Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic-Quintic Nonlinearities

Symmetry breaking bifurcations of solitons are investigated in framework of a nonlinear fractional Schrödinger equation (NLFSE) with competing cubic-quintic nonlinearity. Some prototypical characteristics of the symmetry breaking, featured by transformations of symmetric and antisymmetric soliton families into asymmetric ones, are found. Stable asymmetric solitons emerge from unstable symmetric and antisymmetric ones by way of two different symmetry breaking scenarios. A twisting branch, featured with double loops bifurcation, bifurcates off from the base branch of symmetric soliton solutions and crosses it, then merges into the base branch driven by the competitive nonlinear effect. A supercritical pitchfork bifurcation is bifurcated from the branch of antisymmetric soliton solutions and gives rise to a supercritical pitchfork bifurcation. Stability of the soliton families is explored by linear stability analysis. With the increase of the Lévy index, stability region induced by the twisting loops bifurcation is expanded. However, stability region of the pitchfork bifurcation is shrunk on the parameter plane of the Lévy index and the soliton power.     

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.     

Bright-dark self-coupled vector spatial solitons in biased two-photon photovoltaic photorefractive crystals

This paper predicts that bright-dark self-coupled vector solitons are possible in biased two-photon photovoltaic photorefractive crystals under steady-state conditions. The solutions of these vector solitons can be determined by use of simple numerical integration procedures. When the photovoltaic effect is neglectable, these vector solitons are bright-dark vector screening solitons. When the external bias field is absent, these vector solitons degenerate the bright-dark vector photovoltaic solitons.     

Symmetric and Anti-Symmetric Solitons of the Fractional Second-and Third-Order Nonlinear Schr?dinger Equation

The fractional second-and third-order nonlinear Schr?dinger equation is studied,symmetric and antisymmetric soliton solutions are derived,and the influence of the Levy index on different solitons is analyzed.The stability and stability interval of solitons are discussed.The anti-interference ability of stable solitons to the small disturbance shows a good robustness.     

Steady-state bright-dark vector spatial solitons in biased two-photon photorefractive crystals

We show that bright-dark vector solitons are possible in biased two-photon photorefractive crystals under steady-state conditions. The analytical solutions of these vector solitons can be obtained if the intensities of the two vector components are approximately equal. When the intensities of the two vector components differ, the vector soliton pair solutions can be determined using simple numerical integration procedures. The stability of the bright-dark vector solitons has been investigated numerically.     

Solitons in thermal media with periodic modulation of linear refractive index

We address the existence and properties of solitons in thermal media with periodic modulation of linear refractive index. Many kinds of solitons in such optical lattices, including symmetric and antisymmetric lattices, are found under different conditions. We study the influence of the refractive index difference between two different layers on solitons. It is also found that there do not exist cutoff value of propagation constant and soliton power for shifted lattice solitons. In addition, the solitons launched away from their stationary position may propagate without oscillation when the confinement from lattices is strong.     

Vector NLS solitons interacting with a boundary

We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions (BCs): the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs. The construction is based on the so-called dressing the boundary, which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process. Under the Robin BCs, examples, including boundary-bound solitons, are explicitly derived; under the mixed Neumann/Dirichlet BCs, the boundary can act as a polarizer that tunes different components of the vector solitons. Connection of our construction to the inverse scattering transform is also provided.     

Gap Solitons in Fractional Dimensions With a Quasi‐Periodic Lattice

The existence and stability of gap solitons in the nonlinear fractional Schrödinger equation are investigated with a quasi‐periodic lattice. In the absence of nonlinearity, the exact band‐gap spectrum of the proposed system is obtained, and it is found that the spectrum gap size can be adjusted by the sublattice depth and the Lévy index. Under self‐defocusing nonlinearity, both in‐phase and out‐of‐phase gap solitons have been searched in the first four gaps. It is revealed that in‐phase gap solitons are generally stable in wide regions of their existence, whereas stable out‐of‐phase gap solitons can only exist in the fourth spectrum gap. Linear stability analysis of gap solitons is in good agreement with their corresponding nonlinear evolutions in fractional dimensions. The presented numerical findings may lead to interesting applications, such as transporting of light beams through the optical medium, and other areas connected with the Kerr effect and fractional effect.     

Defect solitons supported by parity-time symmetric defects in superlattices

The existence and stability of defect solitons supported by parity-time (PT) symmetric defects in superlattices are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive defects, zero defects, and negative defects. In the first gap, out-of-phase solitons are stable for positive defects or zero defects, whereas in-phase solitons are stable for negative defects. For both the in-phase and out-of-phase solitons with the positive defect and in-phase solitons with negative defect in the first gap, there exists a cutoff point of the propagation constant below which the defect solitons vanish. The value of the cutoff point depends on the depth of defect and the imaginary parts of the PT symmetric defect potentials. The influence of the imaginary part of the PT symmetric defect potentials on soliton stability is revealed.     

Dynamics of vector solitons in two-component Bose--Einstein condensates with time-dependent interactions and harmonic potential

We present two kinds of exact vector-soliton solutions for coupled nonlinear Schr?dinger equations with time-varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright solitons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our model. At the same time, we obtain the opposite situation for dark--dark solitons.     

亮孤子在宇称时间对称波导中的传输和控制

基于光波在宇称-时间(PT)对称波导中传输的理论模型, 数值研究了亮孤子在呈高斯分布的PT对称克尔非线性平板波导中的传输和控制. PT对称波导, 要求波导的折射率分布呈偶对称, 而增益/损耗分布呈奇对称. 结果表明: 当波导的折射率分布强度为正时, PT对称波导的中心折射率最大, 即使没有自聚焦克尔非线性效应, PT对称波导也可以束缚光波, 形成波浪形光束且长距离传输; 当折射率分布强度为负时, PT对称波导的中心折射率最小, 光波的传输方向发生偏移. 而增益/损耗分布可控制光波的偏移方向: 增益/损耗分布强度为正, 光波向左偏移; 强度为负, 光波向右偏移; 强度为零时, 光波被分为两束. 且当折射率分布强度为负时, 可以很好地抑制相邻亮孤子间的相互作用. 该研究结果可为未来PT对称波导在全光控制方面的应用提供一定的理论依据.     

Stability of solitons in parity-time-symmetric couplers

Families of analytical solutions are found for symmetric and antisymmetric solitons in a dual-core system with Kerr nonlinearity and parity-time (PT)-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of gain, loss, and intercore coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").     

二元玻色-爱因斯坦凝聚体中矢量孤子的转化行为

考虑种内和种间相互作用均为排斥作用,研究了局限于谐振外部势阱中的二元玻色-爱因斯坦凝聚体中灰-灰和黑-黑孤子的动力学行为.结果表明:当谐振势阱的轴向囚禁频率为零时,灰-灰和黑-黑孤子均能保持局域稳定;而当轴向囚禁频率不为零时,凝聚体中的原子向势阱中心聚集,发现灰-灰孤子可以转化成亮-亮孤子.     

Phase interaction of short vector solitons

An interaction of vector solitons in the frame of coupled third-order nonlinear Schrödinger equations taking into account third-order linear dispersion, nonlinear dispersion, and cross-phase modulation terms is considered. Phase nature of the solitons? interaction is shown. In particular, dependence of solitons? trajectories on initial distance between solitons is shown. Conditions of reflection and propagation of solitons through each other are obtained.     

Gap solitons supported by optical lattices in biased centrosymmetric photorefractive crystals

We analyze the existence and stability of gap solitons supported by optical lattices with self-focusing nonlinearity in biased centrosymmetric photorefractive crystals. It is shown that, in first finite bandgap, gap solitons are symmetric in transverse dimension, single humped, entirely positive and linearly stable, while these solitons are antisymmetric with similar profiles, the stable and unstable intervals of the gap solitons are intertwined in the second finite bandgap.     

双光子光折变晶体中两分量矢量空间孤子

为了研究外加偏压双光子光折变晶体中的矢量空间孤子,建立了矢量空间孤子的动态演化方程,给出了矢量空间孤子数值解.采用数值模拟的方法,求解矢量空间孤子的数值表达式,理论预言了稳态条件下亮-亮、暗-暗自耦合矢量空间孤子的存在|同时,数值求解演化方程,分析了亮-亮自耦合矢量空间孤子的演化特性.数值结果表明,无论两孤子分量的强度近似相等还是有较大差别,这些自耦合矢量空间孤子都可以由数值积分程序给出.亮-亮、暗-暗自耦合矢量空间孤子在双光子光折变晶体中稳定存在.     

双光子光折变晶体中两分量矢量空间孤子(英文)

为了研究外加偏压双光子光折变晶体中的矢量空间孤子,建立了矢量空间孤子的动态演化方程,给出了矢量空间孤子数值解.采用数值模拟的方法,求解矢量空间孤子的数值表达式,理论预言了稳态条件下亮-亮、暗-暗自耦合矢量空间孤子的存在;同时,数值求解演化方程,分析了亮-亮自耦合矢量空间孤子的演化特性.数值结果表明,无论两孤子分量的强度近似相等还是有较大差别,这些自耦合矢量空间孤子都可以由数值积分程序给出.亮-亮、暗-暗自耦合矢量空间孤子在双光子光折变晶体中稳定存在.     

Solitons in a system of three linearly coupled fiber gratings

We introduce a model of three parallel-coupled nonlinear waveguiding cores equipped with Bragg gratings (BGs), which form an equilateral triangle. The most promising way to create multi-core BG configuration is to use inverted gratings, written on internal surfaces of relatively broad holes embedded in a photonic-crystal-fiber matrix. The objective of the work is to investigate solitons and their stability in this system. New results are also obtained for the earlier investigated dual-core system. Families of symmetric and antisymmetric solutions are found analytically, extending beyond the spectral gap in both the dual- and tri-core systems. Moreover, these families persist in the case (strong coupling between the cores) when there is no gap in the systems linear spectrum. Three different types of asymmetric solitons are found (by means of the variational approach and numerical methods) in the tri-core system. They exist only inside the spectral gap, but asymmetric solitons with nonvanishing tails are found outside the gap as well. Stability of the solitons is explored by direct simulations, and, for symmetric solitons, in a more rigorous way too, by computation of eigenvalues for small perturbations. The symmetric solitons are stable up to points at which two types of asymmetric solitons bifurcate from them. Beyond the bifurcation, one type of the asymmetric solitons is stable, and the other is not. Then, they swap their stability. Asymmetric solitons of the third type are always unstable. When the symmetric solitons are unstable, their instability is oscillatory, and, in most cases, it transforms them into stable breathers. In both the dual- and tri-core systems, the stability region of the symmetric solitons extends far beyond the gap, persisting in the case when the system has no gap at all. The whole stability region of antisymmetric solitons (a new type of solutions in the tri-core system) is located outside the gap. Thus, solitons in multi-core BGs can be observed experimentally in a much broader frequency band than in the single-core one, and in a wider parameter range than it could be expected. Asymmetric delocalized solitons, found outside the spectral gap, can be stable too.Received: 13 August 2003PACS: 42.81.Dp Propagation, scattering, and losses; solitons - 42.65.Tg Optical solitons; nonlinear guided waves - 05.45.Yv Solitons     

The contrast between defect solitons in parityben time symmetric superlattice and simple-lattice complex potentials

The existence and stability of defect superlattice solitons in parity-time (PT) symmetric superlattice and simple-lattice complex potentials are reported. Compared with defect simple-lattice solitons in similar potentials, the defect soliton in superlattice has a wider stable range than that in simple-lattice. The solitons' power increases with increasing propagation constant. For the positive defect, the solitons are stable in the whole region where solitons exist in the semi-infinite gap. For the zero defect, the solitons are unstable at the edge of the band. For the negative defect, the solitons propagate with the shape of Y at low propagation constant and propagate stably at the large one.     

局域单PT对称势中多级孤子的传输特性研究

具有Parity-Time(PT)对称性的光学系统是近年提出的一种新型光学结构,在光开关、光子信息处理器件等方面具有潜在的应用。研究了局域单PT对称光学系统中双级孤子和三级孤子的存在范围与稳定特性。研究结果表明:多级孤子存在一临界传播常数,传播常数对应了线性模下的本征值。双级孤子和三级孤子仅能在较深的PT对称势中才能稳定地传输。多级孤子的稳定性的范围随着PT对称势的深度增加而扩大;孤子的能量随着传播常数的增大而增加,但随着PT对称势的调制深度的增加而减少。