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.     

飞秒脉冲初始脉宽和啁啾对其自相似演化及压缩的影响

采用自相似抛物脉冲放大器对飞秒脉冲直接进行放大,并以低非线性系数的光子带隙光纤作为脉冲压缩器对放大的脉冲进行压缩.通过分步傅里叶方法研究了飞秒脉冲的初始宽度和啁啾对其自相似演化和压缩的影响.研究结果表明脉冲宽度越宽,脉冲自相似演化程度越差,演化脉冲的压缩质量也越差,压缩脉冲宽度较大,且有基座;脉冲的初始啁啾会严重阻碍其自相似演化,并最终影响脉冲的压缩质量;啁啾越大,脉冲的自相似演化结果越差,脉冲的压缩质量也越差;正的啁啾对脉冲的自相似演化的影响比负啁啾的要大.     

Effects of initial frequency chirp on the linear propagation characteristics of the exponential optical pulse

In this paper, the linear propagation characteristics of the exponential optical pulse with initial linear and nonlinear frequency chirp are numerically studied in a single mode fibre for \be₂<0. It can be found that the temporal full width at half maximum and time-bandwidth product of exponential pulse monotonically increase with the increase of propagation distance and decrease with the increase of linear chirp C for C<0.5, go through an initial decreasing stage near \zeta=1, then increase with the increase of propagation distance and linear chirp C for C\geq0.5. The broadening of pulses with negative chirp is faster than that with positive chirp. The exponential pulse with linear chirp gradually evolves into a near-Gaussian pulse. The effect of nonlinear chirp on waveform of the pulse is much greater than that of linear chirp. The temporal waveform breaking of exponential pulse with nonlinear chirp is first observed in linear propagation. Furthermore, the expressions of the spectral width and time-bandwidth product of the exponential optical pulse with the frequency chirp are given by use of the numerical analysis method.     

Study on pulse compression in tapered holey fibres

This paper proposes three kinds of tapered holey fibres with a multi-layer of holes whose pitch of air holes at the end of untapered and tapered are 5.8 μm and 1.8 μm. The central wavelength which locates in the anomalous dispersion region is 1.55 μm. An adaptive split-step Fourier method is numerically used to study the pulse propagation in tapered holey fibres. For the considered convex tapered holey fibre, at a wavelength of 1.55 μm, a compression factor of 136.7 can be achieved by initial width of 800 fs propagation through a length of 0.8 m. It demonstrates that in anomalous dispersion region, pulse can be compressed with the increase of nonlinearity coefficient and the decrease of dispersion coefficient.     

Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers

The passive nonlinear reshaping in normally dispersive optical fibers in the steady-state regime is studied numerically. It is found that normal dispersion and self-phase modulation are able to provide pulse reshaping towards a parabolic pulse profile at the distances exceeding the optical wave breaking length. However, as compared to the similariton formation in active fibers the resulted pulse shape in passive fibers is strongly depended on the initial pulse parameters and nonlinear and dispersive fiber properties as well. The influence of initial pulse shape, initial chirp, third-order dispersion and loss on the parabolic pulse formation is studied consistently, and estimation of practical conditions which are needed for parabolic pulses formation in a passive fiber is provided.     

级联单模光纤中初始啁啾对高阶孤子脉冲压缩的影响

采用两段级联单模光纤对高阶孤子脉冲进行压缩。两段光纤具有不同的反常色散值,当高阶孤子脉冲在第一段光纤中获得最大程度压缩时,通过转换色散值不同的光纤,使压缩脉冲继续以高阶孤子的形式在第二段光纤中再次被压缩。每段光纤的长度都进行了优化,使得脉冲在每段光纤中都获得最大程度的压缩。基于非线性薛定谔方程,数值研究了初始啁啾对高阶孤子脉冲压缩的影响。研究结果表明,初始啁啾对高阶孤子脉冲的压缩有重要影响。与无初始啁啾时的情形相比,正的初始啁啾能增强每段光纤中脉冲的压缩效果,降低压缩脉冲的基座能量,而负初始啁啾的影响则相反。随着初始啁啾参量Cp的增大,脉冲在每段光纤中的压缩因子均增加,而基座能量、最优光纤长度均减小。     

一种改善损耗光纤中皮秒脉冲孤子效应压缩效果的方法

以常规光纤中的皮秒脉冲孤子效应压缩过程为基础,研究了在有无损耗的光纤中初始啁啾对脉冲压缩的影响。研究发现,在损耗光纤中引入初始啁啾能够抵消光纤损耗对孤子效应压缩的负面影响,从而大大改善了脉冲压缩的效果。如果所选取的啁啾值适当,则可以几乎完全抵消光纤损耗的作用,从而使光脉冲呈现出如同在无损耗的光纤中传输时一样。     

Wave-coupling theory of linear electro-optic effect for ultrashort laser pulses

A wave-coupling theory of linear electro-optic (EO) effect for ultrashort laser pulses has been developed. As one of its applications, the linear EO effect of ultrashort Gaussian pulses propagating in LiNbO₃ crystal is demonstrated, with the intensity lower than the damage threshold. It is found that the EO effect is sensitive to both the azimuth angle and the polar angle of wave vector of light. And the larger the applied electric field, the shorter the crystal used for optimization of EO coupling is. The numerical results show that, with the duration of input pulse changing from 150 fs to 5 fs, the durations of output pulses are broadened due to the group-velocity dispersion, as well as the first- and second-order refractive dispersion. In addition, when input pulse duration is larger than 20 fs, in contrast with zero chirp, the output durations can be slightly compressed if a positive chirp input pulse is used. The validities of slowly varying amplitude approximation and continuous wave approximation are also discussed. The influence of self-phase modulation and cross-phase modulation on the EO effect is also discussed briefly.     

不同入射脉冲强度线性啁啾对BaF2晶体交叉偏振波输出特性影响的数值模拟研究

在超短飞秒激光技术中, 基于BaF₂晶体三阶非线性效应的交叉偏振波技术是目前最重要的提高脉冲时域对比度的手段之一. 针对不同入射脉冲强度下入射脉冲的线性啁啾对BaF₂晶体交叉偏振波的输出特性, 包括转换效率、光谱加宽和时域压缩的影响进行了详细的数值模拟和讨论.特别地, 详细对比研究了非饱和及强入射脉冲情况下线性啁啾对交叉偏振波输出脉冲光谱加宽的影响. 结果表明, 在强入射脉冲情况下, 交叉偏振波的光谱加宽量从非饱和情况下相对于零点线性啁啾时的对称结构, 变得不再具有对称性, 并对产生非对称性的原因进行了详细的物理解释.     

基于可调谐静电啁啾镜的电子脉冲压缩技术

分析了基于双级反射静电系统的电子脉冲压缩技术方法。类比于光子脉冲压缩用多层介质啁啾镜, 将该静电系统称为可调谐静电啁啾镜:根据静电啁啾镜电气结构参数的设置, 入射电子脉冲在系统中U形反射运动飞行时间与其初始轴向能量具有相应不同的色散关系, 也即正负啁啾特性。讨论了该啁啾镜正负啁啾属性的可调谐性及脉冲压缩技术细节, 并给出了计算实例。     

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.     

Pulse propagation through a nonlinear optical amplifier

We report an investigation of pulse propagation through a recently proposed nonlinear amplifier composed of asymmetrical twin-core fibre. While the pulse is amplified and the associated noise is suppressed, we find that the pulse is strongly chirped. While the chirp in the centre of the pulse can be easily eliminated by inserting a short piece of dispersive fibre right after the amplifier, the chirp in the wings may remain and lead to the eventual destruction of the pulse. This residual chirp can be removed through a damped and radiative oscillation by judicious adjustment of the parameters of the amplifier and the dispersive fibre. Finally, we consider the effect of noise in the pulse. We discovered a threshold of the noise amplitude below which the noise is suppressed (which must be a characteristic asset of the nonlinear amplifier). Above the threshold, the noise tends to shift the centre of the pulse.     

Wave-breaking-extended fiber supercontinuum generation for high compression ratio transform-limited pulse compression

Wave-breaking often occurs when a short intense optical pulse propagates in a long normally dispersive optical fiber. This effect has conventionally been avoided in fiber (super-)continuum-based pulse compression because the accumulated frequency chirp of the output pulse cannot be fully compensated by a standard prism (or grating) pair. Thus, the spectral extending capability of the wave-breaking has not been utilized to shorten the compressed pulse. We demonstrate that wave-breaking-free operation is not necessary if a 4f pulse shaper-based compressor is employed to remove both the linear and nonlinear chirp of the output pulse. By propagating a 180 fs (FWHM) input pulse in a nonlinear photonic crystal fiber beyond the wave-breaking limit, we compress the wave-breaking-extended supercontinuum output pulse to the bandwidth-limited duration of 6.4 fs (FWHM). The combination of high compression ratio (28×) and short pulse width represents a significant improvement over that attained in the wave-breaking-free regime.     

Compression dynamics for phase-modulated few-cycle pulses

A theory of compression of short optical pulses with quadratic phase modulation in a dispersive medium has been developed. The results of numerical simulation of the equation for the light wave field are reported. The conditions are found at which a pulse is compressed to one oscillation period. The optimal phase modulation index providing the maximum pulse compression is estimated.     

XPM-induced pulse compression in birefringent dispersion decreasing fiber

The pulse compression induced by cross-phase modulation in birefringent dispersion decreasing fiber is discussed theoretically by solving the coupled Schrödinger equations which include the contribution of the high-order non-linear effects, and third-order dispersion. In particular, it is found that a high quality compressed signal pulse can be obtained by a pump pulse of low intense through the technique. The dependence of optimum compression on the non-linear factor N, time delay τ_d and the dispersive ratio f is also discussed in detail.     

Quasi-adiabatic compression of a plasma column by a longitudinal magnetic field

Approximate 1.5-dimensional MHD equations are derived that describe the quasi-adiabatic compression of a thin plasma column by a longitudinal magnetic field. The parameters of the compressed plasma are obtained analytically as functions of the initial conditions and longitudinal field. The stability of plasma compression against the Rayleigh-Taylor instability is investigated. It is shown that, in the Z-Θ-pinch geometry, increasing the longitudinal magnetic field makes it possible to achieve radial compression ratios of 20–30 without violating the cylindrical symmetry of the column. The possibility of thermonuclear ignition in a thin plasma column in a Z-Θ-pinch configuration is studied. The ranges of the initial plasma densities and temperatures and the initial lengths of the plasma column that are needed to achieve ignition in a plasma compressed by a factor of 20–30 are determined. The parameters of the electromagnetic energy source required to achieve such a high plasma compression are estimated.     

Difference-Frequency Generation Among Ultrashort Optical Pulses in Quasi-Phase-Matching Waveguides

A theoretical model of ultrashort pulse difference-frequency generation (DFG) is presented and developed with quasi-phase matching (QPM) gratings in the undepleted-pump, unamplified-signal approximation. An analytic solution to a case of ultrashort pulse pumped DFG process, including group-velocity mismatching effects and input pulses with frequency chirp and time delay, is obtained. The influences of group-velocity mismatching effects and input signal pulse parameters on the conversion efficiency and output converted pulse characteristics are analyzed and discussed. The results indicate that the conversion efficiency is increased due to the enhancement of pump and signal interaction. The output pulse is inevitable compressed under pulsed pumping and can be compensated by introducing the initial frequency chirp and time delay.     

Wave Breaking in a Class of Nonlocal Dispersive Wave Equations

Abstract

The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in di!erent physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which also incorporate physics of short wavelength scales. The model is identified by a renormalization of an infinite dispersive di!erential operator, followed by further specifications in terms of conservation laws associated with the underlying equation. Several well-known models are thus rediscovered. Wave breaking criteria are obtained for several models including the Burgers-Poisson system, the Camassa-Holm type equation and an Euler-Poisson system. The wave breaking criteria for these models are shown to depend only on the negativity of the initial velocity slope relative to other global quantities.     

色散缓变光纤中增益系数的取值对皮秒脉冲孤子效应压缩的影响

从描述皮秒光脉冲在色散缓变光纤(FSDD)中所满足的非线性Schro¨dinger方程(NLS)出发,数值模拟了高阶皮秒脉冲在增益系数取值不同的色散缓变光纤中的孤子效应压缩,研究分析了增益系数所产生的影响。计算结果表明,对于孤子阶数确定的光脉冲,增益系数有一最佳取值范围,对应于孤子效应压缩的参量———脉冲压缩比有最佳值。讨论了初始啁啾的影响。