KdV孤子的含时微扰理论

研究了周期性含时微扰对KdV(Korteweg de Vries)孤子的影响. 将微扰项展为时间变量的傅里叶级数,发现其常数项是导致长期项的根源. 在一阶近似下,消除长期项,求出了孤子参数(高度、宽度和速度)随时间的缓慢变化. 傅氏级数中的其他项决定了微扰对孤子波形的一阶修正. 关键词： KdV孤子 孤子微扰论     

Soliton-based ultra-high speed optical communications

Multi-terabit/s, ultra-high speed optical transmissions over several thousands kilometers on fibers are becoming a reality. Most use RZ (Return to Zero) format in dispersion-managed fibers. This format is the only stable waveform in the presence of fiber Kerr nonlinearity and dispersion in all optical transmission lines with loss compensated by periodic amplifications. The nonlinear Schrödinger equation assisted by the split step numerical solutions is commonly used as the master equation to describe the information transfer in optical fibers. All these facts are the outcome of research on optical solitons in fibers in spite of the fact that the commonly used RZ format is not always called a soliton format. The overview presented here attempts to incorporate the role of soliton-based communications research in present day ultra-high speed communications.     

One-dimensional nonparaxial bright solitons and their coherent interactions in Kerr media

<正>The existence of one-dimensional bright Kerr solitons is investigated in Kerr media beyond the paraxial approximation. It is found that a nonparaxial soliton with no less than a minimum dimensionless width of about 0.76 can exist, which corresponds to the real width about a wavelength.Besides,the coherent interactions between two nonparaxial bright solitons in Kerr media are also investigated in detail.It is found that their separation and intensity ratio have great influence on the coherent interaction between these two solitons.Furthermore,the effect of the relative phase difference on the nonparaxial interaction is quite different from that on the paraxial interaction.Periodical breath, merging,repulsion,and energy transferring can be realized separately by choosing an appropriate initial relative phase between the coherent solitons.     

非自治拉曼多色孤子的管理和传输

以变系数的非自治非线性薛定谔方程为模型,考虑了一种色散、非线性和自发拉曼散射效应管理下的非自治系统,通过简单变换显式给出了该系统的精确非自治拉曼多色孤子解。基于精确孤子解,解析研究了该拉曼多色孤子在非自治管理系统中的演化特性,发现孤子的中心位置、波数与色散和非线性以及拉曼效应有关,而孤子频移仅与拉曼效应的参数决定,拉曼效应主导了非自治孤子的自频移,引起了孤子的频移在传输过程中不断的发生变化,导致了孤子的多色性。另外,我们数值讨论了该非自治孤子的传输稳定性,结果表明:该非自治拉曼多色孤子在有限的扰动下具有较好的稳定性。     

Dynamics of Nonautonomous Dark Solitons

We solve a generalized nonautonomous nonlinear Schrdinger equation analytically by performing the Hirota's bilinearization method. The precise expression of a parameter , which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton (∈2≠1) while it has no effects on the wave central position.Moreover, the precise expressions of a nonautonomous black soliton's (∈2≠1) width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton's evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.     

暗-暗与亮-暗光伏孤子相互作用

用数值方法分析了平行传播异色光伏暗孤子之间及亮-暗孤子之间的相互作用.结果表明，光伏暗孤子共轴传播能在有限的距离内保持准孤子形态，靠近传播时存在着相互吸引的作用 ，而相距较远传播时表现为一孤子暗区使另一孤子的缓变光场部分发生局部会聚作用.光伏暗孤子与亮孤子的相互作用随距离的不同可使亮孤子光强分布变尖锐或变平缓，以及使亮孤子发生能量转移.从两束信号光共同引起折射率波导这一物理机理对光伏孤子这些相互作用给出定性物理解释. 关键词： 光伏空间孤子 暗孤子 亮孤子 相互作用     

Interactions of adjacent pulsating, erupting and creeping solitons

This paper investigates the adjacent interactions of three novel solitons for the quintic complex Ginzburg--Landau equation, which are plain pulsating, erupting and creeping solitons. It is found that different performances are presented for different solitons due to isolated regions of the parameter space where they exist. For example, plain pulsating and erupting solitons exhibit mutual annihilation during collisions with the decrease of total energy, but for creeping soliton, the two adjacent pulses present soliton fusion without any loss of energy. Otherwise, the method for restraining the interactions is also found and it can suppress interactions between these two adjacent pulses effectively.     

有外加电源的串联光折变晶体回路中的独立空间全息-哈密顿屏蔽孤子对

在由两块垂直于光轴两端面镀上电极的光折变晶体和一个外加电源组成的串联光折变晶体回路中, 在适当的条件下可以形成独立空间全息-哈密顿屏蔽孤子对. 这种孤子对共有四种类型:明-明、暗-暗、明-暗以及暗-明. 当入射光束的空间展宽尺寸远小于晶体宽度时, 孤子对中的哈密顿暗孤子可以通过光感应电流影响另一个孤子, 而哈密顿明孤子和全息孤子则不能影响另一孤子.     

有外加电源的串联光折变晶体回路中的独立空间全息-哈密顿屏蔽孤子对

在由两块垂直于光轴两端面镀上电极的光折变晶体和一个外加电源组成的串联光折变晶体回路中, 在适当的条件下可以形成独立空间全息-哈密顿屏蔽孤子对. 这种孤子对共有四种类型:明-明、暗-暗、明-暗以及暗-明. 当入射光束的空间展宽尺寸远小于晶体宽度时, 孤子对中的哈密顿暗孤子可以通过光感应电流影响另一个孤子, 而哈密顿明孤子和全息孤子则不能影响另一孤子.     

Incoherent interaction between one- and two-dimensional solitons in noncentrosymmetric photorefractive media

The incoherent interaction between solitons with different transverse dimensions in a noncentrosymmetric photorefractive crystal is studied both in theory and in experiment. An anomalous incoherent interaction between one- and two-dimensional solitons, whose attractive and repulsive effects depend on the soliton separation, is numerically demonstrated by employing an anisotropic model. By launching a one-dimensional green beam and a two-dimensional red beam into a biased SBN:60 crystal, the hybrid-dimensional soliton interaction is performed. The experimental results are in good agreement with the numerical ones.     

用正弦变频滤波器抑制孤子间的相互作用

提出用正统变频滤波器抑制孤子间的相互作用，并对上变频滤波器、下变频滤波器、交叉变频滤波器在抑制孤子相互作用方面的效应进行了数值研究。结果表明，正弦变频滤波器是最为有效的。     

Davydov soliton collisions

In this Letter, we study the collisions of Davydov solitons. The collision behaviour is diverse and complicated, and very sensitive to both the initial phases and velocities of the solitons. For some parameter ranges, Davydov solitons are stable to collisions in the sense that the solitons retain their structures, though for some cases, the propagation direction may be altered. For other parameter ranges, significant structural changes may occur: An exchange of energy between solitons, or the merger of two solitons to form a new bound state.     

光致异构聚合物中相互作用光学空间孤子对的垂直光调控

采用数值法研究了在具有光致异构非线性的聚合物中平行传播的光学空间孤子对(信号光)被另一束垂直入射光调控的情况.调节调控光和信号光的初始相位差、调控光入射位置等可以使信号光孤子产生合成、分开等现象，对此给出了物理解释.这种相互作用的空间光孤子被垂直光调控的现象可望应用于光合成、光互联、光波导等方面. 关键词： 光学空间孤子对 相互作用 垂直光调控 光致异构     

Separate holographic screening soliton pairs in a biased series photorefractive crystal circuit

Holographic dark (bright) screening solitons are predicted in one dimension for a series circuit consisting of two photorefractive crystals connected electronically by electrode leads in a chain with a voltage source. Each crystal can support a holographic screening soliton. The two solitons are known collectively as a separate holographic screening soliton pair with three types: bright--bright, bright--dark and dark--dark. The numerical results show that the two solitons in a soliton pair can affect each other through a light-induced current and their coupling can affect their spatial profiles under the limit in which the optical wave has a spatial extent much less than the width of the crystal.     

非均匀系统中非自治孤子的色散和非线性管理

基于包含自发拉曼散射和外电光调制效应的非自治非线性薛定谔方程,采用简单的变换方法,解析研究了三种非均匀系统中非自治孤子的管理和传输。结果发现,在非均匀的非线性渐增或色散渐减光纤系统中都存在精确的啁啾非自治孤子解,都可以实现孤子的放大和压缩,但具有不同的速度、频移和啁啾特性;而在非均匀的色散和非线性均渐减光纤系统中,可以支持无啁啾的非自治孤子,该孤子具有不变的脉宽和振幅以及振荡衰减的速度,孤子的频移仅由自发拉曼散射决定。同时,数值模拟结果进一步证实在三种非均匀管理系统中都可支持非自治孤子的传输。该研究结果为实际非均匀孤子管理系统中实现孤子的压缩和传输提供了理论依据。     

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.     

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     

Two‐dimensional magnetosonic shock wave propagation in dense electron–positron–ion plasmas

Two‐dimensional (2D) magnetosonic wave propagation in magnetized quantum dissipative plasmas is studied. The plasma system is comprised of inertial ions, inertia‐less electrons, and positrons. The multi‐fluid quantum hydrodynamic model is used, in which quantum statistical and quantum tunnelling effects of electrons and positrons are included. Reductive perturbation analysis is performed to derive the Zabolotskaya–Khokhlov equation for the 2D propagation of a magnetosonic shock wave in a magnetized qauntum plasma. The effects of varying the different plasma parameters such as positron density and magnetic field intensity on the propagation characteristics of magnetosonic shock waves are discussed with non‐relativistic degenerate plasma parameters in astrophysical plasma situations.     

Interaction of in-band and in-gap lattice soliton trains in optically induced two-dimensional photonic lattices

We demonstrate the coherent interactions of lattice soliton trains, including in-band solitons (IBSs) and gap soliton trains (GSTs), in optically induced two-dimensional photonic lattices with self-defocusing nonlinearity. It is revealed that the $\pi$-staggered phase structures of the lattice soliton trains will lead to anomalous interactions. Solely by changing their initial separations, the transition between attractive and repulsive interaction forces or reversion of the energy transfer can be obtained. The `negative refraction' effect of the soliton trains on the interaction is also discussed. Moreover, two interacting IBSs can merge into one GST when attraction or energy transfer happens.     

亚皮秒光孤子脉冲在突变界面的反射

本文建立了决定亚皮秒孤子在小突变界面的反射支配方程和边界条件，给出了不同的亚皮秒孤子的界面反射透射特性的数值模拟，讨论了孤子遇到界面后能继续无形变传输的条件。