We investigate linear and nonlinear light propagation in weakly perturbed AlGaAs slab waveguides whose fabrication induced local defects give rise to random multiple scattering. The statistical evaluation of the intensity distribution at the rear facet reveals an abundance of high-amplitude events in the linear regime, contradicting the predictions of the central limit theorem by far. In this article we propose weak successive backscattering to be a generator of high-amplitude events, while a focusing nonlinearity of the Kerr type counterintuitively diminishes them, thus effectively randomizing the intensity distribution. We support our experimental findings with numerical simulations based on the stray matrix approach introduced by Edrei et?al. [ Phys. Rev. Lett. 62, 2120 (1989) ]. This novel proposed mechanism for the formation of extreme events in the context of linear wave dynamics represents the first encounter of the phenomenon in the limit of weak scattering.
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