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We investigate the effects of weak disorder on the time evolution of a wavepacket in an array of optical waveguides with parity-symmetric evanescentcoupling and, open or periodic boundary conditions. For an open array, when thedisorder is unable to suppress the ballistic expansion, we find that the lightpartially localizes to its initial waveguide and the parity-symmetric waveguidewhen a single waveguide is excited. For an array with periodic boundarycondition, the light localizes in the initial waveguide and its antipodalwaveguide. Through a model where the boundaries of the array are only partiallyreflective, we quantify and investigate the continuous crossover between thesetwo regimes. Our results show that disorder-induced localization in finitearrays with very weak disorder is strongly affected by the boundary effectsthat have been hitherto ignored.

Interplay between boundaries and disorder in coupled optical waveguides