Dependence of Ultrafast Electron Emission Characteristics of Graphene Cold Cathode on Femtosecond Photoexcitation Polarization Angle

Ultrafast electron pulses, generated through femtosecond photoexcitation in nanocathode materials, introduce high-frequency characteristics and ultrahigh temporal-spatial resolution to vacuum micro-nano electronic devices. To advance the development of ultrafast electron sources sensitive to polarized light, we propose an ultrafast pulsed electron source based on a vertical few-layer graphene cold cathode. This source exhibits selective electron emission properties for varying polarization angles, with high switching ratios of 277 (at 0°) and 235 (at 90°). The electron emission of the graphene evolves from cosine to sine as the polarization angle increases from 0° to 90°. The variation of electron emission current with polarization angle is intrinsically related to light absorption, local field enhancement, and photothermal conversion efficiency. A physical mechanism model and semiempirical expression were presented to reveal the MPP and PTE mechanisms at different polarization angles. This tunable conversion between mechanisms indicates potential applications in tunable ultrafast optoelectronic devices.

Phase-locked and phase-unlocked multicolor solitons in a fiber laser

Multicolor solitons are nonlinear pulses composed of two or more solitons centered at different frequencies, propagating with the same group velocity. In the time domain, multicolor solitons consist of an envelope multiplying a more rapidly varying fringe pattern that results from the interference of these frequency components. Here, we report the observation in a fiber laser of a novel, to the best of our knowledge, type of dynamics in which different frequency components still have the same group velocity but have different propagation constants. This causes the relative phases between the constituent spectral components to change upon propagation, corresponding to the fringes moving under the envelope. This leads to small periodic energy variations that we directly measure. Our experimental results are in good agreement with realistic numerical simulations based on an iterative cavity map.

Pure-high-even-order dispersion bound solitons complexes in ultra-fast fiber lasers

Temporal solitons have been the focus of much research due to their fascinating physical properties. These solitons can form bound states, which are fundamentally crucial modes in fiber laser and present striking analogies with their matter molecules counterparts, which means they have potential applications in large-capacity transmission and all-optical information storage. Although traditionally, second-order dispersion has been the dominant dispersion for conventional solitons, recent experimental and theoretical research has shown that pure-high-even-order dispersion (PHEOD) solitons with energy-width scaling can arise from the interaction of arbitrary negative-even-order dispersion and Kerr nonlinearity. Despite these advancements, research on the bound states of PHEOD solitons is currently non-existent. In this study, we obtained PHEOD bound solitons in a fiber laser using an intra-cavity spectral pulse shaper for high-order dispersion management. Specifically, we experimentally demonstrate the existence of PHEOD solitons and PHEOD bound solitons with pure-quartic, -sextic, -octic, and -decic dispersion. Numerical simulations corroborate these experimental observations. Furthermore, vibrating phase PHEOD bound soliton pairs, sliding phase PHEOD bound soliton pairs, and hybrid phase PHEOD bound tri-soliton are discovered and characterized. These results broaden the fundamental understanding of solitons and show the universality of multi-soliton patterns.

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.

Optimizing ultrashort pulse in fiber laser based on artificial intelligence algorithm

Ultrashort pulses, characterized by their short pulse duration, diverse spectral content, and high peak power, are widely used in fields including laser processing, optical storage, biomedical sciences, and laser imaging. The complex, highly-nonlinear process of ultrashort pulse evolution within fiber lasers is influenced by numerous aspects such as dispersion, loss, gain, and nonlinear effects. Traditionally, the split-step Fourier transforms method is employed for simulating ultrashort pulses in fiber lasers, which involves traversing multiple parameters within the fiber to attain the pulse's optimal state. The simulation is a significantly time-consuming process. Here, we use a neural network model to fit and predict the impact of multiple parameters on the pulse characteristics within fiber lasers, enabling parameter optimization through genetic algorithms to determine the optimal pulse duration, pulse energy, and peak power. Integrating artificial intelligence algorithms simplifies the acquisition of optimal pulse parameters and enhances our understanding of multiple parameters' impact on the pulse characteristics. The investigation of ultrashort pulse optimization based on artificial intelligence holds immense potential for laser design.

Internal motion within ultrafast asynchronous dual wavelength mode-locked lasers

Realtime spectroscopy access to ultrafast fiber lasers provides new opportunities for exploring complex soliton interaction dynamics. In this study, we employ a time-stretch technique that enables real-time access to both spectral and temporal dynamics, revealing rich nonlinear processes in asynchronous dual wavelength mode-locked pulses in an ultrafast fiber laser. Due to the different group velocities of the two wavelengths, the mode-locked solitons centered at different wavelengths periodically collide with each other. We recorded the entire process of soliton establishment, stabilization, and disappearance, shedding light on the mystery of stable transmission of dual-wavelength mode-locked pulses. These processes were observed for the first time in an ultrafast fiber laser, and the experimental evidence provides important insights into the understanding of nonlinear dynamics in fiber lasers, as well as the potential for improving laser performance for application in dual-comb spectroscopy.

Revealing of long-range soliton interaction induced time and phase dynamics in a mode-locked fiber laser

By means of the dispersive temporal interferometry technique, we carried out a real-time observation of the time separation and relative phase evolutions of two pulses toward harmonic mode-locking. During the separation stage of the buildup process, the time separation increases, while the relative phase decreases synchronously, and the largest change rates are 0.247 fs/r and -0.017 rad/r, respectively. Meanwhile, the two rates show a linear relation with the former 17.4 times larger than the latter. Moreover, a residual phase change rate of -3.89 × 10-4 rad/r is observed in a steady non-uniform dual-soliton state, while such phase change is absent in a uniform four-soliton state. This study unveils the soliton interaction dynamics in lasers, which not only help to reduce timing jitter in multi-soliton mode-locking, but also bring insight to a temporal tweezing of femtosecond pulse.

Controlling intracavity dual-comb soliton motion in a single-fiber laser

Ultrafast science builds on dynamic compositions of precisely timed light pulses, and evolving groups of pulses are observed in almost every mode-locked laser. However, the underlying physics has rarely been controlled or used until now. Here, we demonstrate a general approach to control soliton motion inside a dual-comb laser and the programmable synthesis of ultrashort pulse patterns. Introducing single-pulse modulation inside an Er:fiber laser, we rapidly shift the timing between two temporally separated soliton combs. Their superposition outside the cavity yields ultrashort soliton sequences. On the basis of real-time spectral interferometry, we observe the deterministic switching of intersoliton separation arising from the interplay of attracting and repulsing forces via ultrafast nonlinearity and laser gain dynamics. Harnessing these insights, we demonstrate the high-speed all-optical synthesis of nano- to picosecond pump-probe delays and programmable free-form soliton trajectories. This concept may pave the way to a new class of all-optical delay generators for ultrafast measurements at unprecedented high tuning, cycling, and acquisition speeds.

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.

Single-shot optical imaging with spectrum circuit bridging timescales in high-speed photography

Single-shot optical imaging based on ultrashort lasers has revealed nonrepetitive processes in subnanosecond timescales beyond the recording range of conventional high-speed cameras. However, nanosecond photography without sacrificing short exposure time and image quality is still missing because of the gap in recordable timescales between ultrafast optical imaging and high-speed electronic cameras. Here, we demonstrate nanosecond photography and ultrawide time-range high-speed photography using a spectrum circuit that produces interval-tunable pulse trains while keeping short pulse durations. We capture a shock wave propagating through a biological cell with a 1.5-ns frame interval and 44-ps exposure time while suppressing image blur. Furthermore, we observe femtosecond laser processing over multiple timescales (25-ps, 2.0-ns, and 1-ms frame intervals), showing that the plasma generated at the picosecond timescale affects subsequent shock wave formation at the nanosecond timescale. Our technique contributes to accumulating data of various fast processes for analysis and to analyzing multi-timescale phenomena as a series of physical processes.

Single-Photon Level Dispersive Fourier Transform: Ultrasensitive Characterization of Noise-Driven Nonlinear Dynamics

Dispersive Fourier transform is a characterization technique that allows directly extracting an optical spectrum from a time domain signal, thus providing access to real-time characterization of the signal spectrum. However, these techniques suffer from sensitivity and dynamic range limitations, hampering their use for special applications in, e.g., high-contrast characterizations and sensing. Here, we report on a novel approach to dispersive Fourier transform-based characterization using single-photon detectors. In particular, we experimentally develop this approach by leveraging mutual information analysis for signal processing and hold a performance comparison with standard dispersive Fourier transform detection and statistical tools. We apply the comparison to the analysis of noise-driven nonlinear dynamics arising from well-known modulation instability processes. We demonstrate that with this dispersive Fourier transform approach, mutual information metrics allow for successfully gaining insight into the fluctuations associated with modulation instability-induced spectral broadening, providing qualitatively similar signatures compared to ultrafast photodetector-based dispersive Fourier transform but with improved signal quality and spectral resolution (down to 53 pm). The technique presents an intrinsically unlimited dynamic range and is extremely sensitive, with a sensitivity reaching below the femtowatt (typically 4 orders of magnitude better than ultrafast dispersive Fourier transform detection). We show that this method can not only be implemented to gain insight into noise-driven (spontaneous) frequency conversion processes but also be leveraged to characterize incoherent dynamics seeded by weak coherent optical fields.

Single-shot dynamics of dual-comb generation in a polarization-multiplexing fiber laser

Dual optical frequency combs have been a recurrent case of study over the last decade due to their wide use in a variety of metrology applications. Utilizing a single cavity laser to generate a dual comb reduces system complexity and facilitates suppression of common noise. However, a dual-comb regime in single cavity lasers tends to be more unstable and difficult to achieve. Therefore, having a better understanding about the way they are generated could improve and automate their generation and control. In this paper, we investigate the build-up dynamics and collision of dual comb in a polarization-multiplexing ring-cavity fiber laser using DFT (Dispersive Fourier Transform) method. We observe a bunch of meta-stable short-lived mode-locking states before the laser entered the dual-comb mode-locking state. The energy level of this short-lived initial pulses determines its evolution. If it decreases too much, the pulse will eventually collapse while if it stays above certain level, it will be successfully generated. The results presented in this paper increase the understanding of dual-comb generation inside a single cavity laser and may contribute in future attempts to increase the stabilization of this regime.

Decaying dynamics of harmonic mode-locking in a SESAM-based mode-locked fiber laser

The entire decaying dynamics of harmonic mode-locking (HML) are studied utilizing the dispersive Fourier transform (DFT) technique in a SESAM-based mode-locked fiber laser. It is unveiled that the harmonic solitons do not disappear directly, but undergo transitional processes from the higher-order HML to the lower-order HML and then to the fundamental mode-locking (FML), and finally vanish. The "big corner" can also exist in the decaying process rather than just in the buildup process of HML, and there is at least one "big corner" during the decaying process between the consecutive multi-pulsing states. The energy stabilization phase (ESP) cannot be observed during every transitional process. A breathing behavior and a vibrating soliton molecule are observed in the decaying process from the 2nd HML to the FML and in the decaying process of the FML, respectively. Our work would enrich the understanding of HML behaviors and may contribute to the laser designs.

Temporal soliton dynamics of synchronised ultrafast fibre lasers

Synchronised ultrafast soliton lasers have attracted great research interest in recent decades. However, there is a lack of comprehensive understanding regarding the buildup mechanism of synchronised pulses. Here, we report a dynamic analysis of independent and synchronised solitons buildup mechanisms in synchronised ultrafast soliton lasers. The laser comprises an erbium-doped fibre cavity and a thulium-doped fibre cavity bridged with a common arm. Pulses operating at two different wavelengths formed in the cavities are synchronised by cross-phase modulation-induced soliton correlation in the common fibre arm. We find that the whole buildup process of the thulium-doped fibre laser successively undergoes five different stages: continuous wave, relaxation oscillation, quasi-mode-locking, continuous wave mode-locking and synchronised mode-locking. It is found that the starting time of the synchronised solitons is mainly determined by the meeting time of dual-color solitons. Our results will further deepen the understanding of dual-color synchronised lasers and enrich the study of complex nonlinear system dynamics.

Photonic molecule state transition by collision

We investigate the impact of collisions with two-frequency photonic molecules aiming to observe internal dynamic behavior and challenge their strong robustness. Versatile interaction scenarios show intriguing state changes expressed through modifications of the resulting state such as temporal compression and unknown collision-induced spectral tunneling. These processes show potential for efficient coherent supercontinuum generation and all-optical manipulation.

Investigations on diverse dynamics of soliton triplets in mode-locked fiber lasers

Optical soliton molecules exhibiting behaviors analogous to matter molecules have been the hotspot in the dissipative system for decades. Based on the dispersion Fourier transformation technique, the real-time spectral interferometry has become the popular method to reveal the internal dynamics of soliton molecules. The rising degrees of freedom in pace with the increased constitutes of soliton molecules yield more intriguing sights into the internal motions. Yet the soliton molecules with three or more pulses are rarely investigated owing to the exponentially growing complexity. Here, we present both experimental and theoretical studies on the soliton molecules containing three solitons. Different assemblies of the constitutes are categorized as different types of soliton triplet akin to the geometric isomer, including equally-spaced triplet and unequally-spaced triplet. Typical soliton triplets with different dynamics including regular internal motions, hybrid phase dynamics and complex dynamics involving separation evolution are experimentally analyzed and theoretically simulated. Specifically, the energy difference which remains elusive in experiments are uncovered through the simulation of diverse triplets with plentiful dynamics. Moreover, the multi-dimensional interaction space is proposed to visualize the internal motions in connection with the energy exchange, which play significant roles in the interplays among the solitons. Both the experimental and numerical simulations on the isomeric soliton triplets would release a larger number of degrees of freedom and motivate the potentially artificial configuration of soliton molecules for various ultrafast applications, such as all-optical buffering and multiple encoding for telecommunications.

Collision and dissociation of soliton molecules triggered by gain perturbation in passively mode-locked fiber laser

Soliton molecule has the properties that similar to those of matter molecule, which brings great research value. The rich dynamics of soliton molecules depend on the complex interactions between pulses. As one of the important factors, gain dynamics has multi-dimensional effects on the interactions of soliton molecules. We here study the interaction process of soliton molecules under gain perturbation, and find the oscillation and collision behaviors of pulses within soliton molecules induced by gain perturbation, as well as the pulses recombination through interactions between soliton molecules. We believe that the energy change in the cavity and the energy transfer based on the continuous wave component play an important role in the evolution process of the dissociation of soliton molecules into three-pulses bunch and single pulse. These findings reveal the effects of gain on the motion of soliton molecules and provide a basis for exploring the control dynamics of soliton molecules.

Ultrafast Temporal SU(1,1) Interferometer

Interferometers are highly sensitive to phase differences and are utilized in numerous schemes. Of special interest is the quantum SU(1,1) interferometer which is able to improve the sensitivity of classical interferometers. We theoretically develop and experimentally demonstrate a temporal SU(1,1) interferometer based on two time lenses in a 4f configuration. This temporal SU(1,1) interferometer has a high temporal resolution, imposes interference on both time and spectral domains, and is sensitive to the phase derivative which is important for detecting ultrafast phase changes. Therefore, this interferometer can be utilized for temporal mode encoding, imaging, and studying the ultrafast temporal structure of quantum light.

Two-photon imaging of soliton dynamics

Optical solitary waves (solitons) that interact in a nonlinear system can bind and form a structure similar to a molecule. The rich dynamics of this process have created a demand for rapid spectral characterization to deepen the understanding of soliton physics with many practical implications. Here, we demonstrate stroboscopic, two-photon imaging of soliton molecules (SM) with completely unsynchronized lasers, where the wavelength and bandwidth constraints are considerably eased compared to conventional imaging techniques. Two-photon detection enables the probe and tested oscillator to operate at completely different wavelengths, which permits mature near-infrared laser technology to be leveraged for rapid SM studies of emerging long-wavelength laser sources. As a demonstration, using a 1550 nm probe laser we image the behavior of soliton singlets across the 1800-2100 nm range, and capture the rich dynamics of evolving multiatomic SM. This technique may prove to be an essential, easy-to-implement diagnostic tool for detecting the presence of loosely-bound SM, which often remain unnoticed due to instrumental resolution or bandwidth limitations.

Phase-tailored assembly and encoding of dissipative soliton molecules

Self-assembly of particle-like dissipative solitons, in the presence of mutual interactions, emphasizes the vibrant concept of soliton molecules in varieties of laser resonators. Controllable manipulation of the molecular patterns, held by the degrees of freedom of internal motions, still remains challenging to explore more efficient and subtle tailoring approaches for the increasing demands. Here, we report a new phase-tailored quaternary encoding format based on the controllable internal assembly of dissipative soliton molecules. Artificial manipulation of the energy exchange of soliton-molecular elements stimulates the deterministic harnessing of the assemblies of internal dynamics. Self-assembled soliton molecules are tailored into four phase-defined regimes, thus constituting the phase-tailored quaternary encoding format. Such phase-tailored streams are endowed with great robustness and are resistant to significant timing jitter. All these results experimentally demonstrate the programmable phase tailoring and exemplify the application of the phase-tailored quaternary encoding, prospectively promoting high-capacity all-optical storage.

Real-time Fourier-domain optical vector oscilloscope

To meet the constant demands of high-capacity telecommunications infrastructure, data rates beyond 1 terabit per second per wavelength channel and optical multiplexing are widely applied. However, these features pose challenges for existing data acquisition and optical performance monitoring techniques because of bandwidth limitation and signal synchronization. We designed an approach that would address these limitations by optically converting the frequency limit to an unlimited time axis and combining this with a chirped coherent detection to innovatively obtain the full-field spectrum. With this approach, we demonstrated a real-time Fourier-domain optical vector oscilloscope, with a 3.4-terahertz bandwidth and a 280-femtosecond temporal resolution over a 520-picosecond record length. In addition to on-off keying and binary phase-shift keying signals (128 gigabits per second), quadrature phase-shift keying wavelength division-multiplexed signals (4 × 160 gigabits per second) are simultaneously observed. Moreover, we successfully demonstrate some high-precision measurements, which indicate them as a promising scientific and industrial tool in high-speed optical communication and ultrafast optical measurement.

Single-Shot Reconfigurable Femtosecond Imaging of Ultrafast Optical Dynamics

Understanding ultrafast dynamics in the femtosecond timescale plays a pivotal role in fundamental research and technology innovation. Spatiotemporal observation of those events in real-time requires imaging speeds greater than 1012 frames per second (fps), far beyond the fundamental speed limits of the ubiquitous semiconductor sensor technologies. In addition, a majority of femtosecond events are non-repeatable or difficult-to-repeat since they either work in a highly unstable nonlinear regime or require extreme or rare conditions to initiate. Therefore, the traditional pump-probe imaging approach fails since it heavily depends on precise event repetition. Single-shot ultrafast imaging emerges as the only solution; however, existing techniques cannot reach more than 15×1012 fps, and they only record an insufficient number of frames. Compressed ultrafast spectral photography (CUSP) is proposed to overcome these limitations. Here, CUSP's full design space is explored by manipulating the ultrashort optical pulse in the active illumination. Via parameter optimization, an extraordinarily fast frame rate of 219×1012 fps is achieved. This implementation of CUSP is also highly flexible, allowing various combinations of imaging speeds and numbers of frames (several hundred up to 1000) to be readily deployed in diverse scientific studies, such as laser-induced transient birefringence, self-focusing, and filaments in dielectric media.

Indirect spectrum measurement via random phase modulation and detection in temporal domain

Spectroscopy continues to provide possibilities for a deeper understanding of fundamental physical phenomena. Traditional spectral measurement method, dispersive Fourier transformation, is always limited by its realization condition (detection in the temporal far-field). Inspired by Fourier ghost imaging, we put forward an indirect spectrum measurement to overcome the limitation. The spectrum information is reconstructed via random phase modulation and near-field detection in the time domain. Since all operations are realized in the near-field region, the required length of dispersion fiber and optical loss are greatly reduced. Considering the application in spectroscopy, the length of required dispersion fiber, the spectrum resolution, the range of spectrum measurement and the requirement on bandwidth of photodetector are investigated.

Dichromatic "Breather Molecules" in a Mode-Locked Fiber Laser

Bound states of solitons ("molecules") occur in various settings, playing an important role in the operation of fiber lasers, optical emulation, encoding, and communications. Soliton interactions are generally related to breathing dynamics in nonlinear dissipative systems, and maintain potential applications in spectroscopy. In the present work, dichromatic breather molecules (DBMs) are created in a synchronized mode-locked fiber laser. Real-time delay-shifting interference spectra are measured to display the temporal evolution of the DBMs, that cannot be observed by means of the usual real-time spectroscopy. As a result, robust out-of-phase vibrations are found as a typical intrinsic mode of DBMs. The same bound states are produced numerically in the framework of a model combining equations for the population inversion in the mode-locked laser and cross-phase-modulation-coupled complex Ginzburg-Landau equations for amplitudes of the optical fields in the fiber segments of the laser cavity. The results demonstrate that the Q-switching instability induces the onset of breathing oscillations. The findings offer new possibilities for the design of various regimes of the operation of ultrafast 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.

Dynamics of pulsating solitons derived from asymmetrical dispersive waves

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.

Periodic transition between two evolving soliton pulsation states in an Yb-doped fiber laser

Due to the fascinating features, pulsating solitons attract much attention in the field of nonlinear soliton dynamics and ultrafast lasers. So far, most of the investigations on pulsating soliton are conducted in Er-doped fiber lasers. In this work, we reported the periodic transition between two evolving pulsating soliton states in an Yb-doped fiber laser. By using the real-time measurement techniques, the spectral and temporal characteristics of this transition state were investigated. Two evolving soliton pulsation states have similar evolution process, i.e., from pulsating towards quasi-stable mode-locked states. However, the details of the two processes are different, such as the pulse energy levels, pulsating modulation depths, duration of quasi-stable mode-locked states. The transition between two evolving soliton pulsation states could be attributed to the interaction of the polarizer and the varying polarization states of the pulse inside the laser cavity. The experimental results will contribute to the further understanding of soliton pulsating dynamics in dissipative optical systems.

Novel optical soliton molecules formed in a fiber laser with near-zero net cavity dispersion

Soliton molecules (SMs) are stable bound states between solitons. SMs in fiber lasers are intensively investigated and embody analogies with matter molecules. Recent experimental studies on SMs formed by bright solitons, including soliton-pair, soliton-triplet or even soliton-quartet molecules, are intensive. However, study on soliton-binding states between bright and dark solitons is limited. In this work, the formation of such novel SMs in a fiber laser with near-zero group velocity dispersion (ZGVD) is reported. Physically, these SMs are formed because of the incoherent cross-phase modulation of light and constitute a new form of SMs that are conceptually analog to the multi-atom molecules in chemistry. Our research results could assist the understanding of the dynamics of large SM complexes. These findings may also motivate potential applications in large-capacity transmission and all-optical information storage.

Genetic algorithm optimization of broadband operation in a noise-like pulse fiber laser

The noise-like pulse regime of optical fiber lasers is highly complex, and associated with multiscale emission of random sub-picosecond pulses underneath a much longer envelope. With the addition of highly nonlinear fiber in the cavity, noise-like pulse lasers can also exhibit supercontinuum broadening and the generation of output spectra spanning 100's of nm. Achieving these broadest bandwidths, however, requires careful optimization of the nonlinear polarization rotation based saturable absorber, which involves a very large potential parameter space. Here we study the spectral characteristics of a broadband noise-like pulse laser by scanning the laser operation over a random sample of 50,000 polarization settings, and we quantify that these broadest bandwidths are generated in only [Formula: see text] 0.5% of cases. We also show that a genetic algorithm can replace trial and error optimization to align the cavity for these broadband operating states.

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.

Collision-induced Hopf-type bifurcation reversible transitions in a dual-wavelength femtosecond fiber laser

Collisions refer to a striking nonlinear interaction process in dissipative systems, revealing the particle-like properties of solitons. In dual-wavelength mode-locked fiber lasers, collisions are inherent and periodic. However, how collisions influence the dynamical transitions in the dual-wavelength mode-locked state has not yet been explored. In our work, dispersion management triggers the complex interactions between solitons in the cavity. We reveal the smooth or Hopf-type bifurcation reversible transitions of dual-color soliton molecules (SMs) during the collision by the real-time spectral measurement technique of time-stretch Fourier transform. The reversible transitions between stationary SMs and vibrating SMs, reveal that the cavity parameters pass through a bifurcation point in the collision process without active external intervention. The numerical results confirm the universality of collision-induced bifurcation behavior. These findings provide new insights into collision dynamics in dual-wavelength ultrafast fiber lasers. Furthermore, the study of inter-molecular collisions is of great significance for other branches of nonlinear science.

Experimental realisations of the fractional Schrödinger equation in the temporal domain

The fractional Schrödinger equation (FSE)-a natural extension of the standard Schrödinger equation-is the basis of fractional quantum mechanics. It can be obtained by replacing the kinetic-energy operator with a fractional derivative. Here, we report the experimental realisation of an optical FSE for femtosecond laser pulses in the temporal domain. Programmable holograms and the single-shot measurement technique are respectively used to emulate a Lévy waveguide and to reconstruct the amplitude and phase of the pulses. Varying the Lévy index of the FSE and the initial pulse, the temporal dynamics is observed in diverse forms, including solitary, splitting and merging pulses, double Airy modes, and "rain-like" multi-pulse patterns. Furthermore, the transmission of input pulses carrying a fractional phase exhibits a "fractional-phase protection" effect through a regular (non-fractional) material. The experimentally generated fractional time-domain pulses offer the potential for designing optical signal-processing schemes.

Dark soliton families in quintic nonlinear lattices

We prove that the dark solitons can be stable in the purely quintic nonlinear lattices, including the fundamental, tripole and five-pole solitons. These dark soliton families are generated on the periodic nonlinear backgrounds. The propagation constant affects the forms of these solitons, while the number of poles does not lead to the variation of the backgrounds. The dark solitons are stable only when the propagation constant is moderately large.

Direct Observation of Dynamically Localized Quantum Optical States

Quantum-correlated biphoton states play an important role in quantum communication and processing, especially considering the recent advances in integrated photonics. However, it remains a challenge to flexibly transport quantum states on a chip, when dealing with large-scale sophisticated photonic designs. The equivalence between certain aspects of quantum optics and solid-state physics makes it possible to utilize a range of powerful approaches in photonics, including topologically protected boundary states, graphene edge states, and dynamic localization. Optical dynamic localization allows efficient protection of classical signals in photonic systems by implementing an analogue of an external alternating electric field. Here, we report on the observation of dynamic localization for quantum-correlated biphotons, including both the generation and the propagation aspects. As a platform, we use sinusoidal waveguide arrays with cubic nonlinearity. We record biphoton coincidence count rates as evidence of robust generation of biphotons and demonstrate the dynamic localization features in both spatial and temporal space by analyzing the quantum correlation of biphotons at the output of the waveguide array. Experimental results demonstrate that various dynamic modulation parameters are effective in protecting quantum states without introducing complex topologies. Our Letter opens new avenues for studying complex physical processes using photonic chips and provides an alternative mechanism of protecting communication channels and nonclassical quantum sources in large-scale integrated quantum optics.

Spectro-temporal evolution of mode-locked lasing in fiber frequency-shifted feedback laser

As a type of mode-locked fiber laser, fiber frequency-shifted feedback lasers (FSFLs) have been rarely studied regarding the buildup process of mode locking. We carried out an experimental investigation to show the unique characteristics of the process, such as the direct evolution of the Q switched mode-locked state to the mode-locked state, the unique phenomenon of spectral center frequency oscillation, evolution to a double-pulse state in harmonic mode locking, millisecond stabilization time, and exponentially decreasing change of relative phase per round trip. For the first time, to the best of our knowledge, the double-beam heterodyne method is applied to measure the evolution of laser spectra with pulse width in the nanosecond range. Understanding the unique buildup mechanism may aid in the engineering and application of FSFLs.

Dynamic phase retrieval method for ultrafast and precise vibration sensing based on time stretching

We demonstrate a method for retrieving the phase information from single-shot interference spectra obtained by dispersive Fourier transform, through which the error accumulation during phase retrieval is restrained. A Mach-Zehnder interferometer is proposed for vibration sensing with high speed. We find that relative phase trends at different time delays can be precisely retrieved to improve the signal-to-noise ratio when the time interval jitter between pulses within two arms is less than four times the pulse width. The verification experiment achieves a phase resolution of 5.3 mrad and a high-speed refresh frame rate of 51.8 MHz. Numerical simulations and experiments show that the method is effective for phase demodulation of dynamic interference spectra, and provides a reliable strategy for high-speed, precision sensing.

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

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.

Synchronous and asynchronous pulsating dual solitons in lasers

Pulsating solitons are intriguing objects in laser physics and nonlinear science. Recently, emerging works on the pulsating multi-solitons have raised interest in interactions and synchronizations within multiple breathers. However, with their separation of the order of nanoseconds, the evolution and underlying dynamics of multiple pulsating solitons remain uncharted. In this work, we bring initial insights into the pulsating dual-soliton (PDS) with a separation of three orders of magnitude of the pulse duration. Chaotic, synchronous, and asynchronous pulsations are revealed to be controlled by the pump power. Specifically, two solitons can pulsate synchronously in the form of a frozen limit cycle. The asynchronous PDS at a high pump power brings the rotating limit cycle in the phase space. Unveiling the evolutionary dynamics of PDS, this work has potential in all-optical storage, signal encoding, and time division multiplexing communications.

High energy and low noise soliton fiber laser comb based on nonlinear merging of Kelly sidebands

Optical solitons in mode-locked laser cavities with dispersion-nonlinearity interaction, delivers pulses of light that retain their shape. Due to the nature of discretely distributed dispersion and nonlinearity, optical solitons can emit Kelly-sidebands via the frequency coupling of soliton and dispersive waves. In this paper, we generate a high-energy femtosecond laser comb, by using the intracavity Kelly radiations and 3^rd order nonlinearities. By increasing the intracavity power, the soliton envelop and the Kelly-sidebands merge together via four-wave-mixing, forming a super-continuum spectrum, obtaining 3.18 nJ pulse energy. A supercontinuum span covering from 1100 nm to 2300 nm for further self-referenced f-2f stabilization can be directly achieved by using an amplification-free external supercontinuum technique. Our finding not only demonstrates a non-trivial frequency-time evolution based on 'erbium + χ⁽³⁾' nonlinear gains, but also offers a new opportunity to develop practically compact fiber frequency combs for frequency metrology or spectroscopy.

Dynamics of dissipative soliton molecules in a dual-wavelength ultrafast fiber laser

Optical solitons, particle-like excitations ubiquitous in many fields, can bind to form soliton molecules with striking molecule-like interactions. However, the exotic soliton interactions in soliton molecules are still largely unexplored in dual-wavelength mode-locked fiber lasers. Here, we reveal the dynamics of dissipative soliton molecules with periodic solitons collision in a dual-wavelength ultrafast fiber laser. The soliton molecules with a central wavelength of 1532.8 nm and 1561 nm exhibit conspicuously different evolution characteristics attributed to the difference in gain spectral intensity and trapped potential. The long-wavelength soliton molecule swiftly recovers to the initial state after collision, while the short-wavelength soliton molecule has a remarkable variation in temporal separation and operation state. Moreover, the multiple intensive repulsion and attraction in soliton molecule with energy transfer between leading and trailing solitons, and the formation of triplet soliton molecule in short-wavelength with multiple switching have also been observed. The different oscillating solutions coexisting in dual-wavelength soliton molecules involving oscillating and sliding phase evolution confirm the multistability of the dissipative system. These findings shed new insights into the dynamics of soliton molecules and solitons collision in nonlinear systems.

Superlocalization Reveals Long-Range Synchronization of Vibrating Soliton Molecules

We implement a superlocalization method in the time domain that allows the observation of the external motion of soliton molecules in a fiber ring cavity laser with unprecedented accuracy. In particular, we demonstrate the synchronization of two oscillating soliton molecules separated by several nanoseconds, with intermolecular oscillations following the same pattern as the intramolecular motion of the individual molecules. These experimental findings indicate an interplay between the different interaction mechanisms that coexist inside the laser cavity, despite their very different characteristic ranges, timescales, strengths, and physical origins.

Mutual dynamics between synchronous solitons in a bidirectional mode-locked fiber laser

In this Letter, the mutual dynamics between synchronous solitons in a bidirectional mode-locked fiber laser are studied via dispersive Fourier transform methodology. We explore the spectral evolution and the statistical correlations between solitons with bidirectional propagation, indicating the low and high mutual linear dependences of the spectral energy jitters in stable and breathing mode-locking states, respectively. Moreover, to the best of our knowledge, the oscillating and sliding phase dynamics are experimentally revealed by the interference between bidirectional breathing solitons in ultrafast fiber lasers for the first time. Our findings enrich the understanding of the internal mutual dynamics between bidirectional solitons, which guides the extension of their potential applications, such as Sagnac-effect-based optical sensing.

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.

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

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.

High speed surface defects detection of mirrors based on ultrafast single-pixel imaging

High speed surface defects detection of mirrors is of great significance, for detecting the quality of the mirrors on-site, and ultimately for monitoring the operating states of laser systems. The speeds of conventional proposals are relatively low as they utilize mechanically scanning methods or two-dimensional charge-coupled devices. Here, we propose a high speed surface detection method based on ultrafast single-pixel imaging, which consists of a spatial Fourier optical module for frequency-space mapping and a dispersive Fourier transform module for frequency-time mapping. An optical grating is utilized to map the wideband spectrum of dissipative soliton into the spatial domain under far-field diffraction, where the mirror is inspected. Dispersive Fourier transform is used to map the surface-defects-coded spectral information into the temporal domain, then recorded by a high speed single-pixel detector. The detection system permits continuous single-shot spectra measurement with a frame rate equivalent to the pulse repetition rate (8.4 MHz). We extract amplitude defects by demodulating light intensity, and obtain phase defects by demodulating the interference spectrum with a Mach-Zehnder interferometer structure. Experimental results show that the damaged mirror with a two-dimensional width of 10 × 13 mm can be obtained with a spatial resolution of 90 µm. The obtained phase accuracy after Hilbert transformation is 0.00217 rad, corresponding to a depth resolution of 51 nm. This scheme can find promising applications for surface defects detection of large aperture mirrors, and real-time monitoring of laser systems with high energy.

Intracavity Raman scattering couples soliton molecules with terahertz phonons

Ultrafast atomic vibrations mediate heat transport, serve as fingerprints for chemical bonds and drive phase transitions in condensed matter systems. Light pulses shorter than the atomic oscillation period can not only probe, but even stimulate and control collective excitations. In general, such interactions are performed with free-propagating pulses. Here, we demonstrate intra-cavity excitation and time-domain sampling of coherent optical phonons inside an active laser oscillator. Employing real-time spectral interferometry, we reveal that Terahertz beats of Raman-active optical phonons are the origin of soliton bound-states – also termed “Soliton molecules” – and we resolve a coherent coupling mechanism of phonon and intra-cavity soliton motion. Concurring electronic and nuclear refractive nonlinearities generate distinct soliton trajectories and, effectively, enhance the time-domain Raman signal. We utilize the intrinsic soliton motion to automatically perform highspeed Raman spectroscopy of the intra-cavity crystal. Our results pinpoint the impact of Raman-induced soliton interactions in crystalline laser media and microresonators, and offer unique perspectives toward ultrafast nonlinear phononics by exploiting the coupling of atomic motion and solitons inside a cavity.

Here, the authors demonstrate intra-cavity excitation and time-domain sampling of coherent optical phonons inside an active laser oscillator. They discover that Terahertz crystal vibrations link successive ultrashort solitons which offers an approach to highspeed Raman spectroscopy inside laser cavities.

Internal dynamics in bound states of unequal solitons

The bound states (BSs) of solitons are found to have intriguing internal dynamics in ultrafast lasers. Here, we explore the binding mechanism and internal motions of asymmetric bound state (ABS) solitons constituted by unequal solitons at short-range with their tails directly overlapped. Experiments and simulations show that the periodic energy flux between two solitons, mediated by their overlapped tails, gives rise to a balanced separation and energy distribution across the ABS. The motion mechanisms of strong and weak solitons are discussed in detail. This work provides insights into the binding mechanism and internal dynamics of BSs.

Ultrafast Mueller matrix polarimetry with 10 nanosecond temporal resolution based on optical time-stretch

A fastest full Mueller matrix polarimeter, to the best of our knowledge, based on optical time-stretch has been proposed and demonstrated. Thanks to the time-stretch-based ultrafast spectra detection mechanism, its measurement time could reach 10 ns. Additionally, a novel, to the best of aour knowledge, simpler method to estimate its main systematic error has been proposed and verified. With the proposed method, static measurement of polarizer and wave plate is executed with a maximum coefficient error of below 0.1. Dynamic measurement of a free space electro-optic modulator as fast-changing phase retardation has also been executed to demonstrate the feasibility of the proposed system.

Real-time observation of phase transition of bifurcation evolution in mode-locked lasers

By using the dispersive temporal holography technology, we observe the real-time dynamics of period-doubling bifurcation evolution in an ultrafast fiber laser. The pulse properties including the phase, polarization state, chirp, pulse width, and pulse energy are fully bifurcated, which embody the bifurcation induced "phase transition." There are two types of bifurcation in the laser buildup: one to many bifurcation towards the chaos and the multiple bifurcated pulses back to the stationary state along the reversed trajectory. Both of them can be explained by the rule of the same phase transition. We conclude and illustrate the differences and connections to another common pulsation, the Hopf bifurcation. The findings can promote an understanding of the bifurcations in ultrafast lasers, and are beneficial for an improvement of laser stability.