Metamaterials are playing an important role in modern investigation on electromagnetics of complex media. Double negative (DNG) media, single negative (SNG) media, chiral media or omega media, just to mention a few, are suggesting promising applications, like e.g. electromagnetic cloaking or circuit miniaturization.
Research in this field is focused both on material characterization and manufacture as well as new applications, like those in the area of guided-wave propagation in waveguides containing this type of media.
Wave propagation in waveguiding structures containing metamaterials has been subject to an intense investigation, mostly due to their promising applications to microwave and millimeter-wave guiding and radiating devices. Several types of waveguides involving metamaterials have been already addressed in the literature but, in most cases, this analysis has been limited to single frequency operation.
In this talk the DNG H-guide and respective directional coupler have addressed. The existence of proper leaky modes and the contra-directional coupling have been investigated. Both lossless and lossy lorentzian models have been used to characterize the material dispersion. A rigorous full-wave analysis of the surface and leaky modes was conducted and the approximate coupled-mode theory was used to characterize the directional coupler. Operational diagrams, where the contra-directional coupling is put in evidence, and proper leaky modes emerging at the band gaps of the coupler are the most notorious results.
The DNG ridge waveguide is also analyzed. This three-dimensional open planar waveguide was analyzed using the transverse resonance method and the classical mode-matching technique, while the radiation modes have been discretized through the placement of a perfectly conductor electric plane far above the waveguide. The accuracy of the results was accessed by comparison with the approximate effective index method. The results include the dispersion diagrams of the proper leaky modes.
The effects of material dispersion and loss on the performance of some types waveguides, involving metamaterials, are also investigated. A lossy dispersive Lorentz model is adopted for both the electric permittivity and the magnetic permeability. The dispersion properties and the modal equation root dynamics in the complex plane of the longitudinal wavenumber are analyzed.
Unphysical results may arise when simple dispersion models, disregarding losses, are adopted, therefore violating causality. In fact, according to the Kramers-Kronig relations, a causal dispersive metamaterial model must necessarily include the losses. In the absence of losses and for finite values of the constitutive parameters, unphysical resonances in the longitudinal wavenumber are reported.
This unphysical behavior, disappears when losses are considered in the material model. In fact, as soon as negligible losses are introduced, these resonances turn into improper leaky modes.
The propagation of lossy surface and leaky modes in this type of waveguides is also investigated and its performance is analyzed. Moreover, the effects of metamaterial dispersion and losses may suggest potential applications. Namely, it is shown that, in the presence of small losses, this waveguide exhibits sharp narrow passbands, hence suggesting its application in the design of waveguiding filters.