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.     

宽带喇曼放大器的快速优化设计方法

介绍了一种改进的宽带分布式多泵浦喇曼放大器（DMRA）优化设计方法.通过研究多波长后向泵浦的喇曼放大器传输方程，采用合理的近似得出了快速DMRA的一个简化理论分析模型.通过对模拟退火算法几个优化环节的改进，使其能够更快速地应用于DMRA的多峰值问题的优化设计.利用该方法重点对C+L波段约80 nm带宽范围的DMRA进行了优化，在80 km传输光纤上，设计实现了开关增益10 dB，相对平坦度小于0.12，增益起伏小于1 dB的DMRA.与其他的DMRA设计方法相比，该方法使用较少的泵浦数目就能获得同样的增益带宽及平坦的谱特性.     

An effective numerical method for gain profile optimizations of multi pumped fiber Raman amplifiers

In this paper, we have solved propagation equations of multi-pump fiber Raman amplifier using Runge–Kutta (RK 4th order) numerical method and pump power evolutions along with the fiber length. They are used to calculate the net gain and gain ripple by varying the input signals powers for different fiber lengths. The pump powers are optimized by genetic algorithm and resulting net gain and gain ripple are reported graphically as well as in tabular form. The optimum minimum gain ripple is 0.26 dB for 1 mW input signal powers for 50 km fiber length. By increasing the fiber length gain ripple increases to 0.5 dB for 0.1 mW input signal power. In comparison to other methods reported in the literature, our method is simple to implement and efficient for numerical design of Raman amplification in optical communication systems.     

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.     

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.     

Automatic gain control in Raman amplifier with multi-wavelength pumps

Automatic gain control method in Raman amplifier with multi-wavelength pumping scheme is presented. Monitoring of several channel power and feedback pump control is used in the gain control method. The condition to minimize the gain deviation is investigated by numerical simulation. Two monitoring channels are necessary to confine gain deviation in ±0.2 dB at two pumps C-band Raman amplifier. In the experiment, gain deviation of 1.5 dB is controlled to 0.2 dB at 38/40 channels drop, and fast suppression of transient gain excursion is achieved.     

Optimization of pump parameters for gain flattened Raman fiber amplifiers based on artificial fish school algorithm

In this work, a novel metaheuristic named artificial fish school algorithm is introduced into the optimization of pump parameters for the design of gain flattened Raman fiber amplifiers for the first time. Artificial fish school algorithm emulates three simple social behaviors of a fish in a school, namely, preying, swarming and following, to optimize a target function. In this algorithm the pump wavelengths and power levels are mapped respectively to the state of a fish in a school, and the gain of a Raman fiber amplifier is mapped to the concentration of a food source for the fish school to search. Application of this algorithm to the design of a C-band gain flattened Raman fiber amplifier leads to an optimized amplifier that produces a flat gain spectrum with 0.63 dB in band ripple for given conditions. This result demonstrates that the artificial fish school algorithm is efficient for the optimization of pump parameters of gain flattened Raman fiber amplifiers.     

Multi parameter optimization of Raman Fiber Amplifier using genetic algorithm for S band dense wavelength division multiplexed system

A simple genetic algorithm is implemented to perform multi parameter optimization of Raman Fiber Amplifier for 100 channel S band dense wavelength division multiplexed system at 25 GHz interval. A cost effective system using single Raman pump is investigated aiming at maximum average gain. The single counter propagating pump is optimized to frequency of 211.528 THz and 652.93 mW power level with optimum Raman fiber length of 44.064 Km. There is evidence to show that the optimum solution presents a small gain variation (less than 3 dB) over an effective bandwidth covering 197–199.475 THz. The optimized configuration enabled an adequate system performance in terms of acceptable Q-factor (19.52 dB) and BER (1.46 × 10⁻²¹).     

宽带喇曼/EDFA混合放大器的优化设计

采用改进的模拟退火算法对Raman/EDFA混合放大器的增益谱进行了优化，根据EDFA及Raman的功率传播方程获得了简洁的目标函数.通过对模拟退火算法几个优化环节的改进，使其能够更快速地应用于Raman/EDFA的多峰值问题的优化设计，可以在短时间内获得最优的放大器参量.计算结果表明选择合适的喇曼抽运波长和抽运功率，仅用4个反向抽运的分布式喇曼放大器加C波段的EDFA就可以获得C+L波段约70 nm的带宽、开关增益达到15 dB、最大增益波动小于1.2 dB的平坦增益谱，而且无需额外的平坦滤波器.     

Optimization of Raman gain spectrum using Lagrangian multiplier method

Based on Lagrangian multiplier method (LMM), the gain spectrum of distributed multi-pump Raman amplifier (DMRA) is optimized. Beside of governing rate equations in Raman amplifiers, we consider two applicable constrains on cost function for optimizing the gain spectrum. Because of more accurate and controllable designing of DMRAs, a maximum power for each input pump wave is considered as well as average gain value as two constrains. LMM reduces the optimization problem with constrains to solve a two-point boundary value problem for each solution. This method is applied to minimizing gain ripple of full bandwidth (60 nm) a 100 Km Raman amplifier for different number of pumps.     

A theoretical study of double-pass thulium-doped fiber amplifiers

An efficient fluoride-based thulium-doped fiber amplifier (TDFA) is theoretically demonstrated using a double-pass scheme. A reflector is incorporated in the double-pass TDFA to allow double propagation of the test signal in the gain medium and thus improve the gain of the TDFA. The small signal gain improvement of more than 15 dB is obtained in the 1465 nm region. A gain as high as 42 dB is obtained in this region with 300 mW of 1050 nm pump using 20 m of thulium-doped fiber. However, a noise figure penalty of approximately 1 dB is also obtained in this wavelength region. Differential equations are solved using the Runge-Kutta method in the theoretical analysis. The theoretical result is in agreement with the experimental result.     

增益平坦拉曼放大器优化算法研究

在分析受激拉曼散射耦合方程的基础上，介绍了一种反向设计多波长抽运光纤拉曼放大器的方法，并使用一种改进遗传算法和新型打靶法，讨论了体现特定的高增益和宽带平坦的适应度函数，对抽运波长和功率进行了优化，得到高增益，宽带平坦的增益谱，其开关增益可达15dB，增益带宽达80nm，增益波动小于1dB，这种放大器结构比现有的宽带光纤放大器在增益平坦上有一定的进步。     

Limitation in the intrinsic method of EDFA gain optimization for 32 × 40 Gbit/s WDM systems

The gain flattening of the erbium doped fiber amplifier (EDFA) is one of the most important aspects in the EDFA which the gain is wavelength dependent. For the first time the limitation of EDFA gain optimizing for a 32-channel wavelength division multiplexing (WDM) systems is investigated and reported in this paper. In a 32-channel WDM system the most favorable flatness gain achieved was 23.16 ± 1.51 dB with an average noise figure of 5.70 dB. This outcome proposes that the method does not achieve a uniform spectral gain in a 32-channel WDM system that incorporates a bandwidth of around 25 nm. Based on the simulation results the intrinsic optimization of EDFA causes the poor SNR and peak signal power with great variation over a transmission distance of 480 km single mode fiber.     

双向抽运光纤拉曼放大器的优化设计算法

基于双向抽运拉曼放大器的功率耦合方程 ,采用遗传算法和级链的全局收敛的Broyden方法 ,提出一种优化设计不同形式双向抽运宽带光纤拉曼放大器的自动配置算法。该算法的特点是计算速度快、收敛性好、适应面广。通过对单光纤的分布式、具有不同增益要求的分立式以及不同周期的色散管理结构的分布式双向抽运拉曼放大器的设计表明 :在 10THz的增益带宽内 ,放大器的增益平坦度均优于± 0 .6dB ,表明了该算法的可行性。此方法为采用双向抽运技术的拉曼放大器及其相应的全拉曼光纤传输系统的设计提供了一个公共平台     

Experimental and theoretical studies on a double-pass C-band bismuth-based erbium-doped fiber amplifier

Performance of a Bismuth-based Erbium-doped fiber amplifier is experimentally and theoretically investigated using 1480 nm pumping with double-pass scheme. In the theoretical analysis, the rate and power propagation equations are solved to examine the optimum length for the C-band operation as well as the gain and noise figure characteristics. The calculated small signal gain is 38 dB with gain variation of less than 3 dB. The measured gain is 4 dB lower due to spurious reflections which were ignored in the theoretical analysis. At input signal power of 0 dBm, a gain of 14.5 dB is obtained experimentally with gain variation of less than 1 dB within the wavelength region from 1530 to 1565 nm. The noise figure is less than 12 dB within this region.     

反向抽运光纤喇曼放大器增益特性分析

将打靶法和龙格库塔法两种数值计算方法相结合，对反向抽运光纤喇曼放大器中信号光和抽运光相互作用的耦合微分方程进行数值求解.在分别选取不同参量且取不同值的条件下，详细分析了光纤长度、初始信号光功率、初始抽运光功率、光纤有效面积、喇曼增益系数及光纤对信号光与抽运光的损耗等参量对增益的影响，最后提出了有效提高增益的方法.     

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。     

Gain and gain-flatness improved photonic crystal fiber Raman amplifier based on a dual-pass amplification configuration with single pump laser

A gain and gain-flatness improved L-band dual-pass Raman fiber amplifier (RFA) utilizing a photonic crystal fiber (PCF) as gain medium is demonstrated. By introducing complementary gain spectra of typical forward and backward pumping single-pass RFA using the same PCF, we finally achieve average net gain level of 22.5 dB with a ±0.8 dB flattening gain in 20-nm bandwidth from 1595 nm to 1615 nm, which is rare in RFAs with only one single pump and no flattening filter. Compared with the single-pass pump configurations, gain level, flatness and bandwidth are greatly improved by using the dual-pass amplification configuration. The limitation of this configuration caused by multi-path interference (MPI) noise and stimulated Brillouin scattering (SBS) is also discussed.     

Multistage gain-flattened hybrid optical amplifier at reduced wavelength spacing

In this paper, two stage hybrid optical amplifier (HOA) composed of a single erbium doped fiber amplifier and Raman amplifier is proposed for dense wavelength division multiplexed (DWDM) system and investigate the impact of reduced channel spacing. The performance has been evaluated in the term of gain, gain flatness and noise figure. Also, using gain equalization technique, hybrid optical amplifier that has a gain flatness of 3 dB, and a noise figure of less than 7.4 dB is observed.     

Characteristics of low noise hybrid fiber amplifier

The characteristics of hybrid fiber amplifier (HFA) are investigated. HFA is composed of three stages: short-length EDFA pre-stage, DCF Raman amplifier, and power boosting EDFA. HFA has low noise figure, high output power, and also wide input power dynamic range. Gain control method of HFA is presented experimentally, and the transient gain excursion is suppressed to less than 0.5 dB at 3 dB channel add-drop. HFA can be used as line amplifier in optical transmission link even combined with distributed Raman amplifier due to wide input power dynamic range. The transmission performance of HFA is better than EDFA by more than 1.0 dB of Q-factor in 720 km SMF transmission.