High-frequency solitons in media with induced scattering from damped low-frequency waves with nonuniform dispersion and nonlinearity

The dynamics of high-frequency field solitons is considered using the extended nonhomogeneous nonlinear Schrödinger equation with induced scattering from damped low-frequency waves (pseudoinduced scattering). This scattering is a 3D analog of the stimulated Raman scattering from temporal spatially homogeneous damped low-frequency modes, which is well known in optics. Spatial inhomogeneities of secondorder linear dispersion and cubic nonlinearity are also taken into account. It is shown that the shift in the 3D spectrum of soliton wavenumbers toward the short-wavelength region is due to nonlinearity increasing in coordinate and to decreasing dispersion. Analytic results are confirmed by numerical calculations.     

双折射光纤中斯托克斯波的增益谱

根据激光脉冲在双折射光纤中传输时的混合模方程,考虑拉曼效应后,得出在受激拉曼散射和参量放大共同作用下的增益。数值模拟了当输入泵浦波沿两双折射轴450附近区域传输时,在不同色散区斯托克斯增益谱随输入功率及群速度失配等相关参数的变化关系;结果表明斯托克斯增益谱在不同色散区表现出明显不同的特性,当满足一定条件下,可利用混合模双折射光纤中传输的泵浦波分解出的脉冲序列来分离和提取T频脉冲。     

双折射光纤中斯托克斯波的增益谱

根据激光脉冲在双折射光纤中传输时的混合模方程,考虑拉曼效应后,得出在受激拉曼散射和参量放大共同作用下的增益。数值模拟了当输入泵浦波沿两双折射轴450附近区域传输时,在不同色散区斯托克斯增益谱随输入功率及群速度失配等相关参数的变化关系;结果表明斯托克斯增益谱在不同色散区表现出明显不同的特性,当满足一定条件下,可利用混合模双折射光纤中传输的泵浦波分解出的脉冲序列来分离和提取T频脉冲。     

准孤子对在色散缓变光纤中传输特性的数值研究

用分步富里叶变换法求解色散缓变光纤的光孤子NLS方程，在一定条件下孤子对在该光纤中演变为准孤子，其幅值和宽度发生周期性变化，没有出现通常情况下的周期性离合现象。     

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.     

Third-order dispersion for generating optical rogue solitons

We theoretically and numerically evidence that optical rare and strong temporal events generated in fiber supercontinua originate from convective modulational instabilities. This convective nature is induced by higher-order terms (odd-order dispersion and stimulated Raman scattering) that break the time reversal symmetry of the nonlinear Schrödinger equation. We demonstrate (i) analytically that the third-order dispersion term alone turns the system to be convectively unstable and (ii) numerically that the sign of the curvature of the tail of the probability density function changes (in logarithmic scale) when the third-order dispersion term is added. This latter feature results in more powerful rare events. If, in addition, stimulated Raman scattering is taken into account, both the convective instabilities and the power of extreme events are further enhanced giving rise to a probability density function with a more pronounced curvature.     

高阶色散对高双折射光纤增益谱的影响

根据参量放大和拉曼效应共同作用下的耦合波方程,在考虑高阶色散情况下,当输入泵浦波偏振方向同双折射轴成45时,通过引入拉曼增益的洛伦兹模型,研究了高双折射光纤中,参量放大和拉曼效应共同作用下的增益谱随相关参量的变化关系。结果表明:高双折射光纤中,在不同色散区,不同的输入参量（输入功率、群速度失配等）条件下,参量放大和拉曼效应共同作用下的增益谱受到高阶色散的影响,增益谱的结构、强度和谱宽产生了变化, 高阶色散对增益谱的影响不可忽略;可以利用增益谱在大群速度失配区域远离中心频率偏移的性质,提取T频率脉冲。     

Soliton models in resonant and nonresonant optical fibers

In this review, considering the important linear and nonlinear optical effects like group velocity dispersion, higher order dispersion, Kerr nonlinearity, self-steepening, stimulated Raman scattering, birefringence, self-induced transparency and various inhomogeneous effects in fibers, the completely integrable concept and bright, dark and self-induced transparency soliton models in nonlinear fiber optics are discussed. Considering the above important optical effects, the different completely integrable soliton models in the form of nonlinear Schrödinger (NLS), NLS-Maxwell-Bloch (MB) type equations reported in the literature are discussed. Finally, solitons in stimulated Raman scattering (SRS) system is briefly discussed.     

Inverse dielectric function of a superlattice including local field effects and spatial dispersion

The inverse longitudinal dielectric function of a superlattice is calculated. Local field effects due to the superlattice structure and spatial dispersion due to both the superlattice and atomic structure are taken into account. Two applications are treated i) density Raman scattering from interface and bulk plasmons and ii) optical dielectric constants of superlattices.     

Superradiance and Raman scattering in three-level molecular system

A model is presented for the dynamics of superradiance, coherent and stimulated Raman scattering from an optically pumped three-level system. The evolution of the pumping and two counterpropagating waves in the adjacent transition are taken into account. The results of computer simulation show that by specifying the pumping pulse area, and active medium length and pressure we can control the parameters of the pulses in the adjacent transition. The possibilities of observing coherent Raman scattering dynamics, which are significantly different from that for stimulated Raman scattering, are shown. The results of simulation show that for the ultrashort pumping pulse the superradiative emission in the backward direction is formed within the coherence length near the entrance plane of the active medium.     

Exciton-polariton solitary waves

Effects of the exciton and polariton dispersions and the nonlinear exciton and photon interactions on the properties of polariton solitons in molecular crystals are investigated. Higher-order terms and phase-modulation (chirp) are taken into account. Bright- and dark-soliton solutions of the resulting modified nonlinear Schr?dinger (NLS) equation are presented. Nonlinearity- and dispersion-induced critical points on the polariton dispersion curve are obtained, separating regions with different solutions. Received 2 October 2001 / Received in final form 23 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: Stoychev@issp.bas.bg     

On the excitation of four magnons in Raman scattering

Raman scattering by four magnons in antiferromagnets is studied. It is shown that the excited-state exchange mechanism resulting in two-magnon scattering at the same time gives four-magnon scattering as well. The intensity and line shape of this scattering is computed numerically for simple cubic systems. The agreement with experimental data is fairly good for KNiF₃, if magnon-phonon interaction is taken into account.     

On the types of instability of spatially restricted systems

A classification of instabilities in spatially restricted systems is presented, which generalizes a classification considered in book [1]. It is shown that, if a system has no active boundaries and the waves are not amplified in an infinite homogeneous medium, which corresponds to the absence of solutions of the dispersion equation with the negative imaginary part of the wave vector at the real frequency, then only nonamplified instabilities with a nonlocal resonance can be developed. The development of nonamplified instability is considered in a spatially restricted system through which a flux propagates, when along with natural waves the excitation of the waves of fluxes playing a key role in the development of the instability is taken into account.     

关于顺式聚乙炔共振喇曼谱的理论解释

本文建议以双极化子微观模型,根据多声子晶格弛豫理论解释顺式聚乙炔的喇曼谱。在准一维哈密顿量中考虑了电子与不同声子模的耦合,其耦合常数由红外及喇曼实验数据确定。理论计算结果与实验数据进行了比较和讨论。文中采用的方法可以推广到类似的系统 关键词：     

偏振模色散影响下飞秒孤子的传输特性研究

以Maxwell电磁场理论为基础，在综合考虑了高阶色散、高阶非线性、自相位调制、交叉相位调制、自变陡、脉冲内喇曼散射及偏振模色散等因素的基础上，推导了飞秒孤子脉冲在双折射光纤中传输的耦合非线性薛定谔方程，并利用分步傅里叶方法对该方程进行了数值计算，研究分析了偏振模色散对飞秒孤子传输的影响。结果发现：当Dp≤0.1ps/km1/2时，偏振模色散对系统的影响很小，随着偏振模色散值的增大，系统的传输性能迅速恶化，当偏振模色散值达到0.3ps/km1/2时，系统的传输距离已经不到无偏振模色散时的1/3；若同时考虑光纤的高阶效应，以飞秒孤子作为载体的系统已经不能实现高速长距离的传输。     

Breathers and solitons for the coupled nonlinear Schr?dinger system in three-spine α-helical protein

We mainly investigate the variable-coefficient 3-coupled nonlinear Schr?dinger(NLS) system, which describes soliton dynamics in the three-spine α-helical protein with inhomogeneous effect. The variable-coefficient NLS equation is transformed into the constant coefficient NLS equation by similarity transformation firstly. The Hirota method is used to solve the constant coefficient NLS equation, and then we get the one-and two-breather solutions of the variable-coefficient NLS equation. The results show that, in the background of plane waves and periodic waves, the breather can be transformed into some forms of combined soliton solutions. The influence of different parameters on the soliton solution and the collision between two solitons are discussed by some graphs in detail. Our results are helpful to study the soliton dynamics inα-helical protein.     

(2+1)-D propagation of spatio-temporal solitary waves including higher-order corrections

We study the propagation of bright two-dimensional spatio-temporal solitary waves using a higher-order multi-dimensional non-linear Schrödinger equation. Starting directly from Maxwell's equations, a multiple-scales derivation is presented which results in a generalized first-order vectorial evolution equation that is valid for the non-linear spatio-temporal propagation of a predominantly linearly polarized electric field with large spatial and temporal bandwidths. A reduced version of this full equation including the higher-order linear and non-linear effects of third- and fourth-order dispersion, space–time focusing, shock, stimulated Raman scattering, and ultrafast quintic index saturation, is solved numerically via a modified split-step algorithm. Material parameters corresponding to those of fused silica at λf=1.55 m are used, with the addition of a negative quintic saturation term. Without quintic saturation, the non-linear spatio-temporal wave broadens under the action of the higher-order space–time effects. In addition, in the absence of Raman scattering, the wave undergoes collapse until arrested by the remaining higher-order terms. Frequency down-shifting and spatio-temporal broadening due to Raman scattering are found to have the greatest effect on non-linear spatio-temporal wave propagation. Nevertheless, we demonstrate that quintic saturation effectively stabilizes the wave such that broadening is reduced considerably, permitting nearly stationary propagation over many confocal distances, albeit with substantial down-shift. The resulting spatio-temporal solitary waves should be useful for applications in ultrafast all-optical switching and logic, and the generalized evolution equations will provide a refined starting point for the study of spatio-temporal phenomena in other areas as well.     

双折射色散阶跃光纤中拉曼效应和参量放大增益谱

在拉曼效应和参量放大共同作用下,当激光脉冲在双折射光纤中传输时,根据所遵循的耦合模方程,通过引入平行拉曼增益的洛伦兹模型,导出了当输入泵浦波偏振方向同双折射轴成45°角时,在双折射色散阶跃光纤中拉曼效应和参量放大共同作用所导致的增益,讨论并分析了在不同色散区增益谱随相关参量的变化。结果表明:由于拉曼效应、参量放大、双折射和色散的相互作用,导致增益谱的斯托克斯波与反斯托克斯波彼此不对称;在反常色散区,产生的增益以反斯托克斯波为主,在正常色散区则以斯托克斯波为主;当表征距离的级数m发生变化时,增益谱也随之发生变化,可以利用色散阶跃光纤在适当的级数m位置提取T频率脉冲。     

Rogue wave formation by accelerated solitons at an optical event horizon

Rogue waves, by definition, are rare events of extreme amplitude. At the same time, they are surprisingly ubiquitous, in the sense that they can exist in a wide range of physical contexts and possess probability distributions that exhibit heavier tails than the normal Gaussian distribution. While many mechanisms have been demonstrated to explain the appearance of rogue waves in various specific systems, there is no known generic mechanism or general set of criteria shown to rule their appearance. Presupposing only the existence of a nonlinear Schrödinger-type equation together with a concave dispersion profile around a zero-dispersion wavelength, we demonstrate that solitons may experience acceleration and strong reshaping due to the interaction with continuum radiation, giving rise to extreme-value phenomena. The mechanism appears to be widely independent from interactions specific to the optical context, e.g., the Raman effect or other scattering processes that have no equivalent in other wave-supporting physical systems. In our system, a strong increase in the peak power may appear via reshaping while the pulse energy is nearly conserved. The conservative nature of the proposed reshaping-induced appearance of rogue waves makes this mechanism particularly robust.