Multi-soliton Patterns Research Articles

Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraits

In this study, we investigate the deeper characteristics of the modified Ito equation, which can be applied across various scientific domains to represent systems influenced by noise and randomness. Multi-solitons, including 1-wave, 2-wave, and 3-wave solitons, have been successfully generated using a multiple exponential-function approach. For visual representation, the outcomes are displayed through 3D, 2D, density, and contour plots. The wave transformation is then applied to convert the studied model into an ordinary differential equation. Following this, the dynamic nature of the model is examined from various viewpoints, including bifurcation, chaotic phenomena, multistability, and sensitivity analysis. Bifurcation shows how the solution of a planar system depends on equilibrium points, and when an outward periodic force is implemented to the unperturbed planar system, it reveals chaotic characteristics. These are analyzed using tools such as 3-dimensional and 2-dimensional plots, time scale plots, and Poincaré maps. Additionally, the model’s sensitivity is assessed with varying initial values. The results underscore the effectiveness and relevance of the proposed approaches for examining solitons within a broad spectrum of nonlinear systems.

Exploring multi-soliton patterns, bifurcation analysis, and chaos in (2+1) dimensions: A study on nonlinear dynamics

This study explores the intrinsic characteristics of the (2+1)-dimensional Schwarz-Korteweg-de Vries equation used to describe shallow water waves. The multiple solitons are successfully constructed using a technique involving multiple exponential functions. Graphical representations of the results are provided in 3D, 2D, and density plots to assess the compatibility of the solutions. Also, the dynamic nature of studied equation is examined based on bifurcation and chaos theory for nonlinear systems. Bifurcation signifies how our dynamical system is affected by physical parameters in planar dynamical system. After that, we apply the external force on planar dynamical system to show the chaotic like behavior of the studied model. Such behavior is confirmed by utilizing different chaos detecting tools. The obtained results serve to explain the effectiveness and applicability of the utilized methodologies in comprehend the exact solution and qualitative behavior of nonlinear physical models.

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.

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.

Observation the Multi-Soliton Patterns From the Er-Doped Mode-Locked Fiber Laser Modulated by PtSe2

The passively mode-locked fiber laser can provide an ideal platform to investigate the soliton dynamics for it can be modeled by the complex Ginzburg-Landau equation well. Here, we experimentally studied the formation and dynamics of soliton patterns in an erbium-doped fiber laser mode-locked by PtSe2 based saturable absorber via evanescent field interaction. With the increase of pump power, different soliton patterns, such as single soliton, two solitons and bound soliton, can be observed experimentally. The results can identify the nonlinear optical response of the PtSe2, and may make way for unveiling the nature of the soliton dynamics in the fiber laser system.

Versatile multi-soliton patterns of noise-like pulses in a passively mode-locked fiber laser.

We experimentally report the dynamics of multi-soliton patterns noise-like pulses (NLPs) in a passively mode-locked fiber laser, which the pulse duration can be linearly tuned from 8.21 ns to 128.23 ns by 2.936 ns / 10 mW. Benefiting from the drastically strengthened nonlinear effects in the cavity and the high gain amplification in the unidirectional ring (UR), the transformation from rectangular-shaped NLP to Gaussian-shaped NLP is experimentally achieved. Versatile multi-soliton patterns are observed in NLP regime for the first time, namely, single-scale soliton clusters, high-order harmonic mode-locking, and localized chaotic multiple pulses. In particular, the spectrum evolution with pump power and spectrum stability in 2 hours are also monitored. The obtained results demonstrate the rectangular-shaped NLP can fully transform into Gaussian-shaped NLP, and the multi-soliton patterns can exist in the NLP regime, which contributes to further understanding the nature and mechanism of the NLP in a passively mode-locked fiber laser.

Behavioral similarity of dissipative solitons in an ultrafast fiber laser.

We unveil a new type of dissipative soliton behavior in a net-normal-dispersion bidirectional ultrafast fiber laser. That is, the bidirectional dissipative solitons will always reveal similar spectral and temporal characteristics through common gain and loss modulation, even if the transient instability is involved. The behavioral similarity enables us to accurately design the soliton patterns by introducing seed pulses through loss modulation. As a proof-of-concept application, the precise and flexible manipulation of multi-soliton patterns is demonstrated. These findings will shed new insights into the complex dissipative soliton dynamics and benefit the design of ultrafast lasers with desirable soliton patterns for practical applications.

Optical soliton molecular complexes in a passively mode-locked fibre laser

Ultrashort optical pulses propagating in a dissipative nonlinear system can interact and bind stably, forming optical soliton molecules. Soliton molecules in ultrafast lasers are under intense research focus and present striking analogies with their matter molecules counterparts. The recent development of real-time spectral measurements allows probing the internal dynamics of an optical soliton molecule, mapping the dynamics of the pulses’ relative separations and phases that constitute the relevant internal degrees of freedom of the molecule. The soliton-pair molecule, which consists of two strongly bound optical solitons, has been the most studied multi-soliton structure. We here demonstrate that two soliton-pair molecules can bind subsequently to form a stable molecular complex and highlight the important differences between the intra-molecular and inter-molecular bonds. The dynamics of the experimentally observed soliton molecular complexes are discussed with the help of fitting models and numerical simulations, showing the universality of these multi-soliton optical patterns.

Influence of pseudo-stimulated-Raman-scattering on the modulational instability in an inhomogeneous nonlinear medium

We study the influence of the pseudo-Raman effect on the modulation instability (MI) in an inhomogeneous nonlinear medium. The system is governed by the extended nonlinear Schrodinger (NLS) equation, which is derived from a Zakharov-type system for the interaction between high-frequency and low-frequency waves. The resulting inhomogeneous NLS equation includes a pseudo-stimulated-Raman-scattering term. The model may apply to the propagation of waves in plasmas, surface waves in the ocean, and optical beams in nonlinear waveguides. This nonautonomous model is converted into an autonomous equation by a similarity transformation, allowing us to find MI regions of the system. The results suggest new possibilities for controlling multi-soliton patterns generated by the MI. The MI patterns are also produced by numerical simulations that confirm the analytical results.

A microfiber-based gold nanorod saturable absorber with evanescent field interaction for multi-soliton patterns in a fiber laser

We report on the generation of various multi-soliton patterns in a fiber laser using a microfiber-based gold nanorod saturable absorber (GNR SA). By depositing GNRs onto a microfiber, the nonlinear effect and photo-thermal stability of the GNR SA are both enhanced due to the evanescent field interacting with the nonlinear material GNRs for a relatively long interaction time. Benefiting from a high third-order nonlinear coefficient and the excellent saturable absorption of GNRs, versatile multi-soliton patterns such as random distribution multi-solitons, soliton clusters, soliton molecules, multiple solitons occupying the whole cavity, and soliton flow can be easily obtained by properly adjusting the laser cavity parameter settings. The experimental results contribute to further understanding the physical mechanisms of multi-soliton dynamics, and demonstrate that the microfiber-based GNR SA is an excellent candidate for investigating the nonlinear phenomena in ultrafast fiber lasers.

Versatile patterns of multiple rectangular noise-like pulses in a fiber laser.

We report on the generation of versatile patterns of multiple rectangular noise-like pulses (NLPs) in a fiber laser mode-locked by nonlinear amplifying loop mirror (NALM). Benefiting from the strengthened nonlinear effect of a segment of highly nonlinear fiber (HNLF) in the loop, multiple rectangular NLPs with various patterns are formed depending on the cavity parameter settings. In particular, the multiple rectangular NLPs could possess unequal packet durations, which is different from the conventional multi-soliton patterns. The experimental results contribute to further understanding the characteristics of the rectangular NLP and the dynamics of multi-pulse patterns.

Microfiber-Based Highly Nonlinear Topological Insulator Photonic Device for the Formation of Versatile Multi-Soliton Patterns in a Fiber Laser

We reported on the observation of versatile multi-soliton patterns in an erbium-doped fiber laser with a microfiber-based topological insulator (TI) photonic device. Taking advantage of both the high third-order nonlinear susceptibility and excellent saturable absorption of TI, various multi-soliton formations, such as soliton molecules, bound solitons, and soliton rains could be easily obtained at a low pump power. These results might deepen the understanding of nonlinear dynamics of multi-soliton patterns, and further demonstrate that the TI deposited microfiber could operate as a high-performance photonic device with both highly nonlinear effect and saturable absorption for the related optics applications.

Vector nature of multi-soliton patterns in a passively mode-locked figure-eight fiber laser.

The vector nature of multi-soliton dynamic patterns was investigated in a passively mode-locked figure-eight fiber laser based on the nonlinear amplifying loop mirror (NALM). By properly adjusting the cavity parameters such as the pump power level and intra-cavity polarization controllers (PCs), in addition to the fundamental vector soliton, various vector multi-soliton regimes were observed, such as the random static distribution of vector multiple solitons, vector soliton cluster, vector soliton flow, and the state of vector multiple solitons occupying the whole cavity. Both the polarization-locked vector solitons (PLVSs) and the polarization-rotating vector solitons (PRVSs) were observed for fundamental soliton and each type of multi-soliton patterns. The obtained results further reveal the fundamental physics of multi-soliton patterns and demonstrate that the figure-eight fiber lasers are indeed a good platform for investigating the vector nature of different soliton types.

The formation of various multi-soliton patterns and noise-like pulse in a fiber laser passively mode-locked by a topological insulator based saturable absorber

We experimentally investigated the formation of various multi-soliton patterns and noise-like (NL) pulses in an erbium-doped fiber laser passively mode-locked by a new type of saturable absorber: topological insulator. With the increase of pump power, various multi-soliton operation states—ordered, chaotic and bunched multiple-soliton—were subsequently obtained. Once the pump power exceeds 401 mW, an NL pulse state emerged, with a maximum 3 dB bandwidth of about 9.3 nm. This systematic study clearly demonstrated that a topological insulator could be an effective saturable absorber for the formation of various soliton operation states in a fiber laser cavity.

Reconstruction of multi-soliton interactions using crest data for (2+1)-dimensional KdV type equations

To predict the wave parameters from the interaction patterns of waves (the inverse problem), the corresponding direct problem needs to be solved. In this paper, interaction patterns of multi-soliton solutions of KdV type equations are constructed. The connection between the multi-soliton interaction patterns and the decomposition of a multi-soliton solution into a linear superposition of solitons and interaction solitons is demonstrated. All new concepts are illustrated for three-soliton solutions of the Kadomtshe–Petviashvili equation.

Multi-hump optical solitons in a saturable medium

We investigate multi-hump spatial solitary waves and multi-soliton patterns generated by an incoherent interaction of two optical beams in a medium with saturable (e.g. photorefractive) nonlinearity. Applying a bifurcation analysis and numerical relaxation technique, we reveal different scenarios of creating the multi-hump solitons and find the families of solitary waves composed of two mutually coupled components. We analyse the stability of these solitons to propagation and find that the evolution of a soliton is governed by its modal structure.

Soliton Lattice and Gas in Passive Fiber-Ring Resonators

We consider multisoliton patterns in the model of a synchronously pumped fiber-loop resonator. An essential difference of this system from its long-line counterpart is that, due to the finite length, dynamical regimes may be observed that would be unstable in the infinitely long line. For the case when the effective instability gain, produced by competition of the modulational instability (MI) of the flat background and losses, is small, we have consistently derived a special form of the complex Ginzburg-Landau equation for a perturbation above the continuous wave (cw) background. It predicts bound states of pulses with a uniquely determined ratio of the pulse width to the separation between them. Direct numerical simulations have produced regular soliton lattices at small values of the feeding pulse power, and irregular patterns at larger powers. Evidence for a phase transition between the lattice and gas phases in the model is found numerically. At low power, the width-to-sep aration ratio as found numerically proves to be quite close to the analytically predicted value. We also compare our results with recently published experimental observations of MI-stimulated formation of a pulse array in a mode-locked fiber laser.