Subdiffraction and spatial filtering due to periodic spatial modulation of the gain-loss profile

We investigate light propagation in the materials with periodically modulated gain-loss profile in both transverse and longitudinal directions with respect to the direction of light propagation. We predict the effects of self-collimation (diffraction-free propagation) of the beams, as well as the superdiffusion (spatial frequency filtering) of the beams depending on the geometry of the gain-loss lattice, and justify the predictions by numerical simulations of the paraxial wave propagation equations.