  In a Drude-like model for the conduction electrons of Metal Nanoparticles
(MNPs) in a periodic linear chain, considering dipole-dipole interactions of
adjacent particles, an analytical expression is derived for each particle
permittivity for two different polarizations of incident light: parallel with
and perpendicular to the chain line. A numerical analysis is carried out for a
chain including 10 identical gold Nanoparticles (NPs) for two different sizes
of NPs and two different host media of air and glass. It is shown that in the
parallel case of polarization, interaction of NPs leads to a substantial
increase in the extinction cross section and the red-shift of the Surface
Plasmon Resonance (SPR) wavelength. In comparison with the linear properties of
a single NP, the second and penultimate particles have the most increase in the
extinction cross section and SPR wavelength displacement while the first and
last particles experience the least variations due to the mutual interactions.
For the perpendicular polarization, inversely, the dipolar coupling causes the
decrease in extinction cross section of all particles and the blue-shift of SPR
wavelength. For the parallel polarization, the absolute values of the real and
imaginary parts of complex permittivity of each MNP decrease in comparison with
the single particle case while they increase for the perpendicular state of
polarization.
