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.     

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.     

Simple design method for gain-flattened three-pump Raman amplifiers

We propose a simple and efficient approach to the design of 3-wavelength backward-pumped Raman amplifiers with increased gain flatness over a wide spectral band. Three different methods dealing with the optimization of one or two different simple parameters are studied. Various examples are provided for illustration, and the dependence of both amplifier gain and gain flatness with pump power is shown. Gain flatness in the spectral range of 1,520–1,595 nm of about 1 dB for a 7.5 dB gain and of 1.8 dB for a 13.5 dB gain is demonstrated using only three pumps with wavelengths within the 1,420–1,480 nm interval.     

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.     

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.     

Impact of the all-optical gain-clamping technique on the transience characteristics of cascaded discrete fiber Raman amplifiers

We theoretically analyse the dynamic response of amplifier cascades involving combinations of unclamped and gain-clamped discrete fiber Raman amplifiers (DFRAs) in the worst possible case of power transients. We consider a 64-channel system in which all of the channels except one (i.e. the surviving channel) are modulated to simulate channel add/drop. We vary the number and the position of the gain-clamped DFRAs in the cascade to determine whether a cascade in which only a few amplifiers are gain-clamped (referred to as a mixed cascade) can be as effective as a cascade comprising all gain-clamped amplifiers for controlling the power transients within tolerable limits (for example, 1 dB). We take into account the location of the surviving channel and the operational regime of the amplifiers. Our results show that the location of the gain-clamped DFRAs in a mixed cascade affects the transient characteristics and that it is possible to control the transients within tolerable limits.     

光纤喇曼增益系数的简捷测量

基于小信号开关增益原理,采用抽运光-探测波法,利用SLD(超辐射激光二极管)作为宽带小信号探测光源,快速测量出了标准单模光纤(G.652)的频移为0.5～20 THz内的喇曼增益系数,测量结果和文献中已有的值基本吻合,所测得的光纤喇曼增益系数可用于光纤喇曼放大器的理论和实验研究,该方法同样可以对其他类型光纤的喇曼增益系数进行测量.     

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.     

Effect of sinusoidal ripples in refractive index profile distribution on the performance characteristics of dual concentric core step index fiber Raman amplifier

Phased matched wavelength, effective area, effective Raman gain, and wave guide dispersion are computed from exact numerical solution assuming scalar wave equation in the presence and absence of ripples as imperfections in the refractive index profile in dual cores of single mode fiber Raman amplifier for the first time. It is observed that for larger values of amplitude and lower frequencies, the effective Raman gain increases w.r.t. that calculated with no ripples. However, we assume ripple amplitude up to 5% of core cladding refractive index difference w.r.t. the available data, corresponding to the three ranges of relative ripple amplitudes of 1%, 2%, 3% and ripple frequencies of 1, 2, 3 μm⁻¹. Based on these data, we analyse performance of FRA over frequency shift band of 20–700 cm⁻¹. Uniformity of gain is interestingly seen to be maintained for higher ripple frequency and lower amplitude. However, no prominent effect in coefficient of dispersion and phase matched wavelength is observed within operating range of wavelength. Also, based on available structural parameter, the investigation should find use as a guide to system users to know the limit and promise of existence of ripples.     

Theoretical analysis of gain characteristics of Dy-doped fiber amplifiers

The rate equations and power evolution equations of Dy³⁺-doped fiber amplifiers (DDFA) are proposed, and numerically analyzed. Based on the numerical analysis, several major characteristics of the fiber amplifier are calculated and compared with those of Pr³⁺-doped fiber amplifier (PDFA). The results show that DDFA can achieve better efficiency and wider gain bandwidth than PDFA.     

Multi-channel gain and noise figure evaluation of Raman/EDFA hybrid amplifiers

We present detailed multi-channel experimental characterization of different configurations of single pump hybrid Raman-erbium doped fiber (EDF) amplifiers. The incorporation of an EDF section in a dispersion compensating Raman amplifier is demonstrated to provide superior performance than Raman only system. It is shown that the multi-channel gain spectrum is quite different form the single-channel case. We have also measured the polarization dependent gain (PDG) of the hybrid amplifier configurations and results show that different configurations of hybrid amplifiers have different PDG effects on long-haul optically amplified link.     

An efficient shooting method for fiber amplifiers and lasers

A simple shooting method is proposed for the design of distributed multi-pumped Raman fiber amplifiers (RFAs) and Yb-doped double-clad fiber lasers (DCFLs). Using the proposed method a distributed RFA with 10 pump sources and 1700 mW total input pump power is simulated and high-power Yb-doped DCFL rate equations are solved numerically. The numerical simulation results show that the proposed method has good convergence in the condition of increasing numbers and power of input pump sources.     

Noise performance analysis of bi-directionally pumped distributed fiber Raman amplifiers with consideration of fiber nonlinearity and its impact on EDFA output OSNR

Under small-signal assumption, equivalent noise figure normalized by fiber nonlinearities (NENF) of bi-directionally pumped distributed fiber Raman amplifiers (BiDFRA) is derived. Amplified spontaneous Raman scattering noise and double Rayleigh scattering noise are both included. The relation between NENF and Raman gain, forward Raman gain percentage is investigated under different polarization factor and Rayleigh scattering coefficient. It agrees well with numerical simulation results. Based on the analytical expression, the optical signal-to-nose ratio (OSNR) improvement of hybrid pre-BiDFRA/erbium-doped fiber amplifier (EDFA) compared with sole EDFA is studied. It is shown that there is an optimum Raman gain and forward Raman gain percentage to maximize the OSNR improvement. Finally, some guidelines on BiDFRA design are proposed.     

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 L-band EDFA of high clamped gain and low noise figure implemented using fiber Bragg grating and double-pass method

The L-band erbium-doped fiber amplifier (EDFA) of low noise figure and high clamped-gain using gain-clamped and double-pass configuration is presented in this paper. A total of five different configurations of EDFAs by reflection scheme with single forward pumping schemes are examined and compared here. Among these configurations, we first find the configuration of 1480-nm pumped L-band EDFA with optimum gain and noise figure value. To further minimize the gain variation, a fiber Bragg grating (FBG) with 1615-nm center wavelength and 1-nm bandwidth is determined and added in double-pass L-band EDFA. The gain variation and maximum noise figure of EDFA while channel dropping is investigated. As the number of channel dropping from 32 to 4, the L-band type-A EDFA keep the variation of gain within 2.9 dB and the maximum noise figure below 5 dB with each channel’s input power of −23 dBm.     

A numerical method for solving gain characteristics of Er/Yb codoped waveguide amplifiers

By means of the interpolation and iteration methods to deal with the rate equations and the light propagation equations for the Er³⁺/Yb³⁺ codoped waveguide amplifier (EYCDWA), the gain characteristics in the forward, backward, and bidirectional pumped styles are analyzed. In order to obtain high gain, some parameters such as waveguide length, dopant concentration, pump power, and signal power are optimized. The results show that the pump power and signal power are about 50 mW and 1 mW, respectively, the gain is about 6.5 dB for the 2.0 cm-long EYCDWA with an Er³⁺ ion concentration of 1.5 × 10²⁶ m^–3 and Yb³⁺ ion concentration of 1.9 × 10²⁷ m^–3. Moreover, the upconversion is investigated for the designed device.     

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.