A note on loop-soliton solutions of the short-pulse equation

It is shown that the N-loop soliton solution to the short-pulse equation may be decomposed exactly into N separate soliton elements by using a Moloney-Hodnett type decomposition. For the case N=2, the decomposition is used to calculate the phase shift of each soliton caused by its interaction with the other one. Corrections are made to some previous results in the literature.     

Stability of vortex solitons in the cubic-quintic model

We investigate one-parameter families of two-dimensional bright spinning solitons (ring vortices) in dispersive media combining cubic self-focusing and quintic self-defocusing nonlinearities. In direct simulations, the spinning solitons display a symmetry-breaking azimuthal instability, which leads to breakup of a soliton into a set of fragments, each being a stable nonspinning soliton. The fragments fly out tangentially to the circular crest of the original vortex ring. If the soliton’s energy is large enough, the instability develops so slowly that the spinning solitons may be regarded as virtually stable ones, in accord with earlier published results. Growth rates of perturbation eigenmodes with different azimuthal “quantum numbers” are calculated as a function of the soliton’s propagation constant κ from a numerical solution of the linearized equations. As a result, a narrow (in terms of κ) stability window is found for extremely broad solitons with values of the “spin” s=1 and 2. However, analytical consideration of a special perturbation mode in the form of a spontaneous shift of the soliton’s central “bubble” (core of the vortex embedded in a broad soliton) demonstrates that even extremely broad solitons are subject to an exponentially weak instability against this mode. In actual simulations, a manifestation of this instability is found in a three-dimensional soliton with s=1. In the case when the two-dimensional spinning solitons are subject to tangible azimuthal instability, the number of the nonspinning fragments into which the soliton splits is usually, but not always, equal to the azimuthal number of the instability eigenmode with the largest growth rate.     

光纤孤子包络方程及相关分析

从经典唯象观点出发,提出了相位移动的精确公式,严格推导出光纤孤子包络方程,揭示了原包络函数的唯一性,并合理分析了光纤孤子的形成机制.     

Damping of internal soliton modes in media with quadratic nonlinearity

Optical solitons in media with quadratic nonlinearity and frequency dispersion are theoretically analyzed. Internal soliton modes and the rate of their radiative damping as a function of detuning from the phase-matching condition and the nonlinear shift of phase velocity for different soliton dimensions (d=1, 2, 3) are found. The length of a nonlinear medium required to form a stationary soliton is determined.     

强非局域空间光孤子大相移的理论研究以及应用方案设计

本文发展了郭旗等人的唯像理论,发现在铅玻璃中,孤子随着本身功率或者抽运光孤子功率几十个毫瓦的变化,就会出现π的附加相移.基于抽运光孤子功率对弱信号光孤子相位有着高调制灵敏度的结论,提出了一种较可行的光开关实现方案. 关键词： 强非局域 空间光孤子 大相移     

负折射介质中可控自陡峭效应对孤子传输的影响

研究了具有非线性极化的负折射介质中孤子脉冲的传输特性,着重分析了在常规非线性传输模型中不曾出现的由负折射介质色散磁导率导致的可控自陡峭效应对孤子传输的影响.结果表明,与正自陡峭效应一样,负自陡峭效应同样造成孤子脉冲的非对称、中心偏移和高阶孤子衰减,但脉冲偏移的方向与正自陡峭效应情形相反.此外,利用可控自陡峭效应可以从某种程度上抵消三阶色散效应导致的孤子脉冲偏移,从而实现孤子脉冲中心的无偏移传输.     

Phase jitter in periodically dispersion-managed optical transmission systems

We investigate the phase jitter in long-haul optical transmission systems with periodic dispersion management and amplification. We compare different dispersion-managed soliton systems and a conventional soliton system having the same pulse width and path-averaged dispersion. Using the variational method, we derive the ordinary differential equations for the pulse parameters perturbed by amplifier noise and hence calculate the phase jitter. We verify the analytical results by numerically solving the nonlinear Schrödinger equation using split-step Fourier algorithm. The results suggest that the reduction of nonlinear phase noise in dispersion-managed soliton systems is possible compared to a conventional soliton system. It is also revealed that the phase noise is enhanced in stronger dispersion-managed systems. We also explore the phase noise effect in dispersion-managed quasi-linear systems and find that phase jitter is mitigated in highly dispersive fibers.     

Collision-induced time shift of a dispersion-managed soliton and its minimization in wavelength-division-multiplexed transmission

The formula for the time shift of a dispersion-managed soliton that results from its collision with other solitons in different channels consists of two terms, one related to the frequency shift during collision, and the other related to the residual frequency shift after collision. It is found that an optimal relative delay exists between pulses in adjacent channels after each dispersion-managed span that balances the contributions from the two terms and minimizes the overall time shift, leading to a substantial improvement in transmission performance.     

Large phase shift of spatial solitons in lead glass

A large phase shift of the strongly nonlocal spatial optical soliton (SNSOS) was predicted by Guo et al. [Phys. Rev. E69, 016602 (2004)]. We investigate the phase shift of the SNSOS in lead glass. It is found that the phase shift rate along the propagating direction of such a soliton is one order larger than that of the local soliton. The theory agrees quantitatively with the experiment on the dependence of the phase shift on the degree of nonlocality. We realize a π-phase shift by changing the optical power by about 10?mW around the critical soliton power, which agrees qualitatively with our theoretical result.     

电磁诱导透明系统中的暗孤子

利用电磁诱导透明效应提供的高色散和非线性系数, 研究暗孤子的形成环境以及孤子演化与环境参数的关系. 为了提高电磁诱导透明的稳定性和可操作性, 用双势阱半导体作为基质材料. 将量子理论和经典场理论结合, 获得了非线性薛定谔方程. 以非线性薛定谔方程为基础, 研究暗孤子的形成条件, 以及孤子演化与环境参数的关系. 研究结果表明: 当介质为反常色散同时交叉相位调制为负时, 在该介质中可以形成和传播暗孤子; 暗孤子演化中, 脉宽、灰度与相位相互关联, 脉宽越小、灰度越大, 相位增长越迅速. 此外, 研究了系统的调制不稳定性, 探讨了在调制不稳定下的增益谱.     

Interaction properties of complex modified Korteweg-de Vries (mKdV) solitons

Interaction properties of complex solitons are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries (mKdV) equation, given by the Hirota equation and the Sasa-Satsuma equation, which share the same traveling wave (single-soliton) solution having a sech profile characterized by a constant speed and a constant phase angle. For both equations, nonlinear interactions in which a fast soliton collides with a slow soliton are shown to be described by 2-soliton solutions that can have three different types of interaction profile, depending on the speed ratio and the relative phase angle of the individual solitons. In all cases, the shapes and speeds of the solitons are found to be preserved apart from a shift in position such that their center of momentum moves at a constant speed. Moreover, for the Hirota equation, the phase angles of the fast and slow solitons are found to remain unchanged, while, for the Sasa-Satsuma equation, the phase angles are shown to undergo a shift such that the relative phase between the fast and slow solitons changes sign.     

Tunable Supercontinuum Generated in a Yb~(3+)-Doped Microstructure Fiber Pumped by Ti:Sapphire Femtosecond Laser

We experimentally demonstrate that a tunable supercontinuum(SC) can be generated in a Yb3+-doped microstructure fiber by the concept of wavelength conversion with a Ti:sapphire femtosecond(fs) laser as the pump.Experimental results show that an emission light around 1040 nm in an anomalous dispersion region is first generated and amplified by fs pulses in the normal dispersion region. Then, SC spectra from 1100 to 1380 nm and 630 to 840 nm can be achieved by combined effects of higher-order soliton fission and Raman soliton self-frequency shift in the anomalous dispersion region and self-phase modulation, dispersive wave, and four-wave mixing in the normal dispersion region. It is also demonstrated that the 20 nm change of pump results in a 280 nm broadband shift of soliton and the further red-shift of soliton is limited by OH-absorption at 1380 nm.     

Direct carrier–envelope phase stabilization of a soliton-effect compressed sub-two-cycle pulse source through nonlinear mixing of solitonic and dispersive waves

We present a carrier–envelope phase (CEP) stabilized sub-two-cycle 5.2 fs pulse source based on soliton-effect self-compression of femtosecond laser pulses in millimetre-long highly nonlinear photonic crystal fibres. We employ a simple and efficient scheme to generate a strong (40–60 dB, configuration dependent) CEP beat signal directly from the pulse source via f-to-2f interferometry where the second harmonic of the main soliton pulse is mixed with the isolated dispersive blue/green radiation peak that is also generated in the compression process, obviating the need for additional spectral broadening mechanisms.     

Interactions of solitons with complex defects in Bragg gratings

We examine collisions of moving solitons in a fiber Bragg grating with a triplet composed of two closely set repulsive defects of the grating and an attractive one inserted between them. A doublet (dipole), consisting of attractive and repulsive defects with a small distance between them, is considered too. Systematic simulations demonstrate that the triplet provides for superior results, as concerns the capture of a free pulse and creation of a standing optical soliton, in comparison with recently studied traps formed by single and paired defects, as well as the doublet: 2/3 of the energy of the incident soliton can be captured when its velocity attains half the light speed in the fiber (the case most relevant to the experiment), and the captured soliton quickly relaxes to a stationary state. A subsequent collision between another free soliton and the pinned one is examined too, demonstrating that the impinging soliton always bounces back, while the pinned one either remains in the same state, or is kicked out forward, depending on the collision velocity and phase shift between the solitons.     

The Evolution Feature of Chirp-Dark Soliton in Single-Mode Fiber

The evolution feature of the injected initial-chirp tanh-dark soliton in single-mode fiber is studied in this paper. We analyze the evolution of amplitude, pulse width, frequency chirp and center position shift of dark soliton along with the variation of propagation distance, primarily using Lagrange-Euler's formula and taking the high-order dispersion as perturbation. The results show that the amplitude and pulse width of chirp-dark soliton are all oscillating around a certain critical distance in ideal fiber (β = 0), and the high-order dispersion conduces to generate the asymptotic dark soliton.     

Cusp and loop soliton solutions of short-wave models for the Camassa–Holm and Degasperis–Procesi equations

A simple method is developed for constructing the solutions of the short-wave model equations associated with the Camassa–Holm (CH) and Degasperis–Procesi (DP) shallow-water wave equations. Taking an appropriate scaling limit of the N-soliton solution of the CH equation, we obtain the N-cusp soliton solution for the CH short-wave model. The similar procedure also leads to the N-loop soliton solution for the DP short-wave model. We describe the property of the solutions. In particular, we derive the large-time asymptotics of the solutions as well as the formulas for the phase shift.     

基于强非局域空间光孤子的温度传感器原理

为了让温度传感器在集成化全光控制中找到实现途径,提出一种基于非局域空间光孤子传输的温度传感器的理论方案.以铅玻璃作为非局域空间光孤子的传输介质,通过研究圆柱形铅玻璃中, 中心入射光束在传输过程中的相移问题, 得出在环境温度0.32 ℃的改变就可以引起孤子π相移的结论.此温度改变对相移的调制有望为基于干涉仪原理的温度传感器提供一个可行且灵敏度较高的实现方案.     

Effect of nonlinear dispersion on pulse self-compression in a defocusing noble gas

Media with a negative Kerr index (n₂) offer an intriguing possibility to self-compress ultrashort laser pulses without the risk of spatial wave collapse. However, in the relevant frequency regions, the negative nonlinearity turns out to be highly dispersive as well. Here, we study the influence of nonlinear dispersion on the pulse self-compression in a defocusing xenon gas. Purely temporal (1+1)-dimensional investigations reveal and fully spatio-temporal simulations confirm that a temporal shift of high intensity zones of the compressed pulse due to the nonlinear dispersion is the main effect on the modulational instability (MI) mediated compression mechanism. In the special case of vanishing n₂ for the center frequency, pulse compression leading to the ejection of a soliton is examined, which cannot be explained by MI.     

Dispersive dark optical soliton with Schödinger-Hirota equation by G′/G-expansion approach in power law medium

This paper studies dispersive optical solitons that are governed by the Schrödinger-Hirota equation with power law nonlinearity. The G′/G-expansion method is applied to extract soliton solution to this equation. This approach reveals dark 1-soliton solution to the equation.     

Effect of dark soliton on the spectral evolution of bright soliton in a silicon-on-insulator waveguide

The spectral evolution of bright soliton in a silicon-on-insulator optical waveguide is numerically simulated using the split-step Fourier method. The power and input chirp of the dark soliton and the second-order dispersion are varied to investigate the effect of dark soliton on the spectrum of bright soliton. The simulations prove that the dark soliton modifies the spectral shape of the bright soliton. Further, the variation in the power of dark soliton affects the splitting of bright soliton. Furthermore, the chirped dark soliton can improve the spectral width and flatness. The variation in the dispersion of dark soliton modifies the phase matching of the bright soliton and the dispersive wave emission, thereby affecting the spectral evolution.