Nowadays, metamaterials are receiving a considerable attention in the literature. Double negative (DNG) media, single negative (SNG) media, chiral media or omega media, just to mention a few, are suggesting promising applications like electromagnetic cloaking or circuit miniaturization. Most of the research on the field is mainly focused on material characterization and manufacture. However, there is a certain scarcity of publication in the area of guided-wave propagation in waveguides containing this type of media.
In the last years, the research of this group on the topic has been mainly focused on the analysis of the propagation characteristics of three-dimensional waveguides involving metamaterials. The waveguides addressed so far can be divided into two major groups: Three-dimensional closed waveguides for microwaves and millimeter waves, such as the H-guide or the non-radiative dielectric (NRD) waveguide; Open planar waveguides for integrated optics, such has the ridge waveguide and the rib waveguide. Fully analytical methods have been used when possible, and numerical methods based on the mode matching technique have been used when there is no closed analytical solution for the electromagnetic problem.
In the case of chiral media, the chiral H-guide was considered. The chiral H-guide consists of an H-guide where the common isotropic dielectric slab is replaced by chiral slab. The material dispersion was included in the analysis through the use of the Condon model for the chirality parameter. Since there is no exact solution for this problem, the transverse resonance method together with a classical mode matching technique have been applied. Results include operational and dispersion diagrams, and possible applications lye in the area of reciprocal phase-shifters and mode converters.
Another type of closed structure analyzed is the omega NRD-guide, firstly proposed by this research group, which includes an omega slab. NRD waveguides and couplers involving uniaxial omega media, exhibiting a vertical optical axis, have been addressed. The exact modal equations were derived by the transverse resonance method, since this structure supports a rigorous analysis, which includes pure LSE and LSM modes.
Lately, the DNG H-guide and respective directional coupler have been studied. 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. Future work will include the analysis of the symmetric triple-slab DNG H-guide directional coupler and respective field strength diagrams.
Finally, the DNG ridge waveguide has also been 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.