Plasmon polaritons in cubic lattices of spherical metallic nanoparticles

This is the final version. Available from the American Physical Society via the DOI in this record.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 wave-vector 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 cosS.L. and F.P. acknowledge funding through the Junior Professorship Program of the Ministry of Science, Research and the Arts (MWK) of Baden-Wurttemberg within the project ¨ “Theory of Plasmonic Nanostructures”, through the Carl Zeiss Foundation and the Collaborative Research Center (SFB) 767 of the German Research Foundation (DFG). C.-R.M. would like to acknowledge financial support from the EPSRC Center for Doctoral Training in Metamaterials (Grant No. EP/L015331/1). C.-R.M. and E.M. acknowledge financial support by the Royal Society (International Exchange Grant No. IE140367, Newton Mobility Grant NI160073, Theo Murphy Award TM160190) and by the Leverhulme Trust (Research Project Grant RPG-2015-101). G.W. is grateful to the French National Research Agency ANR (Project No. ANR14-CE26-0005 Q-MetaMat) and the CNRS PICS program (Contract No. 6384 APAG) for financial support. Part of this work was performed on the computational resource bwUniCluster, funded by the MWK and the universities of the state of