Influence of Raman effects in wavelength-division multiplexed soliton systems

Taking into account the delayed Raman response, an expression for the collision-induced frequency shift is derived. In a wavelength-division multiplexed soliton system, solitons undergo cross-frequency shifts owing to collisions, which leads to timing jitter for transmission systems with bit rates of more than 40 Gbits/s per channel.     

Analysis of soliton collisions in a wavelength-division- multiplexed dispersion-managed soliton transmission system

Timing jitter induced by soliton collisions is the leading nonlinear penalty in wavelength-division-multiplexed (WDM) dispersion-managed soliton transmission. Through analysis and numerical simulations we show that consecutive complete collisions together with partial collisions at the system output cause approximately the same amount of timing shift as partial collisions at the system input. We further show that the worst-case timing shift diverges logarithmically with the total number of WDM channels and linearly with the total transmission distance. However, the probability for such worst cases to occur decreases exponentially with channel spacing, total number of WDM channels, and transmission distance. We conclude that only the effects caused by adjacent channels need to be considered in a high channel count WDM system.     

Chirped soliton interaction in strongly dispersion-managed wavelength-division-multiplexing systems

We theoretically analyze nonlinear interactions between chirped solitons in dispersion-managed wavelength-division-multiplexing (WDM) systems. We employ the perturbation method to evaluate frequency and chirp shifts caused by collisions among different WDM channels. It is shown that a chirped soliton suffers less frequency shift and time displacement than an ideal soliton, indicating its potential applicability for WDM systems.     

Dissipative Kerr solitons in optical microresonators with Raman effect and third-order dispersion

Using the mean-field normalized Lugiato–Lefever equation, we theoretically investigate the dynamics of cavity soliton and comb generation in the presence of Raman effect and the third-order dispersion. Both of them can induce the temporal drift and frequency shift. Based on the moment analysis method, we analytically obtain the temporal and frequency shift,and the results agree with the direct numerical simulation. Finally, the compensation and enhancement of the soliton spectral between the Raman-induced self-frequency shift and soliton recoil are predicted. Our results pave the way for further understanding the soliton dynamics and spectral characteristics, and providing an effective route to manipulate frequency comb.     

Soliton collisions in dispersion-managed wavelength-division-multiplexed systems

We show that collision-induced frequency shifts in wavelength-division-multiplexed (WDM) soliton transmission systems are strongly suppressed with increasing dispersion management. We predict new oscillations in the residual frequency shift response, owing to the relative motion induced by the dispersion map, and demonstrate a direct correlation between these oscillations and the modified soliton-collision dynamics. Simple analytical expressions for the oscillation minima are obtained, and implications for WDM soliton system design are discussed.     

Deterministic Raman crosstalk effects in amplified wavelength division multiplexing transmission

We study the deterministic effects of inter-pulse Raman-induced crosstalk in amplified wavelength division multiplexing (WDM) optical fiber transmission lines. We show that the dynamics of pulse amplitudes in an N-channel transmission system is described by an N-dimensional predator-prey model. We find the equilibrium states with non-zero amplitudes and prove their stability by obtaining the Lyapunov function. The stability is independent of the exact details of the approximation for the Raman gain curve. Furthermore, we investigate the impact of cross phase modulation and Raman self and cross frequency shifts on the dynamics and establish the stability of the equilibrium state with respect to these perturbations. Our results provide a quantitative explanation for the robustness of differential-phase-shift-keyed WDM transmission against Raman crosstalk effects.     

非均匀系统中非自治孤子的色散和非线性管理

基于包含自发拉曼散射和外电光调制效应的非自治非线性薛定谔方程,采用简单的变换方法,解析研究了三种非均匀系统中非自治孤子的管理和传输。结果发现,在非均匀的非线性渐增或色散渐减光纤系统中都存在精确的啁啾非自治孤子解,都可以实现孤子的放大和压缩,但具有不同的速度、频移和啁啾特性;而在非均匀的色散和非线性均渐减光纤系统中,可以支持无啁啾的非自治孤子,该孤子具有不变的脉宽和振幅以及振荡衰减的速度,孤子的频移仅由自发拉曼散射决定。同时,数值模拟结果进一步证实在三种非均匀管理系统中都可支持非自治孤子的传输。该研究结果为实际非均匀孤子管理系统中实现孤子的压缩和传输提供了理论依据。     

Simulative analysis of soliton-based DPSK transmission system

The effectiveness of the conventional dispersion compensation techniques: DCF, FBG and OPC to use with soliton transmission is presented. The frequency shifts of solitons induced by collisions between different channels in a soliton WDM system can be reduced by dispersion compensation. The reduction mechanism applied is the cancellation of the shifts generated in both normal and anomalous dispersion regimes. It is analyzed that phase jitter can be reduced by the use of midway spectral inversion.     

Observation of a Raman-induced interpulse phase migration in the propagation of an ultrahigh-bit-rate coherent soliton train

Coherent soliton packets generated in a passively mode-locked fiber laser are transmitted through 23km of dispersion-decreasing fiber. We observe a shift of the phase difference between solitons that is due to intrapulse Raman scattering. We attribute the stability in propagation of these trains to a trade-off between minimizing soliton-soliton interactions by reduction of the pulse width and minimizing this Raman-induced phase migration, which can force the solitons into a deleterious attractive phase relationship. We are thus able to demonstrate the propagation of 177-Gbit/s soliton packets over a distance of 123 soliton periods.     

Raman response function for silica fibers

The commonly used Lorentzian form of the Raman response function for studying propagation of ultrashort pulses in silica fibers does not properly account for the shoulder in the Raman gain spectrum originating from the Boson peak. We propose a more accurate form of this response function and show that its predictions for the Raman-induced frequency shift should be in better agreement with experiments.     

Modified propagation equations for soliton transmission in a polarization-division multiplexing system

The modified coupled averaged propagation equations describing the orthogonally polarized soliton propagation in a random birefringent fibre are derived. These include the third-order dispersion and Raman shift terms. Using these equations, the effects of the third-order dispersion and Raman shift terms are found to reduce the soliton interactions in a polarization-division multiplexing transmission system. This revised version was published online in November 2006 with corrections to the Cover Date.     

非自治拉曼多色孤子的管理和传输

以变系数的非自治非线性薛定谔方程为模型,考虑了一种色散、非线性和自发拉曼散射效应管理下的非自治系统,通过简单变换显式给出了该系统的精确非自治拉曼多色孤子解。基于精确孤子解,解析研究了该拉曼多色孤子在非自治管理系统中的演化特性,发现孤子的中心位置、波数与色散和非线性以及拉曼效应有关,而孤子频移仅与拉曼效应的参数决定,拉曼效应主导了非自治孤子的自频移,引起了孤子的频移在传输过程中不断的发生变化,导致了孤子的多色性。另外,我们数值讨论了该非自治孤子的传输稳定性,结果表明:该非自治拉曼多色孤子在有限的扰动下具有较好的稳定性。     

光相位共轭对分布放大明孤子传输的控制作用

应用数值分析方法研究了在由分布式掺饵光纤放大器级联的传输线中利用反相位、非等振幅输入和光相位共轭器等对孤子间的相互作用和孤子自频率漂移的削弱作用。结果表明,反相对相位、非等振幅输入和光相位共轭器的联合作用可以几乎完全消除几个ps脉宽孤子间的相互作用和孤子自频率漂移,避免了孤子间的能量交换,使孤子光脉冲在由分布式掺饵光纤放大器级联的长距离传输线中稳定传输。     

Cross-phase modulation and multiwavelength adiabatic solitons

In an experimental demonstration of four-channel, wavelength-division-multiplexed repeaterless transmission over 235 km, adiabatic soliton propagation allows for precise spectral characterization of cross-phase modulation effects during initial soliton collisions. Theoretical predictions of the spectral shifts that occur are verified for ultrashort solitons. The relationship between the frequency shift and the initial pulse separation is confirmed by measurement of the bit-error ratio as the pulse spacing is varied at the fiber input. Adiabatic expansion of narrow solitons may help to alleviate the channel restrictions that are required for prevention of soliton collisions at the fiber input.     

Effect of filters on solition collisions in WDM systems with lumped amplifiers and periodically varying dispersion

The effect of frequency-guiding filters on soliton collisions in wavelength-division multiplexing systems with lumped amplifiers and periodically varying dispersion has been investigated. The evolution equations for the soliton frequency shift and time shift are derived. The numerical results indicate that the filters make the frequency shift resulting from soliton collision tend toward zero; thus the system performance is improved considerably.     

Hirota方程的怪波解及其传输特性研究

求出了高阶Hirota方程在可积条件下的一种精确呼吸子解,并基于此呼吸子解得到了Hirota方程的一种怪波解.在此怪波解的基础上研究了怪波的激发,发现对平面波进行周期性扰动可以激发怪波,对平面波进行高斯扰动可以更快地激发怪波,还可以直接在常数项上增加高斯扰动激发怪波.作为一个实例,采用分步傅里叶方法数值研究了在考虑自频移和拉曼增益时怪波的传输特性,自频移使怪波中心发生偏移,拉曼增益使得怪波分裂得更快,而且拉曼增益值越大怪波分裂得越快,但是拉曼增益对怪波的峰值强度没有明显影响.最后数值模拟了相邻怪波之间的相互作用特点,随着怪波之间距离的减小,怪波将合二为一,成为一束怪波,之后再分裂,并分析了拉曼增益和自频移对怪波相互作用的影响.     

孤子光纤中拉曼自频移效应的研究

首次报道孤子光纤中拉曼自频移效庆的研究结果。对满足孤子光纤色散关系条件时含损耗，拉曼延迟效应的广义非线性薛定谔方程进行了微扰分析。求得了拉曼自频移关系表达式。发现改变光纤几何参数可以有效地控制孤子拉曼自频移。     

脉冲内拉曼散射影响下的孤子之间的相互作用及其控制

研究了脉冲内拉曼散射效应影响下的同相和反相相邻孤子脉冲之间的相互作用,分析了孤子之间的相互作用对定时抖动的影响和脉冲内拉曼散射效应对孤子频移的影响。研究结果表明:在脉冲内,在拉曼散射效应的影响下,同相基态孤子脉冲的周期性离合被破坏了,两孤子脉冲一次碰撞后一直处于排斥状态,并且在碰撞后自频移现象十分明显;反相孤子脉冲的影响则较弱,两孤子脉冲都向下降沿发生偏移。引入非线性增益可以有效地控制孤子之间的相互作用,抑制自频移效应和稳定孤子传输。     

波分复用孤子通信系统容量研究

在波分复用(WDM)孤子通信系统中,不同信道的孤子由于载波频率不一样而会发生周期性的碰撞,碰撞将引起孤子到达接收端时间的移动,这个现象限制着邻近信道的最小频率间隔和可以被复用的最大频率范围,即决定了WDM孤子通信系统的最大通信容量。