Quantum theory of plasmon polaritons in chains of metallic nanoparticles: From near- to far-field coupling regime

TL;DR

This paper develops a quantum model for plasmon polaritons in metallic nanoparticle chains, capturing near- and far-field effects, and reveals tunable group velocities and hybrid light-matter states through detailed numerical and analytical analysis.

Contribution

It introduces a comprehensive quantum theory including retardation and Umklapp processes, providing new insights into the dispersion and dynamics of plasmon polaritons in nanoparticle chains.

Findings

Group velocities exhibit almost periodic sign changes and are highly tunable.

Analytical perturbation theory agrees well with numerical results away from eigenfrequency intersections.

Hybridization of light and matter excitations quantified via Hopfield's coefficients.

Abstract

We develop a quantum theory of plasmon polaritons in chains of metallic nanoparticles, describing both near- and far-field interparticle distances, by including plasmon-photon Umklapp processes. Taking into account the retardation effects of the long-range dipole-dipole interaction between the nanoparticles, which are induced by the coupling of the plasmonic degrees of freedom to the photonic continuum, we reveal the polaritonic nature of the normal modes of the system. We compute the dispersion relation and radiative linewidth, as well as the group velocities of the eigenmodes, and compare our numerical results to classical electrodynamic calculations within the point-dipole approximation. Interestingly, the group velocities of the polaritonic excitations present an almost periodic sign change and are found to be highly tunable by modifying the spacing between the nanoparticles. We show that, away from the intersection of the plasmonic eigenfrequencies with the free photon dispersion, an analytical perturbative treatment of the light-matter interaction is in excellent agreement with our fully retarded numerical calculations. We further study quantitatively the hybridization of light and matter excitations, through an analysis of Hopfield's coefficients. Finally, we consider the limit of infinitely spaced nanoparticles and discuss some recent results on single nanoparticles that can be found in the literature.