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. © 2011 SPIE.

Composite materials based on plasmonic nanoparticles allow building metamaterials with very large effective permittivity (positive or negative) or ε-near-zero; moreover, if clustered or combined with other nanoparticles, it is possible to generate also effective magnetic permeability (positive or negative), and an ad-hoc design would result in the generation of double negative materials, and therefore backward wave propagation. However, losses are usually significant and affect the metamaterial performance. In this work, we report on the possibility of adopting fluorescent dye molecules or quantum dots, optically pumped, embedded into the dielectric cores of the employed nanoshell particles, and provide loss-compensation in ordered 3D periodic arrays at optical frequencies. Each spherical nanoshell is modeled as an electric dipole. We consider nanoparticles with gold and silver shells. We then find the modes with complex wavenumber in the metamaterial, and describe the composite material in terms of homogenized effective material parameters (refractive index and permittivity). Furthermore, in case of loss-compensation, we compare the results obtained from modal analysis with the ones computed by using two different homogenization methods: (i) Maxwell Garnett homogenization theory and (ii) Nicholson-Ross-Weir retrieval method. We show the design of two ε-near-zero metamaterials with low losses by simulating gain material made of dyes or quantum dots with realistic parameters. A brief discussion about the employment of the two kinds of active gain materials adopted here is given in the end. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).