Negative refraction and partial focusing in an anisotropic metamaterial realized by a loaded transmission line network

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 ail 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.