  We investigate the effects of weak disorder on the time evolution of a wave
packet in an array of optical waveguides with parity-symmetric evanescent
coupling and, open or periodic boundary conditions. For an open array, when the
disorder is unable to suppress the ballistic expansion, we find that the light
partially localizes to its initial waveguide and the parity-symmetric waveguide
when a single waveguide is excited. For an array with periodic boundary
condition, the light localizes in the initial waveguide and its antipodal
waveguide. Through a model where the boundaries of the array are only partially
reflective, we quantify and investigate the continuous crossover between these
two regimes. Our results show that disorder-induced localization in finite
arrays with very weak disorder is strongly affected by the boundary effects
that have been hitherto ignored.
