Spatio-temporal-spectral imaging of non-repeatable dissipative soliton dynamics

Dissipative solitons (DSs) are multi-dimensionally localized waves that arise from complex dynamical balances in far-from-equilibrium nonlinear systems and widely exist in physics, chemistry and biology. Real-time observations of DS dynamics across many dimensions thus have a broad impact on unveiling various nonlinear complexities in different fields. However, these observations are challenging as DS transitions are stochastic, non-repeatable and often strongly coupled across spatio-temporal-spectral (STS) domains. Here we report multi-dimensional (space xy+discrete time t+wavelength lambda) DS dynamics imaged by STS compressed ultrafast photography, enabling imaging at up to trillions of frames per second. Various transient and random phenomena of multimode DSs are revealed, highlighting the importance of real-time multi-dimensional observation without the need for event repetition in decomposing the complexities of DSs. Due to three-dimensional, stochastic and non-repeatable transitions of dissipative solitons, it is challenging to monitor their full dynamics. Here, the authors resolve the dynamics by wavelength and along two spatial dimensions with up to trillions of frames per second using compressed ultrafast photography.