Ordinary planar waveguide cannot support electromagnetic (EM) wave propagating at frequency below the cut-off frequency of the waveguide, due to the evanescent wave nature of the EM wave in such waveguide. We have found by theoretical analysis that extraordinary EM wave transmission could occur for transverse-electric modes at frequency below the cut-off frequency of the hollow waveguide by inserting different kinds of anisotropic metamaterials (AMMs) in the hollow waveguide. Such transmission of EM energy has no lower cut-off frequency and is due to the conversion of the evanescent wave into propagating mode inside the AMMs, which is quite different from that in the case of waveguide loaded with an isotropic left-handed material slab. We have verified the extraordinary phenomenon by performing circuit analog of the planar waveguide loaded with different kinds of AMMs through realization with transmission line metamaterials.
We have studied the electromagnetic wave propagation in a two-dimensional anisotropic metamaterial (AMM) realized by a periodic structure composed of an anisotropically loaded transmission line (TL) network. The dispersion relation of the TL metamaterial is analysed by rigorous periodic TL theory, which shows hyperbolic dispersion surface in phase space below a certain critical frequency. We have constructed an interface between an isotropic normal medium and an AMM with a properly designed normal TL mesh and the loaded TL network, respectively, and analysed the electromagnetic wave propagation in such a system using microwave circuit simulations. We directly demonstrate the negative refraction of energy flow and the positive refraction of the wave vector, as well as the partial focusing phenomenon in such AMM, have good agreement with the theoretical prediction. When the dissipation is included in the simulation on actual microstrip line structure, we find that the dissipation in the TL metamaterial affects only the magnitude of the propagating energy, not the refraction phenomenon.
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