基于移位算子时域有限差分的色散薄层节点修正算法

提出了一种时域有限差分（FDTD）计算中色散介质薄层问题处理的新算法.对于厚度小于一个元胞尺度的电小尺寸色散介质薄层问题,采用将元胞内电位移矢量和磁感应强度加权平均的方法,求得薄层所在元胞内修正点处的等效介质参数.然后根据常见色散介质模型,包括Debye模型、Lorenz模型、Drude模型等,介电常数和磁导率可以表示为jω分式多项式的特点,结合频域到时域的转换关系（即用/t代替jω）和移位算子方法得到了修正点处的时域本构关系,进而获得时域递推计算式.数值结果表明,该方法具有通用、节省计算时间、节省内存和计算精度良好等优点. 关键词： 色散介质薄层 节点修正 移位算子 时域有限差分     

一种新型高双折射光子晶体光纤特性研究

设计了一种高双折射高非线性光子晶体光纤, 采用全矢量有限元法研究了这种光纤的基模模场、双折射、非线性、有效模面积及色散特性. 数值研究发现, 减小孔间距Λ的大小, 在波长1550 nm 处, 该光纤可获得10^-2 数量级的双折射B, 比普通的椭圆保偏光纤高约两个数量级; 同时, 该光纤可获得42 W^-1·km^-1 的高非线性系数γ. 另外,分别在可见光和近红外波段出现了两个零色散波长, 在波长800–2000 nm 之间具有良好的色散平坦特性. 这种设计为获得高双折射高非线性超平坦色散光子晶体光纤提供了一种新的方法, 该光纤在偏振控制、非线性光学和色散控制方面具有广泛的应用前景. 关键词： 光子晶体光纤 高双折射 高非线性 有限元法     

有限深两层流体中内孤立波造波实验及其理论模型

将置于大尺度密度分层水槽上下层流体中的两块垂直板反方向平推, 以基于 Miyata-Choi-Camassa (MCC)理论解的内孤立波诱导上下层流体中的层平均水平速度作为其运动速度, 发展了一种振幅可控的双推板内孤立波实验室造波方法. 在此基础上, 针对有限深两层流体中定态内孤立波 Korteweg-de Vries (KdV), 扩展KdV (eKdV), MCC和修改的Kdv (mKdV)理论的适用性条件等问题, 开展了系列实验研究.结果表明, 对以水深为基准定义的非线性参数ε 和色散参数μ, 存在一个临界色散参数μ₀, 当μ < μ₀ 时, KdV理论适用于ε ≤μ 的情况, eKdV理论适用于μ < ε ≤√μ 的情况, 而MCC理论适用于ε > √μ 的情况, 而且当μ ≥μ₀ 时MCC理论也是适用的.结果进一步表明, 当上下层流体深度比并不接近其临界值时, mKdV理论主要适用于内孤立波振幅接近其理论极限振幅的情况, 但这时MCC理论同样适用.本项研究定量地表征了四类内孤立波理论的适用性条件, 为采用何种理论来表征实际海洋中的内孤立波特征提供了理论依据. 关键词： 两层流体 内孤立波 双板造波 临界色散参数     

色散效应对光学参量放大器量子起伏特性的影响

解析求解了包含色散、损耗和抽运吃空的含时的Fokker-Planck方程,通过数值计算首先获得了色散时简并参量放大(DOPA)系统的光压缩特性.研究结果表明：色散效应是由非线性极化率从χ″增大到χ″/{1+σ²/}/+2而引起的.随着色散效应的逐渐增大,压缩曲线的形状基本相同,且整体向左收缩,最大压缩趋近于线性理论的结果1/(1+μ).还获得了色散时非简并参量放大(NOPA)系统的光纠缠特性.研究发现：当σ给定,随着抽运参数μ的增大,相应的相位变化也增大,非线性极化率的极性发生多次变化,极性为正阶段的增益大部分被极性为负阶段的衰减所抵消,净增益不大,压缩也不大,最小均方差V₁的值逐渐减小,且整体向右移动,接近于线性理论的结果1/(1+μ). 关键词： 色散 量子起伏 光学参量放大器     

非高斯噪声对惯性棘轮中粒子负迁移率的影响

利用随机模拟方法研究了惯性棘轮中非高斯噪声对负迁移率的影响. 分别模拟了绝对负迁移率(ANM), 非线性迁移率(NNM) 和负微分迁移率(NDM) 等三种反常输运现象. 计算结果表明: 1) 在不同的参数空间里, 非高斯噪声参数q 能够增强或者削弱ANM, 诱导NNM 和NDM; 2) 当q 较大时, 反常输运现象转化为正常输运; 3) 随着q 逐渐增大, 平均速度- 关联时间特性曲线朝着关联时间较小的方向移动并且其峰值逐渐减小. 关键词： 反常输运 负迁移率 非高斯噪声     

具有三个零色散波长的光子晶体光纤中色散波孤子的产生

基于广义非线性薛定谔方程,数值模拟了具有3个零色散波长的光子晶体光纤中孤子的演化过程及其时频特性.结果表明,由于第2个反常色散区的存在,不仅在正常色散区得到了相位匹配的蓝移和红移色散波,还在低频反常色散区得到了高强度的色散波孤子,而且此孤子在高频正常色散区进一步辐射出了蓝移色散波.     

八边形光子晶体光纤色散补偿特性分析

利用多极法对八边形光子晶体光纤的色散补偿特性进行数值模拟,分析了结构参数变化对色散补偿特性的影响;计算了具有相同参数的六边形结构光子晶体光纤的色散系数和非线性系数;研究表明八边形光子晶体光纤比六边形结构的光子晶体光纤的大负色散特性明显提高,非色散系数低,更有利于进行色散补偿.因此,本文设计了一种新型的八边形色散补偿光纤,在λ=1.55μm时色散值为-1434.9ps·nm^-1·km^-1,色散斜率为-4.6338ps·nm^-2· 关键词： 光子晶体光纤 多极法 色散斜率 色散补偿     

强双折射光纤中任意偏振方向矢量调制不稳定性

利用光脉冲在非线性双折射光纤中传播时所遵循的相干耦合非线性薛定谔方程,研究了偏振方向与双折射轴成任意角度时，在反常色散区和正常色散区所产生的调制不稳定性.结果表明，在反常色散区和正常色散区存在不稳定偏振区域和稳定偏振区域，对应不同的不稳定偏振区域，输入临界功率不同，脉冲有不同的增益谱. 关键词： 任意偏振方向 矢量调制不稳定性 非线性光纤 双折射     

反常色散平坦光纤产生平坦宽带超连续谱的数值研究

通过数值计算，对反常色散平坦光纤中高阶孤子压缩效应产生超连续谱进行了系统、深入的研究. 结果表明，反常色散平坦光纤的色散参量二阶微分常量、峰值色散参量及抽运脉冲的脉宽、孤子阶数对该种光纤中平坦超连续谱的形成及所需光纤长度的选取都有着非常重要的影响；进一步研究表明，超连续谱的展宽机理主要来自脉冲的自相位调制效应和群速度色散的共同作用,高阶非线性效应对超连续谱的产生不起决定性作用，在计算中完全可以忽略. 关键词： 反常色散平坦光纤 超连续谱 自相位调制效应 群速度色散     

高斯变迹布拉格光纤光栅中的调制不稳定性

利用激光脉冲在光纤光栅中传播时所遵守的相干耦合非线性薛定谔方程,研究了激光脉冲在高斯变迹布拉格光纤光栅中传输时，在反常色散区和正常色散区所产生的调制不稳定性.结果表明在反常色散区和正常色散区都能产生调制不稳定性；在反常色散区，当输入功率达到一定数值时，产生明显的有规律的增益谱；在正常色散区，在产生调制不稳定性功率区域，调制不稳定性存在并从给定值一直持续到无穷；并且，在反常色散区和在正常色散区，增益谱都受到高斯变迹函数的制约. 关键词： 高斯变迹 布拉格光栅 调制不稳定性 增益     

Numerical method of studying nonlinear interactions between long waves and multiple short waves

Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train (expressed as wave train 2) leads to the energy focusing of the other short wave train (expressed as wave train 3). This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.     

应用非线性薛定谔方程模拟深海内波的传播

本文选取东沙岛以东深海区域,应用描述深海内波的非线性薛定谔方程,采用啁啾的思想,研究了频散和非线性效应之间的关系,模拟了深海内波的传播.数值模拟内波演变趋势与MODIS影像拍摄到的内波演变趋势基本符合,从而验证了应用非线性薛定谔方程模拟深海弱非线性内波传播的合理性. 关键词： 深海内波 啁啾 非线性薛定谔方程 频散和非线性     

Extended acoustic waves in a one-dimensional aperiodic system

We numerically study the propagation of acoustic waves in a one-dimensional system with an aperiodic pseudo-random elasticity distribution. The elasticity distribution was generated by using a sinusoidal function whose phase varies as a power-law, f μ nⁿ\phi \propto n^{\nu}, where n labels the positions along the media. By considering a discrete one-dimensional version of the wave equation and a matrix recursive reformulation we compute the localization length within the band of allowed frequencies. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicates the presence of extended acoustic waves with non-zero frequency for sufficient degree of aperiodicity.     

Giant waves in weakly crossing sea states

The formation of rogue waves in sea states with two close spectral maxima near the wave vectors k ₀ ± Δk/2 in the Fourier plane is studied through numerical simulations using a completely nonlinear model for long-crested surface waves [24]. Depending on the angle θ between the vectors k ₀ and Δk, which specifies a typical orientation of the interference stripes in the physical plane, the emerging extreme waves have a different spatial structure. If θ ≲ arctan(1/√2), then typical giant waves are relatively long fragments of essentially two-dimensional ridges separated by wide valleys and composed of alternating oblique crests and troughs. For nearly perpendicular vectors k ₀ and Δk, the interference minima develop into coherent structures similar to the dark solitons of the defocusing nonlinear Schroedinger equation and a two-dimensional killer wave looks much like a one-dimensional giant wave bounded in the transverse direction by two such dark solitons.     

Predictability of the appearance of anomalous waves at sufficiently small Benjamin–Feir indices

The numerical simulation of the nonlinear dynamics of random sea waves at sufficiently small Benjamin–Feir indices and its comparison with the linear dynamics (at the coincidence of spatial Fourier harmonics near a spectral peak at a certain time t_p) indicate that the appearance of a rogue wave can be predicted in advance. If the linear approximation shows the presence of a sufficiently extensive and/or high group of waves in the near future after t_p, an anomalous wave is almost necessarily formed in the nonlinear model. The interval of reliable forecasting covers several hundred wave periods, which can be quite sufficient in practice for, e.g., avoiding the meeting of a ship with a giant wave.     

Rogue waves: Classification,measurement and data analysis,and hyperfast numerical modeling

The last twenty years has seen the birth and subsequent evolution of a fundamental new idea in nonlinear wave research: Rogue waves, freak waves or extreme events in the wave field dynamics can often be classified as coherent structure solutions of the requisite nonlinear partial differential wave equations (PDEs). Since a large number of generic nonlinear PDEs occur across many branches of physics, the approach is widely applicable to many fields including the dynamics of ocean surface waves, internal waves, plasma waves, acoustic waves, nonlinear optics, solid state physics, geophysical fluid dynamics and turbulence (vortex dynamics and nonlinear waves), just to name a few. The first goal of this paper is to give a classification scheme for solutions of this type using the inverse scattering transform (IST) with periodic boundary conditions. In this context the methods of algebraic geometry give the solutions of particular PDEs in terms of Riemann theta functions. In the classification scheme the Riemann spectrum fully defines the coherent structure solutions and their mutual nonlinear interactions. I discuss three methods for determining the Riemann spectrum: (1) algebraic-geometric loop integrals, (2) Schottky uniformization and (3) the Nakamura-Boyd approach. I give an overview of several nonlinear wave equations and graph some of their coherent structure solutions using theta functions. The second goal is to discuss how theta functions can be used for developing data analysis (nonlinear Fourier) algorithms; nonlinear filtering techniques allow for the extraction of coherent structures from time series. The third goal is to address hyperfast numerical models of nonlinear wave equations (which are thousands of times faster than traditional spectral methods).     

Electrohydrodynamic wave-packet collapse and soliton instability for dielectric fluids in (2 + 1)-dimensions

A weakly nonlinear theory of wave propagation in two superposed dielectric fluids in the presence of a horizontal electric field is investigated using the multiple scales method in (2 + 1)-dimensions. The equation governing the evolution of the amplitude of the progressive waves is obtained in the form of a two-dimensional nonlinear Schrödinger equation. We convert this equation for the evolution of wave packets in (2 + 1)-dimensions, using the function transformation method, into an exponentional and a Sinh-Gordon equation, and obtain classes of soliton solutions for both the elliptic and hyperbolic cases. The phenomenon of nonlinear focusing or collapse is also studied. We show that the collapse is direction-dependent, and is more pronounced at critical wavenumbers, and dielectric constant ratio as well as the density ratio. The applied electric field was found to enhance the collapsing for critical values of these parameters. The modulational instability for the corresponding one-dimensional nonlinear Schrödinger equation is discussed for both the travelling and standing waves cases. It is shown, for travelling waves, that the governing evolution equation admits solitary wave solutions with variable wave amplitude and speed. For the standing wave, it is found that the evolution equation for the temporal and spatial modulation of the amplitude and phase of wave propagation can be used to show that the monochromatic waves are stable, and to determine the amplitude dependence of the cutoff frequencies.Received: 23 November 2003, Published online: 15 March 2004PACS: 47.20.-k Hydrodynamic stability - 52.35.Sb Solitons; BGK modes - 42.65.Jx Beam trapping, self-focusing and defocusing; self-phase modulation - 47.65. + a Magnetohydrodynamics and electrohydrodynamicsM.F. El-Sayed: Permanent address: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt     

光参量振荡器的模型仿真

在傍轴近似条件下建立了OPO的数学模型,通过引入三波混频中时间与空间关系,采用分步傅里叶算法模拟了纳秒级脉冲和连续光波在谐振腔内的三波混频过程。理论模型中考虑了不同频率光波之间的色散关系,可以在高转换效率情况下分析不同泵浦脉冲功率、脉冲时长、腔镜透反射比以及不同种子光输入等情况下的输出波形、功率以及OPO阈值等特性。实验中采用掺杂MgO的周期性极化铌酸锂晶体（MgO∶PPLN）为非线性介质,在输入1.06 m泵浦激光脉冲能量为0.4 mJ时,产生3.8 m闲频光超过0.07 mJ输出,与数值模拟结果0.08 mJ较为符合。     

Low-frequency surface wave propagation along plane boundaries in fluid-saturated porous media

A method of the mechanics of a fluid-saturated porous medium is used to study the propagation of harmonic surface waves along the free boundary of such a medium, along the boundary between a porous medium and a fluid, and along the boundary between two porous half-spaces. It is shown that, at low frequencies (i.e., for waves with frequencies lower than the Biot characteristic frequency), the corresponding dispersion equations in zero-order approximation are reduced to the equations for an “equivalent” elastic medium. For the wave numbers of surface waves, corrections taking into account the generation of longitudinal waves of the second kind at the boundary are calculated. Examples of numerical solutions of dispersion equations for rock are presented.