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We calculate the surface plasmon dispersion relations for a periodic chain ofspherical metallic nanoparticles in an isotropic host, including all multipolemodes in a generalized tight-binding approach. For sufficiently small particles($kd \ll 1$, where $k$ is the wave vector and $d$ is the interparticleseparation), the calculation is exact. The lowest bands differ only slightlyfrom previous point-dipole calculations provided the particle radius $a\lesssim d/3$, but differ substantially at smaller separation. We alsocalculate the dispersion relations for many higher bands, and estimate thegroup velocity $v_g$ and the exponential decay length $\xi_D$ for energypropagation for the lowest two bands due to single-grain damping. For$a/d=0.33$, the result for $\xi_D$ is in qualitative agreement with experimentson gold nanoparticle chains, while for larger $a/d$, such as $a/d=0.45$, $v_g$and $\xi_D$ are expected to be strongly $k$-dependent because of the multipolecorrections. When $a/d \sim 1/2$, we predict novel percolation effects in thespectrum, and find surprising symmetry in the plasmon band structure. Finally,we reformulate the band structure equations for a Drude metal in the timedomain, and suggest how to include localized driving electric fields in theequations of motion.Comment: 19 pages 3 figures To be published in Phy. Rev.

Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation