Complex-ω approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres

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 similar to 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.