Self-collimation in 2D complex and PT-symmetric media

We study propagation light beams in 2D photonic periodic nanostructures with both index and gain/loss modulations. We determine the conditions for complex periodic media with in-phase gain and index modulations to support self-collimation, non-diffractive propagation, with simultaneous non-diffusive broadening of the beam. We also analyze self-collimation in media where index and gain modulations are dephased by a quarter of the spatial period, hence being PT-symmetric. The propagation properties of such PT-symmetric complex media may be reduced to two limiting cases, either to a Photonic Crystal case with a pure index modulation or to a pure gain modulated media, at each side of the PT-transition condition.