We present an experimental study on light propagation within a bulk material, wherein a controlled, weakly disordered, three-dimensional spatial fluctuation of the refractive index is induced. We find that the random, varying potential splits a broad wave into a stable, two-dimensional (2D) caustic network, which persists over extended evolution distance. This network remains stable until 2D branched light flow emerges from the interconnection spots of the network. We thus demonstrate the first-ever observation of the stable two-dimensional branched flow of light and experimentally identify the fundamental length scale at which the two-dimensional branching initiates, as well as its power-law dependence on the correlation length and the strength of the random potential.

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• Light propagation in random media