  When the surface plasmon resonance in a metal-nanoparticle chain is excited
at one point, the response signal will generally decay down the chain due to
absorption and radiation losses. The decay length is a key parameter in such
plasmonic systems. By studying the plasmon lattice Green's function, we found
that the decay length is generally governed by two exponential decay constants
with phase factors corresponding to guided Bloch modes and one power-law decay
with a phase factor corresponding to that of free space photons. The results
show a high level of similarity between the absorptive and radiative decay
channels. By analyzing the poles (and the corresponding residues) of the
Green's function in a transformed complex reciprocal space, the dominant decay
channel of the real-space Green's function is understood.
