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.

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.

Author Correction: Analysis of laser radiation using the Nonlinear Fourier transform.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Analysis of laser radiation using the Nonlinear Fourier transform.

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions.

Breathing dissipative solitons in mode-locked fiber lasers.

Dissipative solitons are self-localized coherent structures arising from the balance between energy supply and dissipation. Besides stationary dissipative solitons, there are dynamical ones exhibiting oscillatory behavior, known as breathing dissipative solitons. Substantial interest in breathing dissipative solitons is driven by both their fundamental importance in nonlinear science and their practical applications, such as in spectroscopy. Yet, the observation of breathers has been mainly restricted to microresonator platforms. Here, we generate breathers in a mode-locked fiber laser. They exist in the laser cavity under the pump threshold of stationary mode locking. Using fast detection, we are able to observe the temporal and spectral evolutions of the breathers in real time. Breathing soliton molecules are also observed. Breathers introduce a new regime of mode locking into ultrafast lasers. Our findings may contribute to the design of advanced laser sources and open up new possibilities of generating breathers in various dissipative systems.

Experimental study on buildup dynamics of a harmonic mode-locking soliton fiber laser.

In this paper, we experimentally investigate the onset dynamics of harmonic mode-locking (HML) in a short-cavity all-polarization-maintaining fiber laser using time-stretch spectroscopy. We observe a transient multi-pulse state evolving into a stable HML state. Moreover, a bunch of metastable short-lived mode-locking states are recorded before the laser entered the HML state. In these transient states, sudden changes including the formation and destruction of single broadband pulses are observed.

On the Q-switching bunch dynamics in the build-up of stretched-pulse mode-locking.

In this paper, we experimentally investigate a rich set of Q-switching bunches in the build-up of stretched-pulse mode-locking of an erbium-doped fiber laser. Interestingly, regular clustering of periodic Q-switched mode-locking states is observed in the self-starting process. Moreover, with time-stretch spectroscopy, we record periodic pulse-to-pulse spectral evolution occurring in these turbulent and rapidly-evolving pre-mode-locking states.

In-cavity soliton self-frequency shift ultrafast fiber lasers.

Lasing wavelengths are generally limited at the gain bands of active materials. In this Letter, we propose and demonstrate a new concept of ultrafast fiber laser based on in-cavity soliton self-frequency shift (SSFS). Benefiting from SSFS, the wavelength of ultrafast fiber lasers can be beyond the gain band of active fibers. SSFS was previously stimulated by transmitting pulses in passive fibers. Triggering SSFS inside a laser cavity has never been reported. We successfully stimulate SSFS in a laser by employing a piece of dispersion-shifted fiber. In-cavity SSFS is expected to be implemented in various ultrafast lasers and is conducive to develop compact wavelength versatile laser sources.

Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser.

We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.

Filter-Based Dispersion-Managed Versatile Ultrafast Fibre Laser.

We present the operation of an ultrafast passively mode-locked fibre laser, in which flexible control of the pulse formation mechanism is readily realised by an in-cavity programmable filter the dispersion and bandwidth of which can be software configured. We show that conventional soliton, dispersion-managed (DM) soliton (stretched-pulse) and dissipative soliton mode-locking regimes can be reliably targeted by changing the filter's dispersion and bandwidth only, while no changes are made to the physical layout of the laser cavity. Numerical simulations are presented which confirm the different nonlinear pulse evolutions inside the laser cavity. The proposed technique holds great potential for achieving a high degree of control over the dynamics and output of ultrafast fibre lasers, in contrast to the traditional method to control the pulse formation mechanism in a DM fibre laser, which involves manual optimisation of the relative length of fibres with opposite-sign dispersion in the cavity. Our versatile ultrafast fibre laser will be attractive for applications requiring different pulse profiles such as in optical signal processing and optical communications.

Gain dependent pulse regimes transitions in a dissipative dispersion-managed fibre laser.

For the first time, we demonstrate the possibility to switch between three distinct pulse regimes in a dissipative dispersion-managed (DM) fibre laser by solely controlling the gain saturation energy. Nonlinear Schrödinger equation based simulations show the transitions between hyper-Gaussian similaritons, parabolic similaritons, and dissipative solitons in the same laser cavity. It is also shown that such transitions exist in a wide dispersion range from all-normal to slightly net-normal dispersion. This work demonstrates that besides dispersion and filter managements gain saturation energy can be a new degree of freedom to manage pulse regimes in DM fibre lasers, which offers flexibility in designing ultrafast fibre lasers. Also, the result indicates that in contrast to conservative soliton lasers whose intensity profiles are unique, dissipative DM lasers show diversity in pulse shapes. The findings not only give a better understanding of pulse shaping mechanisms in mode-locked lasers, but also provide insight into dissipative systems.

Watt-level ultrahigh-optical signal-to-noise ratio single-longitudinal-mode tunable Brillouin fiber laser.

A watt-level ultrahigh optical signal-to-noise ratio single-longitudinal-mode (SLM) tunable Brillouin fiber laser (BFL) has been demonstrated. By optimizing the length of the single mode fiber (SMF) cavity at 11 m and its output ratio at 60%, 1.04 W output power, as well as stable SLM operation is obtained at 2.24 W pump power. The single pass cavity BFL has the advantage that the Brillouin pump frequency does not need to match the cavity mode, thus the stability is greatly improved. As only SMF is used in the cavity, the operating wavelength can be tunable without restriction from the self-lasing cavity mode. Furthermore, it proves that core-pumped single-frequency fiber laser is able to generate watt-level power. The laser demonstrates excellent performance in terms of noise, linewidth, and stability.

Tunable delay slow-light in an active fiber Bragg grating.

We proposed and experimentally demonstrated an extremely simple and feasible slow-light technique to achieve tunable optical delay by using the Er/Yb codoped fiber Bragg grating (FBG). The signal light experiences strong dispersion when it is launched into the reflection edge of FBG, and the group delay value is determined by the signal wavelength and the pump power. In the experiment, a controllable delay of 0.9 ns can be obtained through changing the 980 nm pump power. The group velocity can be slowed down to 5.6x10(7) m/s, which is 19% of the speed of light in free space. It provides a very simple approach to control the light group delay, which is likely to have important implications for practical applications.