  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.
