Complex-ωapproach versus complex-kapproach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres

Abstract

Propagation characteristics of surface plasmon-polaritons (SPPs) in linear chains of metallic nanospheres (LCMNs) can be found from a dispersion equation, by assuming that either frequency or wave number of a SPP is real. In this paper, we present a comparative study of SPP modes corresponding to the two types of complex solutions for an infinitely long LCMN embedded in a gain medium. We show that even though gain predominantly affects the SPP dispersion obtained with real frequency, both solutions result in the same dispersion and attenuation of SPP modes, when Ohmic losses are almost compensated by gain. In this regime, an analytic expression for the propagation length of SPPs exists, and the SPPs' dispersion is determined by a real equation. We also demonstrate that for a given amount of gain (below the amplification limit of ∼1000 cm −1 ), transversely polarized SPPs attenuate slower than longitudinally polarized SPPs and are, therefore, preferable for the purpose of energy transfer in gain-supplied LCMNs. The transmission windows for SPP modes of different polarizations do not overlap each other, which facilitates realization of LCMN-based plasmonic filters. Our results may prove useful in design optimization of all-optical chips for power-efficient optical supercomputers.

Energy transport of surface phonon polaritons propagating along a chain of spheroidal nanoparticles

“…Considering that the coupling among individual resonances of each nanoparticle may guide surface electromagnetic fields along a chain of nanoparticles, these structures have been proposed as potential waveguides of both SPPs and SPhPs. The propagation [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and energy transport [10,19] by SPPs propagating along chains of metallic nanoparticles have been widely investigated by many research groups, while analogous works dealing with SPhPs are scarce [20].…”

Propagation of surface plasmon-polaritons in linear chains of metallic nanoparticles embedded in a gain medium

“…where the dispersion law is found from the real equation Re / 0, which is clearly simpler than Eqs. (1) and (2) [11]. Thereby, we arrive at an important general conclusion that either complex-k or complex-ω solutions of the dispersion equation can be used to describe propagation of SPPs in the low-loss regime, when the Ohmic and radiation losses are almost overcome by gain.…”

“…In this limit, 2 cos , so that Eqs. (1) and (2) reduce to the explicit dependencies 1/ cos ε / 4α ω and 1/ cos ε / 2α ω , respectively [11].…”

“…The local electric field acting on the th nanoparticle , is the vectorial sum of the electric fields generated by other particles and external sources. By decomposing this field to longitudinal (L) and transverse (T) components and setting , the equations for SPP dispersion acquire the form [11] ε / 2α ω ,…”

Guided Plasmon Modes of a Graphene-Coated Kerr Slab

“…The surface conductivity of graphene (σ g ) can be effectively modulated via tuning its chemical potential (μ) through chemical doping, or electrostatic or magnetostatic gating [1]. For Im σ g > 0, graphene behaves as a very thin metal layer capable of supporting transverse magnetic (TM) surface plasmons (SPs) [7][8][9][10][11][12][13]. Tunability of plasmon resonance through the variation of μ, together with a relatively large propagation length and a small localization scale of SPs in the infrared (IR) and terahertz (THz) ranges, are key advantages of graphene SPs over those supported by noble metals like silver and gold [7].…”