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.
Abstract
Soliton explosion refers to a striking nonlinear dynamics in dissipative systems. In this state, a dissipative soliton collapses but returns back to its original state afterwards. Yet, the ...origin of such exotic soliton dynamics remains elusive. Here it is revealed that soliton collision can induce soliton explosions in a mode-locked fibre laser, benefiting from synchronous measurements of the spatio-temporal intensity evolution and the real-time spectra evolution using dispersive Fourier transform. Up to seven nonlinear regimes are observed successively in the laser by increasing the pump power only, including single-pulse mode locking, standard soliton explosions, noise-like mode locking, stable double pulsing, soliton collision induced explosions, soliton molecules, and double-pulse noise-like mode locking. These experimental findings are conducive to understand complex soliton dynamics in many nonlinear dissipative systems.
Abstract
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.
Abstract
Formation of coherent structures and patterns from unstable uniform state or noise is a fundamental physical phenomenon that occurs in various areas of science ranging from biology to ...astrophysics. Understanding of the underlying mechanisms of such processes can both improve our general interdisciplinary knowledge about complex nonlinear systems and lead to new practical engineering techniques. Modern optics with its high precision measurements offers excellent test-beds for studying complex nonlinear dynamics, though capturing transient rapid formation of optical solitons is technically challenging. Here we unveil the build-up of dissipative soliton in mode-locked fibre lasers using dispersive Fourier transform to measure spectral dynamics and employing autocorrelation analysis to investigate temporal evolution. Numerical simulations corroborate experimental observations, and indicate an underlying universality in the pulse formation. Statistical analysis identifies correlations and dependencies during the build-up phase. Our study may open up possibilities for real-time observation of various nonlinear structures in photonic systems.
Solitons can form bound states that are frequently referred to as soliton molecules as they exhibit molecule‐like dynamics. The build‐up phase of the optical soliton molecule remains elusive. Here, ...by means of a time‐stretch technique that enables real‐time access to the spectral and temporal dynamics, rich nonlinear processes involved in the build‐up of soliton molecules are revealed in an ultrafast fibre laser. Specifically, the formation of closely‐ and well‐separated bound solitons are resolved. In both cases, the build‐up phases consist of three nonlinear stages including mode locking, soliton splitting, and soliton interactions. For closely‐separated bound solitons, soliton interactions display wide diversities in repeated measurements, including soliton attraction, repelling, collision, vibration, and annihilation. For well‐separated bound solitons, repulsive interactions dominate the soliton interactions. Numerical simulations corroborate these experimental observations. Furthermore, a conceptually different soliton molecule, the intermittent‐vibration soliton molecule, is discovered and characterized. It is the intermediate state between the vibrational and stationary soliton molecules. The author's findings could assist in the understanding of the build‐up phase of localized structures in different dissipative systems.
Here, using a time‐stretch technique, it is found that the build‐up phases of soliton molecules consist of three nonlinear stages in an ultrafast fibre laser including mode locking, soliton splitting, and soliton interactions. Numerical simulations corroborate the experiments. Besides, a new soliton molecule, termed intermittent‐vibration soliton molecule is discovered and characterized.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
Tunable harmonic mode-locking of (HML) one kind of dissipative solitons (DSs) has been experimentally demonstrated in an Er-doped fiber (EDF) laser for the first time. The laser is mode-locked by ...nonlinear polarization rotation. The repetition rate can be tuned from the 2nd to 10th-order HML. A high repetition rate of 232 MHz (10th- order HML) has been observed in this laser, and the pulse duration after compression is 153-fs with single-pulse energy of 0.5 nJ. The spectral width of the pulses decreases as the harmonic order increases in the experiment, which is demonstrated for the first time, consistent with the numerical study. A rule based on monitoring the pulse spectral width to find desired-order HML is also proposed.
Though normal-dispersion mode-locked fiber lasers generally work on a single-pulse regime due to the large chirp of the pulses, we observe bound states of one kind of dissipative solitons in the ...laser. The separation between the bounded pulses in such soliton molecules increases with the pump power, and also varies with the settings of polarization controllers, which is consistent with other kinds of bounded pulses such as solitons. Our study indicates that the bound state of pulses is an intrinsic feature of mode-locked lasers and is independent of pulse profiles, stimulated by overdriving of mode-locking mechanisms.
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.
There is a growing demand for higher computational speed and energy efficiency of machine learning approaches and, in particular, neural networks. Optical implementation of neural networks can ...address this challenge. Compared to other neuromorphic platforms, fibre-based technologies can unlock a wide bandwidth window and offer flexibility in dimensionality and complexity. Moreover, fibre represents a well-studied, low-cost and low-loss material, widely used for signal processing and transmission. At the same time, mode-locked fibre lasers offer flexibility and control, while the mode-locking effect can be crucial for unlocking ultra-short timescales and providing ultra-fast processing. Here, we propose a mode-locked fibre laser with a non-linear power threshold in both power and spectrum. The advantage of the proposed system is a spectrum width two-branch function dependent on the input signal power. The effect is caused by a transition between two operating regimes and is governed by the input signal power. The proposed design enables receiving a non-linear transfer function in amplitude with a power threshold as an optical analogue of biological neurons with the additional advantage of a non-linear two-branch transfer function in spectrum width. The latter property is similar to the frequency-varied response dependent on stimulus properties in biological neurons. Thus, our work opens new avenues in research into novel types of artificial neurons with a frequency spectrum width variable response and, consequently, spiking neural networks and neural-rate-based coding with potential applications in optical communications and networks with flexible bandwidth, such as 5G and emerging 6G.
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