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

Abstract

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 describes how these waves are altered when the liquid crystal host is a nematic or a cholesteric liquid crystal (NLC or CLC) with or without an applied magnetic field. We find that, in general, the liquid crystal host, either NLC or CLC, alters the dispersion relations of the transverse ($T$) and longitudinal ($L$) waves significantly from the dispersion relations for an isotropic host. We show that by altering the director axis of the liquid crystal relative to the long axis of the metallic chain, that the $T$ branch can be split into two non-degenerate linearly polarized branches (NLC host) or two non-degenerate elliptically polarized branches (CLC host). When an external magnetic field is applied parallel to both the long axis of the metallic particles and the director of the CLC host, we find that the dispersion relations are odd in an exchange in sign for $ω$ for the non-degenerate elliptically polarized $T$ branches. That is, the application of an external magnetic field leads to the realization of a one-way waveguide.