Dichromatic "Breather Molecules" in a Mode-Locked Fiber Laser

Temporal and spatiotemporal soliton molecules in ultrafast fibre lasers

Ultrafast fibre lasers, characterized by ultrashort pulse duration and broad spectral bandwidth, have drawn significant attention due to their vast potential across a wide range of applications, from fundamental scientific to industrial processing and beyond. As dissipative nonlinear systems, ultrafast fibre lasers not only generate single solitons, but also exhibit various forms of spatiotemporal soliton bunching. Analogous to molecules composed of multiple atoms in chemistry, soliton molecules (SMs) - alias bound states - in ultrafast fibre lasers are a key concept for gaining a deeper understanding of nonlinear interaction and hold a promise for advancing high-capacity fibre-optic communications. SMs are particularly notable for their high degree of controllability, including their internal temporal separation, and relative phase differences, thereby suggesting new possibilities for manipulating multi-pulse systems. In this review, we provide a comprehensive overview of recent advancements in the studies of SMs with the multidimensional parameter space in ultrafast fibre lasers. Owing to the flexibility afforded by mode-locking techniques and dispersion management, various types of SMs - with diverse values of the soliton number, relative phase, pulse separation, carrier frequencies, and even modal dispersion - have been experimentally demonstrated. We also discuss other basic nonlinear optical phenomena observed in fibre lasers, including the formation, spatiotemporal pulsations, and interaction dynamics of SMs. Furthermore, we explore the multidimensional control of SMs through approaches such as gain modulation, polarization control, dispersion management, and photomechanical effects, along with their applications to optical data encoding. Finally, we discuss challenges and future development of multidimensional technologies for the manipulation of SMs.

Unveiling the complexity of Arnold's tongues in a breathing-soliton laser

Synchronization occurs ubiquitously in nature and science. The synchronization regions generally broaden monotonically with the strength of the forcing, thereby featuring a tongue-like shape in parameter space, known as Arnold's tongue. Such a shape is universal, prevailing in many diverse synchronized systems. Theoretical studies suggest that, under strong external forcing, the shape of the synchronization regions can change substantially and even holes can appear in the solid patterns. However, experimentally accessing these abnormal regimes is quite challenging mainly because many real-world systems displaying synchronization become fragile under strong forcing. Here, we are able to observe these intriguing regimes in a breathing-soliton laser. Two types of abnormal synchronization regions are unveiled, namely, a leaf- and a ray-like shape. High-resolution control of the loss allows holes to be revealed in the synchronization regions. Our work opens the possibility to study intriguing synchronization dynamics using a simple breathing-soliton laser as a test bed.

Quantum diffusion of pure-quartic solitons in a laser cavity

Ultrashort pulses experience random quantum motion as they propagate through a mode-locked laser cavity, a phenomenon that inevitably affects the recently introduced pure-quartic solitons. Investigating this process is essential, as quantum-limited noise establishes fundamental performance limits for their application. To date, studies on quantum diffusion and the resulting timing jitter of these solitons remain sparse. In this work, we examine the quantum motion of pure-quartic solitons by injecting amplified spontaneous emission noise into the gain medium, measuring their relative position, and performing analyses using Allan variance and timing jitter power spectral density. Our simulation findings reveal that long-range interactions due to pulse tailing can lead to high-frequency noise, which can be effectively filtered out. In the near-zero dispersion regime, we achieve quantum-limited noise levels significantly less than 1 fs. Good agreement is observed between the analytical model and the simulation results. This work provides insights into the noise levels and mechanisms of pure-quartic solitons and can be extended to more complex scenarios, such as pure-quartic Kerr solitons, and studies on the dynamics of higher-order dispersion solitons.

Observation of Optical Chaotic Solitons and Modulated Subharmonic Route to Chaos in Mode-Locked Laser

We reveal a new scenario for the transition of solitons to chaos in a mode-locked fiber laser: the modulated subharmonic route. Its universality is confirmed in two different laser configurations, namely, a figure-of-eight and a ring laser. Numerical simulations of the laser models agree well with the experiments. The modulated subharmonic route to chaos could stimulate parallel research in many nonlinear physical systems.

From breather soliton molecules to chaos in a laser cavity: the scenario of intermittent transitions

Intermittency is widely observed in various nonlinear dynamical systems as an intriguing transient dynamic far from equilibrium. The internal dynamics formed by a pair of interacting optical solitons are often analogized to typical nonlinear systems. However, whether intermittency exists within the intramolecular motion remains to be investigated. Here, we study the intermittent dynamics of soliton molecules in ultrafast lasers, employing balanced optical cross-correlation techniques with sub-femtosecond temporal resolution. We demonstrate the occurrence of the bursting phase of intense variations of pulse separation within regular breather rhythms. In addition, we discover the intermittent transitions route to chaotic soliton molecules, facilitated by gain control. A series of analysis methods are used to assess the chaotic signals, providing compelling experimental evidence that soliton molecules can be analogized to their matter molecule counterparts. Our experimental findings shed light on the non-equilibrium intramolecular dynamics, providing insight into the transition of the attractors within interacting dissipative solitons in laser and fiber resonators.

Phase-locked and phase-unlocked multicolor solitons in a fiber laser

Multicolor solitons are nonlinear pulses composed of two or more solitons centered at different frequencies, propagating with the same group velocity. In the time domain, multicolor solitons consist of an envelope multiplying a more rapidly varying fringe pattern that results from the interference of these frequency components. Here, we report the observation in a fiber laser of a novel, to the best of our knowledge, type of dynamics in which different frequency components still have the same group velocity but have different propagation constants. This causes the relative phases between the constituent spectral components to change upon propagation, corresponding to the fringes moving under the envelope. This leads to small periodic energy variations that we directly measure. Our experimental results are in good agreement with realistic numerical simulations based on an iterative cavity map.

Synchronization, Desynchronization, and Intermediate Regime of Breathing Solitons and Soliton Molecules in a Laser Cavity

We report on the experimental and numerical observations of synchronization and desynchronization of bound states of multiple breathing solitons (breathing soliton molecules) in an ultrafast fiber laser. In the desynchronization regime, although the breather molecules as wholes are not synchronized to the cavity, the individual breathers within a molecule are synchronized to each other with a delay (lag synchronization). An intermediate regime between the synchronization and desynchronization phases is also observed, featuring self-modulation of the synchronized state. This regime may also occur in other systems displaying synchronization. Breathing soliton molecules in a laser cavity open new avenues for the study of nonlinear synchronization dynamics.

Decaying dynamics of harmonic mode-locking in a SESAM-based mode-locked fiber laser

The entire decaying dynamics of harmonic mode-locking (HML) are studied utilizing the dispersive Fourier transform (DFT) technique in a SESAM-based mode-locked fiber laser. It is unveiled that the harmonic solitons do not disappear directly, but undergo transitional processes from the higher-order HML to the lower-order HML and then to the fundamental mode-locking (FML), and finally vanish. The "big corner" can also exist in the decaying process rather than just in the buildup process of HML, and there is at least one "big corner" during the decaying process between the consecutive multi-pulsing states. The energy stabilization phase (ESP) cannot be observed during every transitional process. A breathing behavior and a vibrating soliton molecule are observed in the decaying process from the 2nd HML to the FML and in the decaying process of the FML, respectively. Our work would enrich the understanding of HML behaviors and may contribute to the laser designs.

Photonic molecule state transition by collision

We investigate the impact of collisions with two-frequency photonic molecules aiming to observe internal dynamic behavior and challenge their strong robustness. Versatile interaction scenarios show intriguing state changes expressed through modifications of the resulting state such as temporal compression and unknown collision-induced spectral tunneling. These processes show potential for efficient coherent supercontinuum generation and all-optical manipulation.