Interplay of disorder and PT symmetry in one-dimensional optical lattices

We study a one-dimensional binary optical lattice in the presence of diagonal disorder and alternating gain and loss, and examine the light transport phenomena for localized and extended input beams. In the pure PT-symmetric case, we derive an exact expression for the behavior of light localization in terms of typical parameters of the system. Within the PT-symmetric region light localization becomes constant as a function of the strength of the gain and loss parameter, but outside the PT-symmetric window, light localization increases as the gain and loss parameter increases. When disorder is added, we observe that the presence of gain and loss inhibits (favors) the transport for localized (extended) excitations.