Metamaterials with simultaneously negative permittivity and permeability are usually described as isotropic materials, although they may actually exhibit electrical and/or magnetic anisotropy. Indefinite media are bianisotropic materials characterized by indefinite permittivity and/or permeability tensors, i.e., which eigenvalues do not all have the same sign. These media, only with partly negative permittivity and permeability tensor diagonal elements, may also exhibit certain anomalous properties like negative refraction. In fact, it was demonstrated that negative refraction is not confined to isotropic materials with negative permittivity and permeability, but can also occur in certain classes of uniaxially anisotropic media. Indefinite media are a more realistic description of metamaterials.
In this talk we address the basic properties of electromagnetic wave propagation in waveguides involving indefinite media. A study about the modes propagating in several types of waveguides filled with indefinite media is presented. An adequate dispersion model is used to characterize the media. When compared with the conventional waveguides, several uncommon features are exhibited, such as the coexistence of forward and backward modes and both co- and contra-directional coupling. The application of some of these features to the design of new devices is addressed. As an example, the concept of an indefinite directional coupler is proposed.
Further developments on this topic include the propagation of leaky-modes on indefinite-medium waveguides.