Effect of loss on transverse localization of light in 1D optical waveguide array in the presence of Kerr-type nonlinearity

In this paper we have comprehensive study on the interplay among radiation loss, transverse disorder (diagonal and off-diagonal) and Kerr-type nonlinearity on the light propagation in 1D array of optical waveguides. Our numerical results demonstrate the presence of three distinguished regimes of transverse light expansion at different propagation distances. At short propagation distance, the Kerr-type nonlinearity are dominated and results in the transverse localization of light through the self-trapping mechanism. Radiation loss, causes the light escape from the injected guides, affect the light expansion in middle distance via broadening the light beam width. At longer distance the disorder terms led to the transverse localization of light, again. Also, we compared the propagation of light in edge and middle modes in the presence of the above effects. Our results show that the propagation distance of first localized regime for edge modes is larger than the middle modes since the edge modes can exchange energy with one of the left or right waveguides, while for middle modes there are two ways for energy exchange. Therefore the discrete diffraction can be diminished the nonlinear effects in middle modes faster than the edge modes.