We first investigate the propagation of an initially localized optical beam through an ordered waveguide array in which the real part of the refractive index of all waveguides is the same, while there is a linear gradient loss along the transverse direction . When the optical loss is an increasing function of , the beam injected into every point of the array propagates to the left edge of the array. But for the case at which optical loss is a decreasing function of , the optical beam propagates to the right edge of the array. In both cases, as the beam reaches the array edge, it is first reflected by the edge due to the presence of a repulsive potential near the array boundary, and then its width remains constant. We next study the wave propagation through a disordered array of waveguides in which the real parts of the refractive indices of waveguides are random numbers, and there exists a transverse loss gradient. For different random realizations with the same disorder level, when the beam is injected into the central waveguide, the beam becomes localized near the array edge with the lower loss.
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