Abstract
Bound and leaky modes with complex wavenumber in chains (linear arrays) of plasmonic nanospheres are characterized for both longitudinal and transverse polarization states (with respect to the array axis). The proposed method allows for the description of each mode evolution when varying frequency. As a consequence, full characterization of the guided modes with complex wavenumber is provided in terms of propagation direction, guidance or radiance, proper or improper, and physical or nonphysical conditions. Each nanosphere is modeled according to the single dipole approximation, and the metal permittivity is described by the Drude model. Modal wavenumbers are obtained by computing the complex zeroes of the homogeneous equation characterizing the field in the one dimensional periodic array. The required periodic Green's function is analytically continued into the complex wavenumber space by using the Ewald method. Furthermore, a parametric analysis of the mode wavenumbers is performed with respect to the geometrical parameters of the array.
Highlights
Periodic arrays of plasmonic nanospheres have been studied because of their interesting performance in several practical applications
We want to emphasize that all the aforementioned excellent referenced work did not provide yet a complete characterization and classification of the modes in a linear chain of plasmonic nanospheres, in terms of leaky/bound, proper/improper, forward/backward, including the conditions for their physical existence, which is the goal of the present paper
Received 3 Jun 2011; revised 13 Aug 2011; accepted 17 Aug 2011; published 6 Sep 2011 12 September 2011 / Vol 19, No 19 / OPTICS EXPRESS 18358 it is classified in terms of path deformation in the complex wavenumber domain
Summary
Periodic arrays of plasmonic nanospheres have been studied because of their interesting performance in several practical applications. Several difficulties are still encountered in the analysis and interpretation of mode propagation in one dimensional (1D-periodic, linear chains) and two dimensional (2D-periodic) arrays of metallic nanospheres when varying frequency, for example Based on what it has been published so far it is somehow hard to discern if a mode is physical (excitable) or not. The scope of this paper is the characterization of the bound (non radiating) and leaky (radiating) modes with complex wavenumber in linear chains of plasmonic nanospheres (Fig. 1), accounting for metal losses, as we recently did in [13] for 2D-periodic arrays. We want to emphasize that all the aforementioned excellent referenced work did not provide yet a complete characterization and classification of the modes in a linear chain of plasmonic nanospheres, in terms of leaky/bound, proper/improper, forward/backward, including the conditions for their physical existence, which is the goal of the present paper. The dyadic form of the Ewald representation of the periodic GF evaluation used in this paper is provided in Appendix B
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