Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability

Abstract

We present a detailed analytical study of surface plasmon polaritons SPPs in generalized asymmetric slab waveguides with a core of negative permittivity and permeability. Profiting from the duality principle, we confine ourselves to the analysis of p-polarized TM SPP eigenmodes, which also occur in thin metallic films. It is shown that the left-handed LH structures considered here support a richer variety of SPPs when compared to their metallic counterparts. Depending on the refractive index distribution, the permittivity of each medium and the thickness of the core, a total of 30 solutions to the involved characteristic equation are identified in a unified manner and classified systematically. In order to identify conclusively all SPPs, we follow an analytical methodology based directly on the solution constraints inherent in the associated transcendental equation. This treatment reveals striking features of the formed SPP eigenmodes, such as the existence of “supermodes” when no SPP is supported at one of the slab interfaces. Moreover, our study reveals the opening of gaps in the SPP dispersion diagrams, occurrence of monomodal propagation for specific choices of the material parameters, presence of SPPs with no cutoff thickness and coexistence of three eigenmodes, with double mode-degeneracy points occurring twice. The eigenmodes with negative energy flux that give rise to negative group velocity are identified via a closed-form expression for the time-averaged power flow P in the guide. For each eigenmode, we examine the variation of P with the reduced slab thickness and discuss key features of the effective index geometric dispersion diagram, most of which are unique to the generalized structures studied herein.