Gain/loss periodic spatial modulated materials on a wavelength scale

We predict self-collimation and superdiffusion of light propagating in materials with periodically modulated gain/loss profile. The modulation is parallel and transverse to the light propagation direction and its periodicity is on the wavelength scale. The self-collimation (or diffraction-free propagation) of the beams is found, which is similar to that observed in photonic crystals. The superdiffusion is also predicted, which means a dependence of the beam amplification on the propagation direction, which results in the spatial frequency filtering of the beams. We justify the predictions by the numerical simulations of the paraxial wave propagation equations.