Omega media can be built by embedding small metallic omega-shaped inclusions in a host medium. The analysis of an omega non-radiative dielectric (NRD) waveguide was originally introduced by these authors. Like magnetically biased ferrites, loading common waveguiding structures with omega media causes the field displacement effect. In the latter case, however, this effect is reciprocal, suggesting its application to the design of reciprocal microwave and millimeter wave devices. The field displacement can also affect the coupling coefficient between two parallel coupled omega NRD waveguides. Instead of changing the waveguide separation, the constitutive omega parameter can be used to control the coupling between the two waveguides.
However, due to the inherently dispersive and lossy characteristics of omega media, the influence of the material dispersion and loss must be investigated. This paper addresses the influence of losses and dispersion of omega media in the design of variable NRD directional couplers. A single-resonance model is used for the constitutive parameters, describing the resonant behavior and finite conductivity of the omega inclusions. Moreover, like the case of double negative (DNG) media, the omega medium may also exhibit both negative permittivity and permeability. Taking all these effects into consideration, we present a complete comprehensive modal analysis for both even and odd LSM modes propagating in this structure.