Subharmonic Entrainment Breather Solitons in Ultrafast Lasers

Linear-coupling-induced double-period pulsating vector solitons in lasers

Pulsating solitons is a universal phenomenon originating from the Hopf-type bifurcation in dissipative systems such as lasers and microresonators. Here, we report the vector soliton in a fiber laser pulsating with two periods of different orders of magnitude. The short-period pulsation manifests as the period-tripling facilitated by the linear coupling between orthogonal polarization components, which breaks the self-consistent evolution of the vector soliton over a single round trip (RT). The long-period pulsation arises from the mode competition between the two polarization components mediated by various cavity effects. The interplay between linear coupling and mode competition gives rise to the robust double-period pulsating (DPP) vector soliton. Our results provide a clear physical mechanism for the broadly observed double-period breather, which has a significant value in exploring breathers with complex dynamics and multiple comb spectroscopy.

The dissipative Talbot soliton fiber laser

Talbot effect, characterized by the replication of a periodic optical field in a specific plane, is governed by diffraction and dispersion in the spatial and temporal domains, respectively. In mode-locked lasers, Talbot effect is rarely linked with soliton dynamics since the longitudinal mode spacing and cavity dispersion are far away from the self-imaging condition. We report switchable breathing and stable dissipative Talbot solitons in a multicolor mode-locked fiber laser by manipulating the frequency difference of neighboring spectra. The temporal Talbot effect dominates the laser emission state-in the breathing state when the integer self-imaging distance deviates from the cavity length and in the steady state when it equals the cavity length. A refined Talbot theory including dispersion and nonlinearity is proposed to accurately depict this evolution behavior. These findings pave an effective way to control the operation in dissipative optical systems and open branches in the study of nonlinear physics.

Revealing of long-range soliton interaction induced time and phase dynamics in a mode-locked fiber laser

By means of the dispersive temporal interferometry technique, we carried out a real-time observation of the time separation and relative phase evolutions of two pulses toward harmonic mode-locking. During the separation stage of the buildup process, the time separation increases, while the relative phase decreases synchronously, and the largest change rates are 0.247 fs/r and -0.017 rad/r, respectively. Meanwhile, the two rates show a linear relation with the former 17.4 times larger than the latter. Moreover, a residual phase change rate of -3.89 × 10-4 rad/r is observed in a steady non-uniform dual-soliton state, while such phase change is absent in a uniform four-soliton state. This study unveils the soliton interaction dynamics in lasers, which not only help to reduce timing jitter in multi-soliton mode-locking, but also bring insight to a temporal tweezing of femtosecond pulse.

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.

Real-time revealing of Cherenkov radiation evolution in optical fibers

The generation of Cherenkov radiation (CR) is determined by the phase-matching condition, but the experimental observation on the phase change of its transient process is still incomplete. In this paper, we use the dispersive temporal interferometer (DTI) technique to real-time reveal the buildup and evolution of CR. Experiments show that when the pump power varies, the phase-matching conditions also change, which is mainly affected by the nonlinear phase shift caused by the Kerr effect. Further simulation results propose that both pulse power and pre-chirp management have a significant impact on phase-matching. The CR wavelength can be shortened and the generation position can be moved forward by adding a suitable positive chirp or increasing the incident peak power. Our work directly reveals the evolution of CR in optical fibers and provides a method for optimizing it.

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

Bound states of solitons ("molecules") occur in various settings, playing an important role in the operation of fiber lasers, optical emulation, encoding, and communications. Soliton interactions are generally related to breathing dynamics in nonlinear dissipative systems, and maintain potential applications in spectroscopy. In the present work, dichromatic breather molecules (DBMs) are created in a synchronized mode-locked fiber laser. Real-time delay-shifting interference spectra are measured to display the temporal evolution of the DBMs, that cannot be observed by means of the usual real-time spectroscopy. As a result, robust out-of-phase vibrations are found as a typical intrinsic mode of DBMs. The same bound states are produced numerically in the framework of a model combining equations for the population inversion in the mode-locked laser and cross-phase-modulation-coupled complex Ginzburg-Landau equations for amplitudes of the optical fields in the fiber segments of the laser cavity. The results demonstrate that the Q-switching instability induces the onset of breathing oscillations. The findings offer new possibilities for the design of various regimes of the operation of ultrafast lasers.

Unveiling the complexity of spatiotemporal soliton molecules in real time

Observing the dynamics of 3D soliton molecules can hold great opportunities for unveiling the mechanism of molecular complexity and other nonlinear problems. In spite of this fantastic potential, real-time visualization of their dynamics occurring on femtosecond-to-picosecond time scales is still challenging, particularly when high-spatiotemporal-resolution and long-term observation are required. In this work, we observe the real-time speckle-resolved spectral-temporal dynamics of 3D soliton molecules for a long time interval using multispeckle spectral-temporal measurement technology. Diverse real-time dynamics of 3D soliton molecules are captured for the first time, including the speckle-resolved birth, spatiotemporal interaction, and internal vibration of 3D soliton molecules. Further studies show that nonlinear spatiotemporal coupling associated with a large average-chirp gradient over the speckled mode profile plays a significant role in these dynamics. These efforts may shed new light on decomposing the complexity of 3D soliton molecules, and create an analogy between 3D soliton molecules and chemical molecules.

Dynamics of pulsating solitons derived from asymmetrical dispersive waves

Pulsating soliton (PS) as a local structure of nonlinear systems has induced substantial interest in nonlinear photonics and ultrafast lasers. However, the interaction mechanism between PSs has not been fully studied. Here, the vital role of the asymmetric dispersive wave (DW) in PSs interaction is investigated for the first time. Based on the complex Ginzburg-Landau equation (CQGLE), we find that the asynchronous pulsating soliton molecule (PSM) composed of strong PSs and weak PSs will produce frequency shift due to the asymmetric DW, and the state of the PS can be transferred through the DW during the collision between PSs and PSM. Moreover, we firstly characterize the PS with asymmetric DW in experiment, and observe the drift of PSM, which agree with our simulation that the asymmetric DW can cause the frequency shift of PSMs. Our results provide new insights into the multi soliton interaction of nonlinear systems.

Farey tree and devil's staircase of frequency-locked breathers in ultrafast lasers

Nonlinear systems with two competing frequencies show locking or resonances. In lasers, the two interacting frequencies can be the cavity repetition rate and a frequency externally applied to the system. Conversely, the excitation of breather oscillations in lasers naturally triggers a second characteristic frequency in the system, therefore showing competition between the cavity repetition rate and the breathing frequency. Yet, the link between breathing solitons and frequency locking is missing. Here we demonstrate frequency locking at Farey fractions of a breather laser. The winding numbers exhibit the hierarchy of the Farey tree and the structure of a devil's staircase. Numerical simulations of a discrete laser model confirm the experimental findings. The breather laser may therefore serve as a simple test bed to explore ubiquitous synchronization dynamics of nonlinear systems. The locked breathing frequencies feature a high signal-to-noise ratio and can give rise to dense radio-frequency combs, which are attractive for applications.

Facile Synthesis of Monodispersed Titanium Nitride Quantum Dots for Harmonic Mode-Locking Generation in an Ultrafast Fiber Laser

As a member of the transition metal nitride material family, titanium nitride (TiN) quantum dots (QDs) have attracted great attention in optical and electronic fields because of their excellent optoelectronic properties and favorable stability. Herein, TiN QDs were synthesized and served as a saturable absorber (SA) for an ultrafast fiber laser. Due to the strong nonlinear optical absorption characteristics with a modulation depth of ~33%, the typical fundamental mode-locked pulses and harmonics mode-locked pulses can be easily obtained in an ultrafast erbium-doped fiber laser with a TiN-QD SA. In addition, at the maximum pump power, harmonic mode-locked pulses with a repetition rate of ~1 GHz (164th order) and a pulse duration of ~1.45 ps are achieved. As far as we know, the repetition rate is the highest in the ultrafast fiber laser using TiN QDs as an SA. Thus, these experimental results indicate that TiN QDs can be considered a promising material, showing more potential in the category of ultrafast laser and nonlinear optics.

Transition between noise-like pulses and Q-switching in few-mode mode-locked lasers

Spatiotemporal mode-locked lasers have attracted extensive attention of researchers due to the complex nonlinear evolution process. Compared to single-mode mode-locked lasers, intermodal interactions greatly affect the pulses evolution in spatiotemporal mode-locked lasers. Here, we experimentally investigate the transition process between noise-like pulses and Q-switching pulses in few-mode mode-locked laser by rotating the plates, where a transition state is greatly broadened in the time domain. By means of spectral filtering, we verify that the process is the reconstruction of Q-switching between different modes to noise-like pulses. Furthermore, during the evolution of noise-like pulses, soliton collisions are detected using dispersive Fourier transform technology. Our research contributes to revealing the transient evolution process in few-mode mode-locked lasers, and enriches the study of nonlinear process.

Real-time observation of phase transition of bifurcation evolution in mode-locked lasers

By using the dispersive temporal holography technology, we observe the real-time dynamics of period-doubling bifurcation evolution in an ultrafast fiber laser. The pulse properties including the phase, polarization state, chirp, pulse width, and pulse energy are fully bifurcated, which embody the bifurcation induced "phase transition." There are two types of bifurcation in the laser buildup: one to many bifurcation towards the chaos and the multiple bifurcated pulses back to the stationary state along the reversed trajectory. Both of them can be explained by the rule of the same phase transition. We conclude and illustrate the differences and connections to another common pulsation, the Hopf bifurcation. The findings can promote an understanding of the bifurcations in ultrafast lasers, and are beneficial for an improvement of laser stability.

All-optical dissipative discrete time crystals

Time crystals are periodic states exhibiting spontaneous symmetry breaking in either time-independent or periodically-driven quantum many-body systems. Spontaneous modification of discrete time-translation symmetry in periodically-forced physical systems can create a discrete time crystal (DTC) constituting a state of matter possessing properties like temporal rigid long-range order and coherence, which are inherently desirable for quantum computing and information processing. Despite their appeal, experimental demonstrations of DTCs are scarce and significant aspects of their behavior remain unexplored. Here, we report the experimental observation and theoretical investigation of DTCs in a Kerr-nonlinear optical microcavity. Empowered by the self-injection locking of two independent lasers with arbitrarily large frequency separation simultaneously to two same-family cavity modes and a dissipative Kerr soliton, this versatile platform enables realizing long-awaited phenomena such as defect-carrying DTCs and phase transitions. Combined with monolithic microfabrication, this room-temperature system paves the way for chip-scale time crystals supporting real-world applications outside sophisticated laboratories.

Discrete time crystals are described by a subharmonic response with respect to an external drive and have been mostly observed in closed periodically-driven systems. Here, the authors demonstrate a dissipative discrete time crystal in a Kerr-nonlinear optical microcavity pumped by two lasers.

Synthesis of Hexagonal Structured GaS Nanosheets for Robust Femtosecond Pulse Generation

Gallium sulfide (GaS), with a hexagonal structure, has received extensive attention due to its graphene-like structure and derived optical properties. Here, high-quality GaS was obtained via chemical vapor synthesis and then prepared as a saturable absorber by the stamp-assisted localization-transfer technique onto fiber end face. The stability of the material and the laser damage threshold are maintained due to the optimized thickness and the cavity integration form. The potential of the GaS for nonlinear optics is explored by constructing a GaS-based Erbium-doped mode-locked fiber laser. Stable femtosecond (~448 fs) mode-locking operation of the single pulse train is achieved, and the robust mode-locked operation (>30 days) was recorded. Experimental results show the potential of GaS for multi-functional ultrafast high-power lasers and promote continuous research on graphene-like materials in nonlinear optics and photonics.

Anomalous slowdown of pump light in Raman fiber lasers

Usually, the pump light in lasers should perform fast light owing to operating in the absorption band. In this study, we observe and demonstrate anomalous slowdown of the pump light in a Raman fiber laser. Experiments show that the pump light can be slowed down to sub-nanoseconds at a repetition rate of 50-500 MHz. Theoretical analysis shows that the hole-burning effect is formed at the Raman gain spectrum in the saturation regime, which imposes on the pump light by normal dispersion. Consequently, the pump light experiences an unusual slow light effect rather than the fast light effect after absorption. We believe it has promising potentials in the improvement of ultrashort pulse generation, and may have significant influence on improving the conversion efficiency in pulse-pumped laser systems.