Faraday Rotation and One-Way Propagation of Plasmon Waves on a Nanoparticle Chain

We calculate the dispersion relations of plasmonic waves propagating along a chain of metallic nanoparticles in the presence of both a static magnetic field ${\bf B}$ and a liquid crystalline host. The dispersion relations are obtained using the quasistatic approximation and a dipole-dipole approximation to treat the interaction between surface plasmons on different nanoparticles. For a plasmons propagating along a particle chain in a nematic liquid crystalline host and a field parallel to the chain, we find a small, but finite, Faraday rotation angle. In a cholesteric liquid crystal host and an applied magnetic field parallel to the chain, the dispersion relations for left- and right-moving waves are found to be different. For some frequencies, the plasmonic wave may propagate only in one of the two directions.