Soliton States Research Articles

Some more variety of analytical solutions to (2+1)-Bogoyavlensky-Konopelchenko equation

The goal of this study is to get analytical solutions to the Bogoyavlensky-Konopelchenko equation, which describes an interaction of a long-wavelength wave moving along the x-axis and a Riemann wave-form moving along the y-axis. The equation has been widely used in soliton theory, fluid dynamics, optics, biological systems, and differential geometry. It is a member of the Ablowitz-Kaup-Newell-Segur hierarchy of integrable systems. By exploiting the classical Lie symmetry approach, the equation is reduced to an ordinary differential equation. After solving the second similarity reduction, the authors derived a novel class of solutions for each case. Additionally, the derived solutions comprise some parameters, and various functions might be utilized to explore wave profiles like stationary, dark, and bright soliton, parabolic dark and bright soliton, and progressive nature. Solutions are compared with previous researches [–] to show novelty of results. Solutions can help with numerous applications in physics, such as fluid dynamics, plasma physics, and nonlinear optics.

Passively harmonic mode-locked erbium-doped fiber lasers based on PbSnS2 saturable absorbers

The two-dimensional (2D) material PbSnS2, a type of transition metal dichalcogenides (TMD), is a highly anisotropic layered compound with potential applications in ultrafast optics. We prepared PbSnS2 nanosheets by liquid phase exfoliation, attached them to microfibers to fabricate saturable absorbers (SAs) by optical deposition method, and successfully applied them to a passive erbium-doped fiber laser (EDFL). In addition, the saturable absorption properties of PbSnS2-based SA were confirmed using a balanced two-detector measurement system. The results demonstrate that the PbSnS2-based SA can realize different stable mode-locked states in the same EDFL cavity, including fundamental frequency conventional soliton and 15th harmonic mode-locked states. Among them, the laser produced fundamental frequency mode-locked state with a signal-to-noise ratio of 59.51 dB (6.58 MHz repetition frequency). The HML pulse with a maximum repetition frequency of 98.71 MHz (corresponding to the 15th harmonic) was obtained. The results demonstrate that PbSnS2 is a candidate material for generating ultrafast pulses and has excellent potential for application in ultrafast lasers.

One-dimensional topological phase and tunable soliton states in atomic nanolines on Si(001) surface

Formation of exotic topological states on technologically important semiconductor substrate is significant from the aspects of both fundamental research and practical implementation. Here, we demonstrate one-dimensional (1D) topological phase and tunable soliton states in atomic nanolines self-assembled on Si(001) surface. By first-principles calculations and tight-binding modeling, we reveal that Bi nanolines provide an ideal system to realize a multi-orbital Su–Schrieffer–Heeger (SSH) model, and the electronic properties can be modulated by substrate-orbital-filtering effect. The topological features are confirmed by nontrivial end states for a finite-length nanoline and (anti-)soliton states at the boundary of two topologically distinct phases. We demonstrate that solitons are highly mobile on the surface, and their formation could be controlled by surface B/N doping. As these nanolines can extend several micrometers long without kinks, and quantum transport simulations suggest clear signatures of topological states characterized by transmission resonance peaks, our work paves an avenue to achieve 1D topological phase compatible with semiconductor technology and to engineer the properties with high tunability and fidelity for quantum information processing.

Strong interactions between solitons and background light in Brillouin-Kerr microcombs.

Dissipative Kerr-soliton combs are laser pulses regularly sustained by a localized solitary wave on top of a continuous-wave background inside a nonlinear resonator. Usually, the intrinsic interactions between the background light and solitons are weak and localized. Here, we demonstrate a strong interaction between the generated soliton comb and the background light in a Brillouin-Kerr microcomb system. This strong interaction enables the generation of a monostable single-soliton microcomb on a silicon chip. Also, new phenomena related to soliton physics including solitons hopping between different states as well as controlling the formations of the soliton states by the pump power, are observed owing to such strong interaction. Utilizing this monostable single-soliton microcomb, we achieve the 100% deterministic turnkey operation successfully without any feedback controls. Importantly, it allows to output turnkey ultra-low-noise microwave signals using a free-running pump.

Bright solitons in a spin-orbit-coupled dipolar Bose-Einstein condensate trapped within a double-lattice.

By effectively controlling the dipole-dipole interaction, we investigate the characteristics of the ground state of bright solitons in a spin-orbit coupled dipolar Bose-Einstein condensate. The dipolar atoms are trapped within a double-lattice which consists of a linear and a nonlinear lattice. We derive the motion equations of the different spin components, taking the controlling mechanisms of the dipole-dipole interaction into account. An analytical expression of dipole-dipole interaction is derived. By adjusting the dipole polarization angle, the dipole interaction can be adjusted from attraction to repulsion. On this basis, we study the generation and manipulation of the bright solitons using both the analytical variational method and numerical imaginary time evolution. The stability of the bright solitons is also analyzed and we map out the stability phase diagram. By adjusting the long-range dipole-dipole interaction, one can achieve manipulation of bright solitons in all aspects, including the existence, width, nodes, and stability. Considering the complexity of our system, our results will have enormous potential applications in quantum simulation of complex systems.

Nonlinear instability and solitons in a self‐gravitating fluid

We study a spherical, self‐gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity‐induced dispersion, the emergence of solitons becomes possible. We thus employ a multiscale expansion method to study, in the weakly nonlinear regime, the evolution of small‐amplitude perturbations around the equilibrium state. This way, we derive a spherical nonlinear Schrödinger (NLS) equation that governs the envelope of the perturbations. The effective NLS description allows us to predict a “nonlinear instability” (occurring in the nonlinear regime of the system), namely, the modulational instability, which, in turn, may give rise to spherical soliton states. The latter feature a very slow (polynomial) curvature‐induced decay in time. The soliton profiles may be used to describe the shape of dark matter halos at the rims of the galaxies.

Novel transition dynamics of topological solitons

Continuous phase transitions can be classified into ones characterized by local-order parameters and others that need additional topological constraints. The critical dynamics near the former transitions have been extensively studied, but the latter is less understood. We fill this gap in knowledge by studying the transition dynamics to a parity-breaking topological ground state called the chiral soliton lattice in quantum chromodynamics at finite temperature, baryon chemical potential, and an external magnetic field. We find a slowing down of the soliton’s translational motion as the critical magnetic field approaches, while the local relaxation rate to the solitonic state remains finite. The time required to converge to the stationary state strongly depends on the symmetry of the initial configuration, determining whether translational motion occurs during the dynamic process. Published by the American Physical Society 2024

Vortex solitons in topological disclination lattices

Abstract The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in these systems, as the vortex state in the disclination lattice bifurcates from its linear topological counterpart, while the position of its propagation constant within the bandgap and localization can be controlled by its power. It is shown that vortex solitons are characterized by strong field confinement at the disclination core due to their topological nature, leading to enhanced stability. Simultaneously, the global discrete rotational symmetry of the disclination lattice imposes restrictions on the maximal possible topological charge of such vortex solitons. The results illustrate the strong stabilizing action that topologically nontrivial structures may exert on excited soliton states, opening new prospects for soliton-related applications.

Tunable Three-Wavelength Fiber Laser and Transient Switching between Three-Wavelength Soliton and Q-Switched Mode-Locked States

We report a passive mode-locked fiber laser that can realize single-wavelength tuning and multi-wavelength spacing tuning simultaneously. The tuning range is from 1528 nm–1560 nm, and up to three bands of soliton states can be output at the same time. These results are confirmed by a nonlinear Schrödinger equation model based on the split-step Fourier method. In addition, we reveal a way to transform the multi-wavelength soliton state into the Q-switched mode-locked state, which is period doubling. These results will promote the development of optical communication, optical sensing and multi-signal pulse emission.

Turn-key Kerr soliton generation and tunable microwave synthesizer in dual-mode Si3N4 microresonators.

This study investigates the thermal compensation mechanism in dual-mode Si3N4 microresonators that demonstrates the ease of generation of single-solitons with nearly octave-wide spectral bandwidth. The deterministic creation of soliton frequency combs is achieved by merely switching the wavelength of a tunable laser or a semiconductor diode laser in a single step. The pump frequency detuning range that can sustain the soliton state is 30 gigahertz (GHz), which is approximately 100 times the resonance linewidth. Interestingly, these dual-mode resonators also support the coexistence of primary combs and solitons, enabling their utilization as functional microwave synthesizers. Furthermore, these resonators readily facilitate the generation of diverse multi-solitons and soliton crystals. This work presents a simplified system to access high-performance and versatile Kerr solitons, with wide-ranging applications in optical metrology, microwave photonics, and LiDAR.

Research on the influence of intra-cavity dispersion on pulse characteristics of a quartic soliton fiber laser

Abstract We numerically investigate the influence of higher-order dispersion on the dynamics of quartic solitons in a passively mode-locked fiber laser. The simulation results show that the output pulse characteristics of the quartic soliton fiber laser are not only affected by the intra-cavity net dispersion but also related to the position of the single-mode fiber (SMF). For different intra-cavity net higher-order dispersion values, the quartic soliton undergoes multiple alternations between the stable single soliton state and pulsating state in the fiber laser, and the number and intensity of Kelly sidebands in the output pulse spectrum are significantly different. For different positions of the SMF, the dynamics of the quartic soliton are also different. In addition, we also observe two types of novel pulsation-creeping behavior and time shift. These findings provide new insights into the output characteristics of quartic solitons in fiber lasers.

A multiple soliton state erbium-doped fiber laser based on a MoS2/C saturable absorber

A MoS2/C saturable absorber in erbium-doped fiber lasers is proved to show excellent pulse modulation capabilities.

Enhanced nonlinear effect for generation of both bound state solitons and harmonic mode-locking with high signal-to-noise ratio based on crossed bandpass transmittance filters

Enhanced nonlinear effect for generation of both bound state solitons and harmonic mode-locking with high signal-to-noise ratio based on crossed bandpass transmittance filters

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.

Spatial-multiplexing of nonlinear states in a few-mode-fiber-based Kerr resonantor

The spatial-multiplexing of nonlinear states of different fiber modes are investigated in a few-mode-fiber-based Kerr resonant cavity. We first design a few-mode fiber (FMF) and optimize the chromatic dispersion for both the fundamental mode (LP01) and the higher-order mode (LP11). A spatial-multiplexing resonant cavity is then constructed by the designed fiber for investigating the coexisted nonlinear states in the spatial dimension. It is founded that the overlap interval of nonlinear states varies with different detuning differences. The coexistence of various nonlinear states is demonstrated within the spatially-multiplexing resonant cavity and eight coexistences are found, including stable soliton state and breather, stable soliton state and Turing pattern, breather and Turing pattern, stable soliton state and chaotic state, two Turing patterns, two chaotic states, two breathers and two stable soliton states. Our study not only enhances the understanding of the fundamental physics of the spatial-multiplexing resonator, but also presents a promising avenue for generating dual frequency combs corresponding to distinct transverse modes.

The fourth-order dispersion effect on the soliton waves and soliton stabilities for the cubic-quintic Gross–Pitaevskii equation

A generalized nonlinear Gross–Pitaevskii equation with the third-, fourth-order dispersions, and the cubic, quintic nonlinear terms is considered, which shows that the wave velocity, amplitude, inverse temporal width and wave number of propagating waves are uniquely dependent on the parameters of second-, third- and fourth-order dispersions. We discuss the anomalous dispersion relations of the cubic-quintic Gross–Pitaevskii(CQGP) equation with second-, third- and fourth-order dispersions, and find that the fourth-order dispersion has a significant influence on the characteristics of the obtained soliton wave solutions. In particular, we analyze the effect of the fourth-order dispersion function r(t) on periodic, bright and dark wave solutions of the CQGP model. We report several families of non-autonomous soliton solutions with different amplitude surfaces, and see that the fourth-order dispersion is essential in a broad range of real physical media as it influences the wave dynamics. Some numerical simulations of bright and dark solitons for the CQGP equation with the different external potentials are considered, which shows the external potential plays a certain stabilizing role for the coexistence state of bright and dark solitons. These dynamic analyses play a significant role in improving the dispersive transport of the nonlinear wave in parabolic-law media.

Ultra-short wavelength of 1.7 μ m ultrafast Tm-doped fiber laser

Thulium-doped fiber lasers (TDFLs) operating at 1.7 μm have immense potential for multiphoton microscopy and imaging applications. However, further research and development are needed, particularly in the ultra-short wavelength range below 1720 nm. Herein, we demonstrate the mode-locked TDFL at 1.7 μm, utilizing a microfiber InSb saturable absorber. By employing intracavity filters, optimizing the gain fiber length, and incorporating a broadband evanescent field absorber, we achieve high-performance ultra-short wavelength solitons in the TDFL. The solitons exhibit a central wavelength of 1707 nm, a pulse width of 895 fs, a repetition rate of 23.36 MHz, and a single pulse energy of 1.7 nJ. Moreover, our experiments demonstrate the generation of diverse soliton states, including high-order harmonic and bound solitons. We also explore the dynamics of mode-locking through experimental investigations. Our findings establish a solid foundation for the research and control of diverse 1.7 μm mode-locked operation state, advancing the field of ultrafast fiber lasers in this wavelength band.

Observation of operation states and wavelength-switching in spatiotemporal mode-locked lasers

The construction and investigation of spatiotemporal mode-locked (STML) lasers offer us an opportunity to comprehend and analyze exceedingly intricate high-dimensional nonlinear physical phenomena that underlie diverse behaviors. While the exploration of coherent mode-locking, such as multimode solitons, has been progressing in depth, there remains a dearth of understanding regarding random pulses or extreme events within STML lasers. In this study, an STML laser was constructed and implemented with two operating regimes. The laser demonstrated mutual switching between noise-like pulses and dissipative soliton states, accompanied by corresponding changes in the output spectrum. The transition of the laser's output spectrum from a single wavelength to a synchronous dual-wavelength at noise-like pulses operation was observed for the first time, as far as we all know. These findings contribute to a deeper understanding of spatiotemporal mode-locked lasers.

Soliton states from quadratic electron-phonon interaction

Soliton states from quadratic electron-phonon interaction

The ground state, localization, and chiral edge dynamics of a three-legged bosonic magnetic ladder

Three-legged bosonic/fermionic magnetic ladder, reproducing the main features of magnetic lattice systems, is an ideal model to study the edge-bulk coupling and chiral edge dynamics, which are a hallmark of quantum Hall physics. Here, the ground state transition, localization, and chiral edge (bulk) states of an interacting three-legged bosonic magnetic ladder are studied analytically and numerically. When the system is in a quasi-steady state, using variational analysis, the threshold for the transition from zero momentum state to plane wave state is obtained. The energy spectrum, the ground state diagram, the chiral current of the system are presented, and the chiral current reversal at the state transition point is observed. Furthermore, the localization and its stability in the system are discussed, and rich localized phenomena (diffusion, breather, soliton, and self-trapping) are predicted. Stable soliton/breather prefers to form an edge state, while the self-trapping is favorite to form a bulk state, i.e. localized edge and bulk states are obtained. Particularly, for the unstable soliton in the ground state or metastable state, different kinds of chiral edge/bulk state and edge-bulk coupling are observed. The stability of the localized states, the edge-bulk coupling characteristics, and the chirality of the system depend on the energy band structure of the system. Additionally, a controllable transition between localized edge state and bulk state is realized by quenching the soliton state. We proposed a theoretical evidence to design and manipulate edge-bulk coupling and different kinds of localized/chiral edge (bulk) states in three-legged bosonic magnetic ladder.