Optical solitons in ultrafast fiber lasers, as a result of dual balances between dispersion and nonlinearity as well as gain and loss, enable various soliton interactions. Soliton collisions are among the most intriguing soliton interactions, which fuel the understanding for particle-like properties of solitons. Here, we experimentally investigate the transient dynamics of collisions between a two-soliton molecule and a soliton singlet in a mode-locked fiber laser. By means of the dispersive Fourier transform technique, the evolving spectral interferograms of different collision scenarios are measured in real time. In particular, the “quasi-elastic” collision is observed, which shows that the soliton-molecule state remains unaltered after the collision and the group-velocity difference between the soliton molecule and the singlet is changed. It is directly demonstrated that a bond exchange occurs between the colliding solitons. By tuning the intra-cavity polarization controller, the dynamic processes of other collision outcomes, including the annihilation of a soliton in the soliton molecule as well as the formation of a stable unequally spaced soliton triplet, are also revealed. Our work facilitates a deeper understanding of soliton collision dynamics in ultrafast fiber lasers.

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Real-Time Access to Collisions between a Two-Soliton Molecule and a Soliton Singlet in an Ultrafast Fiber Laser

Modulating chirped Gaussian vector solitons with group-velocity dispersion

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.

Dynamics of pulsating solitons derived from asymmetrical dispersive waves.

Optical structures can serve as low-power high-capacity alternatives of electronic processors for more efficient neuromorphic computing, but can suffer from large footprints and weak scalability. In this work, properly phased time-perturbed microrings side-coupled to a waveguide are utilized to realize a compact processor for linear transformations. We build up a synthetic frequency dimension to provide sufficient degrees of freedom, where the linear time-varying structures enable the linear intermixing and transformation of frequency-multiplexed data. Moreover, non-reciprocal and asymmetric flow of data in the forward and backward modes, due to phasing of the perturbations, helped to build up another synthetic dimension and to avoid physically repeating the processing elements, thus enabling a much more compact and scalable linear processor. 

Recycling forward and backward frequency multiplexed modes in a waveguide coupled to phased time perturbed microrings for low footprint neuromorphic computing

Optical communication refers to the communication mode with optical signal as a carrier [...]

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Special Issue on Advanced Technique and Future Perspective for Next Generation Optical Fiber Communications

Dissipative systems form various self-organized states owing to the abundant attractor structures. The study of the response of different self-organized states under collision perturbation is of great significance for understanding the dissipative nonlinear systems. The collision dynamics of single soliton and soliton molecules can not only assist the stability analysis of attractors, but also reveal the rich physical connotations of soliton interactions. Here, for the first time, the collision processes of single soliton and soliton molecules in different excited states are detected using the dispersive Fourier transform technology. The collision processes include the disintegration and rebuilding of soliton molecules as well as chaotic oscillating evolution, accompanied by the emergence of transition states such as triple binding state, soliton fusion and acceleration. According to whether the soliton molecule can return to its initial excited state, the collisions are classified as elastic and inelastic. The different interaction strength between solitons is an important condition for rebuilding stable soliton molecules. Numerical simulations show that the gain dynamics are the main physical origin of collisions. Our research will stimulate in-depth research on the interaction of self-organized states in nonlinear systems such as chemical molecules, and have potential applications in optical logic gates.

Elastic and inelastic collision dynamics between soliton molecules and a single soliton.

In this article, we design a long short-term memory (LSTM) scheme, combined with dense networks, to realize soliton dynamics prediction in passively mode-locked fiber lasers. Based on the particle characteristic of soliton interaction, we propose to use the separation and relative phase between solitons as characteristic parameters to model and predict the dynamics. The network predicted soliton collision and soliton molecule dynamics accurately. This scheme of precoding physical information with subsequent dynamics prediction not only introduces new prospects for the laser self-optimization algorithm, but also brings new insights for the modeling of nonlinear systems and description of soliton interactions.

Soliton Molecule Dynamics Evolution Prediction Based on LSTM Neural Networks

As a high-throughput data analysis technique, photon time stretching (PTS) is widely used in the monitoring of rare events such as cancer cells, rough waves, and the study of electronic and optical transient dynamics. The PTS technology relies on high-speed data collection, and the large amount of data generated poses a challenge to data storage and real-time processing. Therefore, how to use compatible optical methods to filter and process data in advance is particularly important. The time-lens proposed, based on the duality of time and space as an important data processing method derived from PTS, achieves imaging of time signals by controlling the phase information of the timing signals. In this paper, an optical neural network based on the time-lens (TL-ONN) is proposed, which applies the time-lens to the layer algorithm of the neural network to realize the forward transmission of one-dimensional data. The recognition function of this optical neural network for speech information is verified by simulation, and the test recognition accuracy reaches 95.35%. This architecture can be applied to feature extraction and classification, and is expected to be a breakthrough in detecting rare events such as cancer cell identification and screening.

https://www.mdpi.com/2304-6732/8/3/78/pdf

Optical Machine Learning Using Time-Lens Deep Neural NetWorks

Deep neural networks have enabled the reconstruction of optical soliton molecules with more complex structures using the real-time spectral interferences obtained by photonic time-stretch dispersive Fourier transformation (TS-DFT) technology. In this paper, we propose to use three kinds of deep convolution networks (DCNs), including VGG, ResNets, and DenseNets, for revealing internal dynamics evolution of soliton molecules based on the real-time spectral interferences. When analyzing soliton molecules with equidistant composite structures, all three models are effective. The DenseNets with layers of 48 perform the best for extracting the dynamic information of complex five-soliton molecules from TS-DFT data. The mean Pearson correlation coefficient (MPCC) between the predicted results and the real results is about 0.9975. Further, the ResNets in which the MPCC achieves 0.9906 also has the better ability of phase extraction than VGG which the MPCC is about 0.9739. The general applicability is demonstrated for extracting internal information from complex soliton molecule structures with high accuracy. The presented DCNs-based techniques can be employed to explore undiscovered mechanisms underlying the distribution and evolution of large numbers of solitons in dissipative systems in experimental research.

Congcong Liu

Papers

Elastic and inelastic collision dynamics between soliton molecules and a single soliton.

Soliton Molecule Dynamics Evolution Prediction Based on LSTM Neural Networks

Optical Machine Learning Using Time-Lens Deep Neural NetWorks

Comparing Performance of Deep Convolution Networks in Reconstructing Soliton Molecules Dynamics from Real-Time Spectral Interference

Dynamics of pulsating solitons derived from asymmetrical dispersive waves.