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.     

Two-dimensional spatial solitons in highly nonlocal nonlinear media

We investigate, analytically and numerically, a class of novel higher-order spatial solitons in two transverse-dimensions, in highly nonlocal nonlinear media. The stability of these solutions in propagation is confirmed by direct numerical simulation. Our results demonstrate that the higher-order spatial solitons in highly nonlocal nonlinear media can exist in various forms, such as the fundamental solitons, vortex-ring solitons, multipole solitons, and fractional solitons.     

Two-dimensional multipole solitons in nonlocal nonlinear media

We present the experimental observation of scalar multipole solitons in highly nonlocal nonlinear media, including dipole, tripole, quadrupole, and necklace-type solitons, organized as arrays of out-of-phase bright spots. These complex solitons are metastable, but with a large parameters range where the instability is weak, permitting their experimental observation.     

非局域非线性介质中空间暗孤子的理论和实验研究

对非局域非线性介质中的空间暗孤子进行了研究.理论上运用牛顿迭代法求解非局域非线性薛定谔方程,得到了不同传播常数下的非局域空间暗孤子的数值解,发现在任何非局域程度以及任何传播常数条件下,都存在暗孤子的解,而且孤子的束宽与非局域程度存在一定的关系.实验上,在染料溶液中观测到了空间暗孤子在非局域非线性介质中的形成.利用输入功率所引起的非线性效应强度的变化,分析了背景光波形对暗孤子的影响,数值模拟结果与实验结果相符合. 关键词： 非局域非线性 空间暗孤子     

Gaussian solitons in nonlocal media: variational analysis

Exact solutions of Gaussian solitons in nonlinear media with a Gaussian nonlocal response are obtained. Using the variational approach, we obtain the approximate solutions of such solitons when the degree of the nonlocality is arbitrary. Specifically, we study the conditions for Gaussian solitons that propagate in weakly and highly nonlocal media. We also compare the variational result with the known exact solutions for weakly and highly nonlocal media.     

Observation of attraction between dark solitons

We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems, such as Bose-Einstein condensates with repulsive long-range interparticle interaction.     

Highly noninstantaneous solitons in liquid-core photonic crystal fibers

The nonlinear propagation of pulses in liquid-filled photonic crystal fibers is considered. Because of the slow reorientational nonlinearity of some molecular liquids, the nonlinear modes propagating inside such structures can be approximated, for pulse durations much shorter than the molecular relaxation time, by temporally highly nonlocal solitons, analytical solutions of a linear Schr?dinger equation. The physical relevance of these novel solitons is discussed.     

(1+2)维各向同性介质中的旋转椭圆空间光孤子

从(1+2)维非局域非线性薛定谔方程出发, 通过坐标变换得到了旋转坐标系下的非局域非线性薛定谔方程. 假设响应函数为高斯型, 用虚时间法数值求解了旋转坐标系下的非局域非线性薛定谔方程的静态孤子解, 迭代出了不同非局域程度条件下的静态椭圆孤子数值解. 最后采用分步傅里叶算法, 以迭代的孤子解作为初始输入波形, 模拟了在不同的非局域程度条件下, (1+2)维椭圆空间光孤子的旋转传输特性. 强非局域时, 椭圆光孤子的长轴方向和短轴方向波形都是高斯型, 其他的非局域程度下, 不是高斯型. 由此表明：(1+2)维椭圆光孤子对非局域程度依赖性很强. 旋转角速度和功率均与非局域程度以及孤子的椭圆度有关.     

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.     

Two-dimensional Hermite-Gaussian solitons in strongly nonlocal nonlinear medium with rectangular boundaries

An analytical solution of self-similar waves, Hermite-Gaussian solitons, emerging in a strongly nonlocal thermal nonlinear medium with the rectangular boundaries was found. The theoretical analysis and numerical simulation showed that the Hermite-Gaussian solitons are elliptic and form a rectangular matrix cluster. Moreover, the symmetries of the soliton and matrix cluster depend not only on the boundary conditions, but also on the symmetry and power of the input beam as well as the propagation distance. The particular interest lies in that the intensities of the solitons in the edges of the rectangular cluster are bigger than those on the center, the most intense solitons occurring at four angles.     

非局域表面暗孤子及其稳定性分析

非局域体介质中的暗孤子及表面亮孤子由于在光通信领域的潜在应用而受到极大关注,然而到目前为止却没有对非局域表面暗孤子的研究.在线性介质和非局域非线性介质的分界面上,数值模拟得到了1+1维非局域基态和二阶表面暗孤子,研究了它们的波形与传播常数和介质非局域程度的关系,基于它们的稳定性分析进行了理论推导和数值模拟.稳定性分析结果表明:1+1维非局域基态表面暗孤子在其存在区域总是稳定的,而二阶表面暗孤子是区域不稳定的,其不稳定区域的宽度与传播常数以及介质的非局域程度有关系,且受传播常数的影响更大.加噪声的初始输入传输图验证了稳定性分析结果的正确性.     

不同非局域程度条件下空间光孤子的传输特性

光束在非局域非线性介质中传输由非局域非线性薛定谔方程描述.讨论了在不同非局域程度 条件下，空间光孤子的传输特性.提出了一个基于分步傅里叶算法数值求解孤子波形和分布 的迭代算法.假定介质的非线性响应函数为高斯型，得出了在不同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，不论非局域程度如何，光束都能以 光孤子态在介质中稳定传输.光孤子的波形是从强非局域时的高斯型过渡到局域时的双曲正 割型，形成孤子的临界功率随非局域程度的减弱而减小，光孤子相位随距离线性增大，相位 的变化率随非局域程度的减弱而减小. 关键词： 非局域非线性薛定谔方程 空间光孤子 临界功率 相位     

Observation of multivortex solitons in photonic lattices

We report on the first observation of topologically stable spatially localized multivortex solitons generated in optically induced hexagonal photonic lattices. We demonstrate that topological stabilization of such nonlinear localized states can be achieved through self-trapping of truncated two-dimensional Bloch waves and confirm our experimental results by numerical simulations of the beam propagation in weakly deformed lattice potentials in anisotropic photorefractive media.     

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     

负性介电各向异性向列相液晶中空间光孤子的理论研究

对非局域非线性介质向列相液晶中介电各向异性为负时的情况进行了研究.理论研究表明,负性介电各向异性的向列相液晶具有负的非线性系数.文中给出了其空间非局域响应特征宽度和非线性系数的表达式,并求出了其非局域响应函数;其次,用数值计算的方法给出了其空间孤子的传输结果.最后,研究了光束功率和偏置电压的改变对负性介电各向异性向列相液晶中光束传输的影响,发现偏置电压的改变会导致光束在负性介电各向异性液晶中形成孤子所需的临界功率发生改变.     

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.     

Accessible solitons in three-dimensional parabolic cylindrical coordinates

A class of self-similar beams, named three-dimensional (3D) spatiotemporal parabolic accessible solitons, are introduced in the 3D highly nonlocal nonlinear media. We obtain exact solutions of the 3D spatiotemporal linear Schrödinger equation in parabolic cylindrical coordinates by using the method of separation of variables. The 3D localized structures are constructed with the help of the confluent hypergeometric Tricomi functions and the Hermite polynomials. Based on such an exact solution, we graphically display three different types of 3D beams: the Gaussian solitons, the ring necklace solitons, and the parabolic solitons, by choosing different mode parameters. We also perform direct numerical simulation to discuss the stability of local solutions. The procedure we follow provides a new method for the manipulation of spatiotemporal solitons.     

Stable spinning optical solitons in three dimensions

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schr?dinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.     

Bright and dark spatial solitons in metallic nanowire arrays

We investigate the formation and propagation of bright and dark three-dimensional unstaggered spatial solitons with cylindrical symmetry in a nonlinear nanowire metamaterial. The metamaterial is formed by metallic nanowires embedded in a Kerr-type dielectric host and is modeled using an effective medium approach. Unlike conventional Kerr media, the metamaterial supports bright solitons when the host is a self-defocusing material and dark solitons when the host is a self-focusing material. Our numerical calculations show that the confinement of the spatial-solitons results from the interplay of the host nonlinear response strength and the hyperbolic dispersion of the photonic states in the nanowire array. Subwavelength solitary beams may be observed for sufficiently strong nonlinearities.     

Observation of two-dimensional surface solitons

We report the first experimental observation of two-dimensional surface solitons at the boundaries (edges or corners) of a finite optically induced photonic lattice. Both in-phase and gap nonlinear surface self-trapped states were observed under single-site excitation conditions. Our experimental results are in good agreement with theoretical predictions.