饱和非线性介质中艾里-高斯光束的传输与交互作用

研究了艾里-高斯光束在饱和非线性介质中的传输与交互作用.结果表明,入射光为单艾里-高斯光束时,在一定功率范围内,调节初始振幅与光场分布,可形成传输方向可控的呼吸孤子.当初始振幅增加时,孤子的呼吸周期先减小后增大.入射光为两艾里-高斯光束时,同相位光束相互吸引,两光束中心位置两侧附近产生呼吸孤子和对称孤子对.反相位光束相互排斥,中心位置两侧仅产生对称的孤子对.光场分布越趋于高斯分布,两艾里-高斯光束相互作用就越强,孤子对的数目越少.     

饱和非线性介质中艾里孤子的产生与传输调控

采用分步傅里叶法,通过数值模拟研究了饱和非线性介质中艾里孤子的产生与传输调控。单艾里光束入射时,在一定的初始振幅范围内可以产生稳定传输的呼吸式孤子。初始振幅增加时,孤子的强度增加,呼吸周期变短,但宽度基本保持不变。衰减系数增加时,孤子的平均峰值强度先增大后减小之后再增大,存在两个极值点。光束入射角度为负值时,形成左倾艾里孤子;光束入射角度为正值时,形成右倾艾里孤子。双艾里光束入射时,入射角同为负值可以减弱光束间的相互作用,入射角同为正值可以增强光束间的相互作用。此外,不同的入射角可以控制孤子或孤子对的传输方向。     

有偏压光伏光折变晶体中艾里高斯光束的传输特性

采用分步傅里叶法,数值模拟研究了有偏压光伏光折变晶体中艾里高斯光束的传输特性.结果表明,当艾里高斯光束初始振幅和晶体的外加电场在一定范围内时,可以形成沿直线稳定传输的呼吸式孤子.调节初始振幅或外加电场可以控制孤子的峰值强度和呼吸周期.随着入射光场分布因子的变大,孤子的平均峰值强度先增大后减小,孤子的呼吸周期先变小后变大.随着光束衰减因子的增加,孤子的平均峰值强度先增大后减小,然后再增大.此外,光束入射角为负值时,孤子向左偏移,光束入射角为正值时,孤子向右偏移.入射角只改变孤子的输出位置,不影响孤子的强度、宽度和呼吸周期.     

竞争非局域向列相液晶中艾里高斯光束的相互作用

基于JUNG P S等提出的新型竞争非局域模型数值研究了艾里高斯光束在该模型中的相互作用,采用分步傅里叶算法数值模拟艾里高斯光束在竞争型非局域非线性向列相液晶中的相互作用。结果表明,可以通过调节初始振幅、初始间距、位相差以及非局域程度控制艾里高斯光束间的相互作用。初始振幅增大会使相互作用力增大;分子取向非局域程度的增加导致艾里高斯光束宽度展宽,使反相艾里光束吸引力增强,热非局域程度的改变使初始振幅较大的反相艾里高斯光束由相互排斥作用变为相互吸引作用,使反相艾里高斯光束出现排斥和吸引作用动态平衡;同时还发现增大热非线性系数能使反相艾里高斯光束出现吸引或排斥。     

艾里-厄米-高斯光束在克尔介质中的孤子控制

以非线性薛定谔方程为理论模型,采用分步傅里叶数值模拟方法,讨论了有限能量艾里-厄米-高斯光束在克尔介质中的传输特性以及相互作用。研究表明,通过控制介质的非线性强度和艾里-厄米-高斯光束的初始振幅,可以抑制光束的衍射效应,当它们满足一定条件时,能够产生孤子。通过研究两艾里-厄米-高斯光束的相互作用,发现调整两光束的初始间隔以及相位,可以控制孤子的数量和传输方向。     

高斯型空间光孤子相互作用的数值研究

 通过数值模拟的方法，对高斯孤子在对数型饱和非线性介质中的相互作用进行了研究，考查了两光束间的相对振幅和相对相位对其相互作用的影响。结果表明：高斯孤子之间的相互作用敏感地依赖于两光束间的相对振幅和相对相位。在不同的振幅差异范围内，光束间的主要作用交替地表现为相互排斥和相互吸引，并由于高斯孤子的不稳定性，导致了光束在碰撞后以一种尺寸周期性变化的呼吸模式传输。随着相对相位的增大，两光束间始终持续地表现出强烈的排斥作用，直到相对相位增加到一个2π周期之后。而且碰撞之后，光束也都以呼吸模式进行传输，其分离的角度越大，呼吸就越明显。     

克尔介质中艾里孤子的形成及控制

利用分步傅里叶法,数值研究了艾里光束在自聚焦克尔非线性介质中的传输。结果表明,当较强的非线性作用于艾里光束时,主瓣能量在传输过程中会发生脱落形成具有周期振荡的空间孤子。随着非线性的增强,该孤子的振荡周期与半高宽都减小。调节艾里光束的入射角度时,脱落孤子的传输轨迹随之发生变化,不同于艾里光束的是,艾里孤子的传输始终保持直线传输。     

高斯光束在有外电场的双光子光伏光折变材料中的演化

为了得到一束高斯光束和两束高斯光束的相互作用在有外电场的双光子光伏光折变材料中的演化结果,将高斯光束作为入射波,采用数值方法求解波传播方程。研究结果表明:在外加电场、光强峰值分别与晶体参量匹配的情况下,一束高斯光束能演化为稳定的屏蔽光伏明孤子,而在不匹配时,一束高斯光束在传播过程中则呈现周期性压缩或膨胀现象。同时也发现:在作用距离范围内,同相位的两高斯光束相互吸引,并伴随有融合现象;而相位相反的两高斯光束相互排斥,且其排斥作用随着光束初始间距的减小而增加,当两高斯光束的相位差位于区间(0,π)和(-π,0)时,其相互作用过程中伴有能量的转移,两区间中能量转移方向相反。     

竞争非局域三次五次非线性介质畔孤子的传输特性

研宄空间光孤子在一维竞争非局域三次五次非线性介质中的新解和传输特性.发现亮孤子在竞争非局域三次自散焦和五次自聚焦非线性介质中存在不稳定区间.在一般非局域程度下,对于不同的三次非线性效应,同相位复合两孤子间表现为吸引或排斥的相互作用,并讨论了折射率的变化.在竞争非局域.三次自聚焦和五次自散焦非线性介质中给出了二极、三极和四极孤子能稳定传播的条件,研究发现更高极孤子的传播是不稳定的.还研究了孤子功率与传播常数以及非局域程度的关系.     

高斯光束在有外电场的中心对称光折变材料中的演化

为了研究在有外电场的中心对称光折变材料中一束高斯光束及两束高斯光束相互作用的演化,将高斯光束作为入射波,采用数值方法求解波传播方程.结果表明,当外加电场,光强峰值和束腰参量分别与晶体匹配的情况下,一束高斯光束能演化为稳定的屏蔽空间明孤子,而在不匹配时,一束高斯光束在传播过程中则呈现周期性的压缩或膨胀现象.同时也发现,在作用距离范围内.两束同相位高斯光束相互吸引,并伴随着融合现象,两束反相位高斯光束相互排斥,且排斥作用随着光束初始间距的减小而增加.     

(1+1)维光折变亮屏蔽孤子相互作用的数值分析

利用束传播法对（1+1）维光折变亮屏蔽孤子间的相互作用进行了详细地数值模拟研究.结果表明：两同相孤子相互吸引,并伴有孤子融合现象,且孤子融合发生时的作用距离随着孤子初始间距的增大而增大;两反相孤子相互排斥,且排斥作用随着孤子初始间距的减小而增强;当两孤子的相位差位于区间（0,π）和（－π,0）中时,其相互作用过程将伴有能量转移,但两区间内能量转移的方向相反,并表现出反转对称性;由于孤子间的距离和相对相位对孤子间的相互作用均有很大的影响,因此多个孤子间的相互作用过程非常复杂,但可以通过分析相邻孤子间的相互作用对其进行定性的预测.     

Anomalous interactions of spatial gap solitons in optically induced photonic lattices

We demonstrate coherent interactions between spatial gap solitons in optically induced photonic lattices. Because of the "staggered" phase structures, two in-phase (out-of-phase) bright gap solitons can repel (attract) each other at close proximity, in contrast to soliton interaction in homogeneous media. A reversal of energy transfer direction and a transition between attractive and repulsive interaction forces can be obtained solely by changing the initial soliton separation relative to the lattice spacing.     

光诱导准一维光子晶格中离散空间光孤子的相互作用

基于分步束传播法数值分析了离散空间光孤子在准一维光诱 导光子晶格中的相干与非相干相互作用过程. 结果表明: 对于相干孤子, 同相时相互吸引, 反相时相互排斥. 然而, 由于非线性响应的各向异性, 横向排布的非相干孤子会因间隔波导数目的增加而由相互吸引变为相互排斥. 并且, 沿对角方向排布的两个非相干孤子在孤子相 互作用力和布拉格反射的共同影响下, 会呈现出"钟摆式"振荡传输现象. 研究结果有助于进一步理解非线性各向异性对离散孤子相互作用的影响机制, 并为后续实验研究提供理论参考.     

光诱导平面波导阵列中离散空间光孤子的相干相互作用

采用Petviashvili迭代法对光诱导平面波导阵列中的一维离散空间光孤子进行求解,利用分步束传播法对离散空间光孤子间的相干相互作用进行了详细的数值模拟.探讨了离散孤子间的相位差、孤子光强、波导阵列写入光的强度和周期以及外加电场对相互作用过程的影响.结果表明：离散孤子间的相位差对相互作用的影响与连续介质中的情况类似,不同相位差情况下的相互作用也表现为吸引、排斥以及能量转移等现象.同时,离散孤子间的相干相互作用过程(如融合距离和排斥间距等)均会受到孤子光强、波导阵列写入光的强度和周期以及外加电场大小的影响 关键词： 光诱导平面波导阵列 离散空间光孤子 相干相互作用     

Observation of discrete solitons in optically induced real time waveguide arrays

We report the first experimental observation of discrete solitons in an array of optically induced waveguides. The waveguide lattice is induced in real time by illuminating a photorefractive crystal with a pair of interfering plane waves. We demonstrate two types of bright discrete solitons: in-phase self-localized states and the staggered (pi out-of-phase) soliton family. This experiment is the first observation of bright staggered solitons in any physical system. Our scheme paves the way for reconfigurable focusing and defocusing photonic lattices where low-power (mW) discrete solitons can be thoroughly investigated.     

Incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media

We theoretically investigate the propagation of incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media. It is found that multipole-mode soliton pairs with arbitrary different orders of Hermite-Gaussian shape can exist when the total power of two beams equals the critical power and the ratio of the beam widths for the Gaussian part is inversely proportional to the square root of the ratio of the wave numbers. When the total power does not equal the critical power, the Hermite-Gaussian breather pair exists and their beam widths evolve analogously. For general cases where the ratio of the beam widths is arbitrary, soliton-breather pairs or breather-breather pairs can be formed and their beam widths evolve synchronously in-phase or out-of-phase. Numerical simulations directly based on the nonlocal nonlinear Schrödinger equation are conducted for comparison with our theoretical predictions. The numerical stability analysis shows the higher-order Hermite-Gaussian solitons can not be stable for small nonlocality or for some media like liquid crystals.     

Anomalous dispersion relations by symmetry breaking in axially uniform waveguides

We show that modes of axially uniform waveguides of arbitrary cross section can be made to have anomalous dispersion relations resulting from strong repulsion between two modes. When the axial wave vector k is 0, the two modes have different TE/TM symmetry and thus can be brought arbitrarily close to an accidental frequency degeneracy. For nonzero k, the symmetry is broken causing the modes to repel. When the modes are sufficiently close together this repulsion leads to unusual features such as extremely flattened dispersion relations, backward waves, zero group velocity for nonzero k, atypical divergence of the density of states, and nonzero group velocity at k=0.     

Symbolic computation on the bright soliton solutions for the generalized coupled nonlinear Schrödinger equations with cubic–quintic nonlinearity

Under investigation in this paper are the generalized coupled nonlinear Schrödinger equations with cubic–quintic nonlinearity which describe the effects of the quintic nonlinearity on the ultrashort optical soliton pulse propagation in the non-Kerr media. Via the dependent variable transformation and Hirota method, the bilinear form is derived. Based on the bilinear form obtained, the one-, two- and three-soliton solutions are presented in the form of exponential polynomials with the help of symbolic computation. Propagation and interactions of solitons are investigated analytically and graphically. Evolution of one soliton is discussed with the analysis of such physical quantities as the soliton amplitude, width, velocity, initial phase and energy. Interactions of the solitons appear in the forms of the repulsion or attraction alternately and propagation in parallel. Inelastic and head-on interactions of the solitons are also showed. Finally, via the asymptotic analysis, conditions of the elastic and inelastic interactions are obtained.     

Delay-coupled discrete maps: Synchronization, bistability, and quasiperiodicity

The synchronization transition is studied in delay-coupled logistic maps. For low coupling, in-phase and out-of-phase synchronous dynamics coexist, and with increasing coupling there is a regime of quasiperiodicity before eventual attraction to a fixed point at a critical value of coupling that depends on the nonlinearity. The presence of a region of asynchrony separating two synchronized regimes—termed anomalous behaviour—has been observed earlier in continuous systems and is shown here to occur in delay mappings as well. There are regions of in-phase, anti-phase, and out-of-phase dynamics of periodic as well as chaotic attractors.     

Coherent and Incoherent Interactions between Discrete-Soliton Trains in Two-Dimensional Light-Induced Photonic Lattices

The coherent and incoherent interactions between discrete-soliton trains are numerically investigated in lightinduced two-dimensional photonic lattices. The solutions of discrete-soliton trains for diamond and square lattices are obtained by Petviashvili iteration method. It is found that for both the kinds of lattices, two in-phase （out- of-phase） discrete-soliton trains attract （repel） each other, and the intermediates are always accompanied with energy transfer. While the interaction forces between two incoherent discrete-soliton trains are always attractive.