Exact solution for velocity of plasmon-polariton in metallic nano-chain

In equidistant infinite chain of metallic nanospheres the collective mode of surface plasmons propagates without radiative losses, i.e., the Lorentz friction losses in each nanosphere are compensated by energy income in near-, medium- and far-field from the rest of the chain. Within an approximate approach including numerical studies in Green function framework it has been indicated superluminal propagation of some plasmon-polariton modes. By the exact solution of the nonlinear dynamic equation we demonstrate that the superluminal modes were an artifact of the perturbation solution type and we show that the group velocities for both polarizations are limited by light velocity, though vary in large range depending on chain parameters and are typically one order lower than the light velocity.