Beam dynamics in disordered PT-symmetric optical lattices based on eigenstate analyses

Wave functions will experience a localization process when evolving in disordered lattices. Here, we have demonstrated the effects of disordered $\mathcal{P}\mathcal{T}$-symmetric potentials on wave-function characteristics in optics based on eigenstate analyses. In weak-disorder cases, by using the tight-binding approximation method, a conclusion is obtained that the increasing of the imaginary part of potential can enhance the diffraction, while the increasing disorder will block the diffraction and lead to localization. In the general case, band theory is used for band-structure analysis of three bands. We find that the disorder has a smaller effect on the higher-order band, which is proved by the beam evolutions. Our work may be instructive for realizing beam path control by manipulating the strengths of disorder and gain and/or loss of lattice.