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

TL;DR

This paper investigates how static magnetic fields and liquid crystalline hosts influence plasmonic wave propagation along nanoparticle chains, revealing Faraday rotation, branch splitting, and one-way wave propagation phenomena.

Contribution

It introduces a theoretical framework for understanding Faraday rotation, band splitting, and unidirectional propagation of plasmon waves in nanoparticle chains within liquid crystal environments under magnetic fields.

Findings

Finite Faraday rotation angle observed in nematic hosts.

Magnetic field induces splitting of plasmonic branches proportional to |B|.

Propagation becomes unidirectional in cholesteric hosts at certain frequencies.

Abstract

We calculate the dispersion relations of plasmonic waves propagating along a chain of semiconducting or 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 with both ${\bf B}$ and the director parallel to the chain, we find a small, but finite, Faraday rotation angle. For ${\bf B}$ perpendicular to the chain, but director still parallel to the chain, the field couples the longitudinal and one of the two transverse plasmonic branches. This coupling is shown to split the two branches at the zero field crossing by an amount proportional to $|{\bf B}|$. 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 propagates only in one of the two directions.