非线性光学 非线性光学概论

O437 2006065099 (2 1)维光学孤子在饱和非线性介质中的模式特征= Characteristic of(2 1)D optical soliton modes in satura- ble nonlinear medium[刊,中]/刘雅洁(嘉兴学院物理教研室,浙江,嘉兴(314001))．陆佩…//发光学报．—2006．27 (2)．—143—148从非线性Schr(?)dinger方程出发,应用数学解析的方法．详细讨论了在饱和非线性介质中(2 1)维空间光学孤子存在满足物理意义的自洽解的条件,给出数值计算所需要的边界条件。通过数值计算,给出了基模和一阶模在某一组参数下的部分模式的光场慢变包络、光强度的二维和三维分布的直观图形,以及相应能量(无量纲)。结果表明,孤子的存在不是任意的,而是依赖于一定的能量。当     

锁模光纤激光器中矢量孤子的传输特性研究

以含有慢饱和吸收效应的耦合非线性薛定谔方程组为模型,对锁模光纤激光器中亮亮类孤子对的产生及传输进行了详细地研究。首先,采用拟解法解析得到了慢饱和吸收效应影响下的一组新型的精确亮亮类孤子解;其次,采用分步傅立叶变换法数值研究了啁啾类亮亮孤子解的演化特性,并在输出端将数值结果与精确解进行了比对;最后,数值研究了一定幅度的白噪声干扰下亮亮类孤子解的稳定性。结果表明:一定的参数条件下,锁模光纤激光器中存在亮亮类孤子解,并且该解在一定的白噪声扰动下,可以实现较长距离的稳定传输。     

对数饱和非线性介质中的自洽多模高斯孤子解

通过解对数饱和非线性介质中光场满足的非线性薛定谔方程,得到一组厄米-高斯型的自洽多模解.在借鉴了R.G.Glauber的相干态理论的基础上,合理假设这组解在非线性介质中呈泊松分布,进而得到了在对数饱和非线性介质中存在高斯孤子的结论,并获得高斯孤子解、非线性系数与泊松参量三者之间的关系.该关系说明,若在介质中存在高斯孤子解,其非线性系数必须满足条件a≥1.当α=1,在介质中仅存在单模高斯孤子,其光斑尺寸必须满足的条件W=1/k n0/n2.在该条件下,以"束腰"注入介质中的高斯光束才可以在保持其光斑尺寸不变的情况下传输,否则光斑尺寸会存在一定的振荡.而振荡方式、振荡范围(表示光斑尺寸展宽或压缩及大小)与输入光束光斑尺寸及其一次导数有直接关系.     

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     

Kerr类非线性介质周期结构中的慢Bragg孤子

在耦合模理论的基础上,给出了一维无限大Kerr类非线性介质周期结构中的孤波解,并且指出,孤波的振幅依赖于入射频率以及脉宽两个参量.同时也证明,在布拉格共振极限条件下,孤波解可以简化成所谓的“隙孤子”解或是“慢布拉格孤子”解 关键词： 孤波 慢布拉格孤子 隙孤子 耦合模理论     

光纤布拉格光栅中的隙孤子存在条件

提出光纤布拉格光栅中产生隙孤子的条件和参量制约关系。利用非线性耦合模式方程建立光纤布拉格光栅中孤子的传播方程,通过扰动方法建立了参量的微分方程,计算得到参量近似解。以周期非线性光学介质中隙孤子存在的条件为依据,数学计算分析得到两组参量关系不等式。最终通过数值计算说明了这些参量之间存在制约关系和物理意义。从而理论上说明了在光纤布拉格光栅中隙孤子存在需要选择适当参量。为光纤布拉格光栅中产生隙孤子的实验和进一步的工程应用提供了理论基础。     

高斯光束在对数型非线性介质中自诱导效应

从标量Helmholtz方程出发,推导了对数饱和非线性介质中光场满足的非线性Schr dinger方程(NLSE)。通过与梯度折射率下的光场满足的方程比较,发现高斯光束在对数型饱和非线性介质中可自诱导梯度折射率。利用数值计算,详细地讨论了自诱导梯度折射率对高斯光束传输特性的影响。发现高斯光束在其自诱导的梯度折射率的影响下,呈振荡形式的准稳定的传输。光束注入介质中的初始状态,直接影响着光束的振荡形式(先发散还是先聚焦)、振荡深度(幅度)、振荡周期。得到高斯光束形成孤子的条件,以及若使高斯光束在对数饱和非线性介质中保持小损耗、高稳定的传输,应该使光束在阈值(孤子条件)附近注入介质的结论。     

全正色散耗散孤子掺镱光纤激光器

研究了一种基于非线性偏振旋转被动锁模没有进行色散管理的全正色散掺镱光纤激光器,在无外加滤波器的情况下实验产生了锁模耗散孤子脉冲.耗散孤子的形成是激光器中正光纤色散、非线性效应、腔传输、增益饱和和滤波效应综合作用的结果.实验产生的锁模耗散孤子脉冲能量达1.1nJ.此外,对激光器的数值模拟结果与实验结果相一致,证实了全正色...     

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     

(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.     

(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。     

Stability and instability of nonlinear defect states in the coupled mode equations—Analytical and numerical study

Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled mode equations (NLCME). This system of PDEs, similar in structure to the Dirac equations, has gap soliton solutions that travel at any speed between 0 and the speed of light. A recently considered strategy for spatial trapping or capture of gap optical soliton light pulses is based on the appropriate design of localized defects in the periodic structure. Localized defects in the periodic structure give rise to defect modes, which persist as nonlinear defect modes as the amplitude is increased. Soliton trapping is the transfer of incoming soliton energy to nonlinear defect modes. To serve as targets for such energy transfer, nonlinear defect modes must be stable. We therefore investigate the stability of nonlinear defect modes. Resonance among discrete localized modes and radiation modes plays a role in the mechanism for stability and instability, in a manner analogous to the nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation. However, the nature of instabilities and how energy is exchanged among modes is considerably more complicated than for NLS/GP due, in part, to a continuous spectrum of radiation modes which is unbounded above and below. In this paper we (a) establish the instability of branches of nonlinear defect states which, for vanishing amplitude, have a linearization with eigenvalues embedded within the continuous spectrum, (b) numerically compute, using Evans function, the linearized spectrum of nonlinear defect states of an interesting multiparameter family of defects, and (c) perform direct time-dependent numerical simulations in which we observe the exchange of energy among discrete and continuum modes.     

Mighty morphing spatial solitons and bullets

We give what we believe to be the first closed-form exact expression for the dynamic evolution of nonstationary beams of arbitrary intensity and width propagating in a uniform nonlinear medium and in both two and three dimensions. This shows that periodic and quasi-periodic (nonradiating) beams can exist in a non-Kerr nonlinear medium. The Schr?dinger equation is solved for Gaussian beams in a saturable medium. For one critical (initial) beam width, the Gaussian is a stable stationary soliton or bullet, independent of its intensity; otherwise, it breathes. New quasi-periodic beams (mighty morphing solitons) and bullets (mighty morphs) of elliptical cross section also exist whose ellipticity changes with propagation.     

空气中紫外波长局域涡旋光孤子的解及其稳定性

根据紫外波长光束在空气中传输时的非线性效应得到包含氧分子三光子电离等非线性效应的薛定谔方程。由该非线性薛定谔方程出发,研究了紫外波长光束在空气中传输时局域涡旋光孤子的形成。将涡旋孤子的形成和粒子在势阱中的运动联系起来,讨论了光束在空气中形成局域涡旋光孤子的初始条件。数值求解了柱坐标下的涡旋孤子解,随着初始幅值的变化,方程出现单环、双环等孤子解;分析了孤子解光强分布随着传播常数的变化情况,并得出光束尺度和脉冲能量对应初始幅值的变化关系。同时分析了孤子解的扰动稳定性,验证了Skarka所推导的一般性判据。     

强非局域光晶格中空间孤子的脉动传播

根据强非局域结构中空间孤子的演化方程——非局域非线性薛定谔方程,采用分步傅里叶方法,对一维强非局域光晶格结构中空间孤子的脉动传播进行数值研究.分析了孤子的初始光束能量、非局域程度、光晶格调制强度、光晶格周期以及线性折射率的纵向调制率与空间孤子的脉动传播周期之间的关系,并对影响脉动传播的内在物理机制进行了讨论.同时,还研究了在线性折射率纵向调制情况下强非局域光晶格结构中空间孤子传输的开关行为. 关键词： 非局域非线性薛定谔方程 光晶格 空间孤子 光开关     

C60溶液中的暗空间光孤子及其诱导的柔性光波导

利用Ａｒ^＋激光在C₆₀甲苯溶液中产生的自散焦效应观察到暗空间光孤子以及由它诱导出的柔性光波导现象．通过对非线性薛定谔方程的数值计算，模拟了暗空间孤子的形成过程，获得与实验相符的结果 关键词：     

Evolution of optical pulses in the presence of third-order dispersion

We model the propagation of femtosecond pulses through optical fibres by a nonlinear Schrödinger (NLS) equation involving a perturbing term arising due to third-order dispersion in the medium. The perturbative effect of this higher-order dispersion causes the usual NLS soliton to emit a radiation field. As a result, the given initial pulse propagating through the fibre exhibits nonsolitonic behaviour. We make use of a variational method to demonstrate how an initial pulse by the interaction with the emitted radiation can evolve into a soliton. We also demonstrate that the effect of interaction between the initial pulse and radiation field can be accounted for by including, in the evolution equation, terms associated with self-steepening and stimulated Raman scattering that characterize the optical medium.     

Propagation of light in(2+1)-dimensional nonlinear optical media with spatially inhomogeneous nonlinearities

The(2 1)-dimensional nonlinear Schr(o)dinger(NLS)equation with spatially inhomogeneous nonlinearities is investigated,which describes propagation of light in(2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities.New types of optical modes and nonlinear effects in optical media are presented numerically.The results reveal that the regular split of beam can be obtained in (2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities,by adjusting the guiding parameter.Furthermore,the stability of beam regular split is discussed numerically,and the results reveal that the beam regular split is stable to the finite initial perturbations.     

One-dimensional EM solitons in ultrashort intense laser pulse-partially stripped plasmas

The one-dimensional electromagnetic (EM) envelope solitons in ultrashort intense laser pulse-partially stripped plasmas were discussed based on the wave equation of intense laser pulse propagating in partially stripped plasmas. Under the weakly relativistic assumption, a modified nonlinear Schrödinger (NLS) equation describing the evolution of the EM field was derived. The analytical analysis shows that in the ultra-short broad beam limits, the relativistic nonlinearity and striction nonlinearity cancel each other, and a one-dimensional laser pulse envelope soliton can be formed only due to the polarization nonlinearity. The relationship between the characteristics of soliton and the parameters of laser pulse and partially stripped plasmas was discussed by numerical analysis.