Surface plasmon polaritons and surface phonon polaritons on metallic and semiconducting spheres: Exact and semiclassical descriptions

摘要

We study the interaction of an electromagnetic field with a non-absorbing orabsorbing dispersive sphere in the framework of complex angular momentumtechniques. We assume that the dielectric function of the sphere presents aDrude-like behavior or an ionic crystal behavior modelling metallic andsemiconducting materials. We more particularly emphasize and interpret themodifications induced in the resonance spectrum by absorption. We prove that"resonant surface polariton modes" are generated by a unique surface wave,i.e., a surface (plasmon or phonon) polariton, propagating close to the spheresurface. This surface polariton corresponds to a particular Regge pole of theelectric part (TM) of the S matrix of the sphere. From the associated Reggetrajectory we can construct semiclassically the spectrum of the complexfrequencies of the resonant surface polariton modes which can be considered asBreit-Wigner-type resonances. Furthermore, by taking into account the Stokesphenomenon, we derive an asymptotic expression for the position in the complexangular momentum plane of the surface polariton Regge pole. We then describesemiclassically the surface polariton and provide analytical expressions forits dispersion relation and its damping in the non-absorbing and absorbingcases. In these analytic expressions, we more particularly exhibitwell-isolated terms directly linked to absorption. Finally, we explain why thephoton-sphere system can be considered as an artificial atom (a ``plasmonicatom" or "phononic atom") and we briefly discuss the implication of our resultsin the context of the Casimir effect.