Observation of soliton molecules in a spatiotemporal mode-locked multimode fiber laser

Transverse mode switchable mode-locked laser with narrow bandwidth

Transverse mode switchable ultrashort optical pulses with narrow bandwidths can create potential for exploring what we believe are new physical effects. We demonstrate the generation of transverse mode switchable ultrashort pulses with narrow bandwidths in an all-fiber mode-locked laser by exploring a mode-selective photonic lantern (MSPL). The laser cavity serves not only as a ring resonator but also as an intrinsic spectral filter. For mode-locking with the LP01, LP11a, and LP11b modes, the bandwidths are 3.0 nm, 86.7 pm and 101.7 pm, respectively. The narrowband pulses with higher-order modes are generated by an intrinsic spectral filter due to the spectral-domain intermodal interference. Mode-locked pulses with a signal-to-noise ratio better than 60 dB for LP01, LP11a, and LP11b modes are independently generated, i.e., transverse mode switchable by changing the input port of the MSPL. The mode-locked wavelength can be tuned for the LP11a mode and LP11b mode by adjusting the state of polarization. Furthermore, our experimental results also show that, the slope efficiency of LP11a and LP11b modes can be improved, by the use of LP11 mode pump scheme. We anticipate that, narrowband pulses with complex mode profiles can be generated by simultaneously phase-locked transverse and longitudinal modes.

Spatiotemporal dual-periodic soliton pulsation in a multimode fiber laser

Spatiotemporal mode-locked (STML) fiber lasers have become a new platform for investigating nonlinear phenomena. In this work, spatiotemporal dual-periodic soliton pulsation (SDSP) is firstly observed in an STML fiber laser. It is found that in the SDSP, the long-period pulsations (LPPs) of different transverse modes are synchronous, while the short-period pulsations (SPPs) exhibit asynchronous modulations. The numerical simulation confirms the experimental results and further reveals that the proportion of transverse mode components can manipulate the periods of the LPP and SPP but does not affect the synchronous and asynchronous pulsations of different transverse modes. The obtained results bring the study of spatiotemporal dissipative soliton pulsation into the multi-period modulation stage, which helps to understand the complex spatiotemporal dynamics in STML fiber lasers and discover new dynamics in high-dimensional nonlinear systems.

Wavelength-tunable spatiotemporal mode-locking in a large-mode-area Er:ZBLAN fiber laser at 2.8 µm

We report a tunable spatiotemporally mode-locked large-mode-area Er:ZBLAN fiber laser based on the nonlinear polarization rotation technique. A diffraction grating is introduced to select the operating wavelength. Under the spectral and spatial filtering effects provided by the grating and spatial coupling respectively, stable ps-level spatiotemporally mode-locked pulses around 2.8 µm with a repetition rate of 43.4 MHz are generated. Through a careful adjustment of the grating, a broad wavelength tuning range from 2747 to 2797 nm is realized. To the best of our knowledge, this is the first wavelength-tunable spatiotemporally mode-locked fiber laser in the mid-infrared region.

Diverse mode operation fiber laser mode-locked by nonlinear multimode interference

We present an all-fiber passively mode-locked (ML) laser with a nonlinear multimode interference (NLMI)-based saturable absorber (SA) capable of generating five pulse modes. The SA consists of two centrally aligned graded index multimode fiber (GIMF) with different diameters (105-50 µm) and features a widely adjustable transmission with saturable/reverse-saturable absorption. Based on this, dissipative soliton (DS), Q-switched rectangular pulse (QRP), dissipative soliton resonance (DSR), noise-like pulse (NLP) and bright-dark pulse pairs (BDP) are observed at three dispersions without additional filter. The DS has a pulse energy, bandwidth and duration of up to 1.15 nJ, 17.98 nm and ∼2.78 ps. The achievable pulse duration and energy of DSR and NLP are 5.21, 48.06 ns and 4.53, 5.12 nJ, respectively. Furthermore, it is demonstrated that the BDP is superimposed by a chair-case pulse (CP) and a rectangular pulse (RP) belonging to orthogonal polarization states. The versatility, flexibility, simplicity and energy scalability of the large-core hybrid GIMF-SA, make it interesting and highly attractive in ultrafast photonics.

Periodically tunable multimode soliton pulsation in a spatiotemporal mode-locked fiber laser

Multimode fiber lasers have become a new platform for investigating nonlinear phenomena since the report on spatiotemporal mode-locking. In this work, the multimode soliton pulsation with a tunable period is achieved in a spatiotemporal mode-locked fiber laser. It demonstrates that the pulsation period drops while increasing the pump power. Moreover, it is found that different transverse modes have the same pulsation period, asynchronous pulsation evolution and different dynamical characteristics through the spatial sampling technique and the dispersive Fourier transform technique. To further verify the experimental results, we numerically investigate the influences of the gain and the loss on the pulsation properties. It is found that within a certain parameter range, the pulsation period drops and rises linearly with the increase of the gain and the loss, respectively. The obtained results contribute to understanding the formation and regulating of soliton pulsations in fiber lasers.

Germanene saturable absorber for mode-locked operation in an all-fiber laser with multiple dispersion environments

In this paper, a high-quality germanene-polyvinyl alcohol (PVA) saturable absorber (SA) with a modulation depth of 3.05% and a saturation intensity of 17.95M W/c m 2 was prepared. Stable conventional mode-locking and harmonic mode-locking (HML) were achieved in germanene-based Er-doped fiber lasers (EDFL) using dispersion management techniques. In a cavity with a net dispersion value of -0.22p s 2, the conventional soliton had a center wavelength of 1558.2 nm, a repetition frequency of 19.09 MHz, and a maximum 3 dB spectrum bandwidth of 3.5 nm. The highest repetition frequencies achieved in cavities with net dispersion values of -2.81p s 2, -1.73p s 2, and -1.09p s 2 were 9.48 MHz, 12.75 MHz, and 12.10 MHz for HML, respectively. Furthermore, the effects of dispersion, power, and the polarization state on HML were systematically investigated. Our research results fully demonstrate the capability of germanene as an optical modulator in generating conventional mode-locked and harmonic mode-locked solitons. This provides meaningful references for promoting its application in ultrafast fiber lasers.

All-multimode fiber spatiotemporal mode-locked figure-eight laser based on multimode gain fiber

In this paper, we report for the first time on an all-multimode fiber spatiotemporal mode-locked figure-eight laser operating at 1.0 µm. This laser utilizes a multimode gain fiber and a nonlinear amplifying loop mirror mechanism. It can generate mode-locked noise-like pulses at different central wavelengths. Additionally, we observed the presence of a multi-soliton state within the cavity by reducing intracavity gain. This study contributes to a broader investigation of various pulse phenomena in spatiotemporal mode-locked lasers and provides valuable insights into further exploring the evolution of spatiotemporal dynamics in such systems.

Spatiotemporal mode-locking and dissipative solitons in multimode fiber lasers

Multimode fiber (MMF) lasers are emerging as a remarkable testbed to study nonlinear spatiotemporal physics with potential applications spanning from high energy pulse generation, precision measurement to nonlinear microscopy. The underlying mechanism for the generation of ultrashort pulses, which can be understood as a spatiotempoal dissipative soliton (STDS), in the nonlinear multimode resonators is the spatiotemporal mode-locking (STML) with simultaneous synchronization of temporal and spatial modes. In this review, we first introduce the general principles of STML, with an emphasize on the STML dynamics with large intermode dispersion. Then, we present the recent progress of STML, including measurement techniques for STML, exotic nonlinear dynamics of STDS, and mode field engineering in MMF lasers. We conclude by outlining some perspectives that may advance STML in the near future.

Dissipative soliton resonance in a figure-eight multimode fiber laser

We report, for the first time to the best of our knowledge, a spatiotemporal mode-locked (STML) multimode fiber laser based on nonlinear amplifying loop mirror (NALM), generating dissipative soliton resonance (DSR) pulses. Due to the complex filtering characteristics caused by the inherent multimode interference filtering structure and NALM in the cavity, the STML DSR pulse has wavelength tunable function. What's more, kinds of DSR pulses are also achieved, including multiple DSR pulses, and the period doubling bifurcations of single DSR pulse and multiple DSR pulses. These results contribute to further understand the nonlinear properties of STML lasers and may shed some light on improving the performance of the multimode fiber 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.

Soliton molecules and their scattering by a localized P T-symmetric potential in atomic gases

We propose a physical scheme to study the formation of optical soliton molecules (SMs), consisting of two solitons bound together with a π-phase difference, and the scattering of SMs by a localized parity-time (P T)-symmetric potential. In order to stabilize SMs, we apply an additional space-dependent magnetic field to introduce a harmonic trapping potential for the two solitons and balance the repulse interaction induced by the π-phase difference between them. On the other hand, a localized complex optical potential obeying P T symmetry can be created through an incoherent pumping and spatial modulation of the control laser field. We investigate the scattering of optical SMs by the localized P T-symmetric potential, which exhibits evident asymmetric behavior and can be actively controlled by changing the incident velocity of SMs. Moreover, the P T symmetry of the localized potential, together with the interaction between two solitons of the SM, can also have a significant effect on the SM scattering behavior. The results presented here may be useful for understanding the unique properties of SMs and have potential applications in optical information processing and transmission.

Spatiotemporal mode-locked fiber laser based on dual-resonance coupling long-period fiber grating

Spatiotemporal mode-locked (STML) fiber lasers have become an excellent platform in nonlinear optics research due to the rich nonlinear evolution process. In order to overcome modal walk-off and realize phase locking of different transverse modes, it is usually crucial to reduce the modal group delay difference in the cavity. In this paper, we use long-period fiber grating (LPFG) to compensate the large modal dispersion and differential modal gain in the cavity, realizing the spatiotemporal mode-locking in step-index fibers cavity. The LPFG inscribed in few-mode fiber could induce strong mode coupling, which has wide operation bandwidth based on dual-resonance coupling mechanism. By using dispersive Fourier transform involved intermodal interference, we show that there is a stable phase difference between the transverse modes constituting the spatiotemporal soliton. These results would be beneficial for the study of spatiotemporal mode-locked fiber lasers.

Soliton phenomena in normal and anomalous dispersion regions in Er-doped mode-locked fiber lasers based on Cr2Si2Te6 saturable absorbers

Investigations of optical solitons have always been a hot topic due to their important scientific research value. In recent years, ultrafast lasers based on two-dimensional materials such as saturable absorbers (SAs) have become the focus of optical soliton research. In this work, various soliton operations are demonstrated in Er-doped fiber lasers (EDFLs) based on ${{\rm Cr}_2}{{\rm Si}_2}{{\rm Te}_6}$ SAs. First, a low-threshold passively mode-locked EDFL with traditional soliton output is constructed, and the pump threshold is as low as 10.1 mW. Second, by adjusting the net dispersion of the cavity, stable dissipative soliton operation can also be obtained. Traditional soliton mode-locked operation with controllable Kelly sidebands from first order to fourth order is realized by adjusting the pump power in a double-ended pumped structure, and the SNR is as high as 55 dB. All results prove that ${{\rm Cr}_2}{{\rm Si}_2}{{\rm Te}_6}$ used as SA material has great potential and wide application prospects in investigating optical soliton operations in mode-locked fiber lasers with both normal and anomalous dispersion.

Multimode nonlinear dynamics in spatiotemporal mode-locked anomalous-dispersion lasers

Spatiotemporal mode-locking in a laser with anomalous dispersion is investigated. Mode-locked states with varying modal content can be observed, but we find it difficult to observe highly-multimode states. We describe the properties of these mode-locked states and compare them to the results of numerical simulations. Prospects for the generation of highly-multimode states and lasers based on multimode soliton formation are discussed.

Self-starting spatiotemporal mode-locking using Mamyshev regenerators

Bridging multi-mode fibers and Mamyshev regenerators holds promise for pulse energy scaling in fiber lasers. However, initialization of a multi-mode Mamyshev oscillator remains a practical challenge. Here we report self-starting spatiotemporal mode-locking (STML) in a multi-mode Mamyshev oscillator without active assistance. The first initialized mode-locking is unstable, but stable STML can be attained by increasing the filter separation. Simulations verify the capability of reaching self-starting STML using Mamyshev regenerators and unveil the effect of filter separation on the self-starting ability.

Multimode soliton collisions in graded-index optical fibers

In this work, we unveil the unique complex dynamics of multimode soliton interactions in graded-index optical fibers through simulations and experiments. By generating two multimode solitons from the fission of an input femtosecond pulse, we examine the evolution of their Raman-induced red-shift when the input pulse energy grows larger. Remarkably, we find that the output red-shift of the trailing multimode soliton may be reduced, so that it accelerates until it collides with the leading multimode soliton. As a result of the inelastic collision, a significant energy transfer occurs between the two multimode solitons: the trailing soliton captures energy from the leading soliton, which ultimately enhances its red-shift, thus increasing temporal separation between the two multimode solitons.

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.

Spatiotemporal self-mode-locked operation in a compact partial multimode Er-doped fiber laser

We report spatiotemporal self-mode-locked operation at 1.55 µm with a low pump threshold of 32 mW in a compact partial multimode fiber laser system. Spatial filtering and the saturable absorber, both of which originate from the multimode interference (linear or nonlinear) of the single mode-multimode structure in this hybrid configuration, are well suited to the spatiotemporal self-mode-locked operation. Not only stable multimode conventional solitons with different spectral bandwidths but also a multimode soliton molecule complex with different structural bound-state patterns are obtained. It is found that the spatiotemporal evolution of the multimode solitons is dependent on many factors, such as the operating state, the involved frequency component, and the interaction between solitons. Furthermore, an unstable spatiotemporal mode-locked (STML) state where the beam profiles of the solitons change spontaneously is also observed for a specific multimode fiber state and pump power.

Modal dynamics in multimode optical fibers: an attractor of high-order modes

Multimode fibers (MMFs) support abundant spatial modes and involve rich spatiotemporal dynamics, yielding many promising applications. Here, we investigate the influences of the number and initial energy of high-order modes (HOMs) on the energy flow from the intermediate modes (IMs) to the fundamental mode (FM) and HOMs. It is quite surprising that random distribution of high-order modes evolves to a stationary one, indicating the asymptotic behavior of orbits in the same attraction domain. By employing the Lyapunov exponent, we prove that the threshold of the HOMs-attractor is consistent with the transition point of the energy flow which indicates the HOMs-attracotr acts as a "valve" in the modal energy flow. Our results provide a new perspective to explore the nonlinear phenomena in MMFs, such as Kerr self-cleaning, and may pave the way to some potential applications, such as secure communications in MMFs.

Modal perspective on geometric parametric instability sidebands in graded-index multimode fibers

In this paper, we investigated the geometric parametric instability (GPI) in graded-index multimode fibers through the multimode generalized nonlinear Schrödinger equation. Our results clearly and intuitively indicate that the generations of GPI sidebands are nearly synchronous in the spectrums of all modes, and the shapes of these spectrums are nearly the same. The numerical results show that the energies of the GPI sidebands come from the pump sideband, and these sidebands are carried by similar spatial beam profiles due to the similar modal components. We also found that the large modal dispersion has an influence for the symmetry of these GPI sidebands.

Tunable spatiotemporal mode-locked fiber laser at 1.55 μm

We report the spatiotemporal mode-locked multimode fiber laser operating at 1.55 µm based on semiconductor saturable absorber mirrors with the mode-locking threshold as low as 104 mW. Benefiting from the multimode interference filtering effect introduced in the laser cavity not only the central wavelength can be continuously tuned from 1557 nm to 1567 nm, but also the number of the output pulses can be adjusted from 1 to 4 by simply adjusting the polarization controllers. This work provides a new platform for exploring the dynamic characteristics of spatiotemporal mode-locked pulses at negative dispersion regime. Moreover, this kind of tunable laser has potential applications in fields of all-optical signal processing, fiber sensing and information coding.

Spatiotemporal Mode-Locking in Lasers with Large Modal Dispersion

Dissipative nonlinear wave dynamics have been investigated extensively in mode-locked lasers with single transverse mode, whereas there are few studies related to three-dimensional nonlinear dynamics within lasers. Recently, spatiotemporal mode locking (STML) was proposed in lasers with small modal (i.e., transverse-mode) dispersion, which has been considered to be critical for achieving STML in those cavities because the small dispersion can be easily balanced. Here, we demonstrate that STML can also be achieved in multimode lasers with much larger modal dispersion, where we find that the intracavity saturable absorber plays an important role for counteracting the large modal dispersion. Furthermore, we observe a new STML phenomenon of passive nonlinear autoselection of single-mode mode locking, resulting from the interaction between spatiotemporal saturable absorption and spatial gain competition. Our work significantly broadens the design possibilities for useful STML lasers thus making them much more accessible for applications, and extends the explorable parameter space of the novel dissipative spatiotemporal nonlinear dynamics that can be achieved in these lasers.

Switchable and spacing tunable dual-wavelength spatiotemporal mode-locked fiber laser

We report a switchable and spacing tunable dual-wavelength spatiotemporal mode-locked (STML) laser based on the multimode interference filtering effect in an all-fiber linear cavity. The dual-wavelength STML operations combined with different pulse patterns are achieved. By adjusting the polarization controllers, the dual-wavelength STML pulses can be switched to single wavelength operation, which is tunable up to 35 nm under certain pump powers. Moreover, the dual-wavelength spacing can also be tuned from 8 nm to 22 nm. The obtained results contribute to understanding and exploring the spatiotemporal characteristics operating in the multi-wavelength regime of STML fiber lasers. All-fiber STML lasers with lasing wavelength tunability and flexibility may have applications in the fields of optical communications and optical measurements.

Real-time multispeckle spectral-temporal measurement unveils the complexity of spatiotemporal solitons

The dynamics of three-dimensional (3D) dissipative solitons originated from spatiotemporal interactions share many common characteristics with other multi-dimensional phenomena. Unveiling the dynamics of 3D solitons thus permits new routes for tackling multidisciplinary nonlinear problems and exploiting their instabilities. However, this remains an open challenge, as they are multi-dimensional, stochastic and non-repeatable. Here, we report the real-time speckle-resolved spectral-temporal dynamics of a 3D soliton laser using a single-shot multispeckle spectral-temporal technology that leverages optical time division multiplexing and photonic time stretch. This technology enables the simultaneous observation on multiple speckle grains to provide long-lasting evolutionary dynamics on the planes of cavity time (t) - roundtrip and spectrum (λ) - roundtrip. Various non-repeatable speckly-diverse spectral-temporal dynamics are discovered in both the early and established stages of the 3D soliton formation.

Recent progress in all-fiber ultrafast high-order mode lasers

Ultrafast high-order mode (HOM) lasers are a relatively new class of ultrafast optics. They play a significant role in the fieldsof scientific research and industrial applications due to the high peak power and unique properties of spatial intensity and polarization distribution. Generation of ultrafast HOM beams in all-fiber systems has become an important research direction. In this paper, all-fiber mode conversion techniques, pulsed HOM laser strategies, and few-mode/multi-mode fiber (FMF/MMF) lasers are reviewed. The main motivation of this review is to highlight recent advances in the field of all-fiber ultrafast HOM lasers, for example, generating different HOM pulses based on fiber mode converters and mode-locking in the FMF/MMF lasers. These results suggest that mode selective coupler can be used as a broad bandwidth mode converter with fast response and HOM can be directly oscillated in the FMF/MMF laser cavity with high stability. In addition, spatiotemporal mode-locking in the FMF/MMF is also involved. It is believed that the development of all-fiber ultrafast HOM lasers will continue to deepen, thus laying a good foundation for future applications.

High-power synchronous multi-wavelength solitons from a multimode mode-locked fiber laser system

In this Letter, we implement a multimode fiber (MMF) laser system mode-locked by a nonlinear polarization rotation technique for controllable synchronous multi-wavelength soliton generation. The synchronization of the repetition rates for different wavelengths is realized by the special mode transmission in MMF. For dual-wavelength mode-locking at 1566.7 nm and 1617.2 nm, each of the synchronously mode-locked solitons consists of a train of quasi-periodic beat pulses with a pulse width of 84 fs and period of 162 fs. The total output power reaches 532 mW with optimally balanced two-color intensities. Furthermore, switchable dual- and tri-wavelength synchronized femtosecond pulses are also obtained. In contrast to previous reports, this synchronously mode-locked multi-wavelength is output directly from a laser oscillator, which provides a simpler candidate to achieve pulse synchronization.

Recent advances in real-time spectrum measurement of soliton dynamics by dispersive Fourier transformation

Mode-locking lasers have not only produced huge economic benefits in industrial fields and scientific research, but also provided an excellent platform to study diverse soliton phenomena. However, the real-time characterization of the ultrafast soliton dynamics remains challenging for traditional electronic instruments due to their relatively low response bandwidth and slow scan rate. Consequently, it is urgent for researchers to directly observe these ultrafast evolution processes, rather than just indirectly understand them from numerical simulations or averaged measurement data. Fortunately, dispersive Fourier transformation (DFT) provides a powerful real-time measurement technique to overcome the speed limitations of traditional electronic measurement devices by mapping the frequency spectrum onto the temporal waveform. In this review, the operation principle of DFT is discussed and the recent progress in characterizing the ultrafast transient soliton dynamics of mode-locking lasers is summarized, including soliton explosions, soliton molecules, noise-like pulses, rogue waves, and mode-locking buildup processes.

Harnessing a multi-dimensional fibre laser using genetic wavefront shaping

The multi-dimensional laser is a fascinating platform not only for the discovery and understanding of new higher-dimensional coherent lightwaves but also for the frontier study of the complex three-dimensional (3D) nonlinear dynamics and solitary waves widely involved in physics, chemistry, biology and materials science. Systemically controlling coherent lightwave oscillation in multi-dimensional lasers, however, is challenging and has largely been unexplored; yet, it is crucial for both designing 3D coherent light fields and unveiling any underlying nonlinear complexities. Here, for the first time, we genetically harness a multi-dimensional fibre laser using intracavity wavefront shaping technology such that versatile lasing characteristics can be manipulated. We demonstrate that the output power, mode profile, optical spectrum and mode-locking operation can be genetically optimized by appropriately designing the objective function of the genetic algorithm. It is anticipated that this genetic and systematic intracavity control technology for multi-dimensional lasers will be an important step for obtaining high-performance 3D lasing and presents many possibilities for exploring multi-dimensional nonlinear dynamics and solitary waves that may enable new applications.

All-fiber spatiotemporally mode-locked laser with multimode fiber-based filtering

We demonstrate the first all-fiber multimode spatiotemporally mode-locked laser. The oscillator generates dissipative soliton pulses at 1036 nm with 12 mW average power, 6.24 ps duration, and 24.3 MHz repetition rate. The reported pulse energy (0.5 nJ) represents ∼4 times improvement over the previously reported single-mode all-normal dispersion mode-locked lasers with multimode interference-based filtering. Numerical simulations are performed to investigate the cavity and spatiotemporal mode-locking dynamics. The all-fiber oscillator we present shows promise for practical use since it can be fabricated simply.

Spatio-temporal-spectral imaging of non-repeatable dissipative soliton dynamics

Dissipative solitons (DSs) are multi-dimensionally localized waves that arise from complex dynamical balances in far-from-equilibrium nonlinear systems and widely exist in physics, chemistry and biology. Real-time observations of DS dynamics across many dimensions thus have a broad impact on unveiling various nonlinear complexities in different fields. However, these observations are challenging as DS transitions are stochastic, non-repeatable and often strongly coupled across spatio-temporal-spectral (STS) domains. Here we report multi-dimensional (space xy + discrete time t + wavelength λ) DS dynamics imaged by STS compressed ultrafast photography, enabling imaging at up to trillions of frames per second. Various transient and random phenomena of multimode DSs are revealed, highlighting the importance of real-time multi-dimensional observation without the need for event repetition in decomposing the complexities of DSs.

Due to three-dimensional, stochastic and non-repeatable transitions of dissipative solitons, it is challenging to monitor their full dynamics. Here, the authors resolve the dynamics by wavelength and along two spatial dimensions with up to trillions of frames per second using compressed ultrafast photography.

Spatiotemporal dissipative solitons and vortices in a multi-transverse-mode fiber laser

We introduce a model for spatiotemporal modelocking in multimode fiber lasers, which is based on the (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation (cGLE) with conservative and dissipative nonlinearities and a 2-dimensional transverse trapping potential. Systematic numerical analysis reveals a variety of stable nonlinear modes, including stable fundamental solitons and breathers, as well as solitary vortices with winding number n = 1, while vortices with n = 2 are unstable, splitting into persistently rotating bound states of two unitary vortices. A characteristic feature of the system is bistability between the fundamental and vortex spatiotemporal solitons.

Generation of mode-locked square-shaped and chair-like pulse based on reverse saturable absorption effect of nonlinear multimode interference

In this paper, the phenomenon of reverse saturable absorption of offset-spliced graded index multimode fibers (OS-GIMF) is revealed. And based on that, the stable square-shaped and chair-like mode-locked pulses are demonstrated with the maximum pulse energy of 0.14 µJ and 23.8 nJ respectively, while the OS-GIMF acts as a saturable absorber (SA) in fiber laser. By adjusting polarization controller (PC) and the pump power, square-shaped and chair-like pulse can be switched to each other. This multimode SA could sever as high power light source owing to its high damage threshold, compact structure and low cost.

Bound states of different pulses based on third-order dispersion

Bound states of double pulses with different wavelengths are observed in a Tm-doped passively mode-locked fiber laser with near-zero net cavity group-velocity dispersion and strong third-order dispersion. The double pulses in the bound states exhibit different pulse durations and peak powers. Simulations show that the two pulses experience different compressing and broadening processes during the intra-cavity evolution. This demonstration reveals the existence of a new form of bound states and enriches the nonlinear dynamics of multi-pulse mode locking.

Multiple-soliton in spatiotemporal mode-locked multimode fiber lasers

Experimental observations of spatiotemporal mode-locked multiple-soliton, including harmonic mode locking and multiple pulses, in multimode fiber (MMF) lasers are reported. Numerical simulations are conducted to investigate the nonlinear dynamics of multi-pulsing. The influences of cavity parameters on the spatiotemporal outputs are analyzed by simulations, which agree with the experimental observations qualitatively. This work would contribute to understanding the complex spatiotemporal nonlinear dynamics in MMF lasers.

Optical soliton molecular complexes in a passively mode-locked fibre laser

Ultrashort optical pulses propagating in a dissipative nonlinear system can interact and bind stably, forming optical soliton molecules. Soliton molecules in ultrafast lasers are under intense research focus and present striking analogies with their matter molecules counterparts. The recent development of real-time spectral measurements allows probing the internal dynamics of an optical soliton molecule, mapping the dynamics of the pulses’ relative separations and phases that constitute the relevant internal degrees of freedom of the molecule. The soliton-pair molecule, which consists of two strongly bound optical solitons, has been the most studied multi-soliton structure. We here demonstrate that two soliton-pair molecules can bind subsequently to form a stable molecular complex and highlight the important differences between the intra-molecular and inter-molecular bonds. The dynamics of the experimentally observed soliton molecular complexes are discussed with the help of fitting models and numerical simulations, showing the universality of these multi-soliton optical patterns.

It has recently been shown that optical solitons can form stably bound states, so-called soliton molecules. Here, Wang et al. demonstrate stable soliton molecule complexes and explore the different bonds represented by the inter- and intra-molecular coupling.

Route towards extreme optical pulsation in linear cavity ultrafast fibre lasers

Pathways towards the generation of extreme optical pulsation in a chaotic transition regime in a linear fibre laser cavity configuration are presented. In a thulium mode-locked fibre laser, extreme events that can be controllably induced by manipulating the cavity birefringence for pulse energies exceeding the single soliton pulse operating regime are studied in detail for the first time. While a solitonic pulsation structure at the fundamental repetition rate is maintained, additional energy is shed in a chaotic manner, leading to broader spectral generation and shorter pulse durations whose behaviour deviates significantly from a classical statistical distribution. These pulses display markedly different characteristics from any previously reported extreme events in fibre lasers associated with multiple solitons and pulse bunching, thus presenting a novel observation of extreme pulsation. Detailed noise studies indicate that significant enhancement of relaxation oscillations, modulation instability and the interplay with reabsorption mechanisms contribute in this transient chaotic regime. The extreme pulsation generated in a compact fibre laser without any additional nonlinear attractors can provide an attractive platform to accelerate the exploration of the underlying physics of the chaos observed in mode-locked laser systems and can lead to novel fibre laser cavity designs.