Retardation effects on the dispersion and propagation of plasmons in metallic nanoparticle chains

TL;DR

This paper analytically investigates how retardation influences the dispersion and propagation of plasmons in metallic nanoparticle chains, revealing significant effects on transverse modes and drawing parallels with atomic physics phenomena.

Contribution

The study provides explicit analytical expressions for plasmonic bandstructure including retardation effects, validated against numerical solutions, and explores their impact on plasmon propagation.

Findings

Retardation causes a logarithmic singularity in the transverse plasmon bandstructure.

Retardation significantly affects transverse, but not longitudinal, plasmon propagation.

Analogy established between radiative effects in nanoplasmonics and the cooperative Lamb shift.

Abstract

We consider a chain of regularly-spaced spherical metallic nanoparticles, where each particle supports three degenerate localized surface plasmons. Due to the dipolar interaction between the nanoparticles, the localized plasmons couple to form extended collective modes. Using an open quantum system approach in which the collective plasmons are interacting with vacuum electromagnetic modes and which, importantly, readily incorporates retardation via the light-matter coupling, we analytically evaluate the resulting radiative frequency shifts of the plasmonic bandstructure. For subwavelength-sized nanoparticles, our analytical treatment provides an excellent quantitative agreement with the results stemming from laborious numerical calculations based on fully-retarded solutions to Maxwell's equations. Indeed, the explicit expressions for the plasmonic spectrum which we provide showcase how including retardation gives rise to a logarithmic singularity in the bandstructure of transverse-polarized plasmons. We further study the impact of retardation effects on the propagation of plasmonic excitations along the chain. While for the longitudinal modes, retardation has a negligible effect, we find that the retarded dipolar interaction can significantly modify the plasmon propagation in the case of transverse-polarized modes. Moreover, our results elucidate the analogy between radiative effects in nanoplasmonic systems and the cooperative Lamb shift in atomic physics.