饱和对数非线性介质中非相干孤子碰撞对相干性的改善

基于相干密度理论，数值地研究了饱和对数非线性支持的部分非相干亮孤子对的相互作用.研究表明，两个非相干亮孤子碰撞不仅能增大碰撞区的光强，还可以大大改善部分非相干光束的相干性.同时还研究了非相干性对孤子碰撞的影响，非相干性不仅抑制了孤子间的相干作用如吸引、排斥和能量交换，同时还由于非相干叠加作用而引入了弱的相互吸引. 关键词： 非相干性 饱和对数非线性 空间光孤子     

Feshbach resonance management of vector solitons in two-component Bose—Einstein condensates

We consider two coupled Gross-Pitaevskii equations describing a two-component Bose-Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential,and investigate the dynamics of vector solitons.By using a direct method,we construct a novel family of vector soliton solutions,which are the linear combination between dark and bright solitons in each component.Our results show that due to the superposition between dark and bright solitons,such vector solitons possess many novel and interesting properties.The dynamics of vector solitons can be controlled by the Feshbach resonance technique,and the vector solitons can keep the dynamic stability against the variation of the scattering length.     

Linear superpositions of gap solitons in periodic Kerr media

The existence of a type of soliton in periodic Kerr media constructed as a superposition of noninteracting gap solitons of different kinds (bright, dark, and periodic) is first demonstrated. The periodic modulation of the nonlinearity is used to suppress the cross-phase modulation between component solitons to allow the superimposed beam to propagate for long distances.     

Conservation laws,bilinear forms and solitons for a fifth-order nonlinear Schrödinger equation for the attosecond pulses in an optical fiber

Under investigation in this paper is a fifth-order nonlinear Schrödinger equation, which describes the propagation of attosecond pulses in an optical fiber. Based on the Lax pair, infinitely-many conservation laws are derived. With the aid of auxiliary functions, bilinear forms, one-, two- and three-soliton solutions in analytic forms are generated via the Hirota method and symbolic computation. Soliton velocity varies linearly with the coefficients of the high-order terms. Head-on interaction between the bidirectional two solitons and overtaking interaction between the unidirectional two solitons as well as the bound state are depicted. For the interactions among the three solitons, two head-on and one overtaking interactions, three overtaking interactions, an interaction between a bound state and a single soliton and the bound state are displayed. Graphical analysis shows that the interactions between the two solitons are elastic, and interactions among the three solitons are pairwise elastic. Stability analysis yields the modulation instability condition for the soliton solutions.     

Multisolitons in a two-dimensional Skyrme model

The Skyrme model can be generalised to a situation where static fields are maps from one Riemannian manifold to another. Here we study a Skyrme model where physical space is two-dimensional euclidean space and the target space is the two-sphere with its standard metric. The model has topological soliton solutions which are exponentially localised. We describe a superposition procedure for solitons in our model and derive an expression for the interaction potential of two solitons which only involves the solitons' asymptotic fields. If the solitons have topological degree 1 or 2 there are simple formulae for their interaction potentials which we use to prove the existence of solitons of higher degree. We explicitly compute the fields and energy distributions for solitons of degrees between one and six and discuss their geometrical shapes and binding energies.     

Passive harmonic mode locking of soliton bunches in a fiber ring laser

We report on the experimental observation of passive harmonic mode locking of bunches of single-pulse solitons or twin-pulse solitons in an Erbium-doped fiber ring laser. Experimental investigations on the phenomenon revealed that, although the soliton interaction between the adjacent single-/twin-pulse solitons in a bunch is weaker than that of the pulse interaction in the twin-pulse solitons, a soliton bunch could also function as a unit and form the state of passively harmonic mode-locking. Harmonic mode-locking is one of the intrinsic characteristics of soliton emission in passively mode-locked fiber ring lasers. It can be formed based on the single-pulse soliton, twin-pulse soliton, or bunch of solitons.     

钛宝石飞秒激光器中孤子分子的内部动态探测

孤子是自然界中一种基本的非线性波动传递形式,孤子间的相互作用能够映射出复杂非线性系统的多体动力学过程,具有重要的基础研究价值.被动锁模激光器是研究孤子相互作用的理想平台.光孤子之间的吸引、排斥作用能够形成孤子分子,而时间拉伸色散傅里叶变换(TS-DFT)技术使得实时探测孤子分子动力学成为可能.基于TS-DFT技术,本文实验研究了钛宝石飞秒激光器产生的孤子分子的内部动态,通过改变抽运功率,分别观察到了间隔为180 fs的稳定的孤子分子和间隔为105 fs的具有微弱相位振荡的孤子分子,后者的振动幅度仅为0.05 rad.实验发现受到环境影响,稳定态的孤子分子还能够转变为相位滑动状态.这些间隔为百飞秒量级的光学孤子分子对于研究孤子的近程非线性相互作用具有突出的意义.     

Regimes of operation states in passively mode-locked fiber soliton ring laser

The principal of passively mode-locked fiber soliton ring lasers is summarized, including its three output operation states: normal soliton, bound–solitons and noise-like pulse. The experimental results of the passively mode-locked fiber soliton ring lasers developed by us are given. Bound–solitons with different discrete separations and three-bound–solitons state have been observed in our fiber laser for the first time. The relationship among three operation states in fiber soliton laser is analyzed.     

New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions

In this paper, by the Darboux transformation together with the Wronskian technique, we construct new double Wronskian solutions for the Whitham-Broer-Kaup (WBK) system. Some new determinant identities are developed in the verification of the solutions. Based on analyzing the asymptotic behavior of new double Wronskian functions as t → ±∞, we make a complete characterization of asymptotic solitons for the non-singular, non-trivial and irreducible soliton solutions. It turns out that the solutions are the linear superposition of two fully-resonant multi-soliton configurations, in each of which the amplitudes, velocities and numbers of asymptotic solitons are in general not equal as t → ±∞. To illustrate, we present the figures for several examples of soliton interactions occurring in the WBK system.     

Vector kink-dark complex solitons in a three-component Bose–Einstein condensate

We investigate kink-dark complex solitons(KDCSs) in a three-component Bose–Einstein condensate(BEC) with repulsive interactions and pair-transition(PT) effects. Soliton profiles critically depend on the phase differences between dark solitons excitation elements. We report a type of kink-dark soliton profile which shows a droplet-bubble-droplet with a density dip, in sharp contrast to previously studied bubble-droplets. The interaction between two KDCSs is further investigated. It demonstrates some striking particle transition behaviours during their collision processes, while soliton profiles survive after the collision. Additionally, we exhibit the state transition dynamics between a kink soliton and a dark soliton. These results suggest that PT effects can induce more abundant complex solitons dynamics in multi-component BEC.     

二阶孤子间相互作用引起孤子衰变

对于二阶孤子脉冲对,通过数值求解非线性Schrdinger方程,得到了二阶孤子在光纤中传输时的衰变规律.由于脉冲之间的相互作用,原来的二阶孤子衰变为两个分离的基孤子.二阶孤子对同位相时,相互作用为“吸引”,衰变后峰值小的基孤子位于内侧,二阶孤子对反位相时,相互作用为“排斥”,衰变后峰值小的基孤子位于外侧.两个二阶孤子脉冲间隔越小,反位相时,在相同传输距离处,衰变产生的两个基孤子的分离程度越大.     

脉冲内拉曼散射影响下的孤子之间的相互作用及其控制

研究了脉冲内拉曼散射效应影响下的同相和反相相邻孤子脉冲之间的相互作用,分析了孤子之间的相互作用对定时抖动的影响和脉冲内拉曼散射效应对孤子频移的影响。研究结果表明:在脉冲内,在拉曼散射效应的影响下,同相基态孤子脉冲的周期性离合被破坏了,两孤子脉冲一次碰撞后一直处于排斥状态,并且在碰撞后自频移现象十分明显;反相孤子脉冲的影响则较弱,两孤子脉冲都向下降沿发生偏移。引入非线性增益可以有效地控制孤子之间的相互作用,抑制自频移效应和稳定孤子传输。     

Solitons in anharmonic chains with ultra-long-range interatomic interactions

We study the influence of long-range interatomic interactions on the properties of supersonic pulse solitons in anharmonic chains. We show that in the case of ultra-long-range (e.g., screened Coulomb) interactions three different types of pulse solitons coexist in a certain velocity interval: one type is unstable but the two others are stable. The high-energy stable soliton is broad and can be described in the quasicontinuum approximation. But the low-energy stable soliton consists of two components, short-range and long-range ones, and can be considered as a bound state of these components.     

开环系统中灰光伏孤子的时间及演化特性分析

分析了开环系统中一维灰光伏孤子的时间特性.基于与时间相关的演化方程,用数值方法得到了准稳态和稳态的灰孤子解,分析了形成准稳态灰孤子的物理机制.结果显示准稳态灰孤子的宽度是与光强无关的,并且它们的形成时间和孤子的峰值与背景辐射强度比成反比.这些性质与开环系统中的亮、暗孤子的性质很相似.同时采用波传播的数值解法,分析了它们的传播特性,结果显示它们在小于10％的扰动下是相对稳定的.     

Field and intensity expectation values of quantum solitons in optical fibers

Expectation values of the field and intensity operators are evaluated for quantum solitons in the normalized fundamental soliton states with a Gaussian momentum superposition and a Poisson distribution for photon numbers. The associate quantum diffusion effects are discussed and the conditions which lead to the classical limit are identified. A numerical estimate is given using experimental data.     

Dark and anti-dark vector solitons of the coupled modified nonlinear Schrödinger equations from the birefringent optical fibers

Coupled modified nonlinear Schr?dinger (CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. A new type of the Lax pair and another hierarchy of the infinitely many conservation laws are derived based on the Wadati-Konno-Ichikawa system. By means of the Hirota method, soliton solutions in the normal dispersion regime are obtained. Parametric regions for the existence of dark and anti-dark vector soliton solutions are given. Asymptotic analysis shows that the collision between two solitons (two anti-dark solitons, two dark solitons, or dark and anti-dark solitons) in each polarization direction is elastic. Moreover, there is no energy transfer between two polarization components of each vector soliton, whether dark or anti-dark vector soliton. In addition, dark and anti-dark solitons can coexist on the same background seen from the collision between the dark and anti-dark solitons in one polarization direction. Our graphical analysis shows that the parameters in the CMNLS equations not only determine the regions for the existence of dark and anti-dark soliton solutions but also control the phase and direction of the propagation of the solitons. Finally, through the linear stability analysis, the modulational instability condition is given.     

非局域高次非线性介质中的多极暗孤子

研究一维非局域三-五次非线性模型下,暗孤子和多极暗孤子的新解和传输特性.发现非局域程度和非线性参量变化对暗孤子的峰值和束宽产生影响,并且在特定的竞争非局域非线性参数下存在稳定基态暗孤子和多极暗孤子的束缚态.另外,讨论了在局域自聚焦三次和非局域自散焦五次非线性介质中暗孤子和两极暗孤子的传输特性,发现孤子比在自散焦三次和自聚焦五次的非线性介质中传输更加稳定.进一步研究了单暗孤子和三极暗孤子的功率与传播常数和非局域程度的关系,并讨论了不同类型暗孤子的线性稳定性问题.     

On the Dromion Solutions of a (2+l)-Dimensional KdV-Type Equation

A general curve soliton which is finite on a curved line and localized apart from the curve for a (2+1)-dimensional KdV-type equation is found. For the KdV-type equation, we find that the dromion solutions can be obtained not only by two perpendicular line solitons, two nonperpendicular (with one is parallel to x-axis) line solitons, but also by one line soliton and one curve soliton. Various types of multi-dromion solutions which are constituted by n straight line solitons parallel to the x axis and one curve soliton can be cast in a simple formula with two arbitrary functions. The KdV-type equation is not integrable because it cannot pass through the three nonparallel line soliton test.     

光折变明孤子的自偏转演化特性

利用一维稳态光折变空间光孤子的统一理论，研究了负载电阻对屏蔽、光伏和屏蔽光伏明孤子自偏转特性的影响。结果表明，无论加载电阻与否，这三种类型的光折变明孤子具有类似的自偏转特性，即孤子波沿一个抛物线轨迹运动。调节负载电阻可以改变孤子的偏转幅度，其中屏蔽光伏明孤子的可调范围最大。