We consider the scattering of electromagnetic waves by a left-handed cylinder -i.e., by a cylinder fabricated from a left-handed material -in the framework of complex angular momentum techniques. We discuss both the TE and TM theories. We emphasize more particularly the resonant aspects of the problem linked to the existence of surface polaritons. We prove that the long-lived resonant modes can be classified into distinct families, each family being generated by one surface polariton propagating close to the cylinder surface and we physically describe all the surface polaritons by providing, for each one, its dispersion relation and its damping. This can be realized by noting that each surface polariton corresponds to a particular Regge pole of the S matrix of the cylinder. Moreover, for both polarizations, we find that there exists a particular surface polariton which corresponds, in the large-radius limit, to the surface polariton which is supported by the plane interface. There exists also an infinite family of surface polaritons of whispering-gallery type which have no analogs in the plane interface case and which are specific to left-handed materials.
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.
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