Stability Of Solitons Research Articles

Generation of Terahertz radiation from a soliton cavity in a laser-plasma system

Abstract Using particle-in-cell simulations, we demonstrate a novel mechanism for the generation of terahertz radiation in a laser-plasma system. The radiation originates from current oscillations trapped in a stable soliton cavity created by the laser in the under-dense plasma region. These oscillations behave like a current dipole antenna. The characteristics of the antenna can be controlled by tuning the laser-plasma parameters to achieve the desired output frequency. We discuss the optimum conditions for the physical realization of this mechanism and its potential practical applications.

Exact soliton solutions, bifurcation, sensitivity and stability analysis of the fractional longitudinal wave equation in magneto-electro-elastic circular rod

Exact soliton solutions, bifurcation, sensitivity and stability analysis of the fractional longitudinal wave equation in magneto-electro-elastic circular rod

Enhancing high-order harmonic mode-locking in Er/Yb-Doped fiber lasers with sub-MHz fundamental frequency via optoacoustic resonance

We present an experimental study of a long Er/Yb-doped fiber ring laser with a low fundamental frequency of 0.678 MHz. By solely adjusting the quarter-wave plate in the polarization controller, we uncovered a series of reproducible laser generation regimes. Among these, multiple soliton bunches were harmonically mode-locked to low-order cavity harmonics (from the 3rd to the 8th). Notably, we also identified a regime featuring a stable soliton train harmonically mode-locked to the 472nd cavity harmonic at 320 MHz. This regime demonstrated exceptional harmonic mode-locking stability, with a supermode suppression level of 49 dB corresponding to the timing jitter on the order of a few picoseconds. We attribute this remarkable stability to an exact optoacoustic resonance between the laser repetition rate and the fiber eigen acoustic mode frequencies, specifically identified as R06 and TR2,15. These findings represent a significant advancement in high-performance fiber laser operation, particularly in enhancing the stability of lasers with sub-MHz fundamental frequencies capable to generate regular pulses with much higher repetition rates.

Wave propagation and soliton behavior in biomechanical tissues: A mathematical approach

This study presents a mathematical model for understanding wave propagation and soliton behavior in biomechanical tissues, explicitly focusing on the Achilles tendon. Utilizing the Korteweg-de Vries (KdV) equation, the research incorporates the Achilles tendons’ nonlinear elastic and viscoelastic properties to explore how mechanical waves propagate through this complex tissue. The tendon’s nonlinear elasticity leads to wave steepening, while its viscoelasticity introduces dispersive effects that counteract this steepening, resulting in the formation of solitons—stable, localized waves that maintain their shape as they propagate. Key findings from this study reveal that the formation and propagation of solitons are strongly influenced by the tendon’s mechanical properties. Numerical simulations show that stiffer tendons, characterized by a higher elasticity modulus, support faster soliton propagation, with wave speeds ranging from 18.9 m/s in damaged tendons to 28.6 m/s in stiffened tendons. Additionally, soliton amplitude increases with tissue stiffness, with the highest amplitude observed in stiffened tendons (5.1 mm) and the lowest in damaged tendons (3.2 mm). The study also demonstrates that energy dissipation due to the tendon’s viscoelasticity plays a critical role in soliton behavior. Damaged tendons exhibit the highest energy loss (18.6%), leading to shorter soliton propagation distances, while stiffer tendons retain more energy (96.1%) and allow solitons to travel further distances (up to 180 mm). Moreover, the balance between nonlinearity and dispersion is crucial for maintaining soliton stability. Excessive nonlinearity leads to unstable solitons, while higher levels of dispersion contribute to more stable waveforms.

Pattern formations and their active manipulation in a Rydberg noisy-dressed Bose-Einstein condensate.

We investigate the formation and manipulation of spatial patterns and their structural phase transitions by examining the effects of laser linewidth on the dynamics of Rydberg noise-dressed Bose-Einstein condensates (RnD BECs). We discover that the homogeneous matter wave can transition into various types of self-organized patterns, which are manipulated by tuning the laser linewidth, control field intensity, and atomic density. Remarkably, the system exhibits stable nonlocal matter-wave solitons, vortices, and soliton molecules under specific laser linewidths.

Diffraction managed vortex soliton in competing cubic-quintic nonlinear media

We study analytically and numerically vortex solitons in competing cubic-quintic nonlinear media with normal and anomalous fourth order diffraction (FOD). Bifurcated solutions of vortex solitons are obtained with variational (Lagrangian) approach. Propagation dynamics are demonstrated with split-step Fourier transform, which show that normal (anomalous) FOD can weaken (enhance) the stable propagation distance of vortex solitons. Furthermore, stability of vortex solitons is determined by Vakhitov-Kolokolov (VK) criteria. The upper branch of vortex solitons is unstable, whereas, the lower branch of vortex solitons is robust against perturbations.

Three-component soliton states in spinor F = 1 Bose-Einstein condensates with PT-symmetric generalized Scarf-II potentials

Abstract Introducing PT-symmetric generalized Scarf-II potentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seeking stable soliton states in quasi-one-dimensional spin-1 Bose-Einstein condensates. In scenarios where the spin-independent parameter c_0 and the spin-dependent parameter c_2 vary, we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-II potentials. We obtain analytical soliton states and find that simply modulating c_2 may change the analytical soliton states from unstable to stable. Additionally, we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations, exhibiting distinct behavior in energy exchange. For further investigation, we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components. These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.

Elliptic Hermite-Gaussian soliton and transformations in nonlocal media induced by linear anisotropy.

Elliptic Hermite-Gaussian (HG) soliton clusters in nonlocal media with anisotropic diffractions are studied comprehensively. The relations among solitons parameters, diffraction indices, and the degree of nonlocality are derived analytically with the Lagrangian method. Stable elliptic HG soliton clusters can be obtained when linear diffraction is anisotropic. When the solitons are launched with an initial orientation angle, we also demonstrate numerically mode transformations between HG and Laguerre-Gaussian (LG) solitons induced by linear anisotropy. Our results will enrich the soliton phenomenon with linear anisotropic diffraction and may lead to novel applications in all-optical switching, interconnection, etc.

Wavelength-Switchable Ytterbium-Doped Mode-Locked Fiber Laser Based on a Vernier Effect Filter.

A wavelength-switchable ytterbium-doped mode-locked fiber laser is reported in this article. Two Mach-Zehnder interferometers (MZIs, denoted as MZI1, MZI2) with close free spectral ranges (FSRs) are connected in series to form a Vernier effect sensor. By utilizing the filtering effect of the Vernier effect sensor, the wavelength-switchable output of an ytterbium-doped mode-locked fiber laser is realized. When the 3 dB bandwidth of the Vernier effect filter is set to be 5.31 nm around 1073.42 nm, stable dissipative solitons are obtained. Stretching MZI1 horizontally, the central wavelengths of the pulses can be switched among 1073.42 nm, 1055.38 nm, and 1036.22 nm, with a total tunable central wavelength range of 37.2 nm. When the 3 dB bandwidth of the Vernier effect filter is set to be 4.07 nm, stable amplifier similaritons are obtained. Stretching MZI1 horizontally, the central wavelengths of the pulses are switchable among 1072.71 nm, 1060.15 nm, 1048.92 nm, and 1037.26 nm, with a total tunable central wavelength range of 35.15 nm. Compared with traditional fiber interference filters, the Vernier effect filter has a higher sensitivity, making wavelength switching more convenient and providing a wider tuning range for the ytterbium-doped mode-locked fiber laser.

Spontaneous symmetry breaking and vortices in a tri-core nonlinear fractional waveguide

We introduce a waveguiding system composed of three linearly-coupled fractional waveguides, with a triangular (prismatic) transverse structure. It may be realized as a tri-core nonlinear optical fiber with fractional group-velocity dispersion (GVD), or, possibly, as a system of coupled Gross–Pitaevskii equations for a set of three tunnel-coupled cigar-shaped traps filled by a Bose–Einstein condensate of particles moving by Lévy flights. The analysis is focused on the phenomenon of spontaneous symmetry breaking (SSB) between components of triple solitons, and the formation and stability of vortex modes. In the self-focusing regime, we identify symmetric and asymmetric soliton states, whose structure and stability are determined by the Lévy index of the fractional GVD, the inter-core coupling strength, and the total energy, which determines the system’s nonlinearity. Bifurcation diagrams (of the supercritical type) reveal regions where SSB occurs, identifying the respective symmetric and asymmetric ground-state soliton modes. In agreement with the general principles of the SSB theory, the solitons with broken inter-component symmetry prevail, as stable states, with the increase of the energy in the weakly-coupled system. Three-components vortex solitons (which do not feature SSB) are studied too. Because the fractional GVD breaks the system’s Galilean invariance, we also address mobility of the vortex solitons, by applying a boost to them.

Vortex solitons in rotating quasi-phase-matched photonic crystals.

We present an approach to generate stable vortex solitons (VSs) in rotating quasi-phase-matched photonic crystals with quadratic nonlinearity. The photonic crystal is introduced with a checkerboard structure, which can be realized using available technology. The VSs are constructed as four-peak vortex modes of two types: rhombuses and squares. Control parameters, including the power, rotating frequency, and size of each square cell, affect the distribution and stability range of these VSs. The tightly binding rhombic VSs realize the system's ground state, which features the lowest value of the Hamiltonian. By introducing rotation, stable VSs with topological charges l = ±1 and ±2 are observed, and the VSs turn from a quadrupole to a vortex-like state. The generation and modulation of stable VSs in rotating quasi-phase-matched photonic crystals demonstrate promising applications in optical communication systems, optical tweezers, and quantum information processing, where precise control over light propagation and vortex states is crucial.

Excitation and manipulation of super cavity solitons in multi-stable passive Kerr resonators

We report on the theoretical analysis as well as the numerical simulations about the nonlinear dynamics of cavity solitons in a passive Kerr resonator operating in the multistable regime under the condition of a sufficiently strong pump. In this regime, the adjacent tilted cavity resonances might overlap, thus leading to the co-existence of combinatory states of temporal cavity solitons and the extended modulation instability patterns. The cavity in the regime of multistablity may sustain distinct families of cavity solitons, vividly termed as super cavity solitons with much higher intensity and broader spectra if compared with those in the conventional bi-stable regime. The description of such complex cavity dynamics in the multstable regime requires either the infinite-dimensional Ikeda map, or the derived mean-field coupled Lugiato-Lefever equations by involving multiple contributing cavity resonances. With the latter model, we revealed the existence of different orders of super cavity solitons, whose stationary solutions were obtained by using the Newton-Raphson algorithm. Along this line, with the continuation calculation, we have plotted the Hopf / saddle-node bifurcation curves, thus identifying the existing map of the stable and breathing (super) cavity solitons. With this defined parameter space, we have proposed an efficient method to excite and switch the super cavity solitons by adding an appropriate intensity (or phase) perturbation on the pump. Such deterministic cavity soliton manipulation technique is demonstrated to underpin the multi-level coding, which may enable the large capacity all-optical buffering based on the passive fiber ring cavities.

Solitons in one-dimensional non-Hermitian moiré photonic lattice

We study the excitation and stabilization of gap solitons and dipole solitons in a non-Hermitian moiré photonic lattice with self-focusing effect. The lattice is constituted by superimposition of a parity-time symmetric potential and an anti-parity-time symmetric potential with inconsistent frequencies. We find that the single gap solitons within semi-infinite bandgap can indeed stably persist, and their ss positions within the lattice can be precisely adjusted through controlling the oblique angles and propagation constants of incident solitons. Further study shows that the lattice enables dipole solitons with specific soliton energy to overcome inherent repulsion, facilitating their propagation within the lattice. This work unveils the existence of stable gap solitons supported by non-Hermitian moiré photonic lattices, emphasizing the pivotal roles of propagation constants and incident angles in regulating soliton propagation.

Optical soliton solutions of the stochastic resonant nonlinear Schrödinger equation with spatio temporal and inter-modal dispersion under generalized Kudryashov's law non-linearity

This article investigates optical soliton solutions within the stochastic resonant nonlinear Schrödinger equation (SRNLSE). This equation incorporates both spatio-temporal dispersion (STD) and inter-modal dispersion (IMD), along with multiplicative white noise and generalized Kudryashov's law non-linearity. By applying the extended auxiliary equation method, we identify a range of soliton solutions, including bright, dark, and singular solitons. Additionally, we derive solutions that take the form of Jacobi elliptic functions, Weierstrass elliptic functions, and periodic wave functions. The study provides significant insights into soliton dynamics within nonlinear optical systems affected by stochastic influences and complex dispersion interactions. Specifically, it highlights how the interplay of STD and IMD, coupled with the presence of multiplicative noise, shapes the behavior of solitons. Moreover, we delve into the effects of multiplicative noise on the exact solutions of the NLSE using the Maple software. Our analysis reveals that multiplicative noise, interpreted in the Ito sense, plays a crucial role in stabilizing the soliton solutions, particularly maintaining their stability around the zero state. This finding underscores the importance of noise in influencing the stability and dynamics of solitons in optical systems.

Chiral Bulk Solitons in Photonic Graphene with Decorated Boundaries

AbstractA chiral bulk soliton in a nonlinear photonic lattice with decorated boundaries, presenting a novel approach to manipulate photonic transport without extensive bulk modifications is proposed. Unlike traditional methods that rely on topological edge and corner modes, this strategy leverages the robust chiral propagation of bulk modes. By introducing nonlinearity into the system, a stable bulk soliton, akin to the topological valley Hall effects is found. The chiral bulk soliton exhibits remarkable stability; the energy does not decay even after a long‐distance propagation; and the corresponding Fourier spectrum confirms the absence of inter‐valley scattering indicating a valley‐locking property. The findings not only contribute to the fundamental understanding of nonlinear photonic systems but also hold significant practical implications for the design and optimization of photonic devices.

Modulational instability, generation, and evolution of rogue waves in the generalized fractional nonlinear Schrödinger equations with power-law nonlinearity and rational potentials.

In this paper, we investigate several properties of the modulational instability (MI) and rogue waves (RWs) within the framework of the generalized fractional nonlinear Schrödinger (FNLS) equations with rational potentials. We derive the dispersion relation for a continuous wave (CW), elucidating the relationship between the wavenumber and the instability growth rate of the CW solution in the absence of potentials. This relationship is primarily influenced by the power parameter σ, the Lévy index α, and the nonlinear coefficient g. Our theoretical findings are corroborated by numerical simulations, which demonstrate that MI occurs in the focusing context. Furthermore, we study the RW generations in both cubic and quintic FNLS equations with two types of time-dependent rational potentials, which make both cubic and quintic NLS equations support the exact RW solutions. Specifically, we show that the introduction of these two potentials allows for the excitations of controllable RWs in the defocusing regime. When these two potentials become the time-independent cases such that the stable W-shaped solitons with non-zero backgrounds are generated in these cubic and quintic FNLS equations. Moreover, we consider the excitations of higher-order RWs and investigate the conditions necessary for their generations. Our analysis reveals the intricate interplay between the system parameters and the potential configurations, offering insights into the mechanisms that facilitate the emergence of higher-order RWs. Finally, we find the separated controllable multi-RWs in the defocusing cubic FNLS equation with time-dependent multi-potentials. This comprehensive study not only enhances our understanding of MI and RWs in the fractional nonlinear wave systems, but also paves the way for future research in related nonlinear wave phenomena.

Asymptotic stability of small solitons for one-dimensional nonlinear Schrödinger equations

Asymptotic stability of small solitons for one-dimensional nonlinear Schrödinger equations

Vortex light bullets in rotating Quasi-Phase-Matched photonic crystals

We present a methodology for the generation of stable vortex light bullets (LBs) in rotating Quasi-Phase-Matched (QPM) photonic crystals with quadratic nonlinearity. The photonic crystal is designed with a checkerboard structure, which is feasible to realize by using contemporary technological advancements. Within this framework, square- and rhombus-shaped LBs are observed, both of which are constructed as four-peak vortex mode. The control parameters include the effective phase mismatch, power, rotating frequency, and the size of checkerboard cells. These parameters play key roles in determining the distribution and stability domains of vortex LBs. In contrast to the stable vortex solitons observed in two-dimensional (2D) quadratic systems, the LBs investigated in the 3D rotating system exhibit narrower stability domains within the system’s parameter space. The rotating frequency results in the transition of LBs from quadrupole to traditional vortex modes. Potential applications of this research lie in the field of optical communications and information processing.

Two-dimensional vortex dipole, tripole, and quadrupole solitons in nonlocal nonlinearity with Gaussian potential well and barrier.

In this work, we investigate the dynamics and stability of two-dimensional (2D) vortex dipole, tripole, and quadrupole solitons with fundamental topological charge (m = 1) and higher topological charge (m > 1) in nonlocal nonlinearity with Gaussian potential well and barrier. Both analytical and numerical methods are applied to explore these vortex solitons. The analytical expressions are derived by utilizing the variational approach. The numerical simulations show that nonlocality cannot stabilize the vortex dipole, tripole, and quadrupole beams with topological charge m = 1. Interestingly, it is found that these vortex solitons remain stable during propagation only when the topological charge is m = 2 and when the propagation constants are below specific thresholds, where the vortex beams can maintain their profile no matter whether the nonlocality is weak, intermediate, or strong or how the Gaussian potential barrier height (well depth) increases. Furthermore, for the solitons with higher topological charge (m = 4), another consistent pattern emerges, that is, vortex dipole, tripole, and quadrupole solitons split into stable petal solitons and fundamental solitons with the number of petal solitons corresponding to the number of vortex solitons present. The analytical results are verified by numerical simulations.

The theoretical study of high-order dissipation soliton molecules evolution in a passively mode-locked fiber laser

High-order solitons represent a special form of soliton. Due to the complexity of their spatial structure and dynamic evolution, they have important applications in communication systems such as wavelength division multiplexing and secure communication. However, compared to traditional solitons, research on the spectral evolution of high-order solitons is still insufficient. In this paper, through precise control of laser parameters, the dynamic evolution process from stable dissipative single soliton to complex dissipative 8-order soliton molecules in passively mode-locked fiber lasers was successfully simulated. This demonstrates the complexity of solitons interaction and reveals the regularity of soliton molecules order with variations in four parameters: the small signal gain coefficient, nonlinear coefficient, gain bandwidth and the polarization controller angle. Through deep analysis of the order of soliton molecules, pulse shape and spectral shape of dissipative soliton molecules, we showcase the potential of fine-tuning laser parameters to achieve high-order dissipative soliton molecules. This work provides important references for the optimization design and expanded applications of lasers, further driving the development of high-performance, high-efficiency fiber laser technology.