A chain of metallic particles, of sufficiently small diameter and spacing, allows linearly polarized plasmonic waves to propagate along the chain. In this paper, we consider how these waves are altered when the host is a nematic or cholesteric liquid crystal (NLC or CLC). In an NLC host, with the principal axis (director) oriented either parallel or perpendicular to the chain, we find that the dispersion relations of both the longitudinal () and transverse () modes are significantly altered relative to those of an isotropic host. Furthermore, when the director is perpendicular to the chain, the doubly degenerate branch is split into two nondegenerate linearly polarized branches by the anisotropy of the host material. In a CLC liquid crystal with a twist axis parallel to the chain, the two branches are again found to be split, but are no longer linearly polarized; the dispersion relations depend on the cholesteric pitch angle. To illustrate these results, we calculate the and dispersion relations for both types of liquid crystals, assuming that the metal is described by a Drude dielectric function. The formalism can, in principle, include single-particle damping and could be generalized to include radiation damping. The present work suggests that the dispersion relations of plasmonic waves on a chain of nanoparticles can be controlled by immersing the chain in an NLC or a CLC and varying the director axis or pitch angle by applying suitable external fields.
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