线性偏振激光在相对论等离子体中的调制不稳定性

 从相对论等离体中电磁波的非线性色散方程出发,利用Karpman方法获得了线性偏振波模所满足的非线性控制方程,在非线性色散方程和非线性控制方程的基础上对线性偏振激光在相对论等离体中传播的调制不稳定性进行分析,给出了调制不稳定的时间增长率与扰动态波数之间的函数关系。     

Propagation of the ultrashort laser pulses through the quantum nonlinear medium with resonant properties

The propagation of ultrashort few-cycle laser pulses through a quantum nonlinear medium with resonant properties is studied using the method of slowly varying amplitudes with allowance for dispersion effects. A self-consistent system of nonlinear wave equation for the evolution of laser field and the nonstationary Schrödinger equation that determines the material polarization response is numerically solved. Specific features of the propagation of laser pulse caused by a relatively large spectral width and the nonadiabatic character of the laser pulse are established. The rise of the slowly dumping polarization at the eigenfrequency of the medium and the consequent stretching of the laser pulse are observed. The role of the resonant absorption of the laser energy in the medium is analyzed. The nonlinear spectral broadening is demonstrated for the laser pulse propagating through the medium.     

光孤子脉冲在增益色散和增益饱和非线性介质中的传播

本文获得了增益色散和增益饱和非线性介质中的光孤子脉冲的解析解。数值计算结果表明,在这类介质中光孤子脉冲传输是可能的,然而由于波传输的内禀特性,这种稳定传输被限制在较短的距离内。在高能量脉冲注入的情况下,光孤子脉冲将分裂为不同传输速度的多个光脉冲。     

Nonlinear Dynamics of Circularly Polarized Laser Pulse Propagating in a Magnetized Plasma with q ‐Nonextensive Velocity Distributions

The nonlinear dynamics of a circularly polarized laser pulse propagating in magnetized plasma contains hot nonextensive q ‐distributed electrons and ions is studied theoretically. A nonlinear equation which describes the dynamics of the slowly varying amplitude electromagnetic wave is obtained using the relativistic two‐fluids model. Some nonlinear phenomena include modulational instability, self‐focusing, soliton formation, and longitudinal and transversal evolutions of laser pulse in nonextensive plasma medium are investigated. Results show that the nonextensivity of particles can substantially change the nonlinearity of medium. The external magnetic field enhances the modulation instability growth rate of right‐hand polarization wave but for the left‐hand polarization the growth rate decreases. The spot size of the laser pulse is strongly affected by the plasma nonextensivity. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mode Structure and the Envelope of a Short Pulse in a Graded-Index Optical Fiber with a Longitudinal Inhomogeneity and a Spatial Bending

We consider propagation of a short optical pulse in an optical fiber whose refractive index is strongly dependent on the radial coordinate and is weakly dependent on the longitudinal coordinate with allowance for the possible weak spatial bending of the fiber axis. The three-dimensional nonlinear wave equation modelling the pulse propagation is solved asymptotically with respect to a small parameter specifying the order of magnitude of the pulse amplitude. A relationship between the propagating modes and the eigenvalues and eigenfunctions of the singular Sturm-Liouville problem is established. The pulse propagation is shown to have three scales: the high-frequency carrier is modulated by the envelope which evolves in a two-scale manner and is described by a nonlinear Schrödinger equation whose coefficients depend on the longitudinal coordinate. The transverse distribution of the wave field and the envelope soliton are obtained in terms of elementary functions for several types of transverse and longitudinal inhomogeneities of the fiber. The possibility of controlling the pulse parameters by varying the transverse and longitudinal inhomogeneities of the fiber is pointed out.     

Solitary wave for a nonintegrable discrete nonlinear Schr?dinger equation in nonlinear optical waveguide arrays

We study a nonintegrable discrete nonlinear Schr?dinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.     

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.     

电子等离子体波对超短脉冲激光传播过程的作用

提出等离子体波对光脉冲产生相位调制的观点,把光脉冲在背景等离子体波中传播时的频率移动与脉宽压缩效应统一起来。给出了脉宽演化的方程,它类似于在势阱中运动的经典粒子的能量守恒方程;估算了脉宽压缩对应的等离子体波振幅阈值。数值计算进一步证实这些结论。最后指出实验上用等离子体波压缩短脉冲激光脉宽的可能性。 关键词：     

高阶非线性效应对飞秒脉冲激光器的影响

本文以分段计算法用高阶非线性薛定谔方程讨论了激光器的传输过程,考虑了有三阶色散、高阶非线性效应-自陡峭效应存在时,激光器中飞秒脉冲的传输特性,给出了棱镜对的分离距离与激光器脉宽的关系,并用数值计算法模拟了脉冲在激光器中的传输过程.     

超强线极化激光在e-p等离子体中传播的成丝不稳定性

基于超强线极化激光在正负电子对(e-p)等离子体中的传播方程,讨论了相互作用过程中的成丝不稳定性。得到了电磁波的非线性色散关系和不稳定性增长率,并讨论了传播过程中激光强度和等离子体温度对成丝不稳定性的影响。结果表明,成丝不稳定性的强弱主要由相互作用的非线性效应与受有质动力作用后等离子体密度的减小之间的竞争所决定。     

Nonlinear propagation of optical pulses of a few oscillations duration in dielectric media

Using a semi-phenomenological model of the polarization response of an isotropic solid dielectric that does not resort to the slowly-varying-envelope approximation, we have obtained a nonlinear wave equation for the electric field of a femtosecond light pulse propagating in the given dielectric. Evidence is presented that this equation possesses breatherlike solutions in the region of anomalous group dispersion and does not have any solutions in the form of steady-state traveling solitary video pulses. A universal relation is found linking the minimum possible duration of a breatherlike pulse with the medium parameters. It is shown that such a pulse contains roughly one and a half periods of the light-wave. Zh. éksp. Teor. Fiz. 111, 404–418 (February 1997)     

The gravitational faraday rotation for cylindrical gravitational solitons

By using cylindrical soliton solutions, the nonlinear behavior of gravitational waves in vacuum is studied in terms of a rotation of the polarization vector between two independent modes. This effect was emphasized by Piran, Safier, and Stark as a gravitational analogue of the Faraday rotation. The polarization of the soliton wave is calculated, and it is found that the+mode which was dominant near the axis of symmetry is fully converted to the×mode at some interaction region and then the disturbance propagating along a light cone like a gravitational wave pulse contains both polarizations.     

Nonlinear Characteristics of an Intense Laser Pulse Propagating in Partially Stripped Plasmas

The nonlinear optic characteristics of an intense laser pulse propagating in partially stripped plasmas are investigated analytically. The phase and group velocity of the laser pulse propagation as well as the three general expressions governing the nonlinear optic behavior, based on the photon number conservation, are obtained by considering the partially stripped plasma as a nonlinear optic medium. The numerical result shows that the presence of the bound electrons in partially stripped plasma can significantly change the propagating property of the intense laser pulse.     

Nonlinear Characteristics of an Intense Laser Pulse Propagating in Partially Stripped Plasmas

The nonlinear optic characteristics of an intense laser pulse propagating in partially stripped plasmas are investigated analytically. The phase and group velocity of the laser pulse propagation as well as the three general expressions governing the nonlinear optic behavior, based on the photon number conservation, are obtained by considering the partially stripped plasma as a nonlinear optic medium. The numerical result shows that the presence of the bound electrons in partially stripped plasma can significantly change the propagating property of the intense laser pulse.     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

高斯光束在克尔型非线性介质中的演化特性

由光束在克尔型吸收介质中传输的非线性薛定谔方程,推导了高斯光束注入介质后满足的耦合方程,并分别在不考虑吸收和高阶展开项的情况下,对脉冲的腰斑半径的演化进行了理论分析。发现当注入脉冲满足一定的条件时,脉冲可以以“孤波”的形式传播。当考虑吸收和高阶展开项时,脉冲不存在“孤波”形式,且存在一个阈值,低于阈值的输入,脉冲发生自聚焦;对高于阈值的输入,腰斑半径随着距离的增加而增加,聚焦趋势根本就不存在。     

Research on the nonlinear pulse propagation by numerical analysis

Based on the computation approaches of numerical analysis in electromagnetic, the nonlinear pulse propagation in optical fiber is investigated in this paper. The transforming rule of the shape and spectrum of Gauss pulse are also researched in chirped and non-chirped scenarios from the nonlinear Schrödinger equation (NLSE). Analyzing the transient wave behavior in time domain and frequency domain respectively, the compression effect of chirp is also presented at different propagation distance. Then by the nonlinear Schrödinger equation, we discuss a specific solution in the quasi soliton without distortion, which has the stable propagation properly, and do the numerical simulation in soliton wave. Finally, by selecting proper fiber structure parameters and adjusting the width in soliton pulse, the soliton communication system can be optimized.     

Interaction of acoustic waves in microinhomogeneous media with hysteretic nonlinearity and relaxation

The propagation of a weak high-frequency pulse in the field of an intense standing low-frequency pump wave excited in an acoustic resonator with quadratic hysteretic nonlinearity and relaxation is theoretically investigated. The nonlinear damping coefficient and the carrier phase delay of the weak high-frequency pulse propagating under the action of an intense low-frequency wave are determined.     

具有几个光振荡周期的飞秒激光脉冲

从麦克斯韦方程组出发 ,推导出了具有几个光振荡周期的飞秒激光脉冲在非线性光纤中传输的方程和非线性光纤的折射率。给出了描述具有几个光振荡周期的飞秒激光脉冲在非线性光纤中传输方程的解。研究了在非线性光纤中自相位调制导致具有几个光振荡周期的飞秒激光脉冲频谱展宽 (脉宽压缩 )的详细物理过程。研究了非线性光纤中飞秒光孤子产生的条件     

Dynamics of quadruple laser pulses in under‐dense plasmas

An analysis of dynamics of a quadruple laser pulse propagating through an under‐dense plasma is presented. The Drude model is used to derive the dielectric function of the plasma for relativistic non‐linearity in the electron mass. An approximate numerical solution of the nonlinear Schrödinger wave equation for the field of the laser beam is obtained with the help of the moment theory approach in the Wentzel–Kramers–Brillouin (WKB) approximation. Particular emphases are placed on the variations of spot size, pulse width, and longitudinal phase delay with the distance of propagation through the plasma. Self‐trapping of the laser pulse is also investigated.