色散磁导率对异向介质中的调制不稳定性的影响

基于Drude模型研究了异向介质的色散磁导率对调制不稳定性的影响. 结果表明,在反常色散情形,赝五阶非线性在异向介质的负折射区中增大了调制频谱的范围及增益值,这与常规正折射介质中出现的现象正好相反;自陡峭效应在异向介质中有可能为负值,但无论正负,也无论在正折射区还是负折射区,它都抑制调制不稳定性的产生;二阶非线性色散效应在正、负折射区中分别促进和抑制调制不稳定性的产生. 在正常色散情形,由于二阶非线性色散效应的作用,使本来在常规正折射介质中不可能出现的调制不稳定性现象也能出现,这一特性为在正常色散区形成孤 关键词： 异向介质 调制不稳定性 色散磁导率 二阶非线性色散     

Modulation instability in silicon photonic nanowires

We demonstrate that strong modulation instability (MI) of copropagating optical waves can be observed in Si photonic nanowires with a length of only a few millimeters. We consider two distinct cases, namely one in which one wave propagates in the normal group-velocity dispersion (GVD) region and the other one experiences anomalous GVD, and a second case in which both waves propagate in the anomalous GVD region. In both cases we show that, for comparable optical powers, the peak value of the MI gain spectrum is 2 to 3 orders of magnitude larger than that achieved in optical fibers.     

Modulation Instability in Non-Kerr-like Optical Fibers near the Zero Dispersion Point

Modulation instability (MI) in non-Kerr-like optical fiber near the zero dispersion point is analyzed. Taking into account the fourth order dispersion, new regions of MI are found. The action of the self-steepening is not the same for each region of MI and critical modulation frequency.     

Generation of Bragg solitons through modulation instability in a Bragg grating structure

In this article, we consider the continuous wave (cw) propagation through the nonlinear periodic structure that consists of alternating layers of both positive and negative Kerr coefficients along the propagation direction. We investigate the modulational instability (MI) conditions required for the generation of ultrashort pulses for the nonlinearity management system. We study the occurrence of MI at the top and bottom edges of the photonic band gap (PBG) where the forward and backward propagating waves are strongly coupled because of the presence of the grating structure. We also study the MI when cw is detuned from the edges of the PBG into the anomalous and normal dispersion regimes. In addition, we discuss the existence of gap solitons for the nonlinearity management system in the upper and lower branches of the dispersion curve through the MI gain spectra. We observe the generation of higher order solitons in the nonlinear periodic structure when the input power is increased beyond a certain critical level. Finally, we discuss the generation of higher order Bragg grating solitons through the intensity evolution of the forward and backward propagating fields.     

Modulation Instability in Non Kerr-like Optical Fibers near the Zero Dispersion Point

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Modulation instability in metamaterials with fourth-order linear dispersion,second-order nonlinear dispersion,and three kinds of saturable nonlinearites

The linearized nonlinear propagation equation and its coefficients, gain spectrum of modulation instability (MI) in metamaterials (MMs) with fourth-order linear dispersion, second-order nonlinear dispersion, and three kinds of saturable nonlinearites, are analytically deduced by utilizing the linear stability analysis and Drude electromagnetic model. Then variations of gain spectra of MI with the normalized angular frequencies and the optical power densities are calculated in real units. In the negative refractive region, two kinds of gain spectra are discovered. The first (second) one is close to (far from) the zero perturbation frequencies and it corresponds to the lower (higher) normalized angular frequencies. Moreover, the second one has higher cutoff frequency, which is obviously beneficial to generation of high-repetition-rate pulse trains. While in the positive refractive region, only the first kind of gain spectra is found. With increase of the optical power densities, the peak gains and the spectral widths of MI increase before decrease, but they vary the most rapidly (slowly) for the exponential (conventional) saturable nonlinearities. The MI characteristics and their corresponding applications can be adjusted by several methods.     

Modulational instability in optical fiber with stochastic parameters and noninstantaneous response

We investigate analytically and numerically the modulational instability (MI) in optical fiber, where the effect of noninstantaneous nonlinear response as well as stochastic coefficients are taken into account. Applying the linear stability analysis and stochastic calculus, we show that the MI gain spectrum reads as the maximal eigenvalue of a constant matrix. In the limiting cases of small fluctuations, we give explicit expressions for the MI gain spectra. In the general configurations, we derive an explicit form of the effective matrix and compute numerically the maximal eigenvalue. The moment MI peak is enhanced and the delayed Raman response reduces the maximum MI gain caused by stochasticity both in anomalous and normal dispersion regimes. Numerical simulations of the full stochastic nonlinear Schródinger equation show that, the phenomenon of MI gives rise to periodic pulse arrays of waves train, as well as to a chain of peaks with continuously growing amplitudes.     

单模光纤中受激喇曼散射对调制不稳定性的影响

基于修正的非线性薛定谔方程，利用线性扰动理论和数值方法研究了单模光纤中的调制不稳定性.由于受激喇曼散射的作用，使得喇曼增益谱叠加到光纤中的调制不稳定性增益谱上.这样，原本调制稳定的光纤正常色散区也出现了调制不稳定性；而在反常色散区，随着初始功率的增加，常规的调制不稳定性增益谱的增益和频谱范围均增大，而喇曼增益谱的增益增大但其频谱范围基本不变，这样导致常规的不稳定区域逐渐侵入并最终掩盖喇曼增益区.数值模拟验证了解析结果的正确性，并证明了利用反常色散情形下的调制不稳定性可以产生超短脉冲序列，但这种脉冲序列的进一步传输将会出现喇曼孤子自频移现象.     

Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time

We investigated the spatiotemporal modulation instability (MI) in a medium with a non-instantaneous Kerr response in which the nonlinear contribution to the refractive index is governed by a relaxing Debye type equation. The expression for the MI gain spectrum in non-instantaneous Kerr medium is obtained, which clearly reveals the influence of the finite time of the nonlinear response (relaxation effect) on the spatiotemporal MI. It is shown that, due to the relaxation effect, the spatiotemporal MI can appear for the case of anomalous dispersion and defocusing nonlinearity, while it cannot appear in instantaneous Kerr medium for the same case, and a new MI gain spectrum appears, adding to the conventional MI gain spectrum similar to that in an instantaneous Ker medium. In addition, the bandwidth of MI gain spectrum is extended and the maximum MI gain is reduced with increasing of the relaxation time. Interestingly, spatiotemporal MI can appear for any spatial frequencies in non-instantaneous Kerr medium for any combination of dispersion and nonlinearity. We have performed an experiment of MI in carbon disulfide (CS₂), a typical non-instantaneous Kerr medium, which shows quantitative agreement with the theoretical analyses.     

Investigation of dispersion characteristic in MI- and MII-type single mode optical fibers

Dispersion characteristic of MI and MII type single mode optical fibers is analytically investigated. For this purpose modal analysis of these fibers to obtain possible wave vectors for given system parameters are done. Then using numerical evaluation of the presented analytical relations, chromatic and waveguide dispersions are calculated. The effects of geometrical and optical parameters of the fibers on dispersion characteristics are investigated. In this analysis, we show that with increase of Δ (optical parameter) for MI structure the slope of dispersion curve is decreased and the case is reversed for MII structure. Also, with rising of Q (geometric parameter) for MI structure the slope of dispersion curve is decreased and the situation is reversed for MII structure. Finally, we show that with boosting of R₂ for MII structure the slope of dispersion is increased. As a final result, our simulations show that small values for optical parameters are better in MII structure for multi-channel optical communications. In MI structure to obtain small dispersion slope, Q can be increased that is easy for fabrication in practice. Finally, Q and R₂ are suitable parameters for control of dispersion in the proposed structures.     

光子晶体光纤中调制不稳定现象与超连续光谱的产生

研究了光子晶体光纤中调制不稳定性效应.从非线性薛定谔方程出发，计算和分析了光子晶体光纤中反常色散区以及正常色散区内的调制不稳定性现象，详细讨论了超短脉冲的脉宽、峰值功率、高阶色散和高阶非线性效应（如脉冲内喇曼散射、自陡峭效应）对调制不稳定性产生的影响.结果表明：二阶色散对调制不稳定性的影响要远大于三阶色散，同时也发现随着初始脉冲宽度的减小，调制不稳定性旁瓣增大但是强度有所降低.另外还发现高阶非线效应如自陡峭和喇曼效应会在不同程度上抑制调制不稳定性.     

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.     

正三角型三芯光纤中等腰对称平面波的调制不稳定性分析

详细分析了正三角型三芯光纤中等腰对称平面波的调制不稳定性.等腰对称平面波即两芯中场完全相同,第三芯中场入射功率与其他两芯中不同的平面波,其存在的前提是入射光总功率(P)必须大于某最小值(P_(min)),该最小值取决于光纤的线性耦合系数和非线性系数.对一给定的总功率P≥P_(min),令一芯中的入射功率为P_1,其他两芯中入射功率均为P_2,有两种形式的场分布:一种是P_1始终大于P_2,随着P的增加,P_1越来越大,P_2越来越小,依线性稳定性分析方法,该场分布对应的增益谱主要特征与双芯光纤非对称平面波的增益谱相似;另一种是随着P的增加,P_1越来越小,P_2越来越大,使用同样的分析方法,发现该场分布下增益谱与双芯光纤非对称平面波增益谱截然不同,其显著特征是无扰动下,在正常和反常色散区域均可产生不稳定性增益,且在正常色散区域,零扰动频率对应的增益最强;另一方面,耦合系数色散对增益谱的影响在正常和反常色散区域都非常弱,这与其在双芯光纤中的影响截然不同.该结果对基于多芯光纤的模分复用系统非线性效应的研究具有一定的指导意义.     

Modulation instabilities in randomly birefringent two-mode optical fibers

Modulation instabilities in the randomly birefringent two-mode optical fibers(RB-TMFs) are analyzed in detail by accounting the effects of the differential mode group delay(DMGD) and group velocity dispersion(GVD) ratio between the two modes, both of which are absent in the randomly birefringent single-mode optical fibers(RB-SMFs). New MI characteristics are found in both normal and anomalous dispersion regimes. For the normal dispersion, without DMGD,no MI exists. With DMGD, a completely new MI band is generated as long as the total power is smaller than a critical total power value, named by Pcr, which increases significantly with the increment of DMGD, and reduces dramatically as GVD ratio and power ratio between the two modes increases. For the anomalous dispersion, there is one MI band without DMGD. In the presence of DMGD, the MI gain is reduced generally. On the other hand, there also exists a critical total power(Pcr), which increases(decreases) distinctly with the increment of DMGD(GVD ratio of the two modes) but varies complicatedly with the power ratio between the two modes. Two MI bands are present for total power smaller than Pcr, and the dominant band can be switched between the low and high frequency bands by adjusting the power ratio between the two modes. The MI analysis in this paper is verified by numerical simulation.     

变路径色散管理孤子系统中的调制非稳性研究

本文研究了变路径色散的孤子系统中的调制非稳性.首先采用微扰法对变路径色散的系统中的调制非稳性(MI)进行理论分析,解析出变路径色散系统中的MI特征根表达式,据此得到了色散管理孤子(DMS)系统的特征参数色散管理图强度与MI增益系数关系.研究结果表明,变路径色散系统中的色散管理强度大大影响MI增益的大小以及增益谱范围,而路径平均色散只影响MI增益谱范围.同时,本文结果还表明DMS较普通孤子系统有更强的抑制MI增益的能力.     

Polarization dependent dispersion and its impact on optical parametric process in high nonlinear microstructure fibre

High nonlinear microstructure fibre （HNMF） is preferred in nonlinear fibre optics, especially in the applications of optical parametric effects, due to its high optical nonlinear coefficient. However, polarization dependent dispersion will impact the nonlinear optical parametric process in HNMFs. In this paper, modulation instability （MI） method is used to measure the polarization dependent dispersion of a piece of commercial HNMF, including the group velocity dispersion, the dispersion slope, the fourth-order dispersion and group birefringence. It also experimentally demonstrates the impact of the polarization dependent dispersion on the continuous wave supercontinuum （SC） generation. On one axis MI sidebands with symmetric frequency detunings are generated, while on the other axis with larger MI frequency detuning, SC is generated by soliton self-frequency shift.     

受激拉曼散射对非线性介质波导的时空不稳定性影响

基于非线性包络方程我们研究了平面非线性介质波导中的时空不稳定性,得到了有拉曼散射效应情形下不稳定性调制的增益谱的表达式.结果表明在正常和反常两种群速度色散情形下,拉曼散射效应都会导致出现新的不稳定性区域,并且使原有的每一个谱分量的增益上升从而使谱的范围扩大.并通过分析反常色散情况下四种不同函数分布的非线性色散介质系数对不稳定性增益谱的影响,得到呈双曲函数分布的非线性色散介质最为理想.     

Modulation instability in negative refractive metamaterials with exponential saturable nonlinearity and self-steepening effects

Modulation instability (MI) in negative refractive metamaterials with exponential saturable nonlinearity and the self-steeping effect is investigated by using the standard linear stability analysis and the Drude electromagnetic model. The dispersion relation, instability condition, cut-off frequency, gain spectrum, and their corresponding dimensionless expressions are analytically deduced and then calculated. The results show that, the self-steepening effect will suppress MI by decreasing the cut-off frequency and the maximum gain. And the larger the power density ratio is, more slowly the cut-off frequency and the maximum gain decrease with increase of the self-steepening parameter. Although the sign of the self-steepening parameter does not influence MI but its absolute value must be smaller than a certain value. Depending on different self-steepening parameters, the cut-off frequency and maximum gain may decrease or increase before decrease with increase of the power density ratio. In particular, for large self-steepening parameters, the power density ratio may have a threshold value. When the power density ratio is under this threshold, MI will disappear.     

Asymptotic theory of plane soliton self-focusing in two-dimensional wave media

An asymptotic method is developed to describe a long-term evolution of unstable quasi-plane solitary waves in the Kadomtsev-Petviashvili model for two-dimensional wave media with positive dispersion. An approximate equation is derived for the parameters of soliton transversal modulation and a general solution of this equation is found in an explicit form. It is shown that the development of periodic soliton modulation, in an unstable region, leads to saturation and formation of a two-dimensional stationary wave. This process is accompanied by the radiation of a small-amplitude plane soliton. In a stable region, an amplitude of the modulation is permanently decreasing due to radiation of quasi-harmonic wave packets. The multiperiodic regime of plane soliton self-focusing is also investigated.     

A comparative study of the full dispersion relation, Compton dispersion relation, and Raman dispersion relation of a free-electron laser in helical wiggler and guiding magnetic fields

The full dispersion relation obtained for a free-electron laser in the presence of circularly polarized, periodic, static wiggler and guiding magnetic fields by the kinetic approach incorporating the particle trajectories is reduced to Compton and Raman regime approximations in the case of a tenuous electron beam. The temporal growth rate has been compared between the full dispersion relation and the Compton dispersion relation, as well as between the full dispersion relation and the Raman dispersion relation in the microwave region. The results show the maxima of growths in the full dispersion relation and the Compton dispersion relation, as well as the full dispersion relation and the Raman dispersion relation, are at the same locations, but the growth rates in both regimes are enhanced with respect to the full dispersion relation for the same plasma frequency and cavity parameters.