Rigorous Study of Forward and Backward Waves in Metamaterial Waveguides

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In this paper a rigorous analysis of the TE modes is developed for studying the propagation in a rectangular metallic waveguide fully-filled with anisotropic metamaterial. The wave equation and the dispersion relations are obtained and analyzed. The higher order modes are exploited. Among the particularities of this anisotropic material, the backward and forward waves can both propagate below the cutoff frequency in the guide. The numerical results for TEm0 are obtained and compared to theoretical predictions and to those previously published. Numerical examples show the validity of this method. In some cases, it has been found that the propagation constant in a rectangular waveguide metamaterial slab is complex although the media are lossless.

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Anisotropy; Complex Modes; Metamaterials; Forward and Backward Waves; Waveguide

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