Super energy flows in a waveguide filled with air and left-handed materials

The phenomena of super energy flows are studied theoretically and numerically in a parallel-plate waveguide which is filled with two layered equally-thick different media, i.e. air and specific left-handed materials (LHM) with $\epsilon_{\rm r1}=-1/(1+\delta)+{\rm i}\gamma$ and $\mu_{\rm r1}=-(1+\delta)+{\rm i}\gamma$. In this special waveguide, two-directional super-energy flows are excited by a three-dimensional horizontal electric dipole at the same time, which has transmission patterns different from those of two-dimensional source and three-dimensional vertical electric dipole. We also show that the retardation and loss in LHM are sensitive to the amplitude of super power densities, and the dimensions of waveguide determine the propagating modes, which makes super energy flows more practical.