Self-collimated beams in 2D complex periodic lattices from P- to PT-symmetry

We analyze self-collimation in two-dimensional periodic complex lattices. We consider P-symmetric and PT-symmetric complex lattices with different geometries, where the periodic modulations of both refractive index and gain-loss are either in-phase, or dephased a quarter of wavelength of the modulation. The non-diffractive propagation of light beams is analytically predicted using coupled mode approach and further confirmed by numerical integration of a paraxial model.