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A chain of metallic particles, of sufficiently small diameter and spacing,allows linearly polarized plasmonic waves to propagate along the chain. In thispaper, we describes how these waves are altered when the liquid crystal host isa nematic or a cholesteric liquid crystal (NLC or CLC) with or without anapplied magnetic field. We find that, in general, the liquid crystal host,either NLC or CLC, alters the dispersion relations of the transverse ($T$) andlongitudinal ($L$) waves significantly from the dispersion relations for anisotropic host. We show that by altering the director axis of the liquidcrystal relative to the long axis of the metallic chain, that the $T$ branchcan be split into two non-degenerate linearly polarized branches (NLC host) ortwo non-degenerate elliptically polarized branches (CLC host). When an externalmagnetic field is applied parallel to both the long axis of the metallicparticles and the director of the CLC host, we find that the dispersionrelations are odd in an exchange in sign for $\omega$ for the non-degenerateelliptically polarized $T$ branches. That is, the application of an externalmagnetic field leads to the realization of a one-way waveguide.

Theory of plasmonic waves on a chain of metallic nanoparticles in a liquid crystalline host