Radiative Plasmonic-Polariton Dispersion Relation for a Thin Metallic Foil With Interband Damping Transitions

Plasmons in a thin metallic foil are of two types: (Ritchie, 1957; Ando , 1982; Stratton, 1941) 1) a two-dimensional plasmon (Ritchie, 1957) whose electrostatic dispersion relation has its frequency proportional to the square root of wave number, which propagates along the surface of the foil and 2) a plasmon constituted of collective electron density oscillations across the foil in the nature of capacitor-like discharges perpendicular to the surfaces of the foil (Ando , 1982) . The latter (type 2) occur at the bulk plasma frequency and it has long been known that they produce electromagnetic (EM) radiation (Ferrell, 1958) (whereas type 1 plasmons do not radiate). The object of this research is to carefully examine the coupling of both these plasmon modes to the EM field in producing radiative polaritons. We carry this out using a complex dielectric function approach embodying both types of plasmons in the context of an exact analytic solution for the dyadic EM field Green's function describing radiative plasmonic-polariton propagation for a thin metallic foil (Horing,et al.), including the role of interband damping transitions. In particular, we will formulate and examine the dispersion relation for such polaritons, which is significantly modified from Stern's result (Stern, 1967) by the radiative type 2 plasmon described above and interband damping. The complex dielectric function embodying both type 1 and type 2 plasmons and interband damping involves a frequency dependent imaginary part and is expected to exhibit interesting radiative plasmonic-polariton phenomenology. This expectation is based on a recent calculation we have carried out (Horing) using a generic dielectric function of the Lorentzian type, which produced inhomogeneous (Jackson, 1975) plane wave radiation from excitation of the foil modes. Such inhomogeneous plane waves, which grow locally as a function of distance away from the foil (without violating the causality principle), have been known to occur previously and are discussed in the literature (Stratton, 1941). This local growth of the EM field may contribute to enhanced focusing properties of an array of nanoholes in the foil.