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Transient chaos in the self-organization of dissipative optical solitons.

| Source: Proceedings of the National Academy of Sciences of the United States of America

Transient chaos is a hallmark of complex dynamics in nonlinear systems. Governed by chaotic saddles, it manifests as short-lived yet rich chaotic behavior preceding an abrupt transition to a stable attractor. However, real-time capture and quantitative characterization of such inherently unpredictable and nonrepetitive dynamics remain challenging, obscuring their physical origins. Here, we experimentally demonstrate transient chaos during the self-organization of dissipative optical solitons in

Transient chaos is a hallmark of complex dynamics in nonlinear systems. Governed by chaotic saddles, it manifests as short-lived yet rich chaotic behavior preceding an abrupt transition to a stable attractor. However, real-time capture and quantitative characterization of such inherently unpredictable and nonrepetitive dynamics remain challenging, obscuring their physical origins. Here, we experimentally demonstrate transient chaos during the self-organization of dissipative optical solitons in a mode-locked fiber laser. By reconstructing phase-space trajectories from single-shot measurements, we quantify key dynamical invariants that confirm the deterministic nature of the underlying nonattracting chaotic set. Experimental and numerical results reveal that this complexity arises from coupled nonlinear interactions within unstable multipulse complexes. Furthermore, we identify the emergence of optical rogue waves with extreme amplitudes during the chaotic transient regime. Our results bridge the conceptual gap between optical chaos and mode-locking coherence, providing both an analytical framework and a versatile experimental platform for probing and manipulating transient chaotic dynamics in high-dimensional dissipative systems.

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