Light propagation in synthetic pseudo-passive media with balanced gain and loss

Optical materials exhibiting exotic values of permittivity $\varepsilon $ and/or permeability $\mu $ are often prohibitively lossy. This is especially true for composite optical metamaterials. A natural solution to the problem is to add a gain component and, thereby, to offset the losses. There are two different ways to do so. The first one involves a photonic structure composed of judiciously arranged loss and gain components. A well-known example of such balanced loss-gain structures is the so-called PT symmetric photonic crystals. An alternative approach is to compensate the losses with gain while preserving uniformity of the medium. Here we consider this second case where both constituents are complex such that $\varepsilon =\varepsilon $'$+$i$\varepsilon $''; $\mu =\rho^{2}\varepsilon $* with $\rho $ being real. In this case the material would have a uniform real refractive index n$=\surd \varepsilon \mu =$n*. We demonstrate that this type of pseudo-passive synthetic structures show novel transport characteristics uncommon to regular lossless structures.