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We theoretically investigate plasmon polaritons in cubic lattices ofspherical metallic nanoparticles. The nanoparticles, each supportingtriply-degenerate localized surface plasmons, couple through the Coulombdipole-dipole interaction, giving rise to collective plasmons that extend overthe whole metamaterial. The latter hybridize with photons forming plasmonpolaritons, which are the hybrid light-matter eigenmodes of the system. Wederive general analytical expressions to evaluate both plasmon andplasmon-polariton dispersions, and the corresponding eigenstates. These areobtained within a Hamiltonian formalism, which takes into account retardationeffects in the dipolar interaction between the nanoparticles and considers thedielectric properties of the nanoparticles as well as their surrounding. Withinthis model we predict polaritonic splittings in the near-infrared to thevisible range of the electromagnetic spectrum that depend on polarization,lattice symmetry and wavevector direction. Finally, we show that thepredictions of our model are in excellent quantitative agreement withconventional finite-difference frequency-domain simulations, but with theadvantages of analytical insight and significantly reduced computational cost.

Plasmon polaritons in cubic lattices of spherical metallic nanoparticles