Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics

Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schrödinger or Gross-Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.     

Pyroelectric photovoltaic spatial solitons in unbiased photorefractive crystals

A new type of spatial solitons i.e. pyroelectric photovoltaic spatial solitons based on the combination of pyroelectric and photovoltaic effect is predicted theoretically. It shows that bright, dark and grey spatial solitons can exist in unbiased photovoltaic photorefractive crystals with appreciable pyroelectric effect. Especially, the bright soliton can form in self-defocusing photovoltaic crystals if it gives larger self-focusing pyroelectric effect.     

中心对称双光子光折变低振幅灰孤子时间特性

为了得到中心对称双光子光折变晶体中低振幅灰空间孤子时间特性的结果,基于中心对称光折变晶体中双光子光折变效应的理论模型,推导出了含时间参量的空间电荷场和光波动态演化方程.采用数值方法,得到了低振幅灰孤子强度包络和强度半峰全宽的时间演化特性.结果表明:初始阶段形成宽度较宽的孤子,其宽度随时间单调递减到一个最小值直至稳态孤子的形成;在相同的演化时间内,孤子半峰全宽随着孤子峰值强度与暗辐射比值的增大而变小.研究了不同时间下低振幅灰孤子动态演化特性.     

Grey screening-photovoltaic soliton-induced waveguides

This paper shows that waveguides induced by grey screening-photovoltaic solitons are always single mode for all intensity ratios, which are the ratio between the peak intensity of the soliton and the dark irradiance. It finds that the confined energy near the centre of the grey soliton and the propagation constant of the guided mode increase monotonically with increasing intensity ratio. On the other hand, when the soliton greyness increases, the confined energy near the centre of the grey soliton and the propagation constant of the guided mode reduce monotonically. When the bulk photovoltaic effect is neglected for short circuits, these waveguides become waveguides induced by grey screening solitons. When the external bias field is absent, these waveguides become waveguides induced by grey photovoltaic solitons.[第一段]     

Waveguides induced by grey screening solitons

We investigate the properties of waveguides induced by one-dimensional grey screening solitons in biased photorefractive crystals. The results show that waveguides induced by grey screening solitons are always of single mode for all intensity ratios, i.e. the ratios between the peak intensity of the soliton and the dark irradiance. Our analysis indicates that the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton increase monotonically with intensity ratio increasing. On the other hand, when the soliton greyness increases, the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton decrease monotonically. Relevant examples are provided where photorefractive crystal is of the strontium barium niobate type.     

Domain wall solitons in quantum electron plasmas

We show the existence of new stationary solutions in the form of domain wall soliton in the nonlinear Schrödinger-Poisson equations describing the dynamics of quantum electron plasmas. It is found that the domain wall soliton exists at strong coupling constant regime and shows a different dynamical behavior in comparison with the previously found dark and gray solitons. The robustness and the conservation of the energy of the domain wall solitons is demonstrated by numerical simulations.     

Stability of elliptic vortex solitons in anisotropic nonlocal media

Elliptic vortex solitons are investigated in anisotropic nonlocal media with more general formulations. We address the existence and dynamics of such solitons analytically and numerically. The solution of elliptic vortex solitons depends on the eccentricity of both the input beam and nonlocal response function. With different degrees of nonlocality, we numerically investigate the evolution of the elliptic vortex solitons, and find that, typically, the elliptic vortex solitons with single and double charges collapse into spiraling dipole- and tripolelike soliton clusters, respectively.     

Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.     

Two-component coupled photovoltaic soliton pair in two-photon photorefractive materials under open circuit conditions

The existence and nonlinear dynamics of two-component incoherently coupled composite solitons in two-photon photorefractive materials under open circuit conditions have been investigated. In the steady-state regime, these incoherently coupled solitons can propagate in bright–dark, bright–bright and dark–dark configurations. These photovoltaic soliton families can be established provided that the carrier beams share the same polarization and wavelength. The influence of the gating beam on the dynamics of stable solitons is discussed. Numerical simulations show that these solitons are stable for small perturbation on amplitude.     

暗-暗与亮-暗光伏孤子相互作用

用数值方法分析了平行传播异色光伏暗孤子之间及亮-暗孤子之间的相互作用.结果表明，光伏暗孤子共轴传播能在有限的距离内保持准孤子形态，靠近传播时存在着相互吸引的作用 ，而相距较远传播时表现为一孤子暗区使另一孤子的缓变光场部分发生局部会聚作用.光伏暗孤子与亮孤子的相互作用随距离的不同可使亮孤子光强分布变尖锐或变平缓，以及使亮孤子发生能量转移.从两束信号光共同引起折射率波导这一物理机理对光伏孤子这些相互作用给出定性物理解释. 关键词： 光伏空间孤子 暗孤子 亮孤子 相互作用     

双光子光折变晶体串联回路中独立全息屏蔽空间孤子对

为了得到双光子独立全息屏蔽空间孤子对的结果,基于光折变晶体中的两波耦合和双光子光折变效应,证明在由两块双光子光折变晶体和一个电压源通过导线连接组成的串联回路中存在全息亮(暗)屏蔽孤子。每块晶体中能支持一个全息屏蔽孤子,这两个孤子称为双光子独立全息屏蔽孤子对,有明-明、暗-暗和明-暗三种类型。数值计算结果表明,在光束的空间展宽远小于晶体宽度的极限条件下,孤子对中的两孤子通过光电流和相互耦合能影响到这些孤子的空间包络和动态演化特性。     

超流费米气体中两维孤子的动力学

我们利用解析和数值的方法,研究从Bardeen-Cooper-Schrieffer(BCS)超流到玻色-爱因斯坦凝聚(BEC)渡越的过程里超流费米气体中两维(2D)孤子的形成和演化.基于超流流体力学方程,在准二维和长波近似下,推导描述弱非线性激发带正色散项的Kadomtsev-Petviashvili方程;给出整个BCS-BEC渡越的2D孤子解,以及数值求解孤子在囚禁势中的演化.数值结果显示由于Snake(横向)不稳定性,大振幅的暗孤子会衰变为大量涡旋-反涡旋对,并且这个不稳定性在不同超流区域不同.     

Asymmetrical surface soliton trains

We elucidate the existence, stability and propagation dynamics of multi-spot soliton packets in focusing saturable media. Such solitons are supported by an interface beside which two harmonically photonic lattices with different modulation depths are imprinted. We show that the surface model can support stable higher-order structures in the form of asymmetrical surface soliton trains, which is in sharp contrast to homogeneous media or uniform harmonic lattice modulations where stable asymmetrical multi-peaked solitons do not exist. Surface trains can be viewed as higher-order soliton states bound together by several different lowest order solitons with appropriate relative phases. Their existence as stable objects enriches the concept of compact manipulation of several different solitons as a single entity and offers additional freedom to control the shape of solitons by adjusting the modulation depths beside the interface.     

Self—Steepening and Thired—Order Dispersion Induced Optical Solitons in Fiber

Usually,one considers only the group velocity dispersion(GVD)-and self-phase modulation(SPM)-induced solitons in optic soliton communication while other higher order effects such as the third-order dispersion(TOD),self-steepening(SS),and stimulated Raman scattering are considered only perturbatively,In this paper,we study the existence of the TOD-and SS-induced soliton solutions.The existence conditions of the TOD-and SS-induced bright and dark solitons are quite different from those of the GVD-and SPM-induced solitons.     

Higher-Order Effects Induced Optical Solitons in Fiber

In this paper, we study the existence conditions of the soliton solutions induced by considering the higher-order effects such as the third-order dispersion (TOD), self-steepening (SS), and self-frequency shift arising from stimulated Raman scattering (SRS) simultaneously in optical soliton communication. Based on the Jacobian expansion method, we successfully obtain bright and dark solitons. The results shows that the resultant inclusion is in agreement with Mollenauer et al. [Physical Review Letters 45 (1980) 1095] when the SRS is not considered; while when the SRS is considered, the existence conditions of the higher-order effects induced bright and dark solitons are not only quite different from those of the group velocity dispersion (GVD)-induced and self-phase modulation (SPM)-induced solitons, but also different from those of the TOD- and SS-induced solitons discussed by Mollenauer et al. [Physical Review Letters 45 (1980) 1095].     

Soliton Properties of Light Pulses on the Surface of Ionic Crystals Generated by Strong Nonlinear Effects

In this paper, we theoretically discuss the soliton properties of light pulse transportation on the surface of an ionic crystal having strong nonlinear interactions between ions of unit cells. We analyze in detail the dark solitons when the nonlinear coefficient g is positive and negative, respectively. It is found that whether the nonlinear coefficient g is positive or negative, the dark solitons can be formed over the whole dispersion relation area of surface polaritons considering nonlinear effects. Attention should be paid to the fact that around ωTO, the light pulse can form advanced dark solitons, and there is a switching area from advanced dark soliton to retarded dark soliton near ωTO. We also discuss the effects of higher nonlinear dispersion on the solitons.     

Separate holographic screening soliton pairs in a biased series photorefractive crystal circuit

Holographic dark (bright) screening solitons are predicted in one dimension for a series circuit consisting of two photorefractive crystals connected electronically by electrode leads in a chain with a voltage source. Each crystal can support a holographic screening soliton. The two solitons are known collectively as a separate holographic screening soliton pair with three types: bright--bright, bright--dark and dark--dark. The numerical results show that the two solitons in a soliton pair can affect each other through a light-induced current and their coupling can affect their spatial profiles under the limit in which the optical wave has a spatial extent much less than the width of the crystal.     

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.     

Dark Solitons for the Defocusing Cubic Nonlinear Schrödinger Equation with the Spatially Periodic Potential and Nonlinearity

We study the existence of dark solitons of the defocusing cubic nonlinear Schrödinger (NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincaré map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity.     

Effects of periodic optical lattice potential on dark solitons in a Bose Einstein condensate

This paper investigates the dynamics of dark solitons in a Bose--Einstein condensate with a magnetic trap and an optical lattice (OL) trap, and analyses the effects of the periodic OL potential on the dynamics by applying the variational approach based on the renormalized integrals of motion. The results show that the dark soliton becomes only a standing-wave and free propagation of the dark soliton is not possible when the periodic length of the OL potential is approximately equal to the effective width of the dark soliton. When the periodic length is very small or very large, the effects of the OL potential on the dark soliton will be sharply reduced. Finally, the numerical results confirm these theoretical findings.