Bound States Of Solitons Research Articles

Oscillatory soliton pairs in spin-orbit coupled spin-1/2 Bose-Einstein condensates

Abstract We investigate oscillatory soliton pairs including the bright-bright solitons, dark-dark solitons, bright-dark solitons and beating solitons (beating soliton refers to a type of soliton characterized by components that are each composed of both bright and dark solitons, and the overall density is equivalent to that of a single soliton) in the spin-orbit coupled spin-1/2 Bose-Einstein condensates (BECs). Two important effects that are the spin orbit coupling (SOC) and Raman detuning resonance on these solitons are studied. The results show that the intensity of SOC affects the spatial oscillation of solitons, while Raman detuning resonance affects the temporal oscillation of solitons. Moreover, the oscillatory soliton pairs and their background are affected by gain/loss. Under different gain/loss modulator, the periodic, parabolic, dromion type and line solitons are constructed for bright-bright pairs, and the periodic and parabolic background planes are presented for dark-dark soliton pairs, as well as the bound state solitons on periodic and kink type background planes are obtained for bright-dark soliton pairs. For one-beating soliton pairs, two types of beating solitons including the petal and breather-like are discovered by adjusting the wave number. For two-beating soliton pairs, the interaction between different combinations of the two types of beating solitons mentioned above, especially the X- and Y-type beating solitons, are presented by controlling two wave numbers. Furthermore, we verify the stability of soliton pairs through numerical simulation and the Physics-Informed Neural Network (PINN) methods.

Implementation of multiple soliton state fiber laser using a promising saturable absorber of silver indium phosphorus sulfide.

Based on the nonlinear broadband saturation absorption, ultrafast carrier recovery rate, and ultrashort recovery time of new low dimensional materials, ultrafast photonics has rapidly developed as an interdisciplinary field. We have demonstrated multiple solitons state output in an erbium-doped fiber laser based on saturable absorption characteristic of AgInP2S6. By preparing AgInP2S6 with a modulation depth of 10.3% as a saturable absorber, a soliton mode-locked operation state with a pulse duration of 292fs was achieved. The pulse repetition frequency is 43 MHz, and the signal-to-noise ratio is as high as 82 dB. In addition, a bound state soliton with a pulse width of 332fs and a harmonic mode-locked with a frequency of up to 645 MHz were also achieved. The experimental results support the possibility of AgInP2S6 as a saturable absorber; therefore, AgInP2S6 material may be a strong candidate for future promising saturable absorber materials.

41.6nm/44 fs Mamyshev Yb-doped fiber laser with bound-state solitons and multiple harmonics

A circular Mamyshev Yb-doped fiber laser was experimentally designed, and multiple pulse modes, including single-pulse, bound-state pulse, and harmonic mode-locked pulse, were observed by modulating the seed source and pump power. Single-pulse mode-locking with a single-pulse energy of 68.6 nJ was demonstrated at a repetition frequency of 12.1 MHz with a spectral half-height width of 41.6 nm and a compressed pulse duration of 44 fs. Results were also obtained for bound-state and harmonic mode-locked pulses, both with post-compression pulse durations of less than 100 fs. The experiments provide validation of the dynamics of a wide range of pulses in Mamyshev lasers. These findings have implications for the further exploration and understanding of pulse dynamics within the optical domain.

Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions

Abstract We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrödinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses on the dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions under non-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole or double-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and the spatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons, we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions. In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle” crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one and two dark solitons.

Bound-state solitons in three-wave resonant interactions

Bound-state solitons in three-wave resonant interactions

Copper Functionalized SnSe Nanoflakes Enabling Nonlinear Optical Features for Ultrafast Photonics.

This study enhances the ultrafast photonics application of tin selenide (SnSe) nanoflakes via copper (Cu) functionalization to overcome challenges such as low conductivity and weak near-infrared (NIR) absorption. Cu functionalization enhances concentration, induces strain, and reduces the bandgap through Sn substitution and Sn vacancy filling with Cu ions. Demonstrated by density functional theory calculations and experimental analyses, Cu-functionalized SnSe exhibits improved NIR optical absorption and superior third-order nonlinear optical properties. Z-scan measurements and femtosecond transient absorption spectroscopy reveal better performance of Cu-functionalized SnSe in terms of nonlinear optical properties and shorter carrier relaxation times compared to pristine SnSe. Furthermore, saturable absorbers based on both SnSe types, when integrated into an erbium-doped fiber laser, show that Cu functionalization leads to a decrease in pulse duration to 798 fs and an increase in 3dB spectral bandwidth to 3.44nm. Additionally, it enables stable harmonic mode-locking of bound-state solitons. This work suggests a new direction for improving wide bandgap 2D materials by highlighting the enhanced nonlinear optical propertiesand potential of Cu-functionalized SnSe in ultrafast photonics.

Dual-wavelength erbium-doped mode-locked fiber laser based on CoPS3 saturable absorber

An erbium-doped mode-locked fiber laser based on CoPS3 saturable absorber was successfully constructed and ultrashort pulsed light was obtained. The CoPS3 nanosheets solution was prepared using the liquid-phase exfoliation technique, and then drop-coated onto a tapered fiber as a saturable absorber. The fiber laser based on CoPS3 saturable absorber could output conventional solitons at the central wavelengths of 1557.46 nm or 1532.12 nm, respectively, as well as simultaneously output conventional solitons at dual wavelengths of 1531.56 nm and 1557.32 nm, with the ability to switch between the three operational states. The achieved minimum pulse width was 1.59 ps. In addition to conventional solitons, the laser demonstrated the capability to generate bound-state solitons. This study highlights the effectiveness of CoPS3 as a reliable optical modulator for fiber lasers and illustrates its potential for applications in ultrafast optics.

Riemann-Hilbert approach and multi-soliton solutions of nonlocal Newell-type long wave-short wave equation

This article’s purpose is to investigate the inverse scattering transform of the nonlocal long wave-short wave (LW-SW) equation and its multi-soliton solutions via Riemann-Hilbert (RH) approach. By using spectral analysis to the Lax pair of LW-SW equation, the RH problem can be constructed. However, we consider spectral analysis from the time part rather than the usual space part, since it is hard to obtain the analyticity of the space part. Then the RH problem can be solved and the formula of the soliton solutions can be given. We provide several special soliton solutions including Y-shaped solitons, V-shaped solitons, bound-state solitons and mixed four-soliton solutions. Compared with the local case, the solutions of nonlocal LW-SW equation exhibit distinct characteristics that (i) these soliton solutions are strictly symmetric with respect to x = 0 under special parameter conditions, (ii) the mixed four-soliton solution, which combines Y-type and bound-state solitons, is novel.

Statistics of Extreme Events in Integrable Turbulence.

We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schrödinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result to two fundamental scenarios of the generation of integrable turbulence: (i)the asymptotic development of the spontaneous modulational instability of a plane wave, and (ii)the long-time evolution of strongly nonlinear, partially coherent waves. In both cases, involving the bound state soliton gas dynamics, the analytically obtained values of the kurtosis are in perfect agreement with those inferred from direct numerical simulations of the fNLSE, providing the long-awaited theoretical explanation of the respective rogue wave statistics. Additionally, the evolution of a particular nonbound state gas is considered, providing important insights related to the validity of the so-called virial theorem.

Spatiotemporal modulated solitons in a quasi-one-dimensional spin-1 Bose–Einstein condensates

In this paper, we investigate the nonautonomous bright/dark solitons in a quasi-one-dimensional spin-1 Bose–Einstein condensates through a three coupled Gross–Pitaevskii (GP) system with space–time-dependent external potential and temporally modulated gain/loss distributions. Based on the Hirota bilinear method, we analytically construct the bright soliton solutions when the coupled GP system exhibits attractive interactions, while we obtain the dark soliton solutions when the coupled GP system exhibits repulsive interactions. The influence of spatiotemporal modulated external potentials, such as the gain/loss distribution Γ(t), on bright/dark soliton dynamics is analyzed in detail via the analytical solutions. By taking different Γ(t), we obtain different types of bright solitons, including periodic, dromion-like and parabolic solitons, and also derive dark solitons on different backgrounds, such as periodic, parabolic and kink backgrounds. We analyze the regulatory effects of different wavenumber ratios on the attraction and squeezing of bound-state solitons. Through the asymptotic analysis, we find that the interactions between two solitons are elastic. In addition, we conduct research on the forward and inverse problems of the above results via the parallel hard-constraint physical informed neural network (phPINN) method. The predicted solitons and potential functions are in good agreement with the exact solitons and potential in the system.

Application of femtosecond mode-locked SnTe thin films and generation of bound-state solitons

In the realm of ultrafast laser technology, the exploration of two-dimensional materials as saturable absorbers (SA) has garnered significant research interest. Our research investigates the characteristics of SnTe thin films, a topological crystalline insulator material, as a potential saturable absorber for ultrafast lasers. Using the molecular beam epitaxy (MBE) technique, we analyze the films’ morphology and composition through atomic force microscopy (AFM) and successfully deposit SnTe epilayers on Au(111)/mica substrates. Through the utilization of SnTe-SA, an erbium-doped fiber laser is fabricated, demonstrating a pulse output with a width of 276 fs and a center wavelength of 1560 nm, highlighting the potential of SnTe films in manufacturing ultrafast optical devices. Additionally, tightly bound solitons with a soliton interval of 1.01 ps are observed, contributing to the exploration of soliton nonlinear dynamics.

Switchable Single- to Multiwavelength Conventional Soliton and Bound-State Soliton Generated from a NbTe2 Saturable Absorber-Based Passive Mode-Locked Erbium-Doped Fiber Laser.

As a member of transition metal dichalcogenides (TMDs), NbTe2 has a work function of 5.32 eV and a band gap of 0 eV at the Fermi level, which enables it to possess broadband absorption characteristics and has huge potential in optoelectronic devices. In this work, a combination of liquid phase exfoliation (LPE) and optical deposition methods (ODMs) were used to fabricate a NbTe2 saturable absorber (SA). Based on the NbTe2 SA, a ring passive mode-locked erbium-doped fiber laser (PML-EDFL) was constructed by adding NbTe2 SA into the laser cavity. A switchable single- to multiwavelength (dual/triple/quadruple) conventional soliton (CS) and a bound-state soliton (BS) were observed for the first time. The results reveal that NbTe2 SA has excellent saturable absorption characteristics (modulation depth of 2.6%, saturation intensity of 177.4 MW/cm2, and unsaturated loss of 63.8%) and can suppress mode competition and stabilize multiwavelength oscillation. This study expands the applications of NbTe2 nanosheets in ultrafast optoelectronics. The proposed switchable PML-EDFL has extensive applications in high-capacity all-optical communication, high-sensitivity optical fiber sensing, high-precision spectral measurements, and high-energy-efficiency photon neural networks.

Multi-soliton solutions, breather-like and bound-state solitons for complex modified Korteweg–de Vries equation in optical fibers

Under investigation in this paper is a complex modified Korteweg–de Vries (KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.

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

Switching and vector characteristics of bound-state solitons in a graphene-based mode-locked fiber laser

A passive mode-locked erbium-doped fiber laser based on graphene operating in the anomalous dispersion state is designed in this paper. In this experiment, the complete convert process from traditional soliton pulses to soliton rains and bound-state (BS) soliton pulses, and ultimately to traditional soliton pulses, is achieved by adjusting the pump power and polarization controller (PC) to control factors such as nonlinearity, dispersion, and birefringence in the cavity. In the BS soliton state, switching between the 0 phase and π phase BS solitons is achieved. We also replaced the 20/80 coupler with the 30/70 coupler to achieve the soliton rains by varying the energy alteration of the intracavity pulse. When the pump power is increased to 350 mW, the laser generates multi-pulses and eventually forms a new BS. In addition, we also studied the soliton vector characteristics during this conversion process and found the polarization-locked vector soliton (PLVS). The research results enrich nonlinear vector soliton dynamics and provide valuable data for further theoretical studies.

Soliton and bound-state soliton mode-locked fiber laser based on polarization-dependent grating.

We demonstrate the generation of solitons and bound-state solitons in a passively mode-locked fiber laser based on the nonlinear polarization rotation effect by polarization-dependent helical grating. The CO2-laser-inscribed grating has a high polarization-dependent loss of 24.4 dB at 1558.4 nm, which has facilitated the achievement of stable mode locking. The soliton laser could generate 548.9 fs pulses at 1560.59 nm with a spectrum bandwidth of 5.45 nm and a signal-to-noise ratio of 75.2 dB. Through adjustment of the polarization controller and pump power, a bound-state soliton mode-locked pulse with a spectral modulation period of 3.11 nm was achieved and the temporal interval between the two solitons was 2.19 ps. Furthermore, its repetition rate can be easily manipulated by varying the pump power. The results indicated that the polarization-dependent helical grating is an excellent polarizer that could be applied in an ultrafast fiber laser.

Conservation laws, bound-state solitons and modulation instability for a variable-coefficient higher-order nonlinear Schrödinger equation in an optical fiber

Under investigation in this paper is a variable-coefficient sixth-order nonlinear Schrödinger equation, which describes the propagation of attosecond pulses in an optical fiber. Based on Lax pair, infinitely-many conservation laws are constructed. With the aid of auxiliary functions, bilinear forms are derived. In addition, the one- and two-soliton solutions are obtained via the Hirota method. The influences of variable coefficients for soliton velocity and profile are discussed. Particularly, the interaction periods and soliton separation factor of bound-state solitons are analyzed. Finally, modulation instability is investigated. The reported results could be used to understand related soliton molecule and optical instability phenomena in nonlinear optics.

Binary Darboux transformation and interactions of solitons for a higher-order matrix nonlinear Schrödinger equation

In this paper, we present two- and three-soliton solutions for a higher-order matrix nonlinear Schrödinger equation based on the binary Darboux transform constructed, and analyze various types of interaction properties of solitons. For the two solitons, our analytical results reveal four major features that are associated to interaction dynamics: breather-like solitons, bound-state solitons, bound states of the solitons with one/two peaks and bound states of one soliton and another soliton with breather-like structure. In addition, we graphically analyze the related properties with regard to interactions of three solitons, and seven different types of interesting appearances about soliton interactions are obtained, including shape-changing and shape-preserving interactions.

Observation of the extracavity propagation of amplified bound-state soliton pulses emitted from a SWNT mode-locked fiber laser

We have experimentally investigated the extracavity propagation of amplified bound-state soliton pulses from a passively single-wall carbon nanotube mode-locked fiber laser. Under proper configuration of pump power and state of polarization, bound-state pulses exhibit a modulated optical spectrum. Except for the two main center wavelengths of 1557.3 and 1560.5 nm, additional five sidelobes centered at 1548.9, 1552.8, 1565.5, 1569.0 and 1573.1 nm are observed. Besides, the propagation after the extracavity erbium-doped fiber amplification is also investigated. It is demonstrated the significant change of the pulse separation is experimentally obtained when adjusting the extracavity PC before the autocorrelator, which is attributed to the coherent nonlinear soliton-soliton interaction. In addition, when different lengths of single-mode fiber after extracavity amplifier is removed or added, the significant change of the pulse separation is also observed, which matches well with the simulated evolution of pulse separation with respect to the SMF length. The pulse separation change of amplified bound soliton pulses is experimentally and theoretically investigated. These results provide further physical understanding of the generation and extracavity propagation of bound-state soliton pulses.

Data-driven nondegenerate bound-state solitons of multicomponent Bose–Einstein condensates via mix-training PINN

In this paper, by modifying loss function MSE and training area of the physics-informed neural network (PINN), we proposed two neural network models: mix-training PINN and prior information mix-training PINN. We demonstrated the advantages of these models by simulating nondegenerate bound-state solitons (NDBSSs) of multicomponent Bose–Einstein condensates (BECs). Numerical experiments showed that our proposed models are not only simulate the NDBSSs of multicomponent BECs, but also significantly improve the simulation capability. Compared with original PINN, the prediction accuracy of our proposed models are improved by one to three orders of magnitude. By testing the inverse problem of multicomponent BECs, it is also proved that these models have good performance.