Optimization of the power ratios of the bidirectional pumping at two wavelengths for erbium-doped fiber amplifiers

The gain and noise factor spectra of erbium-doped fiber amplifiers with pumped according to a copropagating three-level scheme and according to a counterpropagating quasi-two-level scheme in the regime of unsaturated gain in the C band have been simulated numerically. It has been shown that, at the total pump power up to 30 mW and at the optimized power ratio of the copropagating and counterpropagating pumps, the inhomogeneity of the gain in the C band does not exceed 0.25 dB at the noise factor of 4.2–4.7 dB.     

Influence of polarization mode dispersion value in dispersion-compensating fibers on the polarization dependence of Raman gain

Polarization mode dispersion (PMD) of amplifying or transmitting fibers may significantly change the polarization dependence of Raman gain. Experimental results are presented that show low polarization dependence of the Raman gain in dispersion-compensating fibers with high PMD values for both copropagating and counterpropagating pumping configurations. The measured data demonstrate that it is possible to avoid the need for depolarization of a pump source in Raman amplifiers.     

光纤拉曼放大器中增益的偏振相关特性研究

提出了一种改进的、可用于计算偏振相关拉曼增益的光纤拉曼放大器的非线性耦合波方程。建立了单模双折射光纤拉曼增益的数学模型,分析了线偏振抽运光以与光纤快轴成45°激励的单模双折射光纤拉曼放大器模型与实际具有随机双折射的光纤拉曼放大器的拉曼增益偏振相关特性的等价性。基于上述模型,提出了一个可定量表征单模光纤偏振模色散统计特性的拉曼增益偏振相关因子,用以替代常规的光纤拉曼放大器非线性耦合波方程中的偏振相关因子。计算结果与已报道文献的实验数据非常吻合。同时对抽运增益在同向和反向抽运方式下截然不同的增益偏振相关特性给出了合理的解释。     

Fiber Bragg gratings for dispersion compensation in optical communication systems

Dispersion compensating fibers (DCF) are the most widely used technology for dispersion compensation. A DCF without Raman amplification introduces extra loss in the system, thus increasing the need for gain in the discrete amplifiers and degrading the noise performance. The idea to additionally use the DCF as a Raman gain medium was originally proposed by Hansen et al. in 1998. [1] This was quickly followed by Emori et al., who demonstrated a broadband, loss less DCF using multiple-wavelength Raman pumping. [2] DCF is a good Raman gain medium, due to a relatively high germanium doping level and a small effective area. To get sufficient gain with a reasonable pump power, a discrete Raman amplifier has to contain several kilometers of fiber, adding extra dispersion to the system that must be handled in the overall dispersion management. Dispersion compensating Raman amplifiers integrates two key functions: dispersion compensation and discrete Raman amplification into a single component.     

Gain ripple minimization in fiber Raman amplifiers based on variational method

In this paper, the variational method is employed for minimizing the gain ripple of multi-wavelength fiber Raman amplifiers. The variance of gain spectrum of the fiber Raman amplifier is regarded as the cost function, restriction on total pump power and average gain is given as the constraints of the minimization problem. It is shown that the minimization problem with any necessary constraints on the pump powers, average gain and signal to noise ratio, is reduced to a two-point boundary value problem. The method gives the entire possible local and global solutions. The method is applied to different examples of fiber Raman amplifiers with different lengths from 25 km to 100 km and different numbers of pumps from 4 to 20 to determine the pump powers and wavelengths for minimum gain ripple. It was obtained for a 100 km fiber Raman amplifier the gain ripple can be about 0.1 dB with on-off gain more than 20 dB.     

Gain-clamped discrete Raman amplifier with suppressed low-frequency relative intensity noise pump-to-signal transfer

We demonstrate an optically gain-clamped discrete Raman amplifier with a suppressed low-frequency relative intensity noise transfer from pump sources to an input amplified signal, which is accomplished by employing a cascaded second-order Raman fiber resonator as an optical amplification. The input signal dynamic range for a 3-dB gain compression is controllable without affecting the clamping level. In addition, we find that the Raman net gain is unsusceptible to fiber parameters such as the gain and attenuation coefficients at the pump, first-, and second-order Stokes lines. These characteristics fit our proposed gain-clamped discrete Raman amplifier for practical deployment although it works at the expense of the efficiency.     

多波长抽运宽带光纤拉曼放大器的数值模拟与优化

采用平均功率分析算法对多波长抽运宽带光纤拉曼放大器进行了细致的数值模拟，并根据多抽运拉曼增益谱的特点和不同抽运波长对增益斜率的不同影响提出了一种新的有效的抽运优化算法，并利用这种方法对10波长抽运的光纤拉曼放大器进行了优化，获得了70nm带宽上增益谱波动低于0．5dB的结果。     

The moment method for fiber Raman amplifier gain ripple minimization

We aim to propose a novel fiber Raman amplifier modeling based on the moment method, which is previously introduced for modeling the inhomogeneous Erbium doped fiber amplifiers and recently employed to analyze the fiber Raman amplifier with continuous pump spectrum. In this model, the number of governing equations is independent of the number of signals and according to the degree of accuracy it is proportional to the number of pumps. This method is employed to analyze the Raman fiber amplifiers with an arbitrary input signal line shape and to minimize the gain ripple of the fiber Raman amplifier with respect to the pump powers and pump frequencies.     

分布式光纤拉曼放大器在长距离光传输系统中的优化设计

同时考虑接收光信噪比(OSNR)及非线性失真影响，对分布式光纤拉曼放大器在长距离光传输系统中的最优抽运方式进行了研究.利用变分法原理获得了在不记双瑞利背散射(DRB)影响时的最优信号功率分布函数——均匀分布，但考虑双瑞利散射影响时则不存在解析的最优分布函数.在分别考虑长、短光纤跨距的情况下，比较了三种具有代表性的分布式光纤拉曼放大方式，即双向二阶拉曼抽运、双向一阶拉曼抽运和拉曼+掺铒光纤放大器混合放大方式的性能.指出通过优化一阶抽运波长以及一阶到二阶抽运功率比，对称结构的双向二阶抽运在绝大部分情况下可以在 关键词： 光纤拉曼放大器 双瑞利背散射 变分法 光纤非线性     

双向抽运拉曼光纤放大器性能的研究

对双向抽运拉曼光纤放大器(RFA)的噪声特性、增益饱和及抽运功率转换效率进行了详细研究。结果表明,双向抽运拉曼光纤放大器的噪声特性介于前向抽运与后向抽运之间,但主要取决于前向抽运方式所导致的噪声特性;双向抽运方式的饱和功率低于单向抽运方式的饱和功率,同前向抽运与后向抽运提供的增益比例有关;双向抽运方式的抽运功率转换效率同信号光功率及前、后向抽运提供的增益有关,当信号光功率较低时,增加前向抽运的比例可取得较高的抽运功率转换效率,而信号光功率较高时,增加后向抽运的比例可取得较高的抽运功率转换效率。研究一种配置(情况3)的双向抽运拉曼光纤放大器,可以完全补偿100km传输线路的损耗(包括无源器件的损耗),最低光信噪比为30．21dB。     

多波长双向抽运光纤拉曼放大器的优化设计

通过合理分析提出了便于计算多波长双向抽运光纤拉曼放大器信号及噪声功率的实用数值模型,给出求解信号和噪声功率的快速算法。在定义抽运方向度为前向抽运功率与总抽运功率值的比值后,通过对计算结果的分析发现信道平均放大自发辐射噪声功率随着抽运方向度的提高而单调递减;而信道平均双重瑞利散射噪声功率相对抽运方向度的变化曲线始终成U字形。不同的增益下存在对应的最优抽运方向度,在此抽运方向度下放大器总噪声最低。进而考虑在信号非线性失真的条件下提出了抽运方向度优化的衡量指标。优化后的多波长双向抽运方式不仅能保证对所有信道的平坦放大,而且其综合性能明显高于后向抽运方式。     

掺铒光纤放大器中抽运问题的理论分析

依据掺铒光纤放大器的速率方程和光传输方程,在不计放大自发辐射的情况下,得出了抽运功率和信号增益在放大器中沿光纤分布的隐函形式的解析表达式,并利用数值模拟对三种抽运方式下的放大器特性进行了分析。     

Suppression of pump-to-Stokes relative intensity noise transfer in Raman fiber laser by injection of modulated signal

A feasible approach is theoretically demonstrated that suppresses the relative intensity noise (RIN) transfer from pump sources to the proposed Raman fiber laser (RFL) output at the first-order Stokes line. The technique is accomplished by injecting a modulated signal at second-order Stokes shift from the pump wavelength according to the monitored RFL output, which indirectly consumes the pump power fluctuations and results in suppression of the RIN transfer to the RFL output. With the RFL used as a pump source for co-pumped Raman fiber amplifiers, further calculation results show that the Q-factor penalty due to RIN transfer can be dramatically reduced.     

Polarization switching of stimulated Raman scattering in optical fibers by dual-frequency pumping

Experiments are presented showing that under dual-frequency, orthogonal-polarization pumping, stimulated Raman scattering in optical birefringent fibers can be suppressed in one of the two fiber axes. For relatively small-frequency spacing and group-velocity mismatch between the pumps, Stokes light is suppressed along the polarization direction of the highest-frequency pump, owing to the orthogonal component of the Raman gain.     

交叉增益调制型波长转换器噪声特性的研究

对基于半导体光放大器的交叉增益调制型波长转换器相向和同向两种工作方式进行了研究。实验上分别实现了两种工作方式在1550nm波段的波长转换,比较了相同外部条件下两种工作方式的噪声特性,在全面考虑放大自发辐射噪声及其消耗载流子,增益谱的色散性和有源区内部损耗等因素的基础上,运用放大器的分段模型,计算了不同条件下两种方式的输出噪声功率,结果表明：相向型工作方式受放大自发辐射噪声的影响要远大于同向工作方式,输出放大自发辐射噪声功率的大小主要取决于载流子浓度的高低,而载流子空间分布的不均匀程度则决定两种工作方式输出噪声功率的差值大小。     

双重瑞利散射导致的多路干涉噪声对光纤喇曼放大器噪声系数的影响

在没有对喇曼增益分布做任何假设的情况下,利用所推导的光纤喇曼放大器噪声系数的解析表达式,研究了不同光纤长度、不同信号输入功率、不同增益、不同瑞利散射下双重瑞利散射导致的多路干涉噪声对喇曼放大器噪声系数的影响.结果表明随着光纤长度,信号输入功率、喇曼增益和瑞利散射的增加,多路干涉噪声对噪声系数的劣化越严重.但通过合理的优化光纤长度、控制喇曼增益可以取得噪声和增益间的最佳平衡.     

掺铒光纤放大器的理论模拟与全局分析

基于Giles模型并考虑了ASE噪音,对各种泵浦方式下的掺铒光纤放大器(EDFA)进行了数值模拟.提出了一种新的分析方法(增益噪音指数全局分析法),直观有效地分析了EDFA的增益和噪音指数与掺铒光纤长度和泵浦功率的依赖关系,并对各种EDFA的性能作了全面的比较.     

Utilization of stimulated Raman Scattering as secondary pump on hybrid remotely-pump l-band Raman/erbium-doped fiber amplifier

An L-band remotely-pumped erbium-doped fiber amplifier incorporating a secondary pumping scheme utilizing stimulated Raman Scattering (SRS) was demonstrated. 1423 nm Raman laser was employed to generate SRS which became the secondary pump source. The amplifier displayed excellent gain of up to 27.3 dB at 1570 nm for −30 dBm input. Noise figures were also kept to a minimum, with the highest figure measured at 11 dB which was influenced by imperfection of the C/L coupler utilized in this architecture. Overall transmission performance was measured as well and demonstrated an encouraging outcome with gain as high as 24 dB while the noise figure was maintained at about 11 dB. The L-band signal amplification was also contributed by the stimulated Raman scattering along the transmission fiber. The outcome of this study emphasized the feasibility of secondary pumping scheme using SRS in L-band gain enhancement.     

Flat gain spectrum design of Raman fiber amplifiers based on particle swarm optimization and average power analysis technique

In this work, the modified particle swarm optimization is used as an optimization tool to determine the set of wavelengths and power levels of pumps that delivers a flat gain spectrum for Raman fiber amplifiers. The average power analysis technique is used as a numerical method to solve the coupled Raman amplifier equations. By combining the modified particle swarm optimization and average power analysis technique an efficient algorithm for the design of flat-gain-spectrum broadband Raman fiber amplifiers is constructed. Application of this algorithm to the design of flat-gain-spectrum broadband Raman fiber amplifiers shows that the design efficiency of the new method is improved by 1-2 orders of magnitude compared with similar implementations previously reported in the literature. A 4-backward-pump gain-flattened Raman amplifier with bandwidth of 100-nm and maximum gain ripple of <1.0 dB is designed to demonstrate the technique.     

General and effective dynamic gain spectrum control of broadband raman amplifiers with multi-wavelength pumping

An effective feedback algorithm is proposed to dynamically control the gain spectra of multi-wavelength pumped broadband Raman amplifiers. Based on Raman coupling power equations, a simple saturation factor is introduced to achieve the adjusting matrix. By using this method, efficient pump adjustment can be carried out to accomplish wide-range dynamic gain spectrum control (larger than 22 dB dynamic range) as well as automatic gain clamping even for 90 nm bandwidth, highly-saturated RAs. Moreover, this algorithm can be well applied to different fiber types as well as pumping schemes. Some useful guidelines are also demonstrated.