The collective wave type plasmon polariton self-modes in the metallic (Au, Ag) nano-chain were determined and analyzed with respect to the nano-sphere size and chain separation parameters. At some regions for parameters, the undamped modes were identified when the interaction had been assumed as the near-field-zone dipole coupling. These modes were found on the rim of stability of the linear theory, which indicates artifact of the model of near-field coupling. Inclusion of the medium- and far-field zone contributions to dipole interaction removes, however, instability and allows for fully analytical demonstration of quenching of irradiation losses of plasmon polaritons in the chain to the level of only ohmic attenuation. The plasmon polariton dispersion and the group velocity of plasmon polariton wave packets were examined with respect to nano-sphere and chain parameters and mode polarization. Previous numerical results related to long-range plasmon polariton propagation in the chain are transparently interpreted within the analytical approach.
Keywords: Lorentz friction; Metallic nano-chain; Plasmon polariton; Plasmons; Undamped propagation.