Elliptical Gaussian solitons in synthetic nonlocal nonliear media

This paper studies analytically and numerically the dynamics of two-dimensional elliptical Gaussian solitons in a "double-self-focusing" synthetic nonlocal media featuring elliptical and circular Gaussian response with different degrees of nonlocality.Based on the variational approach,it obtains the approximately analytical solution of such Gaussian elliptical solitons.It also computes the stability of the solitons by numerical simulations.     

Surface superlattice solitons in nonlocal nonlinear media

We analyse surface solitons at the interface between a one-dimensional photonic superlattice and a uniform medium with weak nonlocal nonlinearity. We demonstrate that in deep lattices there exist three kinds of surface solitons when the propagation constant exceeds a critical value, including two on-site solitons and one off-site soliton. These three kinds of surface solitons have unique dynamical properties. If the relative depth of the superlattice is low, there is only one kind of off-site soliton; however, the solitons of this kind can propagate stably, unlike their deep superlattice counterparts. Dipole surface solitons are also investigated, and the stable domain is given.     

Elliptic incoherent accessible solitons in strongly nonlocal media

We study the propagation of elliptic incoherent accessible solitons in strongly nonlocal media with noninstantaneous Kerr nonlinearity. For this soliton to exist, the coherence properties of the incoherent beam should be anisotropic. The total power of the incident beam should also equal to a critical value which depend on the beam width as well as the coherence properties. When initial parameters of the beam do not satisfy the existence conditions, the elliptic incoherent accessible solitons will undergo linear harmonic oscillation in different states. Corresponding properties are studied in detail.     

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     

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.     

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.     

强非局域介质中1+1维高斯型损耗空间双孤子的相互作用

研究了1+1维高斯型双光束在含小损耗的强非局域非线性介质中的传输特性。通过对该介质中光束传输遵循的非局域非线性薛定谔方程进行近似简化,得到了含小损耗强非局域非线性介质中1+1维高斯型双光束传输模型。在此基础上运用解析的方法研究了双光束传输的演化规律,得到了准双孤子解。经过进一步分析发现,在传输过程中两光束中心的轨迹为艾里函数;两光束会准周期性地碰撞、分离;随着传输距离的增大,两光束中心之间的最大距离会越来越大。另一方面,当损耗逐渐增大时,两光束的碰撞空间周期将变短,同时两光束中心之间的最大距离也越来越大。     

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     

强非局域介质中1+1维高斯型损耗空间双孤子的相互作用

研究了1+1维高斯型双光束在含小损耗的强非局域非线性介质中的传输特性。通过对该介质中光束传输遵循的非局域非线性薛定谔方程进行近似简化,得到了含小损耗强非局域非线性介质中1+1维高斯型双光束传输模型。在此基础上运用解析的方法研究了双光束传输的演化规律,得到了准双孤子解。经过进一步分析发现,在传输过程中两光束中心的轨迹为艾里函数;两光束会准周期性地碰撞、分离;随着传输距离的增大,两光束中心之间的最大距离会越来越大。另一方面,当损耗逐渐增大时,两光束的碰撞空间周期将变短,同时两光束中心之间的最大距离也越来越大。     

强非局域非线性介质中的二维库墨-高斯孤子簇

利用自相似技术求解一个在强非局域非线性条件下的(2+1)维非线性薛定谔方程,得到一个精确的库墨-高斯解析解,数值模拟与解析解的一致性表明,这种库墨-高斯孤子形成了一类空间孤子簇.发现这种非局域孤子具有较大的相移.     

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     

Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity

We investigate the properties of fundamental, multi-peak, and multi-peaked twisted solitons in three types of finite waveguide lattices imprinted in photorefractive media with asymmetrical diffusion nonlinearity. Two opposite soliton self-bending signals are considered for different families of solitons. Power thresholdless fundamental and multi-peaked solitons are stable in the low power region. The existence domain of two-peaked twisted solitons can be changed by the soliton self-bending signals. When solitons tend to self-bend toward the waveguide lattice, stable two-peaked twisted solitons can be found in a larger region in the middle of their existence region. Three-peaked twisted solitons are stable in the lower (upper) cutoff region for a shallow (deep) lattice depth. Our results provide an effective guidance for revealing the soliton characteristics supported by a finite waveguide lattice with diffusive nonlocal nonlinearity.     

强非局域非线性介质中光束传输的空间光孤子解

利用1+2维Snyder-Mitchell模型讨论了柱坐标系下光束传输过程，得到了强非局域非线性介质中光束稳定传输的拉盖尔高斯型解，即空间光孤子解，并得到了入射光束稳定传输的临界功率.图示展现了几个低阶光孤子解，并发现了强非局域非线性介质中存在圆环形光孤子. 关键词： 强非局域非线性介质 拉盖尔高斯(Laguerre-Gauss)解 高阶空间光孤子     

Solitons in optical lattices with nonlocal nonlinearity

The propagation of spatial solitons is systematically investigated in nonlocal nonlinear media with an imprinted transverse periodic modulation of the refractive index. Based on the variational principle and the infinitesimal approximation of Maclaurin series expansion, we obtain an analytical solution of such nonlocal spatial solitons and an interesting result that the critical power for such solitons propagation is smaller than that in uniform nonlocal self-focusing media. It is found that there exist thresholds in modulation period and lattice depth for such solitons. A stable spatial soliton propagation is maintained with proper adjustment of the modulation period and the lattice depth.     

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.     

相位调制高斯光束在强非局域非线性介质中的传输特性

利用(1+1)维Snyder-Mitchell模型和空间正弦相位调制的方法，讨论了如何控制高斯光束在平面波导中的传输问题，发现只要适当地选择调制参数就可得到稳定对称的三、五和六束子光束的共同传输，其独特全新的相互作用过程在光开关、编码器和分光器上有潜在的应用价值. 关键词： 强非局域非线性介质 空间相位调制 空间光孤子相互作用特性 光开关     

非局域非线性克尔介质中两极孤子的变分解

利用变分法对一种假设的两极孤子进行了研究,得到了该两极孤子的参数耦合方程,并对由参数耦合方程得到的结果进行了数值模拟.结果表明,在光束能量较高,趋近于强非局域的情况下,两极孤子横向强度呈一阶厄米-高斯型分布;光束能量较低的弱非局域情况下,两极孤子的两个强度峰之间有一个平台出现.此两极孤子模型还可退化为高斯光束,得到高斯孤子解.     

Collapse arrest in a two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam in nonlocal nonlinear media

Propagation dynamics of a two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam are investigated numerically in local and nonlocal nonlinear media. The self-healing and collapse of the beam crucially depend on the distribution factor b and the topological charge m. With the aid of nonlocality, a stable Airy Gaussian beam and an Airy Gaussian vortex beam with larger amplitude can be obtained, which always collapse in local nonlinear media. When the distribution factor b is large enough, the Airy Gaussian vortex beam will transfer into quasi-vortex solitons in nonlocal nonlinear media.     

偏离束腰入射对非局域非线性介质中高斯光束演化的影响

从1+1维强非局域模型出发，讨论了偏离束腰入射的高斯光束在非局域非线性介质中的传输 特性，得到了精确的解析解.结果表明，在聚焦介质中偏离束腰入射时，不论入射功率多大 ，光束束宽将发生周期性波动，光孤子不复存在，这与从高斯光束束腰入射的情况有本质的 不同；入射功率决定了光束平均束宽的大小，入射位置决定了光束初始的演化趋势.比较了在入射位置相同的条件下，聚焦介质、散焦介质和线性均匀介质中光束的演化.给出了“空 间啁啾”的定义，偏离束腰入射的物理本质是光束的不同入射位置对应不同的初始空间啁啾 .空间啁啾的概念， 关键词： 非局域非线性介质 空间光孤子 高斯光束     

椭圆高斯光束在强非局域非线性介质中的传输特性

研究了傍轴椭圆高斯光束在强非局域非线性介质中的传输特性，得到了其各参量的演化方程 及其精确解析解.通过对束宽演化方程及其精确解析解的进一步分析，发现傍轴椭圆高斯光 束在强非局域非线性介质中传输时，两横向方向束宽作周期性变化.不管初始功率为多大， 光束都将周期性的由椭圆高斯光束演化为圆对称高斯光束，再由圆对称高斯光束演化为椭圆 高斯光束；并且在演化的过程中，椭圆的半长轴和半短轴会作周期性交替变化.另外，在一 定初始功率下，傍轴椭圆高斯光束可以保持某一横向方向的束宽不变，得到光孤子. 关键词： 强非局域非线性介质 非局域非线性薛定谔方程 椭圆高斯光束 参量演化方程 空间孤子