In this paper, complex modes in a linear chain of gold nanospheres are analyzed, accounting for metal losses. Dispersion
diagrams are computed for travelling modes with both longitudinal and transverse (with respect to the array axis)
polarization states. The procedure outlined in this work allows for the description of single mode evolution varying
frequency, thus the modal dispersion diagrams are composed by the superposition of all the different modes in the one
dimensional array. Each nanoparticle is modeled as an electric dipole, by adopting the single dipole approximation, and
the complex zeroes of the homogeneous equation characterizing the field in the periodic structure are computed. The
Ewald method is employed to analytically continue the periodic Green's function into the complex spectral domain and
to achieve rapid convergence. Full characterization of the modes is provided in terms of their direction of propagation
(forward/backward), their guidance and radiation properties (bound/leaky), the position of their wavenumber on the
Riemann sheet (proper/improper), and also in terms of their possible physical excitation in the structure by a source in
proximity of the array or a defect (physical/nonphysical modes). Understanding the modes excitable in this kind of
structures is essential for possible applications in which the linear chain can be employed, from near-field enhancement
to SERS, and innovative sensors.
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