  Nanoparticle chain waveguide based on negative-epsilon material is
investigated through a generic 3D finite-element Bloch-mode solver which
derives complex propagation constant ($k$). Our study starts from waveguides
made of non-dispersive material, which not only singles out "waveguide
dispersion" but also motivates search of new materials to achieve guidance at
unconventional wavelengths. Performances of gold or silver chain waveguides are
then evaluated; a concise comparison of these two types of chain waveguides has
been previously missing. Beyond these singly-plasmonic chain waveguides, we
examine a hetero-plasmonic chain system with interlacing gold and silver
particles, inspired by a recent proposal; the claimed enhanced energy transfer
between gold particles appears to be a one-sided view of its hybridized
waveguiding behavior --- energy transfer between silver particles worsens.
Enabled by the versatile numerical method, we also discuss effects of
inter-particle spacing, background medium, and presence of a substrate. Our
extensive analyses show that the general route for reducing propagation loss of
e.g. a gold chain waveguide is to lower chain-mode frequency with a proper
geometry (e.g. smaller particle spacing) and background material setting (e.g.
high-permittivity background or even foreign nanoparticles). In addition, the
possibility of building mid-infrared chain waveguides using doped silicon is
commented based on numerical simulation.
