Dynamics of wave packets and soliton interaction in terms of the third-order nonlinear Schrödinger equation

We present the results of numerical study of the evolution of wave packets and envelope soliton interaction in terms of the third-order nonlinear Schrödinger equation. It is shown that an arbitrary initial pulse evolves to a few solitons and a linear quasiperiodic wave. The interaction of solitons is accompanied by the radiation of part of the wave field in the form of a linear quasiperiodic wave from the interaction region, amplification of the soliton with larger amplitude and attenuation of the soliton with smaller amplitude.     

Short Envelope Solitons. Isotropic and Anisotropic Media

Within the framework of the third-order approximation of the nonlinear wave dispersion theory, we find new classes of short scalar and vector solitons of lengths about several wavelengths. Short scalar solitons are found within the framework of a third-order nonlinear Schrödinger equation (NSE-3) including both the nonlinear dispersion terms and the third-order linear dispersion term. The interaction of such solitons is studied, and the soliton stability is proved. Short vector solitons are found within the framework of a coupled third-order nonlinear Schröodinger equation (CNSE-3). Interaction and stability of such solitons are studied.     

Enhanced pulse compression induced by the interaction between the third—order dispersion and the cross—phase modulation in birefringent fibres

In this paper,we report on the enhanced pulse compression due to the interaction between the positive third-order dispersion (TOD) and the nonlinear effect (cross-phase modulation effect) in birefringent fibres.Polarization soliton compression along the slow axis can be enhanced in a birefringent fibre with positive third-order dispersion,while the polarization soliton compression along the fast axis can be enhanced in the fibre with negative third-order dispersion.Moreover,there is an optimal third-order dispersion parameter for obtaining the optimal pulse compression.Redshifted initial chirp is helpful to the pulse compression,while blueshifted chirp is detrimental to the pulse compression.There is also an optimal chirp parameter to reach maximum pulse compression.The optimal pulse compression for TOD parameters under different N-order solitons is also found.     

高阶孤子在光纤中传输的数值研究

通过数值求解非线性薛定谔方程,得到了二阶和三阶孤子的传输特性,并和一阶孤子做了比较.对于二阶孤子和三阶孤子间的相互作用做了分析,讨论了三阶色散对高阶孤子相互作用的影响,得出随着三阶色散的增大,会使孤子的衰变具有新的特性,将会导致光孤子通信的误码率加大.     

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.     

Soliton coupling in birefringent optical fiber with third-order dispersion

Nonlinear coupling of polarized solitons in birefringent optical fiber in the presence of third-order dispersion is considered in the framework of the coupled nonlinear Schrödinger equations. The influence of third-order dispersion on the interaction between solitons is investigated. For sufficiently strong third-order dispersion the interaction may even become repulsive. The stable conditions for solitons of partial pulses are analyzed and amplitude threshold, which decreases with third-order dispersion coefficient decreasing, for the capture of solitons of partial pulses into a coupled two-component pulse is obtained.     

Femtosecond second-order solitons in optical fiber transmission

A propagation of the femtosecond second-order solitons in an optical fiber is studied. We show that a generalized nonlinear Schrödinger equation well describes the propagation of the second-order soliton even containing only a few optical cycles. The propagations of a 50 fs and a 10 fs second-order soliton in an optical fiber are numerically simulated. It is found that, for the case of 10 fs second-order soliton, the soliton decay is dominated by the third-order dispersion, in contrast to the case of 50 fs second-order solitons, where the soliton decay is dominated by the delayed Raman response. It is also found that the exact delayed Raman response form must be used for the propagation of the 50 fs or less than 50 fs second-order soliton.     

Short Envelope Solitons in Nonconservative Media

We consider the dynamics of short envelope solitons within the framework of the third-order nonlinear Schrödinger equation with allowance for both linear losses and pumping by an external wave field. An equation for the soliton amplitude is derived. The stationary value of the soliton amplitude is found.     

Dark-in-the-Bright solitary wave solution of higher-order nonlinear Schrödinger equation with non-Kerr terms

We present new type of Dark-in-the-Bright solution also called dipole soliton for the higher order nonlinear Schrödinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and subject to constraint relation among the parameters in optical context. This equation could be a model equation of pulse propagation beyond ultrashort range in optical communication systems. The solitary wave solution is composed of the product of bright and dark solitary waves. This type of pulse shape to be formed both the group velocity dispersion and third-order dispersion must be compensated. We also investigated the stability of the solitary wave solution under some initial perturbation on the parametric conditions. We have shown that the shape of pulse remains unchanged up to 20 normalized lengths even under some very small violation in parametric conditions.     

钛宝石飞秒激光器中孤子分子的内部动态探测

孤子是自然界中一种基本的非线性波动传递形式,孤子间的相互作用能够映射出复杂非线性系统的多体动力学过程,具有重要的基础研究价值.被动锁模激光器是研究孤子相互作用的理想平台.光孤子之间的吸引、排斥作用能够形成孤子分子,而时间拉伸色散傅里叶变换(TS-DFT)技术使得实时探测孤子分子动力学成为可能.基于TS-DFT技术,本文实验研究了钛宝石飞秒激光器产生的孤子分子的内部动态,通过改变抽运功率,分别观察到了间隔为180 fs的稳定的孤子分子和间隔为105 fs的具有微弱相位振荡的孤子分子,后者的振动幅度仅为0.05 rad.实验发现受到环境影响,稳定态的孤子分子还能够转变为相位滑动状态.这些间隔为百飞秒量级的光学孤子分子对于研究孤子的近程非线性相互作用具有突出的意义.     

Phase interaction of short vector solitons

An interaction of vector solitons in the frame of coupled third-order nonlinear Schrödinger equations taking into account third-order linear dispersion, nonlinear dispersion, and cross-phase modulation terms is considered. Phase nature of the solitons? interaction is shown. In particular, dependence of solitons? trajectories on initial distance between solitons is shown. Conditions of reflection and propagation of solitons through each other are obtained.     

Soliton formation in the propagation of phase-modulated femtosecond pulses through an optical fiber with a cubic nonlinearity

A way of soliton self-formation upon propagation of femtosecond light pulses through an optical fiber with a cubic nonlinearity is described with allowance for the dispersion of the nonlinear response of the medium. For soliton formation to occur, a low-frequency phase modulation of the initial pulse is necessary. Several solitons formed in this way differ in both maximal intensities and group velocities. The duration of an individual soliton may be several (up to ten) times smaller than the initial duration of the input pulse.     

Cascade compression induced by nonlinear barriers in propagation of optical solitons

We investigate the nonlinear tunneling of optical solitons through both dispersion and nonlinear barriers by employing the exact solution of the generalized nonlinear Schrödinger equation with variable coefficients. The extensive numerical simulations show that the optical solitons can be efficiently compressed when they pass through adequate engineered nonlinear barriers. A cascade compression system in a dispersion decreasing fiber with nonlinear barriers on an exponential background is proposed and the cascade compression of optical pulses is further investigated in detail. Finally, the stability to various initial perturbations of the cascade compressed optical soliton and the interaction between two neighboring compressed solitons were investigated too.     

三阶色散和受激拉曼散射效应对呼吸孤子作用的相互平衡

以高阶复系数Ginzburg-Landau方程为模型,就高阶非线性效应(比如:三阶色散、自陡峭、自频移等)对呼吸孤子传输特性的影响进行了详细的分析,结果表明:当各高阶非线性效应单独作用时,可能会导致呼吸孤子形状的不对称或脉冲中心偏移等现象,但是,当它们共同作用于呼吸孤子时,适当的参数选取可以使它们对呼吸孤子的影响相互抵消,从而使呼吸孤子实现保型传输。     

色散渐变光纤中相移控制研究

相移控制能有效的避免孤子间的相互作用.通过利用符号计算和双线性方法,本文解析研究用于描述色散渐变光纤传输特点的非线性Schr?dinger方程,并得到该方程的双孤子解.基于所得到的双孤子解,通过研究发现,当色散渐变光纤中的群速度色散呈Gauss型变化时,可以利用该类光纤实现孤子相移控制,从而避免孤子相互作用,提高光通信系统中信号传输质量.此外,本文还将讨论色散渐变光纤中各类参数对相移控制的影响.本文结论还有助于逻辑门和全光开光的研究.     

具有随机色散的光时分复用系统中色散管理孤子相互作用

本文采用变分法和数值方法研究了具有随机色散的光时分复用系统中色散管理孤子相互作用.发现随机色散增强了孤子间相互作用, 产生了导致孤子淹没的振幅和间隔涨落.相互作用距离与初始间隔、初始相对相位、脉宽和初始相对振幅有关.     

Linear approximation in pulse propagation problems in nonlinear media

It seems obvious that the manifestation of nonlinear effects (such as shock wave and soliton formation) is possible only at comparatively high levels of nonlinearity. Nevertheless, there are well-known examples where a disturbance which is as small as one pleases ceases in time to be linear, and must be described in nonlinear terms. This, e.g., is the situation for the well-known Korteweg-de Vries (KdV) equations, which for an impulsive initial condition of definite sign has an asymptotic solution described by a set of solitons and by a rapidly oscillating wave packet. There will in fact always be at least one soliton asymptotically, no matter how small the initial pulse amplitude [1]. Another example is shock wave (triangular pulse) attenuation at large distances (or times) within the framework of the Burgers equation; the wave remains a shock wave even though its amplitude decreases to zero [1]. It is thus necessary to indicate a criterion which might be used to establish the nature of the asymptotic solution. The aim of the present note is the definition of such a criterion; that is, a relation between nonlinearity and dispersion (dissipation) in which nonlinear effects are manifested only above some threshold level.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 11, pp. 1706–1708, November, 1978.     

Dispersion managed dissipative solitons with higher order nonlinearity and frequency-selective feedback

We present the generation and interaction dynamics of dispersion managed soliton in a dissipative cubic-quintic nonlinear optical fiber coupled with frequency-selective feedback. Analytically, perturbative variational method is used to obtain evolution equations for different soliton parameters that are subsequently solved to study the propagation characteristics of the dispersion managed dissipative solitons (DMDS). The DMDSs show breather like characteristics and are found to be robust against certain level of initial noise. Both the standard Gaussian and more generic super-Gaussian pulse profile are shown to yield stable DMDS. Interaction of two DMDSs of same phase may lead to a bound state. By varying the temporal separation and phase difference between the DMDSs the bound state can be switched between low to high speed regime.     

Ultraslow optical solitons in a four-level tripod atomic system

We investigate possible formation and propagation of localized, shape-preserving nonlinear optical pulse in a resonant, lifetime-broadened four-level tripod atomic system via electromagnetically induced transparency (EIT). We prove both analytically and numerically that although in anomalous dispersion regimes near resonance a superluminal optical soliton may appear, such soliton suffers serious absorption. However, by choosing appropriate parameters to make the system work in normal dispersion regimes and within an EIT transparency window, ultraslow optical solitons with very low light intensity can form and propagate stably in the system.