The Evolution Feature of Chirp-Dark Soliton in Single-Mode Fiber

The evolution feature of the injected initial-chirp tanh-dark soliton in single-mode fiber is studied in this paper. We analyze the evolution of amplitude, pulse width, frequency chirp and center position shift of dark soliton along with the variation of propagation distance, primarily using Lagrange-Euler's formula and taking the high-order dispersion as perturbation. The results show that the amplitude and pulse width of chirp-dark soliton are all oscillating around a certain critical distance in ideal fiber (β = 0), and the high-order dispersion conduces to generate the asymptotic dark soliton.     

数值模拟高阶色散和非线性对光孤子传输的影响

光孤子传输中的高阶色散以及高次非线性效应是光纤通讯发展的重要制约因素。从光孤子在光纤中的一般传输方程出发, 在较大的入纤功率的前提下, 综合考虑了高阶色散、五次非线性和损耗因素, 得到其具体传输方程, 并据此从理论上分析了高阶色散和非线性对光孤子传输性能的影响。本文采用分步傅里叶方法, 以MATLAB为实现工具, 实现高阶色散和非线性对光孤子传输影响的模拟计算, 并深入分析了高阶色散和非线性导致的孤子脉冲频移现象。计算结果表明: 在入射功率较大的时候, 高阶色散效应不可忽略。当五次非线性γ2>0时,孤子脉冲主峰发生微小频移; 而当五次非线性γ2<0时, 孤子脉冲主峰基座产生微小频移; 当高阶色散β3>0时频率出现红移, 而当β3<0时, 频率出现蓝移。     

Observation of high-order polarization-locked vector solitons in a fiber laser

We report on the experimental observation of a new type of polarization-locked vector soliton in a passively mode-locked fiber laser. The vector soliton is characterized by the fact that not only are the two orthogonally polarized soliton components phase-locked, but also one of the components has a double-humped intensity profile. Multiple phase-locked high-order vector solitons with identical soliton parameters and harmonic mode locking of the vector solitons were also obtained in the laser. Numerical simulations confirmed the existence of stable high-order vector solitons in the fiber laser.     

A deep learning method for solving high-order nonlinear soliton equations

We propose an effective scheme of the deep learning method for high-order nonlinear soliton equations and explore the influence of activation functions on the calculation results for higher-order nonlinear soliton equations. The physics-informed neural networks approximate the solution of the equation under the conditions of differential operator, initial condition and boundary condition. We apply this method to high-order nonlinear soliton equations, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg–de Vries equation. The results show that the deep learning method can be used to solve high-order nonlinear soliton equations and reveal the interaction between solitons.     

A Novel Envelope Soliton Solution to the Granular Crystal Model

A theoretical work on envelope solitons to a one-dimensional granular chain model is reported. In the small amplitude approximation, we analytically solve the equation of motion with the help of the semidiscrete multiple-scale method. Our results show that the granular chain model can support an asymmetric high-order envelope soliton under the certain condition. It is found that the second-harmonic term of this high-order envelope soliton has an additional phase. In addition, the influence of both the material parameter and the static load on the localized features of the high-order envelope soliton is discussed.     

Effects of high-order dispersions on dark-bright vector soliton propagation and interaction

The dynamics of dark-bright vector solitons is investigated in a birefringent fiber with the high-order dispersions,and their effects on vector soliton propagation and interaction are analyzed using the numerical method.The combined role of the high-order dispersions,such as the third-order dispersion (TOD) and the fourth-order dispersion (FOD),may cause various deformation of the vector soliton and enhance interaction.These effects depend strictly on the sign of the high-order dispersions.Results indicate that the disadvantageous effects can be reduced effectively via proper mapping of the high-order dispersions.     

Soliton Propagation near Zero-Dispersion Wavelength in Birefringence Fiber

fiom coupled nonlinear Schrodinger equation which describes the birefringence near zero-dispersion wavelength, we derive the evolution feature of soliton parameters and get the differential equation describing the evolution of interval between solitons along with propagation distance. At the same time, we have made detailed numerical research on the propagation in dissipation system of standard fundamental soliton. The result shows that for attractive potential, the distance of oscillation increases dong with the loss increases. For repulsive potential, the distance of oscillation diverges faster along with the loss increases. If selecting the proper-optical fiber of high-order dispersion, the interaction between solitons in birefringence fiber can be eliminated.     

Numerical simulation of propagation of a femtosecond optical soliton in a single-mode fiber with allowance for the imaginary part of Raman response

We consider the effect of Raman inertial response of a medium on the stability of a first-order femtosecond soliton. Numerical solution to the high-order nonlinear Schrödinger equation, with the complex Raman term, describing propagation of a femtosecond optical soliton in a single-mode fiber, is obtained. It is shown that a soliton solution of the high-order nonlinear Schrödinger equation exists under certain conditions imposed on the equation coefficients. These conditions lead to limitations on the wavelength, fiber type, and the highest energy. Results of numerical solutions are in agreement with available experimental data.     

Supercontinuum broadening in all-normal dispersion photonic crystal fiber by means of soliton compression in standard single-mode fiber

Using standard single-mode fiber as high-order soliton compressor for broadening supercontinuum in an 80 m long all-normal dispersion photonic crystal fiber is investigated experimentally and numerically. An analytical formula for calculating proper fiber input power to generate the broadest supercontinuum is derived. The numerical results show that the formula is more accurate in high power level corresponding to the soliton order which is larger than two. The measured supercontinuum ? 20 dB bandwidth is broadened from 84.2 nm to 277.1 nm by using a 20 m long standard single-mode fiber without enhancing fiber input power. Numerical calculations of the amplitude noise in the output spectra show that using soliton compression effect can efficiently broaden the spectral bandwidth and not generate obvious noises.     

量子孤子在光纤中的传播特性

利用线性近似和分步傅里叶变换法，分析了量子孤子在无耗光纤中的传播规律.量子孤子在光纤中的行为由量子非线性薛定谔方程（QNSE）描述,用线性近似法求解此方程，将量子噪声与经典部分分离，着重讨论了孤子量子噪声的演化行为，分析了高阶色散对噪声压缩的影响.结果表明：在较短的传输距离内，孤子的压缩性依然存在，但无论初始时压缩参数如何，随着传输距离的增加，压缩比会达到一个极限;在负色散区，三阶色散对压缩效应无影响.     

Broadband dynamic phase matching of high-order harmonic generation by a high-peak-power soliton pump field in a gas-filled hollow photonic-crystal fiber

Hollow-core photonic-crystal fibers are shown to enable dynamically phase-matched high-order harmonic generation by a gigawatt soliton pump field. With a careful design of the waveguide structure and an appropriate choice of input-pulse and gas parameters, a remarkably broadband phase matching can be achieved for a soliton pump field and a large group of optical harmonics in the soft-x-ray-extreme-ultraviolet spectral range.     

Soliton dynamics of megawatt ultrashort light pulses in a hollow photonic-crystal fiber: Effect of high-order dispersion and retarded nonlinearity

The properties of megawatt optical solitons in hollow photonic-crystal fibers (PCFs) are studied. We demonstrate regimes where high-power laser pulses can be compressed to a few cycles of light field and identify the main tendencies in the soliton dynamics of ultrashort laser pulses in hollow PCFs originating from dispersion properties and limited transmission band of such waveguides. The influence of retarded nonlinearity on the soliton dynamics of high-power laser pulses in a hollow PCF is analyzed. In a multisoliton regime, retarded nonlinearity and high-order dispersion are shown to result in the formation of high-power pulses displaying no oscillations of their temporal envelope, which would be typical of standard high-order solitons.     

Four-wave mixing between a soliton and noise in a system with large amplifier spacing

Depletion of soliton energy by four-wave mixing between a soliton and amplifier noise in a system with 100-km amplifier spacing is studied. Dispersion exponentially decreasing fiber is used as transmission fiber. Improvement of the system by the use of a sliding-frequency filter to reduce noise power and the depletion of soliton energy is shown. The system can be further improved by compensation for depleted soliton energy.     

孤子效应分布式光纤传感器的理论分析

针对目前分布式光纤传感器的优缺点，提出利用孤子效应的拉曼散射分布式光纤传感器系统构想。研究了高阶孤子对分布式光纤传感器的作用，对系统的性能参数进行分析，并在现有器件水平上分析了实现的可能性和存在的难点。     

The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq–Burgers equation

This paper studies the coupled Burgers equation and the high-order Boussinesq–Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink (soliton) solutions and multiple-singular-kink (soliton) solutions are derived for the two equations.     

High-order breather,M-kink lump and semi-rational solutions of potential Kadomtsev-Petviashvili equation

N-kink soliton and high-order synchronized breather solutions for potential Kadomtsev-Petviashvili equation are derived by means of the Hirota bilinear method,and the limit process of high-order synchronized breathers are shown.Furthermore,M-lump solutions are also presented by taking the long wave limit.Additionally,a family of semi-rational solutions with elastic collision are generated by taking a long-wave limit of only a part of exponential functions,their interaction behaviors are shown by three-dimensional plots and contour plots.     

Numerical investigation of soliton molecules with variable separation in passively mode-locked fiber lasers

Soliton molecules evolution is numerically investigated in a passively mode-locked fiber laser based on the nonlinear polarization rotation (NPR) technique. Peak-to-peak separation of soliton molecules can be controlled by changing either pump strength or cavity linear phase delay appropriately. Moreover, soliton molecules with intensity-independent evolution, separation-independent evolution and large intensity-vibrating evolution are numerically found, respectively. The characteristics of soliton molecules evolution versus linear phase delay or pump strength are given. Periodic stable evolution regimes are found. The separation-controllable soliton molecules can be attributed to the mutual effects of phase delay, Kerr nonlinearity and other parameters of the cavity.     

Suppression of stimulated Brillouin scattering with phase modulator in soliton pulse compression

A phase modulator is employed in the scheme of soliton pulse compression with dispersion shifted fiber （DSF）. Stimulated Brillouin scattering （SBS） effect, as a negative influence here, can be dramatically suppressed after optical phase modulation. The experimental result shows that the launched power required for high-order soliton pulse compression has been significantly increased by 11 dB under the condition of 100-MHz phase modulation. Accordingly, the experiment of picosecond pulse compression generated from electro-absorption sampling window （EASW） has also been implemented.     

Phase jitter in periodically dispersion-managed optical transmission systems

We investigate the phase jitter in long-haul optical transmission systems with periodic dispersion management and amplification. We compare different dispersion-managed soliton systems and a conventional soliton system having the same pulse width and path-averaged dispersion. Using the variational method, we derive the ordinary differential equations for the pulse parameters perturbed by amplifier noise and hence calculate the phase jitter. We verify the analytical results by numerically solving the nonlinear Schrödinger equation using split-step Fourier algorithm. The results suggest that the reduction of nonlinear phase noise in dispersion-managed soliton systems is possible compared to a conventional soliton system. It is also revealed that the phase noise is enhanced in stronger dispersion-managed systems. We also explore the phase noise effect in dispersion-managed quasi-linear systems and find that phase jitter is mitigated in highly dispersive fibers.     

Soliton solutions for a generalized fifth-order KdV equation with t-dependent coefficients

We consider a generalized fifth-order KdV equation with time-dependent coefficients exhibiting higher-degree nonlinear terms. This nonlinear evolution equation describes the interaction between a water wave and a floating ice cover and gravity-capillary waves. By means of the subsidiary ordinary differential equation method, some new exact soliton solutions are derived. Among these solutions, we can find the well known bright and dark solitons with sech and tanh function shapes, and other soliton-like solutions. These solutions may be useful to explain the nonlinear dynamics of waves in an inhomogeneous KdV system supporting high-order dispersive and nonlinear effects.