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

We study the interaction of an electromagnetic field with a non-absorbing or absorbing dispersive sphere in the framework of complex angular momentum techniques. We assume that the dielectric function of the sphere presents a Drude-like behavior or an ionic crystal behavior modelling metallic and semiconducting materials. We more particularly emphasize and interpret the modifications 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 sphere surface. This surface polariton corresponds to a particular Regge pole of the electric part (TM) of the $S$ matrix of the sphere. 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 the 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 dispersion relation and its damping in the non-absorbing and absorbing cases. In these analytic expressions, we more particularly exhibit well-isolated terms directly linked to absorption. Finally, we explain why the photon-sphere system can be considered as an artificial atom (a ``plasmonic atom" or ``phononic atom") and we briefly discuss the implication of our results in the context of the Casimir effect.