Interplay of disorder and $\mathcal{PT}$-symmetry

We examine a one-dimensional $\mathcal{PT}$-symmetric binary lattice in the presence of diagonal disorder. We focus on the wave transport phenomena of localized and extended input beams for this disordered system. In the pure $\mathcal{PT}$-symmetric case, we derive an exact expression for the evolution of light localization in terms of the typical parameters of the system. In this case localization is enhanced as the gain and loss parameter in increased. In the presence of disorder, we observe that the presence of gain and loss inhibits (favors) the transport for localized (extended) excitations.