Plasmon polaritons in cubic lattices of spherical metallic nanoparticles

TL;DR

This paper provides a theoretical framework for understanding plasmon polaritons in cubic lattices of metallic nanoparticles, predicting their dispersions and eigenstates with analytical formulas and validating with simulations.

Contribution

It introduces a Hamiltonian-based analytical model for plasmon polaritons in nanoparticle lattices, incorporating retardation effects and dielectric properties, with predictions matching numerical simulations.

Findings

Predicted polaritonic splittings in near-infrared to visible spectrum.

Dispersion relations depend on polarization, lattice symmetry, and wavevector.

Model offers analytical insights with reduced computational cost.

Abstract

We theoretically investigate plasmon polaritons in cubic lattices of spherical metallic nanoparticles. The nanoparticles, each supporting triply-degenerate localized surface plasmons, couple through the Coulomb dipole-dipole interaction, giving rise to collective plasmons that extend over the whole metamaterial. The latter hybridize with photons forming plasmon polaritons, which are the hybrid light-matter eigenmodes of the system. We derive general analytical expressions to evaluate both plasmon and plasmon-polariton dispersions, and the corresponding eigenstates. These are obtained within a Hamiltonian formalism, which takes into account retardation effects in the dipolar interaction between the nanoparticles and considers the dielectric properties of the nanoparticles as well as their surrounding. Within this model we predict polaritonic splittings in the near-infrared to the visible range of the electromagnetic spectrum that depend on polarization, lattice symmetry and wavevector direction. Finally, we show that the predictions of our model are in excellent quantitative agreement with conventional finite-difference frequency-domain simulations, but with the advantages of analytical insight and significantly reduced computational cost.