We present results of modeling of waveguides modes propagation coefficients in cylindrical tree-layer waveguide in this work. Intermediate layer is LHM (Left-Handed-Mcdium) metamaterial with negative index of refraction. The outer and inner layers are conventional materials with positive index of refraction RHM (Right-Handed-Medium). Our results indicate that in such waveguides exist complex waves and waves with a significant slowdown of phase.
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