Long-range speckle correlations play an essential role in wave transport through disordered media, but have rarely been studied in other complex systems. Here we discover spatio-temporal intensity correlations for an optical pulse propagating through a multimode fiber with strong random mode coupling. Positive long-range correlations arise from multiple scattering in fiber mode space and depend on the statistical distribution of arrival times. By optimizing the incident wavefront of a pulse, we maximize the power transmitted at a selected time, and such control is significantly enhanced by the long-range spatio-temporal correlations. We provide an explicit relation between the correlations and the enhancements, which closely agrees with experimental data. Our work shows that multimode fibers provide a fertile ground for studying complex wave phenomena, and the strong spatio-temporal correlations can be employed for efficient power delivery at a well-defined time.
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