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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 consider how these waves are altered by an anisotropic host (such asa nematic liquid crystal) or an applied magnetic field. In a liquid crystallinehost, with principal axis (director) oriented either parallel or perpendicularto the chain, we find that the dispersion relations of both the longitudinal($L$) and transverse ($T$) modes are significantly altered relative to those ofan isotropic host. Furthermore, when the director is perpendicular to thechain, the doubly degenerate $T$ branch is split by the anisotropy of the hostmaterial. With an applied magnetic field ${\bf B}$ parallel to the chain, thepropagating transverse modes are circularly polarized, and the left and rightcircularly polarized branches have slightly different dispersion relations. Asa result, if a linearly polarized transverse wave is launched along the chain,it undergoes Faraday rotation. For parameters approximating that of a typicalmetal and for a field of 2T, the Faraday rotation is of order 1$^o$ per teninterparticle spacings, even taking into account single-particle damping. If${\bf B}$ is perpendicular to the chain, one of the $T$ branches mixes with the$L$ branch to form two elliptically polarized branches. Our calculationsinclude single-particle damping and can, in principle, be generalized toinclude radiation damping. The present work suggests that the dispersionrelations of plasmonic waves on chain of nanoparticles can be controlled byimmersing the chain in a nematic liquid crystal and varying the director axis,or by applying a magnetic field.

Plasmonic Waves on a Chain of Metallic Nanoparticles: Effects of a Liquid Crystalline Host or an Applied Magnetic Field