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

Abstract

Plasmons in a thin metallic foil are of two types: (Ritchie, 1957;Ando et al., 1982;Stratton, 1941) 1) a twodimensional 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 et al., 1982) . The latter (type 2) occur at the bulk plasma frequency p 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.

Electromagnetic wave transmission through a subwavelength nano-hole in a two-dimensional plasmonic layer

“…We have examined the transmission of electromagnetic waves through a nano-hole in a thin plasmonic semiconductor screen for normal incidence of the wave train. This analysis is based on our previously constructed [4], [5], [6] closed-form dyadic electromagnetic Green's function for a thin plasmonic/excitonic layer, which is here adapted to embody a nano-hole (Section 3 above). The resulting closed-form dyadic Green's function is employed in the study of electromagnetic wave transmission through both the hole as well as through the screen itself (Section 4 above).…”

“…Following the position-space inversion of the differential operator in the brackets on the Left Hand Side, carried out in the analysis of Refs. [4], [5] and [6], Eq. ( 5) may be written in the form of a full integral equation as…”

“…However, all of the works we have cited above assume the screen to be a perfect metallic conductor, whereas intense current interest is focussed on plasmonic semiconductors. To address such systems and incorporate the issue of boundary conditions we employ an integral equation formulation [4], [5], [6] describing electromagnetic wave transmission through a nano-hole in a thin plasmonic layer in terms of the dyadic Green's function for the associated vector Helmholtz problem [7], [8], [9], [10]. Interesting electromagnetic phenomena, including enhanced transmission through a nano-hole in an opaque screen, have been discussed in the literature mostly for a metallic thick screen [11], [12], [13], [14].…”

Origin of the low frequency radiation emitted by radiative polaritons excited by infrared radiation in planar La2O3films

“…Here we describe an additional route nature follows to produce radiation from polaritons: the outburst of far IR (FIR) or microwave radiation by radiative polaritons (RPs) at room temperature in simple planar dielectric films, where polaritons cannot propagate. Indeed, RPs [17] and radiative plasmons [18,19] are unable to propagate in planar dielectric layers because of the lack of periodic structures acting as waveguides and enabling constructive interference [20]. The RPs have a group velocity faster than the speed of light in vacuum c [17][18][19], but their inability to propagate suggests that they do not behave as superluminal wave pockets [21,22].…”

“…Indeed, RPs [17] and radiative plasmons [18,19] are unable to propagate in planar dielectric layers because of the lack of periodic structures acting as waveguides and enabling constructive interference [20]. The RPs have a group velocity faster than the speed of light in vacuum c [17][18][19], but their inability to propagate suggests that they do not behave as superluminal wave pockets [21,22]. Therefore, this work describes the energy-release mechanism in RPs with group velocity faster than c upon generation in planar dielectric layers illuminated by IR radiation.…”