  Here we discuss the theory and analyze in detail the guidance properties of
linear arrays of metamaterial/plasmonic small particles as nano-scale optical
nanotransmission lines, including the effect of material loss. Under the
assumption of dipolar approximation for each particle, which is shown to be
accurate in the geometry of interest here, we develop closed-form analytical
expressions for the eigen-modal dispersion in such arrays. With the material
loss included, the conditions for minimal absorption and maximum bandwidth are
derived analytically by studying the properties of such dispersion relations.
Numerical examples with realistic materials including their ohmic absorption
and frequency dispersion are presented. The analytical properties discussed
here also provide some further physical insights into the mechanisms underlying
the sub-diffraction guidance in such arrays and their fundamental physical
limits. Possibility of guiding beams with sub-wavelength lateral confinement
and reasonably low decay is discussed offering the possible use of this
technique at microwave, infrared and optical frequencies. Interpretation of
these results in terms of nanocircuit concepts is presented, and possible
extension to 2-D and 3-D nanotrasnsmission line optical metamaterials is also
foreseen.
