The omega H-guide is an H-guide where the common isotropic slab is replaced by an omega slab. It consists of an omega slab, sandwiched between two metal plates. If the spacing is less than half of the free-space wavelength, lateral radiation from the structure is prevented, since higher-order parallel-plate waveguide modes are below cutoff, and the TEM parallel-plate waveguide mode is not excited provided that symmetry with respect to the y axis is maintained.

Omega materials are artificial media built by including metallic omega shaped particles in a host isotropic medium. These planar inclusions can be seen as a combination of a wire and a loop antenna. When an external electrical field is applied to an omega particle, it induces an electrical dipole moment parallel to the wire and a magnetic moment orthogonal to the loop. Therefore, omega materials exhibit magneto-electric coupling.

This paper addresses the influence of the material dispersion and losses of the omega medium on the propagation characteristics of the waveguide. A single-resonance lossy model was used for the material constitutive parameters of the omega medium. This paper addresses, for the first time, the propagation of proper leaky modes, which are known to propagate in this type of waveguide, in a lossy dispersive omega H-guide.

The inherently dispersive and lossy characteristics of an omega medium affect its operation in the microwave and millimeter wave regimes. The resonant behavior of the inclusions and its finite conductivity causes the medium to be lossy and dispersive, even in small frequency bands near the resonance. Moreover, above the resonant frequency, the omega medium may behave like a double negative (DNG) metamaterial, therefore exhibiting simultaneously negative permittivity and permeability.

Two frequency bands are analyzed: one below and another above the resonance frequency of the omega particles. Below this resonance frequency there are no significant effects arising from dispersion and losses. However, above the resonance frequency the super-slow modes and the proper leaky modes are strongly affected by the dispersion and losses. These effects may suggest potential applications.