Optimal parameter relations to realize high-power transmission in planar waveguide filled with lossy left-handed material

In a planar waveguide filled with two-layered equal-thickness media, in which one is air and the other is a lossy left-handed medium (LHM) with the relative permittivity εr1=-(1+δ)+iγε and permeability μr1=-1/(1+δ)+iγμ, we show rigorously that extremely high power densities can be generated and transmitted along the waveguide. In such a lossy super waveguide, the poles in the relevant integrals are complex, whose real parts represent the wavenumbers of guided modes propagating along the waveguide and imaginary parts denote the attenuations of guided modes. We find that optimal values of the retardation parameter δ exist once the loss in LHM is given to make the transmitted power be maximum. Compared with the conventional air-filled waveguide, at an observation point 10 wavelengths away from the source, the transmitted power density in the lossy super waveguide can be 10000 times larger even when the loss is as high as 10-4 and the retardation is as large as -0.0085