Physical systems with co-existence and interplay of processes featuring distinct spatio-temporal scales are found in various research areas ranging from studies of brain activity to astrophysics. Complexity of such systems makes their theoretical and experimental analysis technically and conceptually challenging. Here, we discover that radiation of partially mode-locked fibre lasers, while being stochastic and intermittent on short time scale, exhibits periodicity and long scale correlations over slow evolution from one round trip to another. The evolution mapping of intensity auto-correlation function allows us to reveal variety of spatio-temporal coherent structures and to experimentally study their symbiotic co-existence with stochastic radiation. Our measurements of interactions of noisy pulses over a time scale of thousands of non-linear lengths demonstrate that they have features of incoherent temporal solitons. Real-time measurements of spatio-temporal intensity dynamics are set to bring new insight into rich underlying nonlinear physics of practical active- and passive-cavity photonic systems.
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