Three-Wave Mixing of Dipole Solitons in One-Dimensional Quasi-Phase-Matched Nonlinear Crystals

A quasi-phase-matched technique is introduced for soliton transmission in a quadratic[χ^((2))]nonlinear crystal to realize the stable transmission of dipole solitons in a one-dimensional space under three-wave mixing.We report four types of solitons as dipole solitons with distances between their bimodal peaks that can be laid out in different stripes.We study three cases of these solitons:spaced three stripes apart,one stripe apart,and confined to the same stripe.For the case of three stripes apart,all four types have stable results,but for the case of one stripe apart,stable solutions can only be found atω_(1)=ω_(2),and for the condition of dipole solitons confined to one stripe,stable solutions exist only for Type1 and Type3 atω_(1)=ω_(2).The stability of the soliton solution is solved and verified using the imaginary time propagation method and real-time transfer propagation,and soliton solutions are shown to exist in the multistability case.In addition,the relations of the transportation characteristics of the dipole soliton and the modulation parameters are numerically investigated.Finally,possible approaches for the experimental realization of the solitons are outlined.

Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation

We show that the nonlinear stage of the dual-wavelength pumped modulation instability(MI)in nonlinear Schrödinger equation(NLSE)can be effectively analyzed by mode truncation methods.The resulting complicated heteroclinic structure of instability unveils all possible dynamic trajectories of nonlinear waves.Significantly,the latticed-Fermi-Pasta-Ulam recurrences on the modulated-wave background in NLSE are also investigated and their dynamic trajectories run along the Hamiltonian contours of the heteroclinic structure.It is demonstrated that there has much richer dynamic behavior,in contrast to the nonlinear waves reported before.This novel nonlinear wave promises to inject new vitality into the study of MI.

Navigation Finsler metrics on a gradient Ricci soliton

In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.

Nondegenerate Soliton Solutions of(2+1)-Dimensional Multi-Component Maccari System

For a multi-component Maccari system with two spatial dimensions,nondegenerate one-soliton and two-soliton solutions are obtained with the bilinear method.It can be seen by drawing the spatial graphs of nondegenerate solitons that the real component of the system shows a cross-shaped structure,while the two solitons of the complex component show a multi-solitoff structure.At the same time,the asymptotic analysis of the interaction behavior of the two solitons is conducted,and it is found that under partially nondegenerate conditions,the real and complex components of the system experience elastic collision and inelastic collision,respectively.

Data-Driven Ai-and Bi-Soliton of the Cylindrical Korteweg-de Vries Equation via Prior-Information Physics-Informed Neural Networks

By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by simulating Ai-and Bi-soliton solutions of the cylindrical Korteweg-de Vries(cKdV)equation.

Three-Soliton Interactions and the Implementation of Their All-Optical Switching Function

As a key component in all-optical networks,all-optical switches play a role in constructing all-optical switching.Due to the absence of photoelectric conversion,all-optical networks can overcome the constraints of electronic bottlenecks,thereby improving communication speed and expanding their communication bandwidth.We study all-optical switches based on the interactions among three optical solitons.By analytically solving the coupled nonlinear Schr¨odinger equation,we obtain the three-soliton solution to the equation.We discuss the nonlinear dynamic characteristics of various optical solitons under different initial conditions.Meanwhile,we analyze the influence of relevant physical parameters on the realization of all-optical switching function during the process of three-soliton interactions.The relevant conclusions will be beneficial for expanding network bandwidth and reducing power consumption to meet the growing demand for bandwidth and traffic.

Observation of stable bound soliton with dual-wavelength in a passively mode-locked Er-doped fiber laser

A phase-locked bound state soliton with dual-wavelength is observed experimentally in a passively mode-locked Erdoped fiber（EDF） laser with a fiber loop mirror（FLM）. The pulse duration of the soliton is 15 ps and the peak-to-peak separation is 125 ps. The repetition rate of the pulse sequence is 3.47 MHz. The output power is 11.8 mW at the pump power of 128 mW, corresponding to the pulse energy of 1.52 nJ. The FLM with a polarization controller can produce a comb spectrum, which acts as a filter. By adjusting the polarization controller or varying the pump power, the central wavelength of the comb spectrum can be tuned. When it combines with the reflective spectrum of the fiber Bragg grating, the total spectrum of the cavity can be cleaved into two parts, then the bound state soliton with dual-wavelength at 1549.7 nm and 1550.4 nm is obtained.

Dual-wavelength dissipative soliton operation of an erbium-doped fibre laser using a nonlinear polarization rotation technique

We report on the generation of dual-wavelength dissipative solitons in a passively mode-locked fibre laser with a net normal dispersion using the nonlinear polarization rotation （NPR） technique. Taking the intrinsic advantage of the intracavity birefringence-induced spectral filtering effect in the NPR-based ring laser cavity, the dual-wavelength dissipative solitons are obtained. In addition, the wavelength separation and the lasing location of the dual-wavelength solitons can be flexibly tuned by changing the orientation of the polarization controller.

Comprehensive analysis of pure-quartic soliton dynamics in a passively mode-locked fiber laser

The understanding of soliton dynamics promotes the development of ultrafast laser technology. High-energy purequartic solitons(PQSs) have gradually become a hotspot in recent years. Herein, we numerically study the influence of the gain bandwidth, saturation power, small-signal gain, and output coupler on PQS dynamics in passively mode-locked fiber lasers. The results show that the above four parameters can affect PQS dynamics. Pulsating PQSs occur as we alter the other three parameters when the gain bandwidth is 50 nm. Meanwhile, PQSs evolve from pulsating to erupting and then to splitting as the other three parameters are altered when the gain bandwidth is 10 nm, which can be attributed to the existence of the spectral filtering effect and intra-cavity fourth-order dispersion. These findings provide new insights into PQS dynamics in passively mode-locked fiber lasers.

Physics-Informed Neural Network Method for Predicting Soliton Dynamics Supported by Complex Parity-Time Symmetric Potentials

We examine the deep learning technique referred to as the physics-informed neural network method for approximating the nonlinear Schr¨odinger equation under considered parity-time symmetric potentials and for obtaining multifarious soliton solutions.Neural networks to found principally physical information are adopted to figure out the solution to the examined nonlinear partial differential equation and to generate six different types of soliton solutions,which are basic,dipole,tripole,quadruple,pentapole,and sextupole solitons we consider.We make comparisons between the predicted and actual soliton solutions to see whether deep learning is capable of seeking the solution to the partial differential equation described before.We may assess whether physicsinformed neural network is capable of effectively providing approximate soliton solutions through the evaluation of squared error between the predicted and numerical results.Moreover,we scrutinize how different activation mechanisms and network architectures impact the capability of selected deep learning technique works.Through the findings we can prove that the neural networks model we established can be utilized to accurately and effectively approximate the nonlinear Schr¨odinger equation under consideration and to predict the dynamics of soliton solution.

Matrix integrable fifth-order mKdV equations and their soliton solutions

We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifthorder mKdV equations are given.

Serum level changes of inflammatory cytokines in patients with moderate to severe acne vulgaris treated with dual-wavelength laser

Background:Acne vulgaris(AV)is a common inflammatory skin disease.Although various mechanisms have been indicated in the etiopathogenesis of AV,the exact pathophysiology remains unknown.Various lasers have been used to treat AV;however,the serum level changes of inflammatory cytokines after laser therapy have not been elucidated.We aimed to investigate the relationship between inflammatory changes and remission on the opposite side in patients with moderate to severe AV after treating half of the face with 595-and 1064-nm dualwavelength laser.Methods:In total,18 patients(9 male and 9 female)between 16 and 35 years of age with moderate to severe AV were evaluated in the study.Disease severity was classified according to the Pillsbury grading system of acne.Patients were randomized to receive a series of two treatment sessions at intervals of 2 weeks and followed up at 2 weeks after the final treatment.A 3 mL blood sample was drawn from every subject each time,and serum levels of inflammatory cytokines such as interleukin(IL)-6,IL-8,and IL-22 were determined using enzyme-linked immunosorbent assay at baseline and 2 weeks after each treatment.Improvement was determined by a blinded assessment of photographs taken before and after the final evaluation.Results:Inflammation was significantly reduced on both the treated and untreated sides,and symptoms of AV lesions were alleviated.All patients showed a significant increase in serum IL-22 levels after the first laser therapy,with no significant difference in serum IL-6 and IL-8 levels.After the second laser therapy,serum IL-6,IL-8,and IL-22 levels were significantly decreased.No significant side effects such as bruising,edema,hyperpigmentation,hypopigmentation,or scarring were reported.Conclusion:Half-face treatment with 595-and 1064-nm dual-wavelength laser for moderate and severe AV showed a significant effect of full-face remission,which was associated with a gradual decrease in IL-6,IL-8,and IL-22 levels after half-face topical treatment.This suggests that reducing inflammatory cytokine levels in the serum can relieve inflammation in non-therapeutic sites.This laser treatment is effective,economical,and painless.

Flat soliton microcomb source

Mode-locked microcombs with flat spectral profiles provide the high signal-to-noise ratio and are in high demand for wavelength division multiplexing(WDM)-based applications,particularly in future high-capacity communication and parallel optical computing.Here,we present two solutions to generate local relatively flat spectral profiles.One microcavity with ultra-flat integrated dispersion is pumped to generate one relatively flat single soliton source spanning over 150 nm.Besides,one extraordinary soliton crystal with single vacancy demonstrates the local relatively flat microcomb lines when the inner soliton spacings are slightly irregular.Our work paves a new way for soliton-based applications owing to the relatively flat spectral characteristics.

All-optical switches based on three-soliton inelastic interaction and its application in optical communication systems

In high-speed optical communication systems,in order to improve the communication rate,the distance between pulses must be compressed,which will cause the problem of the interaction between optical pulses in optical communication systems,which has been widely concerned by researches.In this paper,the bilinear method will be used to analyze the coupled high-order nonlinear Schro¨dinger equations and obtain their three-soliton solutions.Then,the influence of the relevant parameters in the three-soliton solution on the soliton inelastic interaction is studied.In addition,the constraint conditions of each parameter in the three-soliton solution are analyzed,the inelastic interaction properties of optical solitons under different parameter conditions are obtained,and the relevant laws of the inelastic interaction of solitons are studied.The results will have potential applications in the soliton control,all-optical switching and optical computing.

Effective Control of Three Soliton Interactions for the High-Order Nonlinear Schrodinger Equation

We take the higher-order nonlinear Schrodinger equation as a mathematical model and employ the bilinear method to analytically study the evolution characteristics of femtosecond solitons in optical fibers under higherorder nonlinear effects and higher-order dispersion effects.The results show that the effects have a significant impact on the amplitude and interaction characteristics of optical solitons.The larger the higher-order nonlinear coefficient,the more intense the interaction between optical solitons,and the more unstable the transmission.At the same time,we discuss the influence of other free parameters on third-order soliton interactions.Effectively regulate the interaction of three optical solitons by controlling relevant parameters.These studies will lay a theoretical foundation for experiments and further practicality of optical soliton communications.

All-Optical Switches for Optical Soliton Interactions in a Birefringent Fiber

Interactions among optical solitons can be used to develop photonic information processing devices such as alloptical switches and all-optical logic gates. It is the key to achieve high-speed, high-capacity all-optical networks and optical computers, which is also important in academy. We study the properties of all-optical switches of optical solitons in birefringent fibers, based on the coupled nonlinear Schr¨odinger equations. It is found that under different initial conditions we can achieve all-optical switching functions. We also study the influence of different physical parameters of birefringent fibers on all-optical soliton switching. The relevant conclusions are conducive to achieving the all-optical switching function of optical solitons in birefringent fibers, providing useful guidance for widespread applications of optical soliton all-optical switches in birefringent fibers of communications.

High-order effect on the transmission of two optical solitons

For optical solitons with the pulse width in the subpicosecond and femtosecond scales in optical fibers,a modified model containing higher-order effects such as third-order dispersion and third-order nonlinearity is needed.In this paper,in order to study the dynamic mechanism of femtosecond solitons in different media,we take the nonlinear Schr?dinger equation considering higher-order effects as the theoretical model,discuss the propagation of solitons in single-mode fibers,and explore the third-order dispersion and third-order nonlinear effects on the generation of optical solitons.The exact solution of the theoretical model is obtained through the bilinear method,and the transmission characteristics of two solitons with exact soliton solutions in actual fiber systems are analyzed and studied.The influence of various conditions on the transmission and interaction of optical solitons is explored.Methods for optimizing the transmission characteristics of optical solitons in optical communication systems are suggested.The relevant conclusions of this paper have guiding significance for improving the quality of fiber optic communication and increasing bit rates.

Special breathing structures induced by bright solitons collision in a binary dipolar Bose–Einstein condensates

We numerically investigate the breathing dynamics induced by collision between bright solitons in a binary dipolar Bose–Einstein condensates, whose dipole–dipole interaction and contact interaction are attractive. We identify three special breathing structures, such as snakelike special breathing structure, mixed breathing structure, and divide breathing structure.The characteristics of these breathing structures can be described by breathing frequency ?, maximum breathing amplitude A and lifetime τ, which can be manipulated by atomic number Ni and interspecies scattering length a12. Meanwhile, the above breathing structures can realize the process of quasi-transition with a reasonable Ni and a12. Additionally, the collision of two special breathing structures also can bring more abundant breathing dynamics. Our results provide a reference for the study of soliton interactions and deepen the understanding of soliton properties in a binary dipolar Bose–Einstein condensates.

Real-time observation of soliton pulsation in net normal-dispersion dissipative soliton fiber laser

We present experimental observations of soliton pulsations in the net normal-dispersion fiber laser by using the dispersive Fourier transform(DFT) technique. According to the pulsating characteristics, the soliton pulsations are classified as visible and invisible soliton pulsations. The visible soliton pulsation is converted from single-into dual-soliton pulsation with the common characteristics of energy oscillation and bandwidth breathing. The invisible soliton pulsation undergoes periodic variation in the spectral profile and peak power but remains invariable in pulse energy. The reason for invisible soliton pulsation behavior is periodic oscillation of the pulse inside the soliton molecule. These results could be helpful in deepening our understanding of the soliton pulsation phenomena.

Influence of the initial parameters on soliton interaction in nonlinear optical systems

In nonlinear optical systems,optical solitons have the transmission properties of reducing error rate,improving system security and stability,and have important research significance in future research on all optical communication.This paper uses the bilinear method to obtain the two-soliton solutions of the nonlinear Schrödinger equation.By analyzing the relevant physical parameters in the obtained solutions,the interaction between optical solitons is optimized.The influence of the initial conditions on the interactions of the optical solitons is analyzed in detail,the reason why the interaction of the optical solitons is sensitive to the initial condition is discussed,and the interactions of the optical solitons are effectively weakened.The relevant results are beneficial for reducing the error rate and promoting the communication quality of the system.