmon Resonance

Abstract

A forced damped harmonic oscillator model of the dipole plasmon mode is illustrated by the theoretical derivation and the simulation based on the metal ellipsoids. The analytical expression of the restoring force is derived. The displacement of the oscillator, which is the phenomenological relative displacement of the free negative and positive charge systems in solids, can be represented by the accumulated charges on the surface of the nanoparticles based on the derived results. With the help of the finite-difference time-domain method, the dependence of the resonance wavelengths and the surface charge distributions on the geometric parameters and the materials has been verified by the ellipsoids evolved from 10 nm radius spheres. As an essential feature of an oscillator, the phase shifts, which are between the accumulated surface charges (the displacement of the oscillator) and the electric field of the incident light, are also illustrated by the numerical simulation. For the silver nanoparticle with the radius of 10 nm, the phase shifts are consistent with the feature of a forced damped harmonic oscillator. For the large silver nanoparticle with the radius of 50 nm, the magnitudes of the phase shifts have some deviations due to the nonuniform electric field along the light propagation. By this oscillator model, we confirm that localized surface plasmon resonance arises from the collective motion of free charges modulated by the bound charges of the lattice background and the dielectric medium. The forced damped harmonic oscillator model is a clear picture for the dipole localized surface plasmon resonance.