Surface Plasmon Dispersion Relations in Chains of Metallic Nanoparticles: Exact Quasistatic Calculation

TL;DR

This paper provides an exact quasistatic calculation of surface plasmon dispersion relations in chains of metallic nanoparticles, including multipole modes, revealing new effects at small particle separations and high multipole orders.

Contribution

It introduces a generalized tight-binding approach that accounts for all multipole modes and provides detailed dispersion relations, group velocities, and decay lengths for nanoparticle chains.

Findings

Exact dispersion relations for small particles ($kd \,\ll\, 1$) including multipole modes.

Identification of significant deviations from dipole approximations at small interparticle separations.

Prediction of novel percolation effects and symmetry in plasmon band structures at high particle-to-separation ratios.

Abstract

We calculate the surface plasmon dispersion relations for a periodic chain of spherical metallic nanoparticles in an isotropic host, including all multipole modes in a generalized tight-binding approach. For sufficiently small particles ($kd \ll 1$, where $k$ is the wave vector and $d$ is the interparticle separation), the calculation is exact. The lowest bands differ only slightly from previous point-dipole calculations provided the particle radius $a \lesssim d/3$, but differ substantially at smaller separation. We also calculate the dispersion relations for many higher bands, and estimate the group velocity $v_g$ and the exponential decay length $\xi_D$ for energy propagation for the lowest two bands due to single-grain damping. For $a/d=0.33$, the result for $\xi_D$ is in qualitative agreement with experiments on gold nanoparticle chains, while for larger $a/d$, such as $a/d=0.45$, $v_g$ and $\xi_D$ are expected to be strongly $k$-dependent because of the multipole corrections. When $a/d \sim 1/2$, we predict novel percolation effects in the spectrum, and find surprising symmetry in the plasmon band structure. Finally, we reformulate the band structure equations for a Drude metal in the time domain, and suggest how to include localized driving electric fields in the equations of motion.