Most metamaterials exhibit pronounced anisotropic properties that are crucial for the understanding of their superior optical behavior, especially when they are integrated into the structure of a plasmonic waveguide. In this paper, we analytically solve the dispersion relation for a slot plasmonic waveguide filled with an anisotropic-stratified metamaterial and reveal that it supports two modes featuring relatively long propagation lengths in the limit of vanishing slot thickness. We classify these modes according to their physical origin and study the variation of their dispersion properties with material parameters. 1. Introduction The ultimate goal of optics is to enable a perfect control of the interaction between light and matter. This goal has been brought closer by the recent advances in nanotechnology that have made possible the fabrication of optical metamaterials [1, 2]. The unusual electromagnetic properties of metamaterials are expected to enable a new generation of optical devices. In developing design strategies and new concepts for such devices, it is paramount that anisotropic properties of metamaterials are considered along with their other material features. Moreover, even the ways in which common devices operate require revisions when ordinary materials in their design are replaced by anisotropic metamaterials. A considerable amount of theoretical effort has been recently devoted to the analysis of optical propagation through different types of metamaterial structures, including uniaxial dielectrics [3] and indefinite media [4, 5], metal–dielectric heterostructures [6] and superlattices [7], and strongly anisotropic waveguides [8]. In this paper, we reexamine the guiding properties of slot plasmonic waveguides filled with an anisotropic medium. Our work is intended to demonstrate that integration of plasmonic waveguides with anisotropic optical metamaterials not only brings additional freedom to their design, but can also lead to new physical phenomena that may benefit the waveguide performance. The plasmonic waveguide discussed here consists of an anisotropic medium of thickness embedded between two metals of permittivity . We assume that the medium's permittivity is described by a constant, diagonal tensor with its principle axes parallel to the waveguide's edges. Even though the permeability has similar anisotropic properties, only one component of its tensor affects the transverse magnetic (TM) modes, which are of primary interest for plasmonic waveguides. This allows us to describe the permeability using a single parameter . As
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