Dispersion relation and density of states of coupled plasmon modes in periodic chains of metallic nanoparticles

Energy transmission through one-dimensional chains of equally spaced metallic nanoparticles has been studied via the propagation of coupled surface-plasmon modes. These modes are characterized by well-defined dispersion relation $\omega(k)$ and group velocity $v_g=d\omega/dk$ in a band. The nanoparticles are routinely modelled by Drude metallic spheres and the coupled plasmon modes are calculated in the point-dipole approximation. When the particles approach and finally touch, these bands can differ significantly from those obtained by the point-dipole approximation due to strong multipolar interaction among the particles. In this regard, we have calculated the coupled plasmon modes by a tight-binding approach, taking fully multipolar interactions into account. For approaching particles, the dipolar bands move from the visible down to the infrared region and $\omega(k)$ becomes almost independent of $k$. Concomitantly, the group velocity $v_g$ showed an intriguing non-monotonic behavior versus the particle spacing. When the spacing decreases, $v_g$ increases initially but decreases when the particles approach and touch. For moderate spacing, $v_g$ can be reduced drastically to $0.01 c$, except at $kd=0$ and $kd=\pi$, resulting in a slow propagation. Thus one can tune the propagation of plasmon modes by simply varying the spacing between the particles.