Generation and time jitter of the loose soliton bunch in a passively mode-locked fiber laser

We report a regime of the loose soliton bunch in an erbium-doped passively mode-locked fiber laser. In this state,every soliton bunch consists of multiple pulses. The amount of multiple pulses inside the soliton bunch increase as the pump power rises. Moreover, the temporal average pulse-to-pulse separation decreases in general with the increase of the pump power. Further, the spatial-temporal sequences based on the dispersive Fourier transformation technique show that pulse-to-pulse interactions and time jitter can result in pulse forking inside the soliton bunch. Finally, we theoretically demonstrate the soliton bunch with different pulse-to-pulse separations.     

The elliptic function waves and solitons in thermal nonlocal media

An analytical solution is obtained in thermal nonlocal media by considering the weakly and strong nonlocal limit, respectively. In weakly nonlocal case the elliptic function wave solutions, which become soliton under limited condition, are present, while in strongly nonlocal case the solutions are bright soliton and multi-hump soliton. These results are well in good agreement with numerical ones in other references [8].     

Periodic solitons in nonlocal nonlinear media

We identify periodic solitons in nonlocal nonlinear media: multi-hump soliton solutions propagating in a fully periodic fashion. We also demonstrate recurrences and breathers whose evolution is statistically periodic and discuss why some systems support periodic solitons while others do not.     

Propagation characteristics of chirped soliton in periodic distributed amplification systems with variable coefficients

Propagation characteristics of chirped soliton in periodic distributed amplification systems with variable coefficients are investigated by using the split-step Fourier method. The soliton pulse still maintains soliton characteristics after propagation in the system. The shape of output spectrum is still with a single peak. The temporal FWHM of an unchirped soliton performs a slight oscillation with the increase of propagation distance. The oscillation amplitude is slightly increased with the increase of the gain or loss parameter σ. The chirped soliton is obviously and periodically compressed and broadened with the increase of propagation distance in the system. The lager the value of chirp parameter |C| and σ is, the greater the variation of temporal width with the distance is. The effect of chirp on temporal width of soliton in a amplification system is greater than that in a loss system. Three types of numerical experiments show that the soliton with different perturbations can stably propagate along the fiber. In practical applications, one can obtain a suitable soliton pulse by controlling the parameters of the fiber system.     

Passive harmonic mode-locking of a soliton Yb fiber laser at repetition rates to 1.5 GHz

We report passive harmonic mode locking of a soliton Yb fiber laser at repetition rates continuously scalable up to 1.5 GHz. The laser generates transform-limited 500 fs pulses, with pulse energies of 30-100 pJ. At the 31st harmonic (1.3 GHz), the cavity supermodes are suppressed by 35 dB, and the pulse-to-pulse timing jitter is 6 ps.     

Multi-soliton generation with extremely narrow free spectrum range for multiplexed sensors via optical network

We propose a new system of multiplexer sensors using the localized soliton pulse generated by a microring resonator in optical networks. A large bandwidth signal is generated by a soliton pulse propagating within the microring resonator, which is allowed to form the multiplexed sensors. Two forms of soliton pulses are generated and localized, i.e. temporal and spatial solitons. The required soliton pulses with specified wavelengths can be localized and formed the sensing. This is formed by using an optical add/drop multiplexer incorporating in the optical network, where the localized soliton pulses are available for add/drop signals to/from the optical network. The change in physical parameter measured the change in soliton wavelength, which formed the measurement.     

带弱"平台"皮秒光孤子的数值研究

通过数值求解变系数非线性薛定谔方程,发现光纤系统对带有弱“平台”的皮秒光孤子有独特的传输特性。在常参数光纤系统中,这种光孤子体现“呼吸”特性,而在特殊的分布参数光纤系统中,则能较平稳地传输。     

Control of interaction between femtosecond dark solitons in inhomogeneous optical fibers

In this paper, we present exact femtosecond one- and two-dark soliton solutions for a variable-coefficient higher-order nonlinear Schrödinger equation via modified Hirota method. The propagation and interaction of femtosecond dark solitons are investigated in inhomogeneous fiber systems. Elastic collision, bound oscillation and parallel propagation can be achieved in both Gaussian distributed parameter system and exponentially periodic distributed parameter system by choosing the appropriate distributed parameters and soliton parameters. The results may be beneficial to the realization of interaction control of femtosecond dark solitons in communication systems.     

Special Property of Group Velocity for Temporal Dark Soliton

We investigate the speed of temporal dark soliton based on an optical coherent medium. It is demonstrated that the temporal dark soliton is described by a nonlinear Schrodinger equation whose coefficients are decided by the coherent medium. It is found that the speed of temporal dark soliton not only relies on the linear responses including GV parameter, group velocity dispersion parameter as well as the amplitude of dark soliton, but also relies on the nonlinear response like self-phase modulation parameter. Additionally, the dark soliton in anomalous-dispersion regime propagates slower than bright soliton, while in normal-dispersion regime it inversely propagates faster than bright soliton. The complicated property of the speed for dark soliton is quite different from the bright soliton whose speed is commonly only related to the group velocity parameter. We attribute this feature to the modulation instability of the nonlinear system.     

Kac-moody lie algebras and soliton equations: II. Lax equations associated with A1(1)

The soliton equations associated with sl(2) eigenvalue problems polynomial in the eigenvalue parameter are given a unified treatment; they are shown to be generated by a single family of commuting Hamiltonians on a subalgebra of the loop algebra of sl(2). The conserved densities and fluxes of the usual ANKS hierarchy are identified with conserved densities and fluxes for the polynomial eigenvalue problems. The Hamiltonian structures of the soliton equations associated with the polynomial eigenvalue problems are given a unified treatment.     

Stabilised bright solitons in Bose-Einstein condensates in an expulsive parabolic and complex potential

The exact solitonic solutions of the one-dimensional nonlinear Schr?dinger equation, which describes the dynamics of bright soliton in Bose—Einstein condensates with the time-dependent interaction in an expulsive parabolic and complex potential, are obtained by Darboux transformation. The results show that one can compress a bright soliton into an assumed peak of matter wave density by adusting the experimental parameter of the ratio of axial oscillation to radial oscillation or feeding parameter. Especially,when parameters satisfy the relation λ=2γ, the soliton is stable with time evolution without changing its shape and amplitude.     

变路径色散管理孤子系统中的调制非稳性研究

本文研究了变路径色散的孤子系统中的调制非稳性.首先采用微扰法对变路径色散的系统中的调制非稳性(MI)进行理论分析,解析出变路径色散系统中的MI特征根表达式,据此得到了色散管理孤子(DMS)系统的特征参数色散管理图强度与MI增益系数关系.研究结果表明,变路径色散系统中的色散管理强度大大影响MI增益的大小以及增益谱范围,而路径平均色散只影响MI增益谱范围.同时,本文结果还表明DMS较普通孤子系统有更强的抑制MI增益的能力.     

Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion

Soliton propagation in a cascaded dispersion-managed optical amplifier system with zero net dispersion is examined. We present a qualitative physical explanation for the recently discovered fact that a soliton with finite energy can propagate down a fiber line with zero or normal average dispersion. We describe a specific practical system for the main properties of such a soliton, namely, the dependence of the soliton power on the pulse width at chirp-free points and the soliton average energy and width at chirp-free points as functions of the dispersion-allocation (strength of the map) parameter.     

Moving bright solitons in a pseudo-spin polarization Bose-Einstein condensate

We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.     

Multiple bright and dark soliton solutions in three component spinor Bose-Einstein condensates

We investigate a quasi one dimensional spin-1 Bose-Einstein Condensates (BEC) in the absence of an external confinement governed by a system of three coupled Gross-Pitaevskii (GP) equation. Based on the Lax-pair, we construct one soliton solution employing gauge transformation method. In addition, the multiple bright and dark soliton solutions are obtained by properly choosing amplitude dependent parameter in the Lax-pair. The results of the paper emphasizes the richness in the structure of soliton solutions admitted by the spin components, a phenomenon which has never been brought out to the fore. We have also extended the gauge transformation method to generate two soliton solutions.     

Spatial solitons in photonic lattices with large-scale defects

We address the existence,stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium.Several families of soliton solutions,including flat-topped,dipole-like,and multipole-like solitons,can be supported by the defected lattices with different heights of defects.The width of existence domain of solitons is determined solely by the saturable parameter.The existence domains of various types of solitons can be shifted by the variations of defect size,lattice depth and soliton order.Solitons in the model are stable in a wide parameter window,provided that the propagation constant exceeds a critical value,which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium.We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.     

Dissipative solitons in active Bragg gratings

Motionless and moving bright dissipative solitons in an optical fiber with a Bragg grating and non-linear amplification and absorption are found numerically and studied. These solitons form a one-parameter family whose parameter—the soliton velocity—can continuously change in a certain range. The presence of saturation of the nonlinearity is necessary for stability of such solitons. Neglect of saturation of the cubic-in-field polarization of the medium results in the instability of the possible localized structures.     

Stable Soliton Propagation in a System with Spectral Filtering and Nonlinear Gain

Stable soliton propagation in a system with linear and nonlinear gain and spectral filtering is investigated. Different types of exact analytical solutions of the cubic and the quintic complex Ginzburg-Landau equation (CGLE) are reviewed. The conditions to achieve stable soliton propagation are analyzed within the domain of validity of soliton perturbation theory. We derive an analytical expression defining the region in the parameter space where stable pulselike solutions exist, which agrees with the numerical results obtained by other authors. An analytical expression for the soliton amplitude corresponding to the quintic CGLE is also obtained. We show that the minimum value of this amplitude depends only on the ratio between the linear gain and the quintic gain saturating term.     

Stable Soliton Propagation in a System with Spectral Filtering and Nonlinear Gain

Stable soliton propagation in a system with linear and nonlinear gain and spectral filtering is investigated. Different types of exact analytical solutions of the cubic and the quintic complex Ginzburg-Landau equation (CGLE) are reviewed. The conditions to achieve stable soliton propagation are analyzed within the domain of validity of soliton perturbation theory. We derive an analytical expression defining the region in the parameter space where stable pulselike solutions exist, which agrees with the numerical results obtained by other authors. An analytical expression for the soliton amplitude corresponding to the quintic CGLE is also obtained. We show that the minimum value of this amplitude depends only on the ratio between the linear gain and the quintic gain saturating term.     

Interaction of two dark solitons in nonlinear left-handed materials

A system of coupled nonlinear Schrödinger equations (CNLS) has dark soliton solutions. In nonlinear left-handed materials, the interaction of two of these dark solitons with the same parameter κ can generate new electromagnetic envelops that are quite different from a single soliton, even including a ‘bright’ envelop. But the new-generated envelops can also propagate steadily in the materials, we call them quasi-soliton. Numerical calculations demonstrate that varying either the parameter κ or the distance between the two solitons will change the envelop shape of the quasi-soliton remarkably. And an analysis of the phenomena is presented.