Description and characterization of the complex modes in a linear chain of gold nanospheres

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.