(1+1)维强非局域非线性介质中的高阶模呼吸子

基于强非局域非线性介质中的Snyder-Mitchell模型,利用分离变量法得到了(1 1)维光束传输的厄米-高斯型解析解.比较厄米-高斯型解析解与非局域非线性薛定谔方程的数值解,证实了,在强非局域条件下,该厄米-高斯型解与数值解完全吻合.对厄米-高斯光束的传输特性进行研究,结果表明,光束束宽会出现周期性的压缩或者展宽现象.并且得到了实现厄米-高斯光束稳定传输的临界功率、厄米-高斯孤子解及传输常量,临界功率与厄米-高斯光束的阶数无关,但传输常量随阶数的增加而增加.高斯呼吸子和高斯孤子就是基模厄米-高斯呼吸子和基模厄米-高斯孤子.     

非局域非线性介质中光束传输的拉盖尔-高斯变分解

光束在非局域非线性介质中的传输过程由非局域非线性薛定谔方程描述.1+2D非局域非线性薛定谔方程可以转化为圆柱坐标系下的变分问题.通过展开介质响应函数并合理假设试探解求解变分方程,得到光束在强非局域非线性介质中的拉盖尔-高斯解.满足一定条件时,拉盖尔-高斯光束将形成光孤子或退化为高斯光束. 关键词： 非局域非线性介质 强非局域性 变分法 拉盖尔-高斯光束     

非局域克尔介质中厄米高斯光束传输的变分研究

在非局域非线性克尔介质中,通过对介质实对称响应函数的泰勒展开,简化了非局域非线性薛定谔方程所对应的Lagrange密度,进而利用变分法对光束的传输问题进行了分析.求出试探解各个参量的演化方程并得到了自聚焦介质中的厄米高斯型光束的精确解析解,当输入功率达到临界功率时,即形成高阶空间光孤子(厄米高斯孤子),其最低阶(基模光孤子)就是高斯孤子.通过数值模拟发现解析解与数值解符合得很好. 关键词： 非局域克尔介质 变分法 厄米高斯光束 空间光孤子     

强非局域非线性介质中光束传输的厄米高斯解

利用强非局域非线性介质中空间对称实响应函数的泰勒展开简化了非局域非线性薛定谔方程 ，文章基于强非局域非线性空间中的线性模型得到了矩空间1+D(D=1，2)维的厄米高斯 型解，得到了高阶孤子波的解析式，高斯解是最低阶孤子，即基模光孤子，并得到了入射光 束的临界功率．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非对称 光孤子． 关键词： 高阶孤子 强非局域介质 厄米高斯     

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     

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     

微扰法求解铅玻璃中的涡旋空间光孤子

在量子力学的微扰理论框架下,利用微扰法求解得到了1+2维强非局域非线性介质——铅玻璃中二阶微扰修正的"类拉盖尔高斯型"涡旋孤子的近似解析解。从非局域非线性薛定谔方程(NNLSE)出发,以铅玻璃中的真实折射率与Snyder-Mitchell(SM)模型中描述的抛物线型折射率的差值为微扰,以SM模型中的拉盖尔高斯孤子解为基态解,求得了铅玻璃材料中二阶微扰修正的"类拉盖尔高斯型"涡旋孤子的解析解。拓扑荷值分别为1、2、3、4的微扰修正的"类拉盖尔高斯型"光孤子比未加微扰的拉盖尔高斯型光孤子更稳定,非常接近孤子真解的传输行为。     

(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.     

非线性光学

非线性光学概论O4372007032364向列相液晶中强非局域空间光孤子的实验观察=Experi-mental observation of strong nonlocal optical spatial soli-tons in nematic liquid crystals[刊,中]/张涛(华南师范大学信息光电子科技学院传输光学实验室,广东省高校光子信息技术重点实验室.广东,广州(510006)),胡巍…//光学学报.?2007,27(1).?143-147通过实验对向列相液晶中的非局域空间光孤子的传输进行了研究。理论上基于非线性的液晶孤子传输方程,采用高斯形式的试探解,得到了孤子传输的解析解,以及对液晶中的非局域孤子和Snyder等提出的强非局域…     

光弹在库墨-高斯晶格中传输特性的研究

基于分布傅里叶算法及快速虚时间演化迭代法, 研究了光弹在线性和非线性散射异相调制的库墨-高斯晶格中传输的特性. 结果表明, 线性和非线性相位调制显著地改变了光弹的形状及其稳定范围, 并且非线性调制深度通过传播常数控制稳定性区域的宽度, 稳定时空光孤子的能量随着非线性调制深度的加强而增长. 关键词： 时空光孤子 库墨-高斯晶格 快速虚时间演化迭代法     

The elliptic function waves and solitons in thermal nonlocal media

An analytical solution is obtained in thermal nonlocal media by considering the weakly and strong nonlocal limit, respectively. In weakly nonlocal case the elliptic function wave solutions, which become soliton under limited condition, are present, while in strongly nonlocal case the solutions are bright soliton and multi-hump soliton. These results are well in good agreement with numerical ones in other references [8].     

Incoherently coupled vector dipole soliton pairs in nonlocal media

We investigate the incoherently and strongly coupled Manakov vector dipole soliton pairs in nonlocal nonlinear media. We use variational approach, to describe analytical properties of these solutions in a strongly nonlocal regime. We show that the presence of fundamental component improve stability of the dipole nonlocal soliton. In the limit of highly nonlocal nonlinearity, the evolution behaviors of the vector solitons is determined by their total power.     

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.     

Wave propagation in fluid-filled single-walled carbon nanotube on analytically nonlocal Euler–Bernoulli beam model

An analytically nonlocal Euler–Bernoulli beam model for the wave propagation in fluid-filled single-walled carbon nanotube (SWCNT) is established. The governing equations with the nonlocal effects are derived on the variational principle, and used in the wave propagation analysis of the SWCNT beam. Compared with the partially nonlocal Euler–Bernoulli beam models used previously, the analytically nonlocal model presented in the present study predicts well the effects of the stiffness enhancement and the wave damping at the high wavenumber or the strong nonlocal effects area for the fluid-filled SWCNT beam. Though the analytical model is less sensitive than the partially nonlocal model when the moving velocity of the internal fluid is high enough, it simulates more of the high-order nonlocal effecting information than the partially nonlocal model does in many cases.     

有界非局域非线性介质中空间光孤子传输的研究

对有界非局域非线性介质边界对孤子传输的影响进行了研究.基于非局域非线性薛定谔方程以及热传导的泊松方程,采用格林函数法求出了强非局域介质铅玻璃的响应函数和临界功率;从光线方程出发得到了偏离材料中心入射的光束中心振荡轨迹以及周期的解析解.通过数值模拟证明了该结果在不靠近样品边界的范围内都是准确的. 关键词： 空间光孤子 铅玻璃 非局域非线性     

Propagation of four-petal Gaussian beams in strongly nonlocal nonlinear media

The propagation of four-petal Gaussian beams in strongly nonlocal nonlinear media has been studied. The analytical solution and the analytical second-order moment beam width are obtained. For the off-waist incident and the waist incident cases, the intensity pattern evolves periodically during propagation in strongly nonlocal nonlinear media. Under the off-waist incident condition, the second-order moment beam width varies periodically during propagation, whatever the input power is. But under the waist incident condition, there exists a critical power. When the input power equals the critical power, the second-order moment beam width remains invariant, otherwise the second-order moment beam width varies periodically. Numerical simulations based on the nonlocal nonlinear Schrödinger equation are carried out for comparison with the theoretical predictions. The results show that the numerical simulations are in good agreement with the analytical results in the case of strong nonlocality.     

Free torsional vibration of nanotubes based on nonlocal stress theory

A new elastic nonlocal stress model and analytical solutions are developed for torsional dynamic behaviors of circular nanorods/nanotubes. Unlike the previous approaches which directly substitute the nonlocal stress into the equations of motion, this new model begins with the derivation of strain energy using the nonlocal stress and by considering the nonlinear history of straining. The variational principle is applied to derive an infinite-order differential nonlocal equation of motion and the corresponding higher-order boundary conditions which contain a nonlocal nanoscale parameter. Subsequently, free torsional vibration of nanorods/nanotubes and axially moving nanorods/nanotubes are investigated in detail. Unlike the previous conclusions of reduced vibration frequency, the solutions indicate that natural frequency for free torsional vibration increases with increasing nonlocal nanoscale. Furthermore, the critical speed for torsional vibration of axially moving nanorods/nanotubes is derived and it is concluded that this critical speed is significantly influenced by the nonlocal nanoscale.     

Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media

In the framework of nonlinear wave optics,we report the evolution process of a dipole breathing wave in lossy nonlocal nonlinear media based on the nonlocal nonlinear Schr?dinger equation.The analytical expression of the dipole breathing wave in such a nonlinear system is obtained by using the variational method.Taking advantage of the analytical expression,we analyze the influences of various physical parameters on the breathing wave propagation,including the propagation loss and the input power on the beam width,the beam intensity,and the wavefront curvature.Also,the corresponding analytical solutions are obtained.The validity of the analysis results is verified by numerical simulation.This study provides some new insights for investigating beam propagation in lossy nonlinear media.