Lévy flight of superdiffusive light in coupled waveguide lattices

Exotic light behavior in certain disordered one-dimensional optical waveguide lattices with selectively doped gain/loss operating away from the PT symmetry regime is reported. Here, we establish that such open systems host a unique Lévy flight even in the absence of scatterers following Lévy distribution. Owing to the interplay between gain/loss and disorder, the critical transition distance from the ballistic to diffusive domain is reduced and also a superdiffusive propagation distance has been revealed after a certain propagation distance. The stable propagation characteristics of light have been investigated in the form of an intensity distribution for various gain/loss levels, effective beam width variation with length, the center of mass dynamics, and the probability density function. A qualitative analysis indicates that such fabrication feasible lattices may host disordered lasing in the form of a Lévy-type distribution in the output intensity and may also find applications in image transport.