From breather solitons to chaos in an ultrafast laser: The scenario of cascading short and long-period pulsations

Dissipative breather solitons are typical manifestations of the complex gain dynamics of ultrafast lasers. As a paradigm in nonlinear dynamics, the research of dissipative breather solitons is driven by their fundamental importance and practical applications, such as in the generation of optical frequency combs. To date, there is a significant lack of research on the relationship between breather solitons and chaos in ultrafast fiber lasers, which involves extremely subtle tuning of laser parameters. Here, we provide a systematic investigation of breather solitons transitioning to chaos following the scenario of cascading short and long-period pulsations. A series of analyses, including synchronous time-frequency analysis, laser output power analysis, and maximum Lyapunov exponent analysis, cooperatively provide an unambiguous verification of the existence of chaos. In addition, numerical simulations not only well reproduced the experimental results, but also revealed the distinctive transient relaxation oscillations during the transition process of breather solitons with different breathing rhythms. Our findings may contribute to the chaotic dynamics in laser cavities and open new possibilities for promoting the applications of chaotic solitons in optical communication and storage.