An accurate rigorous modal theory has been applied to investigate the propagation characteristics in a rectangular waveguide filled with multilayer left-handed and right-handed metamaterials. It is shown that such a waveguide supports different passbands below the waveguide's cutoff frequency, and the number of passbands is related to the corresponding layers of different left-handed metamaterials (LHMs) filled in the waveguide. The rigorous modal analysis of this structure reveals in detail how the waveguide geometry and left-handed metamaterial parameters may be selected to design rectangular waveguides supporting double or triple below-cutoff passbands. The efficient power transmissions in these below-cutoff passbands are validated by using the full-wave simulation software HFSS. These structures supporting multiple below-cutoff passbands could find applications in waveguide components requiring miniaturization and multiband properties, such as miniaturized multifunctional antennas and filters.
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