Soliton Molecules Research Articles

Quintic Dispersion Soliton Frequency Combs in a Microresonator

AbstractChip‐scale optical frequency combs have attracted significant research interest and can be used in applications ranging from precision spectroscopy to telecom channel generators and lidar systems. In the time domain, microresonator based frequency combs correspond to self‐stabilized soliton pulses. In two distinct regimes, microresonators are shown to emit either bright solitons in the anomalous dispersion regime or dark solitons (a short time of darkness in a bright background signal) in the normal dispersion regime. Here, the dynamics of continuous‐wave‐laser‐driven soliton generation is investigated in the zero‐group‐velocity‐dispersion regime as well as the generation of solitons that are spectrally crossing different dispersion regimes. In the measurements, zero‐dispersion solitons with multipeak structures (soliton molecules) are observed with distinct and predictable spectral envelopes that are a result of fifth‐order dispersion of the resonators. Numerical simulations and the analysis of bifurcation structures agree well with the observed soliton states. This is the first observation of soliton generation that is governed by fifth‐order dispersion, which can have applications in ultrafast optics, telecom systems, and optical spectroscopy.

Nonlinear superposition between lump soliton and other nonlinear localized waves for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

In the previous studies, the authors have reported the lump soliton collided with other nonlinear localized waves for (2+1)-dimensional Korteweg–de Vries–Sawada-Kotera–Ramani equation. However, this work will introduce a novel restrictive condition to reveal the nonlinear superposition between a lump soliton and other nonlinear localized waves. Under the premise of the acquired N-soliton solutions, the nonlinear superposition structures among lump soliton, stripe solitons, resonance Y-type solitons and breather waves guarantee that the lump soliton does not collide with other localized waves by means of the long wave limit approach, soliton resonance method and symbolic computation. Meanwhile, a variety of soliton molecules are yielded through nonlinear superposition and velocity resonance mechanisms. The obtained solutions in this work will bring about new perception of the interaction behavior between lump soliton and other nonlinear localized waves, and provide more brand new insights into the nonlinear phenomena triggered by the areas of plasma physics, fluid dynamics and nonlinear optics.

Unveiling manipulation mechanism on internal dynamics of soliton triplets via polarization and gain control

Self-assembly of ultrashort pulses highlights the complex patterns of dissipative solitons, termed soliton molecules in consideration of the particle-like behaviors. Multi-constituent temporal patterns release the degrees of freedom of versatile internal motions, emphasizing the molecular-analogous soliton dynamics and the advanced laser applications. Beyond previous studies, exploring the artificial manipulation of the intra-molecular dynamics would spread a new research horizon of ultrafast science. Here, we report the research on the manipulation mechanism on the internal dynamics under a tri-soliton model via the implementation of the polarization and gain control. Assisted with real-time spectral interferometry, both the binding separations and the relative phases are retrieved to unfold the intra-molecular dynamics of soliton triplets. Particularly, we present the switching among tri-soliton states identified by different binding separations and phase-evolving velocities, and further unveil the universal rules of the internal dynamics. All these findings provide an evident manifestation of the artificial manipulation on the temporal distributions and intra-molecular dynamics, as well as enable promising access to rapid multi-pulse reconfiguration applicable to fiber laser platforms.

Novel soliton molecules and interaction wave solutions in a (2+1)-dimensional Sawada–Kotera equation: a multi-linear variable separation method

Novel soliton molecules and interaction wave solutions in a (2+1)-dimensional Sawada–Kotera equation: a multi-linear variable separation method

Vector pulsating solitons and soliton molecules under higher-order effects in passively mode-locked fiber lasers

We numerically study the transport dynamics of vector solitons in ytterbium-doped fiber lasers based on a coupled Ginzburg-Landau equation with higher-order effects. By adjusting the small signal gain coefficient and intracavity birefringence, the number of soliton molecules can be manipulated, the transmission of synchronous and asynchronous vector solitons and the generation of chaotic pulse sequences can be realized. Synchronous vector solitons can be generated when the intracavity birefringence is relatively low, the stable transmission of multi-soliton molecules and the interaction between soliton molecules can be achieved. By changing the value of the phase delay, periodic pulsating solitons can be produced. Furthermore, the phenomenon of the pulse train from the period-doubling to chaos can also be observed. With the enhancement of the intracavity birefringence, asynchronous vector solitons can also achieve stable transmission in the cavity, which the amplitudes and widths of two components are opposite with the different phases. The proposed model has universal application value and the numerical results have guiding significance for studying polarization tunable lasers and exploring the nonlinear mechanism in fiber lasers.

A new method of generating the lump molecules and localized interaction solutions to the (2+1)-dimensional SK equation

The (2+1)-dimensional Sawada-Kotera (SK) equation is an important integrable model, which has wide applications in rivers, lakes, atmosphere, the conformal field and quantum gravity gauge field. In this paper, we introduce a new method for constructing the lump molecules in the SK equation. Then, by using this method and imposing the complexification restrictions, velocity resonant principle, we obtain some hybrid wave solutions, which include the interactions between a lump molecule and two separated solitons, between a lump-lump-soliton molecule and a single soliton, between a lump molecule and a soliton molecule, between a lump molecule and a breather, as well as the lump-lump-breather molecule. Dynamical behaviors of these solutions are analyzed theoretically and graphically. The method introduced can be effectively used to study the wave solutions of other nonlinear PDEs. The results obtained not only enrich the types of soliton molecules, but also can be helpful in the study of the propagation behaviors of nonlinear waves.

Spectral pulsations of evolving soliton molecules in an anomalous dispersion fiber laser

We investigate in detail the spectral pulsation of evolving soliton molecules in an anomalous dispersion fiber laser by utilizing the dispersive Fourier transform technique. The spectral pulsations of an evolving soliton molecule with different properties were achieved in our experiments, such as single-period and double-period pulsation. This type pulsation is characterized by the fact that the soliton molecules periodically experience oscillation in spectral profile and peak power due to the periodic vibration evolution of the internal pulses. However, the continuous weak energy exchange between the two solitons inside the soliton molecules results in an almost invariable pulse energy. In addition, analytical fitting models are given to further reveal the spectral pulsation phenomenon of the evolving soliton molecules. These experimental findings can shed some light on the dynamics of soliton molecules in fiber 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.

Strategies for accessing the multipulse regime of mode-locked fiber lasers

Important ongoing research on mode-locked fiber lasers aims at developing new types of multisoliton regimes, such as soliton molecules, molecular complexes, or soliton crystals. The on-demand generation of such multipulse structures is a major challenge, whereas experiments generally involve a tedious trial-and-error adjustment of the laser parameters. Here we present an approach based on a gradual and calibrated adjustment of the system configuration, which employs efficient parameter routes to reach well-defined multipulse regimes. Our numerical simulations show that once the mode-locking threshold is reached, we can adjust the laser parameters gradually to force the evolution of the laser dynamics towards multipulse structures with fewer distortion in their intensity profiles, which are accessible at reduced pump power levels.

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.

Few-Layered Violet Phosphorene Nanostructures as Saturable Absorbers for Stable Soliton Mode-Locking Operations in an Ultrafast Fiber Laser

Two-dimensional (2D) layered nanosheets of violet phosphorene (VP) have great potential in optoelectronic applications owing to their unique electronic, mechanical, and optical properties. Herein, the nonlinear optical (NLO) properties of liquid-phase-exfoliated (LPE) VP nanosheets based on a side-polished D-shaped fiber (DSF) were experimentally investigated by a homemade dual-balance detection fiber system at the near-infrared band. A strong saturable absorption response was observed. The corresponding modulation depth and saturation intensity were determined as ∼1.57 and ∼68.1 MW/cm2, respectively. As an application, a VP-DSF saturable absorber mode-locked erbium-doped fiber laser was realized for the first time, generating ultrashort pulses with a pulse width of 799 fs. Moreover, the stable soliton molecule mode-locking pulses with a pulse width and time interval of 816 fs and 20.5 ps, respectively, were obtained by adjusting the polarization state in the same laser cavity. The experimental results demonstrated the potential use of VP-based nanomaterials in ultrafast photonics applications.

Bright matter-wave bound soliton molecules in spin-1 Bose–Einstein condensates with non-autonomous nonlinearities

This work deals with matter-wave bright soliton molecules in spin-1 Bose–Einstein condensates described by three-component Gross–Pitaevskii equations with non-autonomous nonlinearities that can be tuned by Feshbach resonance management. Notably, it portrays the possibility to generate bright bound soliton molecules with the help of an exact analytic solution under a controlled velocity resonance mechanism. Results show that these soliton molecules experience the effects of time-varying nonlinearities and modulate themselves during propagation by keeping their stable properties. Significantly, the chosen periodic and kink-like nonlinearities expose the snaking, bending, compression, and amplification of multi-structured soliton molecules along with appreciable changes in their amplitude, velocity, width, and oscillations of the molecule profiles. The present results will add significant knowledge to a complete understanding beyond the known interaction dynamics of matter-wave bright solitons in spinor condensates.

Nonlocal symmetries and interaction solutions for the (n + 1)-dimensional generalized Korteweg–de Vries equation

The (n + 1)-dimensional generalized KdV equation is presented in this paper, and we further investigate its nonlocal symmetries by different methods. It can be seen that the symmetrical transformations obtained by different nonlocal symmetries are usually equivalent. Based on the obtained Lie point symmetry as well as the mth finite symmetrical transformations, we obtain its soliton molecules and multiple soliton solutions. Additionally, for the case of n = 4 various types of interaction solutions among solitons and periodic waves are obtained by the similarity reduction method.

Isomeric dynamics of multi-soliton molecules in passively mode-locked fiber lasers

The self-assembly of optical solitons propagating in nonlinear dissipative systems spreads the concept of soliton molecules. Assisted with the real-time spectral interferometry, plentiful internal dynamics has been probed within the multi-pulse patterns, emphasizing the striking analogies with the matter molecules. Therefrom, these particle-like behaviors would yield more intriguing landscapes toward the extended degrees of freedom considering increased constituents. Here, we transfer the concept of “isomer” to the experimental investigation on the unexplored isomeric dynamics of soliton molecules in parallel. Particularly, two isomers for soliton triplets and four isomers for soliton quadruplets are captured under different self-assembled forms, within each of which the binding separations and relative phases of the constituents are governed by mutual soliton interactions. With the diverse separation-phase evolving trajectories mapped in the interaction plane, detailed insights into the temporal distribution and the transient dynamics are displayed with respect to a panorama of the isomeric dynamics. The perspective of optical isomers shed new light on the analogy with matter molecules, and the underlying isomeric dynamics may stimulate the artificial manipulation of various soliton molecules for ultrafast applications.

Manipulation of tunable soliton molecule generation in a fiber laser

On-demand soliton molecule (SM) generation is an advanced coherent multipulse technique in the field of nonlinear optics. Experimentally generating controllable SMs is a significant challenge. Here, we propose to manipulate the generation of tunable SMs in a mode-locked fiber laser based on the self-constructed cascaded compound filtering effect. The cascaded compound filter is achieved by incorporating nonlinear polarization rotation (NPR) filtering into two-stage Lyot filtering for performing a multiplication operation between these two filtering functions. Tunable SMs with flexible parameters of the internal soliton spacings from 4.64 to 6.47 ps, pulse numbers from 2 to 26 and some special phases of ∼ π and ∼ 0.5π are experimentally created on demand by adjusting the cascaded compound filtering profiles. The simulation of SM generation in a fiber laser is carried out to reproduce the transient processes of experimental observations, which reveals that cascaded compound filtering is beneficial for manipulating the generation of SMs. Our research provides a good platform for studying coherent multipulse generation in a dissipative nonlinear system and a novel method for manipulating tunable SM generation.

Exact solutions of the nonlocal higher-order Chen–Lee–Liu equation

The subject of this paper is a nonlocal higher-order Chen–Lee–Liu equation, which can be reduced from the generic deformation of generalized Kaup–Newell hierarchy involving the higher-order effects in optical fibers. With the help of the Darboux transformation, soliton molecules, breather molecules, double periodic solutions and various kinds of mixed soliton solutions are displayed, whose dynamic behaviors based on the parameters are graphically demonstrated.

In2S3 nanoflakes-based saturable absorber for multi-state soliton generation

Attributing to their excellent photoelectric properties, metal sulfides are potential alternatives for femtosecond photonics. Here, indium sulfide nanoflakes are employed as saturable absorbers. The morphology and chemical composition of In2S3 nanoflakes are characterized. An In2S3 nanoflakes-based SA is fabricated by the method of evanescent light deposition with modulation depth of 2.7 % and saturable intensity of 5 MW/cm2. Stable mode locking with central wavelength of 1530 nm, 3 dB bandwidth of 4.9 nm, pulse duration of 733 fs and fundamental repetition rate of 8.18 MHz is obtained. By carefully adjusting of polarization controller and pumping power, harmonic mode locking with repetition rate of 538 MHz could be achieved. By changing the length of single mode fiber and altering the angle of PC, harmonic soliton molecules centered at 1560 nm are generated with spectral modulation period of 1.3 nm and pulse interval of 4.96 ps. The multi-state soliton generation of the laser confirms the excellent nonlinear absorption characteristics of In2S3 in the communication band, which could be expected to enable more practical instrumentations for spectroscopy, optical sensing and optoelectronics, etc.

Engineered zero-dispersion microcombs using CMOS-ready photonics

Normal group velocity dispersion (GVD) microcombs offer high comb line power and high pumping efficiency compared to bright pulse microcombs. The recent demonstration of normal GVD microcombs using CMOS foundry-produced microresonators is an important step toward scalable production. However, the chromatic dispersion of CMOS devices is large and impairs the generation of broadband microcombs. Here, we report the development of a microresonator in which GVD is reduced due to a coupled-ring resonator configuration. Operating in the turnkey self-injection locking mode, the resonator is integrated in a hybrid manner with a semiconductor laser pump to produce high-power efficiency combs spanning a bandwidth of 9.9 nm (1.22 THz) centered at 1560 nm, corresponding to 62 comb lines. Fast, linear optical sampling of the comb waveform is used to observe the rich set of near-zero GVD comb behaviors, including soliton molecules, switching waves (platicons), and their hybrids. Tuning of the 20 GHz repetition rate by electrical actuation enables servo locking to a microwave reference, which simultaneously stabilizes the comb repetition rate, offset frequency, and temporal waveform. This integrated hybrid system could be used in coherent communications or for ultrastable microwave signal generation by two-point optical frequency division.

Real-time buildup dynamics of additive dissipative soliton in mode-locked fiber lasers

Multi-soliton operation is a universal phenomenon in mode-locked lasers, which is generally considered to be generated from pulse splitting or pulse shaping of dispersive waves. Here, we experimentally unveiled the formation dynamics of additive dissipative soliton (ADS) in mode-locked fiber lasers by means of the time stretched technique. Two distinct evolution ways can be observed during the ADS formation process. One way is pulse splitting which corresponds to the soliton molecules with relatively close separation, while the other one is generated from background noise which corresponds to multi-solitons with loose separation. Due to the environmental perturbation, the former process undergoes transient quasi-periodic dissipative soliton explosion before the soliton molecules are stable and the latter way may suffer transient standstill before the formation of additive soliton. These findings could provide some assistance for further enhancing the comprehension of the buildup of multiple soliton and soliton molecules in dissipative systems.

Oscillating soliton molecules induced by strong vector-mode coupling

Soliton molecules, composed of closely spaced pulses with strong internal interactions, have been in-depth studied in fiber lasers due to their fascinating evolution dynamics and potential applications in high-speed optical communications. Here we demonstrate a type of oscillating soliton molecules in a mode-locked fiber laser constituted by single-mode and polarization-maintaining fibers. Ascribing to the unequal coupling between two orthogonal-polarized vector modes, the constituent pulses of soliton molecules possess different intensities and further result in a dual-roundtrip and large-period oscillation. Numerical simulations reproduce the critical experimental phenomena and show that two vector modes display diverse departing behavior in polarization-maintaining fiber. This work sheds light on the role of strong birefringence on vector solitons, providing a flexible nonlinear system to generate and study oscillating soliton molecules.