Propagation properties of spatial optical solitons in different nonlocal nonlinear media with arbitrary degrees of nonlocality

We address the physical features exhibited by spatial optical solitons propagating in nonlocal Kerr-type media with Gaussian-shaped response and exponential-decay response, respectively. An iteration algorithm based on the split-step Fourier method is developed to obtain the numerical solutions of the solitons for the nonlocal nonlinear Schrödinger equation with arbitrary degrees of nonlocality. Our numerical results show that the soliton properties in the normalized system are different with the change of the degree of nonlocality and with the different responses. The profiles undergo a gradual and continuous transition from a Gaussian-shaped function in the strongly nonlocal case to a hyperbolic secant function in the local case for the Gaussian-shaped response, but for the exponential-decay response, the soliton profile is not Gaussian-shaped even in the strongly nonlocal cases. For the same response function, the stronger the nonlocality is, the higher the critical powers for solitons are and the larger of the phase shifts of the solitons. For the same degrees of nonlocality, when the degrees of nonlocality is larger enough, both the critical power and the phase shift for the Gaussian-shaped response are larger than that for the exponential-decay response.     

Dynamics of surface dipole and tripole solitons in nonlocal nonlinear media with optical lattice field

We find the existence conditions for stationary dipole and tripole surface solitons formed at the interface of a nonlocal nonlinear medium and a lattice with linearly modulated frequency. We investigate how the degree of nonlocality, the depth, and the modulation frequency of the optical lattice field affect on the existence of the surface solitons and their dynamics. The relationship between the power and the model parameters is identified. The stability of the surface dipole and tripole solitons is numerically investigated.     

The （l＋l）-dimensional spatial solitons in media with weak nonlinear nonlocality

We study the propagation of (1+1)-dimensional spatial soliton in a nonlocal Kerr-type medium with weak nonlocality. First, we show that an equation for describing the soliton propagation in weak nonlocality is a nonlinear Schr?dinger equation with perturbation terms. Then, an approximate analytical solution of the equation is found by the perturbation method. We also find some interesting properties of the intensity profiles of the soliton.     

Multipole surface solitons supported by the interface between linear media and nonlocal nonlinear media

We address multipole surface solitons occurring at the interface between a linear medium and a nonlocal nonlinear medium. We show the impact of nonlocality, the propagation constant, and the linear index difference of two media on the properties of the surface solitons. We find that there exist a threshold value of the degree of the nonlocality at the same linear index difference of two media, only when the degree of the nonlocality goes beyond the value, the multipole surface solitons can be stable.     

Stable high-dimensional solitons in nonlocal competing cubic-quintic nonlinear media

We find and stabilize high-dimensional dipole and quadrupole solitons in nonlocal competing cubic-quintic nonlinear media. By adjusting the propagation constant, cubic, and quintic nonlinear coefficients, the stable intervals for dipole and quadrupole solitons that are parallel to the x-axis and those after rotating 45° counterclockwise around the origin of coordinate are found. For the dipole solitons and those after rotation, their stability is controlled by the propagation constant, the coefficients of cubic and quintic nonlinearity. The stability of quadrupole solitons is controlled by the propagation constant and the coefficient of cubic nonlinearity, rather than the coefficient of quintic nonlinearity, though there is a small effect of the quintic nonlinear coefficient on the stability. Our proposal may provide a way to generate and stabilize some novel high-dimensional nonlinear modes in a nonlocal system.     

非局域克尔介质中空间光孤子的相互作用

研究了强非局域克尔介质中光束的演化规律，通过相位分析得到了空间孤子相互作用所满足 的非局域非线性薛定谔方程的简化近似模型，并获得了双光束传输的解析解.结果表明在传 输过程中相互作用的高斯光束的相位决定于它们的输入总功率.以振幅一强一弱共同传输的 高斯光束为例进行了具体研究，得到了强光和弱光的解析式，相位分析显示弱光在相当短的 传输距离之内能产生大的相移，可以通过对强光能量的调控来实现对弱光的相位调制. 关键词： 非局域克尔介质 空间光孤子 孤子相互作用 相位调制     

Propagation of coupled dipole-mode beams in nonlocal thermal media

The mutual trapping of two dipole-mode beams is investigated numerically in nonlocal thermal media. Results show that the incoherent attraction of perpendicularly aligned dipole-mode beams can enhance the stability of their composite structure. When the powers of the dipole components are identical, the larger the power, the shorter the stable distance. While when the powers are different, the closer the powers, and the longer the stable distance. Furthermore numerical results proved that the coupled solitary structures exhibit stable propagation for much larger distances than the corresponding scalar cases.     

Dipole solitons in nonlocal nonlinear media with anisotropy

We investigate the existence and stability of dipole-mode solitons in two-dimensional models of nonlocal media with anisotropic Kerr nonlinearity analytically and numerically. We obtain the approximate solution of such elliptic dipole solitons by using the variational approximation. The dynamics of such dipole-mode solitons is governed by the eccentricity of both the input beam and the nonlocal response function. We also compute the stability of the solitons by direct numerical simulations. The effects of the anisotropy of the nonlocal response function on the propagation of the dipole beam are also discussed in detail.     

Spatial optical solitons in fifth order and seventh order weakly nonlocal nonlinear media

We analytically study the (1 + 1)-dimensional spatial optical solitons in weakly nonlocal nonlinear media with cubic–quintic nonlinearity (fifth order nonlinear media) and cubic–quintic–septic nonlinearity (seventh order nonlinear media). Explicit solutions are derived, which include optical bright solitons, singular solutions and singular triangular periodic solution.     

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.     

亚强非局域空间光孤子的相互作用

研究了亚强非局域空间光孤子的相互作用规律,从光线方程出发得到了孤子光束中心的演化性质以及相互作用周期的解析解.发现亚强非局域条件下孤子的初始间距和非局域特征长度的关系对孤子的相互作用周期有很大的影响,在斜入射时存在一个最大入射角, 小于这个角度孤子才会吸引.数值模拟验证了理论解析的结果. 关键词： 亚强非局域 相互作用 空间光孤子 全光开关     

(1+2)维空间光孤子在非局域克尔介质中的传输特性

 从非局域非线性薛定谔方程出发,采用分步傅里叶算法数值讨论了在一定的非局域程度条件下,（1+2）维空间光孤子的传输特性, 数值求解了光孤子各特性参量。假定非局域克尔介质的响应函数为高斯型,得出了在一定的非局域程度条件下空间光孤子的数值解,并数值证明了它们的稳定性。结果表明:（1+2）维光孤子对非局域程度依赖性很强。在一定的非局域程度下,光束能以光孤子态在非局域克尔介质中稳定传输。强非局域时,光孤子的波形是高斯型,其它的非局域程度下,不是高斯型。当非局域程度较弱时,不存在孤子解。     

Propagation of nonlocal optical solitons in lossy media with exponential-decay response

Propagation of optical solitons in lossy nonlocal media with exponential-decay response was investigated theoretically. The analytical solutions of nonlocal solitons and breathers are obtained by variational approach which is applied to a (1 + 1)D nonlocal nonlinear Schrödinger equation. The critical power of soliton and period of breathers are also obtained in the absence of the loss. When the loss is relatively small, the average beam width of breathers has a trend to expand during propagation. The analytical results are confirmed by numerical simulation.     

Variational solutions for Hermite--Gaussian solitons in nonlocal nonlinear media

The physical features exhibited by Hermite--Gaussian (HG) beams propagating in nonlocal nonlinear media with Gaussian-shaped response are discussed with an approximate variational method. Using direct numerical simulations, we find that the beam properties in the normalized system are different with the change of the degree of nonlocality. It is shown that initial HG profiles break up into several individual beams with propagation when the degree of nonlocality $\alpha$ is small. HG beams can propagate stably when $\alpha$ is large enough.     

Dark incoherent spatial solitons in logarithmically saturable nonlinear media

This paper studies numerically the dark incoherent spatial solitons propagating in logarithmically saturable nonlinear media by using a coherent density approach and a split-step Fourier approach for the first time. Under odd and even initial conditions, a soliton triplet and a doublet are obtained respectively for given parameters. Simultaneously, coherence properties associated with the soliton triplet and doublet are discussed. In addition, if the values of the parameters are properly chosen, five and four splittings from the input dark incoherent spatial solitons can also form. Lastly, the grayness of the soliton triplet and that of the doublet are studied, in detail.     

非局域程度对向列相液晶中空间光孤子的影响

理论分析了非局域程度对向列相液晶中(1+2)维空间光孤子的影响.得到了非线性系数以及特征长度和预倾角的关系,并且给出了强非局域性的非线性薛定谔方程,最终得到了单孤子和临界功率的解析解.实验上,通过改变偏压从而间接测量了向列相液晶中的临界功率,并与数值模拟结果相结合与理论结果进行了比较,发现基本相符. 关键词： 空间光孤子 非线性系数 非局域程度 临界功率     

强非局域非线性介质中的涡旋光孤子

满足强非局域条件时，光束在非局域非线性介质的传输过程由Snyder-Mitchell模型描述.在旋转柱坐标系下求解了Snyder-Mitchell模型，得到涡旋光孤子的自相似旋转解析解.结果表明，涡旋光孤子解在径向是惠特克函数与幂函数的乘积，光束的光强呈环形分布，光束绕光束中心旋转. 关键词： 非局域非线性介质 强非局域性 涡旋光孤子 惠特克函数     

强非局域非线性介质中拉盖尔-高斯型光孤子相互作用

利用强非局域非线性介质中傍轴光束传输的线性模型(修正的Snyder-Mitchell模型)讨论了两束共线(即光束中心和传输方向都相同)拉盖尔-高斯型光孤子的传输过程. 改变双光束的相对阶数和相对强度比,叠加光场在传输截面上的光强分布呈现出多样性,通过叠加的方法在该介质中产生了多环形光孤子. 一定条件下传输光束在传输过程中会出现旋转现象,叠加光场成为旋转光场,给出了旋转光束的旋转条件以及旋转速度. 进一步利用拉盖尔-高斯光束在传输过程中特有的螺旋相位特点分析了光场截面强度多样性产生的物理机理. 关键词： 强非局域非线性介质 拉盖尔-高斯型光孤子 共线传输 涡旋相位     

Spinning solitons in cubic-quintic nonlinear media

We review recent theoretical results concerning the existence, stability and unique features of families of bright vortex solitons (doughnuts, or ‘spinning’ solitons) in both conservative and dissipative cubic-quintic nonlinear media.     

Propagation of the two-dimensional elegant Hermite-cosh-Gaussian beams in strongly nonlocal nonlinear media

In this paper, two-dimensional elegant Hermite-cosh-Gaussian beams are introduced and an analytical expression for the beam propagation through an optical ABCD system is derived by using Collins formula. By considering the transfer matrix of the strongly nonlocal nonlinear media, the propagation properties of a two-dimensional elegant Hermite-cosh-Gaussian beam through these media are investigated.