反向抽运光纤拉曼放大器偏振相关增益的数值计算

基于反向抽运方式的光纤拉曼放大器(FRA)的非线性耦合方程,采用数值计算的方法首次系统研究了单抽运多信号传输的FRA系统中各因素——光纤偏振模色散(PMD)、抽运光输入功率、抽运光波长、信号光输入功率、光纤长度及光纤损耗系数等对由抽运-信号拉曼相互作用所产生的偏振相关增益(PDG)的影响;比较了单抽运多信号FRA系统与单抽运单信号FRA系统中由抽运-信号拉曼相互作用所产生的PDG的大小;总结了各参数对降低由抽运-信号拉曼相互作用所产生的PDG的效果。研究结果表明,单抽运多信号FRA系统中的PDG主要由抽运-信号拉曼相互作用产生,并且光纤的PMD值和抽运光功率对PDG的影响较明显。     

Efficient Pump Depolarizer Analysis for Distributed Raman Amplifier With Low Polarization Dependence of Gain

This paper discusses a method of reducing the polarization dependence of gain (PDG) of a distributed Raman amplifier. Reducing its PDG is important for a Raman amplifier because it is higher than that of an erbium-doped fiber amplifier and can degrade transmission performance. Raman PDG is determined primarily by two factors, namely 1) polarization-mode dispersion (PMD) of the transmission fiber and 2) degree of polarization (DOP) of the pump source. The authors propose a simple analytical model to show the required pump light DOP for a given transmission fiber's PMD and the allowable PDG. For instance, a low pump DOP of 5% produces a low PDG of 0.2 dB under typical fiber PMD conditions, in which the analytical model agrees well with experiment. Subsequently, to achieve the required DOP, the pump source configuration is investigated in detail. The authors used one length of polarization-maintaining fiber (PMF) as an efficient pump depolarizer and evaluated its performance for various pump light spectra. It has been shown that the DOP following the depolarizer is determined simply by Fourier transformation of the pump light spectrum. The analysis in this paper has led to the important result that a Fabry-Perot laser diode pump with a short piece of PMF is effective in achieving a low pump DOP due to its multimode spectrum when the length of the PMF is properly adjusted for the longitudinal-mode spacing frequency. It has been verified that a Raman amplifier's PDG can be reduced by the proposed efficient depolarizer sufficiently for a PDG-reduced Raman amplifier repeater to be applicable to long-haul transmission systems     

Calculation of penalties due to polarization effects in a long-haulWDM system using a Stokes parameter model

We derive a Stokes parameter model to calculate the penalties due to the combination of polarization mode dispersion (PMD), polarization dependent loss (PDL), and polarization dependent gain (PDG) in long-haul, dense wavelength division multiplexed (WDM) systems. In this model, we follow the Stokes parameters for the signal and the noise in each channel instead of following the full time domain behavior of each channel. This approach allows us to determine the statistical distribution of penalties with up to 10⁵ fiber realizations and 40 channels. We validate this model to the extent possible by comparison to full numerical simulations. Using this model, we find that the interaction of PMD and PDL is the major source of penalties and that the effect of PDG is negligible in WDM systems with more than ten channels     

Polarization-dependent gain due to signal-signal Raman interaction in low-PMD fiber

We study polarization-dependent gain (PDG) due to signal-signal Raman interaction (SSRI). We find that SSRI-induced PDG can be significant when the fiber polarization-mode dispersion (PMD) is low. If the PMD from the discrete optical components is also small, the accumulated PDG grows almost linearly with the number of the span.     

双向多泵浦光纤拉曼放大器偏振相关增益研究

基于光纤拉曼放大器(FRA)的非线性耦合方程,采用数值计算的方法首次系统分析了双向多泵浦FRA系统中的偏振相关增益(PDG)特性。根据4个泵浦光源配置的不同,FRA有14种结构。首先整体分析了这14种不同FRA结构中PDG的特点;然后对其中一种结构FRA系统中PDG的特性进行了更具体的分析,包括泵浦-信号、泵浦-泵浦以及信号-信号拉曼相互作用所产生的PDG。研究结果表明,当泵浦总数目一定时,反向泵浦数目越多,其PDG均值越小;当泵浦总数目和反向泵浦数目都一定时,PDG的大小与反向泵浦光波长关系不大;双向多泵浦FRA系统中的PDG主要由泵浦-信号拉曼相互作用所产生的PDG决定。以上结果对有效降低双向多泵浦FRA系统中的PDG有重要的参考价值。     

Extending transmission distance of high-density WDM systems usingpost transmitter fiber Raman amplifiers

The authors investigate the behavior of multichannel signals in a high-density wavelength division multiplexing (WDM) system with the consideration of stimulated Raman scattering. A parameter to evaluate the depth of Raman crosstalk is provided, and the transmission distance limitation imposed by Raman crosstalk is analyzed. To extend the system transmission distance, a post-transmitter fiber Raman amplifier is used. The allocation of signal channels on the pump gain profile is discussed. It is found that there exists an optimum pump power which results in a maximum amplifier gain. The example shows that the transmission distance limitation imposed by Raman crosstalk can be extended by 20 km for a 30-channel system with 0.25-dB/km fiber loss     

A tunable wavelength conversion and wavelength add/drop scheme based on cascaded second-order nonlinearity with double-pass configuration

A selective and tunable wavelength conversion and wavelength add/drop scheme based on sum- and difference-frequency generation (SFG+DFG) is proposed, in which the concept of "double-pass" is introduced. An arbitrary channel can be dropped from a wavelength division multiplexing (WDM) signal and added to another WDM signal at arbitrary wavelength. The channel to be dropped is selected and depleted (dropped) by adjusting the pump 1 through sum frequency generation (SFG) during the forward propagation. Subsequently, the difference frequency generation (DFG), taking place during the backward propagation, is employed to convert (add) the dropped channel to another channel in another WDM signal by adjusting the pump 2. For the dropped and added channel, the phase matching of SFG and DFG are nearly perfect and the theoretical expressions are derived under the assumption that the two pumps are undepleted. The power of pump 1 is optimized to deplete the dropped channel completely, while that of pump 2 is chosen to maximize the output power of the added channel. Numerical calculations are performed to investigate the propagation of the other channels whose phase is mismatched. To suppress the crosstalk, the spacing of the WDM channels is chosen to be 0.2 nm (25 GHz). We have also compared our scheme with others (such as the single-pass scheme and the double waveguide scheme) and shown that ours possesses several distinct advantages.     

Transient gain dynamics in saturated Raman amplifiers

This paper provides a detailed analysis of transient gain dynamics in saturated Raman amplifiers fed by wavelength division multiplexed (WDM) signals. Such dynamics are due to a pump saturation effect, known as pump-mediated signal-to-signal crosstalk, which is equivalent to the well-known cross-gain modulation in EDFAs. We provide for the first time a simple block-diagram model of the Raman amplifier, whose state is represented by the relative pumps depletion sensed by the signals. With such model, we are able to prove that the time constants of the Raman gain transients are of the same order as the pump–signal walk-off times. For counter-propagating pumps, the model is very accurate in predicting both the steady-state gain and the transient gain dynamics, with more than an order of magnitude improvement in computation time with respect to the direct solution of the signals and pumps propagation equations. The value of such model is therefore in the simulation of dynamic WDM networking scenarios in which the input powers have large swings in time. The model also extends to the co-propagating pump and well captures the time constants involved in the transients, although the accuracy in the predicted power levels is worse than that of the counter-propagating pump case.     

Adaptive dispersion equalization by monitoring relative phase shiftbetween spacing-fixed WDM signals

This paper proposes a novel adaptive dispersion equalization system that equalizes the temperature-induced dispersion fluctuation in long-span ultra-high-speed optical transmission systems. The system monitors the dispersion fluctuation by measuring the relative delay between two wavelength division multiplexed (WDM) signals, and equalizes the dispersion fluctuation by wavelength tuning. A variable-dispersion equalizer can be used instead of wavelength tuning. Adaptive equalization is successfully demonstrated in 40-Gb/s (8-ps-RZ pulses) 400-km transmission. Furthermore, the proposed equalization system is shown to be applicable to WDM systems that use dispersion and dispersion slope compensation. Since the sensitivity to the dispersion fluctuation is improved by extending the wavelength spacing of the signal and monitor channels, the system is shown to operate even when polarization-mode dispersion (PMD) of the transmission fiber must be taken into account     

高双折射取样啁啾光纤光栅的研究与应用

为实现高速光纤通信系统中的偏振模色散(PMD)补偿,提出了基于高双折射线性啁啾光纤光栅(Hi-BiLCFBG)的线性应变梯度悬臂梁作为PMD补偿器,同时考虑到波分复用(WDM)系统中不同信道PMD值不同,提出了取样啁啾(CSP)与周期啁啾(CGP)的等效,利用带有CSP的高双折射取样光纤光栅(Hi-Bi SFBG)制成多信道PMD补偿器,不同信道等效的啁啾系数不同,从而可同时实现多个信道的PMD补偿。实验中,实现了40Gb/s的传输系统中最大58.6 ps的差分群时延(DGD)补偿,补偿后,信号眼图张开度有明显改善,从而证明了该PMD补偿器的有效性与可行性。     

Bidirectional unrepeatered 43 Gb/s WDM transmission with C/L band-separated Raman amplification

A novel wavelength arrangement using C- and L-band-separated Raman preamplification is proposed for application to bidirectional unrepeatered transmission systems operating with multiple 43 Gb/s channels. The proposed wavelength allocation makes it possible to greatly mitigate Raman gain depletion by the counter-propagating signals. The authors have achieved bidirectional unrepeatered transmission of 32 /spl times/ 43 Gb/s channels (= 1.28 Tb/s) over 200 km with Raman preamplifiers using the proposed technique. They found that the system performance of bidirectional transmission with C/L band-separated Raman preamplification is degraded by nonlinear interactions between the high power Raman pump lights and the WDM signals. The root cause can be described in terms of nondegenerate four-wave mixing induced by beating between the WDM signals and two longitudinal modes of the Raman pump light. A solution avoiding ND-FWM was demonstrated in a 32 /spl times/ 43 Gb/s transmission experiment.     

A generalized suboptimum unequally spaced channel allocationtechnique. I. In IM/DD WDM systems

Four-wave mixing (FWM) is the most serious fiber nonlinearity associated with low-input optical power levels in long-haul multichannel optical systems employing dispersion-shifted fiber. To reduce the crosstalk due to FWM, a generalized suboptimum unequally spaced channel allocation (S-USCA) technique is proposed and investigated. Even though the developed technique is useful in combating FWM crosstalk in wavelength division multiplexing (WDM) lightwave systems with up to 12 channels, its main virtue is in designing multichannel WDM lightwave systems with more than 12 channels. Comparisons of power penalty due to FWM between equal channel spacing (ECS) systems and the S-USCA systems are presented. It is shown that for an intensity modulation/direct detection (IM/DD) transmission system operating in an optical bandwidth of 16 nm with 0 dBm (1 mW) peak optical input power per channel, while a conventional ECS WDM system with 0.84-nm channel spacing cannot even achieve a bit-error rate (BER)=10^-9, the suboptimum technique developed in this paper, for the same minimum channel spacing, can achieve a BER=10^-9 with an FWM crosstalk power of less than 1 dB at the worst channel in a 20-channel WDM system     

分布拉曼光纤放大的实验研究

采用符合ITU-T标准的G波段40信道波分复用(WDM)光源对分布式拉曼放大器(DRA)的特性进行了实验研究。对不同抽运方式及不同光纤长度的分布式拉曼放大器性能作了较为详细的报道。在抽运功率相同的条件下，选用50km单模光纤对比研究了不同抽运方式的拉曼放大器增益和噪声。通过对不同光纤长度的分布式拉曼放大器的实验研究发现，在较低抽运功率且输入信号功率较低的情况下，随着光纤长度增加，拉曼增益也增加，有效噪声系数减小。研究了分布式拉曼放大器对波分复用通信系统信噪比的改善，实验发现不同抽运功率下，拉曼放大器对系统信噪比的改善随抽运功率增加而增加，但是不成线性关系，而且最终会出现饱和。     

Signal light amplification by stimulated Raman scattering in anN-channel WDM optical fiber communication system

The use of forward and backward Raman amplification in an N -channel wavelength-division-multiplexing (WDM) optical-fiber communication system is analyzed. Analytical expressions for the signals, the pumps, and the amplified spontaneous scattered power (ASSP) are presented. The crosstalk among the signal channels is analyzed in terms of system parameters. It is found that the crosstalk is negligible while low pump power is used and becomes significant if high pump power is used. The signal-to-ASSP ratio can be improved by increasing pump power; however, the improvement is small when pump power is already high. A 300-km repeater spacing with more than 20-dB signal-to-ASSP ratio is calculated     

Raman-enhanced regenerative ultrafast all-optical fiber XPM wavelength converter

The Raman gain enhancement of a regenerative ultrafast all-optical cross-phase modulation (XPM) wavelength converter (WC) is quantitatively investigated and experimentally demonstrated to operate error free at 40 and 80 Gb/s. The regenerative nature of the converter is shown by experimentally demonstrating a negative 2-dB power penalty at 80 Gb/s. It is also shown that the Raman gain greatly enhances the wavelength conversion efficiency at 80 Gb/s by 21 dB at a Raman pump power of 600 mW using 1 km of highly nonlinear fiber. An analytical theory based on nonlinear phase-shift enhancement of the fiber-effective length is presented and shows the relationship between a nonlinear enhancement and Raman gain as a function of pump power and fiber design parameters. Measured parameters are used in the analytical model, and a good fit between experiment and theory is shown for two different types of fiber: one dispersion-shifted and one highly nonlinear fiber. The ultrafast response time of Raman gain makes this technique applicable to fiber-based ultrafast WCs. In addition, the applicability to other nonlinear fiber wavelength conversion techniques is discussed.     

Dependence of cross-phase modulation on channel number in fiber WDMsystems

The phase term appearing in the expression for cross-phase modulation due to the optical Kerr effect depends on the sum of the powers carried by each wavelength channel. For this reason, one might expect that the amount of cross-phase modulation would increase with increasing channel number, causing increased interference among channels and hence limiting the total number of channels that a WDM system can support. However, computer simulations of multichannel systems have shown no change in signal distortion as the number of wavelength channels is increased from four to eight. In a simulated three-channel system, the signal distortion of the central channel approaches that of a single-channel system as the wavelength separation is increased to approximately 2 nm. Thus, even a moderate amount of dispersion tends to cancel out the influence of cross-phase modulation, so that beyond a certain wavelength spacing, additional channels do not interfere with the channel under consideration. From these observations, we conclude that cross-phase modulation does not limit the number of wavelength channels that a single optical fiber can support. However, self- and cross-phase modulation are not the only nonlinear effects influencing fiber lightwave systems. Stimulated Raman scattering tends to transfer optical power from short-wavelength channels to channels operating at longer wavelength, degrading their signal-to-noise ratio. The efficiency of this process increases with increasing wavelength spacing. Clearly, a compromise needs to be reached between the conflicting requirements imposed by the optical Kerr effect and by stimulated Raman scattering     

宽带平坦增益光纤喇曼放大器泵浦配置的快速搜索算法

本文提出了一种用于宽带平坦增益喇曼光纤放大器的泵浦配置的快速搜索算法,该算法只需要指定放大器采用的介质光纤参数、信号功率水平、放大器的目标增益和允许采用的泵浦数,就能够搜索到最小均方误差意义下泵浦的配置结果.算法利用最小均方差意义下的最佳逼近,把搜索波长的遗传算法和确定功率积分的具有线性约束条件的二次型凸规划问题结合起来,从而加快了搜索速度.     

Compensating unflattened WDM chips spectra using dynamic backward-pumped fiber Raman amplifiers technology

Fiber Raman amplifiers (FRAs) with multiple pumps are proposed to realize dynamic gain equalization for a spectral chips signal with a non-flattened broadband light source (BLS) in a spectrum-sliced wavelength-division multiplexing (WDM) network. In FRAs with multiple pumps, the gain profile can be adjusted via appropriate specification of the relative position of the pump wavelengths and the power of the pump waves. This paper combines a pump-power control algorithm and a genetic algorithm (GA) to establish the optimal pump spectrum for any specified gain spectrum in the WDM system. The method flattens the power spectra of WDM chips by identifying the optimal pump wavelengths and pump power of backward-pumped FRAs. It avoids the conventional requirement for time-consuming trial-and-error adjustments or intensive numerical simulations. Simulation results show that the scheme is simple, effective, and applicable for various BLSs in a spectrum-sliced WDM transmitter.     

Mitigation of polarization-mode dispersion in multichannel lightwave transmission systems

We propose a novel polarization-mode dispersion (PMD) compensation scheme for wavelength-division-multiplexing (WDM) systems, in which many WDM channels share one or a few PMD compensators at receiver site. It is shown, both analytically and numerically, that this scheme can achieve virtually the same performance as that using per-channel-based PMD compensation.     

Transmission of optical communication signals by distributed parametric amplification

For the first time, to the authors' knowledge, distributed parametric amplification (DPA), i.e., the use of a transmission fiber itself for parametric amplification of communication signals is proposed and demonstrated. To account for the inevitable fiber loss, solutions were derived for the distributed amplifier, with either one or two pumps: They are obtained in terms of confluent hypergeometric functions. Low-penalty DPA of a 10-Gb/s nonreturn-to-zero (NRZ) signal over a 75-km dispersion-shifted fiber (DSF), is demonstrated by using only 66.5 mW of pump power. Three adjacent channels have been simultaneously transmitted, with little penalty due to nonlinear crosstalk. It is experimentally verified that DPA requires less pump power than distributed Raman amplification (DRA), for similar power penalties.