Instabilities in a dissipative soliton-similariton laser using a scalar iterative map

Voltage-controlled nonlinear optical properties in gold nanofilms via electrothermal effect

Dynamic control of the optical properties of gold nanostructures is crucial for advancing photonics technologies spanning optical signal processing, on-chip light sources and optical computing. Despite recent advances in tunable plasmons in gold nanostructures, most studies are limited to the linear or static regime, leaving the dynamic manipulation of nonlinear optical properties unexplored. This study demonstrates the voltage-controlled Kerr nonlinear optical response of gold nanofilms via the electrothermal effect. By applying relatively low voltages (~10 V), the nonlinear absorption coefficient and refractive index are reduced by 40.4% and 33.1%, respectively, due to the increased damping coefficient of gold nanofilm. Furthermore, a voltage-controlled all-fiber gold nanofilm saturable absorber is fabricated and used in mode-locked fiber lasers, enabling reversible wavelength-tuning and operation regimes switching (e.g., mode-locking-Q-switched mode-locking). These findings advance the understanding of electrically controlled nonlinear optical responses in gold nanofilms and offer a flexible approach for controlling fiber laser operations.

Collision dynamics between soliton molecules and a single soliton: exploding soliton pair and periodic soliton explosions

Inherent periodic collisions in dual-wavelength mode-locked fiber lasers (MLFLs) stimulate various intra-cavity collision dynamic phenomena. Analogous to the collision of matter particles, collisions between optical soliton molecules (SMs) and single solitons (SSs) have been observed by the real-time spectral measurements. It is demonstrated that the energy accumulation after the collision caused by internal motion within bound pulses leads to soliton pair (SP) explosions, while the periodic soliton explosions with another cavity parameter setting are almost unaffected by the collision. Additionally, the collision between a SP and a SS is reproduced through numerical simulations, and the collision-induced double Hopf-type bifurcation of SP is predicted. These findings provide novel insights, to the best of our knowledge, for further understanding the complex collision dynamics in dual-wavelength MLFLs and will help in the design of high-performance dual-comb sources.

Bidirectional mode-locked erbium-doped fiber laser based on an all-fiber gold nanofilm saturable absorber

We demonstrate a bidirectional mode-locked erbium-doped fiber laser by incorporating gold nanofilm as a saturable absorber (SA). The gold nanofilm SA has the advantages of high stability and high optical damage threshold. Besides, the SA exhibits a large modulation depth of 26% and a low saturation intensity of 1.22 MW/cm2 at 1.56 μm wavelength band, facilitating the mode-locking of bidirectional propagating solitons within a single laser cavity. Bidirectional mode-locked solitons are achieved, with the clockwise pulse centered at 1568.35 nm and the counter-clockwise one at 1568.6 nm, resulting in a slight repetition rate difference of 19 Hz. Moreover, numerical simulations are performed to reveal the counter-propagating dynamics of the two solitons, showing good agreement with the experimental results. The asymmetric cavity configuration gives rise to distinct buildup and evolution dynamics of the two counter-propagating pulses. These findings highlight the advantage of the gold nanofilm SA in constructing bidirectional mode-locked fiber lasers and provide insights for understanding the bidirectional pulse propagation dynamics.

Observation of the "invisible" pulsation of soliton molecules in a bidirectional ultrafast fiber laser

A novel optical soliton dynamics phenomenon, called "invisible" pulsation, has gradually attracted extensive interest in recent years, which can only be identified effectively with the help of real-time spectroscopy technique, i.e., dispersive Fourier transformation (DFT). In this paper, based on a new bidirectional passively mode-locked fiber laser (MLFL), the "invisible" pulsation dynamics of soliton molecules (SMs) is systematically studied. It is indicated that the spectral center intensity, pulse peak power and relative phase of SMs are periodically changed during the "invisible" pulsation, while the temporal separation inside the SMs is constant. The degree of spectral distortion is positively correlated with the pulse peak power, which verifies that self-phase modulation (SPM) is the inducement of spectral distortion. Finally, the universality of the SMs "invisible" pulsation is further experimentally verified. We believe our work is not only conducive to the development of compact and reliable bidirectional ultrafast light sources, but also of great significance to enrich the study of nonlinear dynamics.

Quantification of dissipative effects in a complex Ginzburg-Landau equation governed laser system by tracing soliton dynamics

The concept of dissipative solitons has provided new insight into the complex pulse dynamics in mode-locked lasers and stimulated novel laser cavity designs. However, most of these studies are restricted to qualitative regimes, because it is difficult to quantify dissipative effects in a mode-locked laser. Meanwhile, the quantification of dissipative effects is a general problem that can be also encountered in other dissipative systems. In this paper, we demonstrate a method for quantifying dissipative effects in a mode-locked laser based on analyzing the soliton dynamics traced by time-stretch dispersive Fourier transform. As a result, we are able to quantitatively reproduce the evolution of the pulse that seeds mode-locking through simulations and gain a deeper understanding of the whole process. The obtained physical picture of mode-locking allows us to propose a simple method to quantify the energy threshold for mode-locking buildup and the stability of mode-locked states. A parameter is introduced to evaluate mode-locking conditions, which can serve as a criterion for designing mode-locked lasers. This work opens up new possibilities in the diagnosis and improvement of mode-locked lasers and studies of soliton physics.

Creeping and erupting dynamics in a pure-quartic soliton fiber laser

Pure-quartic solitons (PQSs) are gradually becoming a hotspot in recent years due to their potential advantage to achieve high energy. Meanwhile, the fundamental research of PQSs is still in the fancy stage, and exploring soliton dynamics can promote the development of PQSs. Herein, we comprehensively and numerically investigate the impact of saturation power, small-signal gain, and output coupler on PQS dynamics in passively mode-locked fiber lasers. The result indicates that altering the above parameters makes PQSs exhibit pulsating or creeping dynamics similar to traditional solitons. Moreover, introducing an intra-cavity filter combined with intra-cavity large fourth-order dispersion makes PQSs go through stationary, pulsating to erupting. That is, the intra-cavity filter changes PQS dynamics. These findings provide new insights into PQS dynamics in fiber lasers.

Machine learning analysis of instabilities in noise-like pulse lasers

Neural networks have been recently shown to be highly effective in predicting time-domain properties of optical fiber instabilities based only on analyzing spectral intensity profiles. Specifically, from only spectral intensity data, a suitably trained neural network can predict temporal soliton characteristics in supercontinuum generation, as well as the presence of temporal peaks in modulation instability satisfying rogue wave criteria. Here, we extend these previous studies of machine learning prediction for single-pass fiber propagation instabilities to the more complex case of noise-like pulse dynamics in a dissipative soliton laser. Using numerical simulations of highly chaotic behaviour in a noise-like pulse laser operating around 1550 nm, we generate large ensembles of spectral and temporal data for different regimes of operation, from relatively narrowband laser spectra of 70 nm bandwidth at the -20 dB level, to broadband supercontinuum spectra spanning 200 nm at the -20 dB level and with dispersive wave and long wavelength Raman extension spanning from 1150-1700 nm. Using supervised learning techniques, a trained neural network is shown to be able to accurately correlate spectral intensity profiles with time-domain intensity peaks and to reproduce the associated temporal intensity probability distributions.

Quantum limited timing jitter of soliton molecules in a mode-locked fiber laser

Soliton molecules in mode-locked lasers are expected to be ideal self-organization patterns, which warrant stability and robustness against perturbations. However, recent ultra-high resolution optical cross-correlation measurements uncover an intra-molecular timing jitter, even in stationary soliton molecules. In this work, we found that the intra-molecular timing jitter has a quantum origin. Numerical simulation indicates that amplified spontaneous emission (ASE) noise induces a random quantum diffusion for soliton pulse timing, which cannot be compensated by soliton binding mechanism. By suppressing indirectly coupled timing jitter at close-to-zero cavity dispersion, a record-low 350 as rms intra-soliton-molecular jittering is obtained from an Er-fiber laser in experiment. This work provides insight into the fundamental limits for the instability of multi-soliton patterns.

Intracavity incoherent supercontinuum dynamics and rogue waves in a broadband dissipative soliton laser

Understanding dynamical complexity is one of the most important challenges in science. Significant progress has recently been made in optics through the study of dissipative soliton laser systems, where dynamics are governed by a complex balance between nonlinearity, dispersion, and energy exchange. A particularly complex regime of such systems is associated with noise-like pulse multiscale instabilities, where sub-picosecond pulses with random characteristics evolve chaotically underneath a much longer envelope. However, although observed for decades in experiments, the physics of this regime remains poorly understood, especially for highly-nonlinear cavities generating broadband spectra. Here, we address this question directly with a combined numerical and experimental study that reveals the physical origin of instability as nonlinear soliton dynamics and supercontinuum turbulence. Real-time characterisation reveals intracavity extreme events satisfying statistical rogue wave criteria, and both real-time and time-averaged measurements are in quantitative agreement with modelling.

In this work the authors perform a combined numerical and experimental study of noise-like pulse multiscale instabilities in dissipative laser systems. They reveal an underlying multiscale dynamics and report the observation of rogue wave events.

Synthesis and dissociation of soliton molecules in parallel optical-soliton reactors

Mode-locked lasers have been widely used to explore interactions between optical solitons, including bound-soliton states that may be regarded as "photonic molecules". Conventional mode-locked lasers normally, however, host at most only a few solitons, which means that stochastic behaviours involving large numbers of solitons cannot easily be studied under controlled experimental conditions. Here we report the use of an optoacoustically mode-locked fibre laser to create hundreds of temporal traps or "reactors" in parallel, within each of which multiple solitons can be isolated and controlled both globally and individually using all-optical methods. We achieve on-demand synthesis and dissociation of soliton molecules within these reactors, in this way unfolding a novel panorama of diverse dynamics in which the statistics of multi-soliton interactions can be studied. The results are of crucial importance in understanding dynamical soliton interactions and may motivate potential applications for all-optical control of ultrafast light fields in optical resonators.

Optimal conditions for self-starting of soliton mode-locked fiber lasers with a saturable absorber

With the recently developed single-shot time-stretch dispersive Fourier transform technique, we investigate the buildup process of an all-polarization-maintaining soliton mode-locked fiber laser. Considering the multi-pulse competitions and the evolution of the survived pulse, we find an optimal range of intra-cavity energy for self-starting related to the saturation energy of the employed saturable absorber. Under the conditions, one dominant pulse can build up quickly against the others, and it finally drives to single-pulse operation. The conclusions drawn here hold for other soliton mode-locked lasers.

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

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.