Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis

TL;DR

This paper analyzes electromagnetic surface polaritons on metallic and semiconducting cylinders using complex angular momentum techniques, revealing their spectral properties and potential applications in photonic systems.

Contribution

It introduces a Regge pole approach to characterize surface polariton modes and derives analytical expressions for their dispersion and damping.

Findings

Surface polaritons are generated by a unique surface wave near the cylinder surface.

The spectrum of resonant modes can be semiclassically constructed from Regge trajectories.

Analytical expressions for dispersion relation and damping of surface polaritons are provided.

Abstract

We revisit scattering of electromagnetic waves from metallic and semiconducting cylinders in the framework of complex angular momentum techniques. We prove that "resonant surface polariton modes" are generated by a unique surface wave, i.e. a surface polariton, propagating close to the cylinder surface. This surface polariton corresponds to a particular Regge pole of the $S$-matrix of the cylinder. From the associated Regge trajectory we can construct semiclassically the spectrum of the complex frequencies of the resonant surface polariton modes which can be considered as Breit-Wigner-type resonances. Furthermore, by taking into account Stokes' phenomenon, we derive an asymptotic expression for the position in the complex angular momentum plane of the surface polariton Regge pole. We then describe semiclassically the surface polariton and provide analytical expressions for its the dispersion relation and its damping. All these features allow us to consider the photon-cylinder system as a kind of artificial atom where the photon plays the role of the electron. Finally, we briefly discuss the implication of our results for two-dimensional photonic crystals.