Ultrafast breather lasers and fractal routes to chaos

ABSTRACT

Ultrafast breathing-soliton laser was demonstrated as a platform for studying synchronization within a single laser oscillator. We developed a unified theoretical model for breather lasers, which clarifies distinct formation mechanisms under net-normal and near-zero cavity dispersion. This framework accounts for experimentally observed differences in pump-power accessibility relative to stationary mode locking, oscillation periods, spectral profiles, and synchronization behavior across the two dispersion regimes. In parallel, genetic algorithms were demonstrated as an effective strategy for exploring such complex experimental parameter spaces. This approach enables self-optimization of breather lasers and facilitates access to new dynamical regimes, including fractal frequency-locked breathers and super-rogue-wave structures. We further revealed multiple novel phenomena of synchronization dynamics, such as anomalous Arnold tongues, modulated subharmonics, and fractal frequency combs. Sequential modulated subharmonics ultimately evolute to chaotic state and were theoretically identified a newly-found fourth route to chaos, presenting an indisputable answer to the long-exploring fundamental question: “Are there other relatively universal routes to chaos” beyond the conventional framework that only three universal routes have been recognized over half a century: the Ruelle-Takens scenario (quasi-periodicity route), the Feigenbaum scenario (period-doubling route), and the Pomeau-Manneville scenario (intermittency route), paving a way for further theoretical and experimental exploration on nonlinear complexity and critical phenomena. Together, these findings enhance our understanding of nonlinear dissipative systems and reinforce mode-locked fiber lasers as a versatile testbed for investigating complex dynamics.

BIOGRAPHY

Heping Zeng is a professor at East China Normal University. He received his BS degree from Peking University in 1990, PhD from the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences in 1995. His research mainly focuses on precision measurements and quantum detection. He is a Fellow of Optica and Foreign member of Academia Europaea.