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.     

New trend for optical signal-to-noise ratio of disturbed Raman fiber amplifier

In a distributed Raman fiber amplifier (DRFA), Raman amplification allows a lower signal launch powers to transverse the span above the noise floor while still increasing the optical signal-to-noise ratio (OSNR). It improves the noise figure and reduces the nonlinear penalty of fiber systems. In this paper, we demonstrate a new trend of OSNR at different pump configurations: forward, backward and bidirectional pumping for DRFAs as a function of fiber length. We also present the variation of OSNR with both input pump power and input signal power. It is found that forward pumping provides the highest OSNR, reaching its maximum value of 37 dB. However, backward pumping provides the smallest OSNR that has its maximum of 22 dB and the bidirectional pumping provides the moderate OSNR between the others having its peak of 26 dB.     

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.     

Simulation analysis of crosstalk among channels with fiber Raman amplifiers at 10 Gb/s

We have investigated the effects of crosstalk in fiber Raman amplifiers (FRAs) by propagating signals through the Raman fiber. We have observed that quality factor reduces for lesser channel spacing. We have able to propagate the signals in two channels with spacing of 20 GHz and quality factor above 25 dB was obtained. The effect of signal input power and injected pump power on crosstalk and signal interference ratio (SIR) has analyzed. It is observed that the signal gain and the injected pump power should be limited to the value well below the threshold of Raman amplification to ensure small crosstalk and high SIR. The effect of Raman fiber length on crosstalk is also studied and it is observed that for high values of Raman fiber length, SIR reduces considerably.     

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.     

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).     

掺铒光纤放大器的增益特性

采用980nm无铝InGaAs/InGAsP/InGaP高功率量子阱激光器泵浦掺铒光纤放大器。在泵浦功率为20mW时,增益为33dB,最大增益系数6．7dB/mW,饱和输出功率为6dBm,并给出掺铒光纤长度和泵浦功率与增益特性的关系。以及输出功率与增益特性的关系。     

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.     

多泵浦光纤喇曼放大器的模拟分析

通过使用综合理论模型对不同配置条件下的多泵浦分布式光纤喇曼放大器的增益谱进行了数值模拟研究,该理论模型包含了瑞利散射、放大自发辐射和不同交互效应,包括泵浦与泵浦、泵浦与信号和信号与信号之间的交互与能量转移.模拟研究了泵浦源功率、泵浦源波长间隔及光纤损耗对喇曼增益谱的影响,结果表明设计多泵浦光纤喇曼放大器需要对泵浦源功率、泵浦源波长间隔光纤损耗谱进行综合考虑,需对泵浦源功率、泵浦源波长间隔进行合理配置.在本文的泵浦源波长设定条件下,考虑实际光纤的损耗谱特性,为了获得大的增益带宽和小的增益不平坦度,短波长泵浦源和最长波长的泵浦源需要更高的泵浦功率,中间波长泵浦源的功率应较低.     

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.     

Shooting algorithm and particle swarm optimization based Raman fiber amplifiers gain spectra design

An initial value determination method with a contraction factor for the counter-pumped Raman coupled equations is proposed. This method is used in conjunction with initial guess correction mechanism of Newton's method to construct a new efficient shooting algorithm for the solution of counter-pumped Raman coupled equations. The particle'swarm optimization is used to find the optimal wavelengths and powers for the pumps. By combining the new shooting algorithm and particle swarm optimization a powerful approach to the design of gain spectra for Raman fiber amplifiers is developed. Using this approach a counter-pumped broadband Raman fiber amplifier in C + L-band is designed and optimized. An average on-off gain of 9.3 dB for a bandwidth of 95 nm is obtained using only 4 pumps, with an in-band ripple level of ± 0.7 dB.     

Investigation of the optical gain and noise figure for multi-channel amplification in EDFA under optimized pump condition

We present the results of an investigation of optical gain and noise figure for simultaneous multi-channel amplification of an erbium doped fibre amplifier (EDFA) under optimized pump condition. Different pump configurations with varying input signal levels show interesting features on gain flatness. In the experiment, population inversion along the fibre length which determines the gain-spectra and noise characteristics of the amplifier is adjusted through optimized fibre length and injected pump power in order to minimize the gain-tilt at C-band. It is observed that bi-directional pumping manifests the best combination of low noise and high gain of EDFA which are useful as in-line repeaters in WDM network. We obtain 30 ± 1.5 dB intrinsically flat small signal gain from 1538 nm to 1558 nm band of wavelength with noise figure <4 dB for 16-channel simultaneous amplification in a single stage EDFA without gain flattening filter.     

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.     

Design of Raman-parametric fiber amplifier for wavelength division multiplex transmission system

We optimize the novel configuration of a hybrid fiber amplifier - Raman assisted-fiber-based optical parametric amplifier （R-FOPA）, in which the parametric gain and Raman gain profiles are combined to achieve a flat composite gain profile. The pump powers and the fiber length in the hybrid amplifier are effectively optimized by genetic algorithm （GA） scheme. The optimization results indicate that the RFOPA can achieve a 200-nm flat bandwidth spectrum with the gain of 20 dB and ripple of less than 4 dB.     

Inherently gain flattened L band TDFA based on W-fiber design

We present here a detailed theoretical analysis for realizing an inherently gain flattened L⁺ band thulium doped fiber amplifier (TDFA), based on a depressed inner-clad (W-fiber) design, wherein the inherent gain flattening is achieved by an optimized bend induced leakage loss. The leakage loss characteristics of W-fiber have been used to suppress higher wavelength amplified stimulated emission (ASE) in the designed TDFA, which otherwise depletes the population inversion in the amplifier, making it almost impossible to obtain high gain for wavelengths in and close to the conventional L-band. It has been shown through simulations that 20 dB net gain (±0.3 dB ripple) is achievable over 32 nm bandwidth (1604-1636 nm), using this design pumped with 160 mW of power. We also show that inherent gain flattening leads to redistribution of power among signal wavelengths, and hence an inherently gain-flattened TDFA is much more efficient as compared to a configuration that uses discrete filters for gain flattening. The net gain value and gain flattening of the designed TDFA module have been tested against tolerance with respect to fiber parameters as well as bend radius. This is for the first time to the authors knowledge that inherently gain flattened L⁺ band operation has been shown using TDFAs.     

A global design of an erbium-doped fiber and an erbium-doped fiber amplifier

A global design of an erbium-doped fiber and an open-loop erbium-doped fiber amplifier (EDFA) in a steady-state operation is discussed by applying genetic algorithms. Taking a signal gain and a bandwidth as objective functions, 7 parameters of the EDFA (erbium concentration, core radius, erbium-doped radius, refractive index difference, fiber length, pumping wavelength and signal power) are optimized by solving optical propagation equations, assuming a homogenous two-level active medium and a single-mode propagation. There is evidence to show that the 1480 nm pump utilized in usual EDFAs is not an optimal choice, which should be chosen around 1460 nm. The optimal core radius ranges 0.465–0.548 μm on pumping power 50–200 mW. Under different design objects and with different pumping powers, however, there are different optimal Er-doped concentrations, reflective index differences and fiber lengths. As a single fiber EDFA, 35 dB signal gain or 35 nm bandwidth is obtained with the 7 optimal parameters, 100 mW pumping power and 0.001 mW input signal power.     

Gain-clamped dual-stage L-band EDFA by using backward C-band ASE

A dual-stage L-band gain-clamped erbium-doped fiber amplifier (GC-EDFA) by using backward C-band amplified spontaneous emission (ASE) is proposed. Compared with other similar GC-EDFAs, the proposed structure has higher and flatter clamped gain in L-band because of its optimal pump power and EDF length. The flatness from 1570 nm to 1600 nm arrives 0.77 dB, the bandwidth of 3 dB is more than 35 nm and the maximal input signal power arrives −15 dBm.     

级联掺磷光纤喇曼激光器的解析优化

讨论了二级级联喇曼光纤激光器的解析解和优化设计.通过引入几何平均功率、增益因子和归一化光纤有效长度,将描述泵浦光和斯托克斯光沿喇曼增益光纤分布的微分方程组简化成代数方程组,在对泵浦光采用线性传播近似后,获得了二级级联喇曼激光器的解析解.所获得的解析解同数值模拟结果吻合得很好.利用该解析解可方便和快速地讨论级联喇曼激光器的优化设计,计算不同泵浦功率下的最佳光纤长度、输出光纤光栅反射率和转换效率.泵谱功率越大,最佳光纤长度越短,最佳输出光纤光栅反射率越小.     

High-gain and low-noise-figure erbium-doped fiber amplifier employing dual stage quadruple pass technique

A high-gain and low-noise-figure (NF) erbium-doped fiber amplifier (EDFA) was demonstrated utilizing a new technique called the dual-stage quadruple pass (DSQP) with filters. An efficient amplification occurs at the signal wavelength of 1550 nm when it travels along the DSQP amplifier. The highest gain of 62.56 dB with a low noise figure of 3.98 dB was achieved for an input signal power of −50 dBm and pump powers of 10 and 165mW in the second and first stage amplifiers respectively.     

800 mW/1484 nm highly efficient two-cascaded phosphosilicate Raman fiber laser pumped by Nd:YVO4 solid-state laser

Using 1064 nm CW Nd:YVO₄ solid-state laser as a pump, 1-km phosphosilicate fiber and cascaded cavities with two pairs of fiber Bragg grating mirrors for 1239 and 1484 nm, we obtained a CW 800 mW/1484 nm Raman fiber laser (RFL) for an actual incident pump power of about 2 W (Nd:YVO₄ power of 6.90 W). The conversion efficiency is as high as 40%. To the best of our knowledge, this is the highest conversion efficiency of RFL pumped by solid-state laser. The output power instability at 1484 nm in half an hour is less than 3%. In addition, the numerical simulations are also performed. Good agreement between the results of numerical simulation and the results of the experiment has been demonstrated.