Wave propagation through photonic waveguide lattices in the presence of optical gain and loss.

We investigate the effects of gain and loss on the light propagation through a lattice of coupled optical waveguides. We demonstrate that superdiffusive transport becomes diffusive in the presence of optical loss after a critical propagation distance as in [Phys. Rev. Lett.113, 123903 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.123903]. However, when optical gain is introduced in the lattice of coupled waveguides, the beam broadening slows down from a superdiffusive to a highly subdiffusive regime after another critical distance. The critical distance decreases with increase of loss or gain in the waveguide lattice. For equal gain and loss, the value of critical distance in the array of active waveguides is much smaller than that in the case of lattice of lossy waveguides. Furthermore, we find that the effective width in the case of lossy waveguides decreases with increase of loss at the same propagation distance. Our results confirm that the regime of beam broadening does not depend on whether the gain is introduced in the waveguides or in their surroundings.