Theory of Plasmonic Waves on a Chain of Metallic Nanoparticles in a Liquid Crystalline Host

Linearly polarized plasmonic waves can propagate along a chain of metallic particles, of sufficiently small diameter and spacing. We have calculated the dispersion relations for these plasmonic waves when the host is either a nematic or a cholesteric liquid crystal (NLC or CLC). An NLC is found to alter the dispersion relations of both transverse ($T$) and or longitudinal ($L$) waves significantly from those for an isotropic host. If the NLC director is perpendicular to the metallic chain, the doubly degenerate $T$ branch is split into two linearly polarized branches. Similar results are obtained for a CLC with twist axis parallel to the chain, except that the $T$ branches are elliptically polarized. When a magnetic field is applied parallel to the chain, the dispersion relations for the $T$ branches are no longer symmetric about $k=0$ and the chain may act as a one-way waveguide at certain frequencies. We present numerical examples assuming spherical metal particle with a Drude dielectric function.