Research has shown that passively mode-locked fiber lasers produce chaotic output, which has caught the attention of physicists, chemists, and bio-scientists owing to their wide bandwidth, good random characteristics, and strong anti-interference. In passively mode-locked fiber lasers, soliton pulsations and soliton explosions with period bifurcation characteristics have been demonstrated to be effective paths to chaos as far as 20 years ago. However, due to the lack of real-time spectrum measurement techniques, the earlier research investigated their theoretical aspect. In recent years, the rise of the dispersive Fourier transform technique has activated an upsurge of their experimental research. The present work first discussed the theoretical model of passively mode-locked fiber lasers, the computational analysis method of soliton dynamics, and the related theory of dispersive Fourier transform technique. In addition, we presented and evaluated the progress of the theoretical and experimental research on soliton pulsations as well as on soliton explosions in passively mode-locked fiber lasers. Finally, we proposed the future research directions of the soliton pulsations and soliton explosions that offer great promise for scientific discoveries.

2D MBenes, the latest derivatives of bulk ternary or quaternary transition metal boride (MAB) phases, have gradually attracted increasing research attention as novae in the flatland. However, the fabrication of MBenes is still a great challenge at present, leading to the lack of reported MBene applications in the photonic field (e.g., ultrafast lasers). Hence, we successfully fabricated few-layer Mo 4/3 B 2−x T z MBenes by selectively etching nanolaminated 3D parent boride (Mo 2/3 Y 1/3 ) 2 AlB 2 . Density functional theory calculations were used to theoretically analyze its electronic and optical properties. By employing the Z-scan technique, the nonlinear absorption characteristics of Mo 4/3 B 2−x T z MBenes from the visible to mid-infrared regime were revealed for the first time. Compared with mainstream 2D materials and common MXenes, Mo 4/3 B 2−x T z has more potential as a nonlinear optical (NLO) material, such as stronger nonlinear absorption (about 100 times of graphene) and lower saturation intensity (about 1% of black phosphorus). Furthermore, by integrating Mo 4/3 B 2−x T z as a saturable absorber (SA) into three similar gain fiber-based laser resonators, broadband stable ultrafast pulses were obtained with pulse durations of 358.7 ps (1 μm), 582.3 fs (1.5 μm), and 2.31 ps (2 μm). Innovation in MBenes as SA will allow the design of novel photonic systems and devices with broadband functionality, opening a promising paradigm for the conscious design of high-performance NLO materials.