Interface entangled plasmon-plasmariton modes

A theoretical study of the propagating electromagnetic surface waves confined to a plane vacuum-homogeneous jellium interface is carried out. A classification of the entangled surface plasmon (L) and plasmariton (T) modes, which we name surface jellions, is given. The collective mode structure is obtained using the Weyl (angular spectrum) expansion of the screened electromagnetic jellium propagator G. The pole structure of G relates to the collective-mode pattern. The surface jellion dispersion relation is a central concept in our analyses. We derive this for interfaces with and without self-consistently determined surface currents, i.e., for so-called active and passive boundary conditions. A numerical calculation of the dispersion relation is carried out for the hydrodynamic model. For this model the dispersion relation has three branches in the region of strong surface plasmon-plasmariton coupling. Starting from a finite-relaxation time τ calculation, the surface jellion eigenmode structure is obtained in the limit τ→∞. Exponentially confined surface jellion eigenmodes carry electromagnetic momentum along the surface, and we calculate the T, L, and TL parts of the momentum, emphasizing numerical data for the hydrodynamic model. It is shown that the entangled TL part carries a momentum backflow. The energy carried by the confined surface jellions is expressed in terms of an equivalent mass concept. The equivalent mass formulation is useful for a harmonic-oscillator description of the surface jellions and their quantization. The equivalent mass of the three branches of the hydrodynamic jellion dispersion is calculated numerically and the T, L, and TL contributions to the equivalent mass are determined. All numerical calculations presented in the article are carried out as a function of the surface jellion wave number along the surface.