Modeling and optimizing of low-repetition-rate high-energy pulse amplification in high-concentration erbium-doped fiber amplifiers

Starting from the modeling of isolated ions and ion-pairs, a closed form rate and power evolution equations for pulse amplification in high-concentration erbium-doped fiber amplifiers (EDFAs) are constructed. According to the equations, the effects of ion-pairs on the performance of a high-concentration EDFA in steady state including upper-state population, ASE powers without input signal are analyzed numerically. Furthermore, the effects of ion-pairs on the dynamic characteristics of low-repetition-rate pulse amplification in the EDFA including the storied energy, output pulse energy and evolution of pulse waveform distortion are systematically studied by using the finite-difference method. The results show that the presence of the ion-pairs deteriorates amplifier performance, such as the upper-state population, ASE power, storied energy, output pulse energy, and saturated gain, etc. For the high-concentration EDFA, the optimum fiber length should be modified to achieve a better performance. The relations between the evolution of pulse waveform distortion or output pulse energy and the input pulse peak power are also discussed. The results can provide important guide for the design and optimization of the low-repetition-rate pulse amplification in high-concentration EDFAs.     

宽带放大器用碲基掺铒光纤结构参量的设计考虑

利用光波导理论及均匀展宽四能级模型，研究了宽带放大器用阶跃型折射率分布碲基掺铒光纤的结构参量—纤芯半径和相对折射率差的设计考虑.理论研究表明，在单模传输条件下，为获取最大信号增益，宜选择相对折射率差大的碲基掺铒光纤来构建光纤放大器.相对折射率差一定的情况下，在高泵浦功率、小信号输入或光纤长度短于各信道最佳增益长度时，选择纤芯半径大的碲基掺铒光纤可以得到大的信号增益；反之，宜选择纤芯半径小的碲基掺铒光纤.     

Effect of Cascading Amplification Stages on the Performance of Serial Hybrid Fiber Amplifier

Abstract

This study demonstrates simulation and experimental validation of a wideband serial hybrid Raman/erbium-doped fiber amplifier. Two configurations are adopted; in type A, a Raman amplifier is the first stage, and in type B, an erbium-doped fiber amplifier is the first stage. At low input signal power, the average gain level is 20 dB with a flat gain bandwidth of 40 nm for both configurations. The noise figure in type B is dominated by the erbium-doped fiber amplifier and produces lower values and flatter spectra than in type A. The gain of the proposed hybrid amplifiers is affected more by the second amplification stage.     

高浓度镱铒共掺磷酸盐光纤放大器增益特性

在忽略高能级的自发辐射和光纤损耗的情况下，利用速率方程和传输方程理论研究了高浓度Er³⁺/Yb³⁺共掺磷酸盐玻璃光纤放大器的增益特性，讨论了Er³⁺浓度、Yb³⁺浓度、抽运光功率、信号光功率、光纤长度对放大器增益的影响，并与单掺铒光纤放大器进行了比较.由于Yb³⁺的敏化作用降低了铒离子的团簇效应，减少了离子间相互作用，共掺光纤的增益和效率明显高于单掺光纤.数值计算表明，3.2cm长Er³⁺/Yb³⁺共掺光纤在980nm的20dBm(100mW)抽运功率下，1532nm处的增益可达10dB. 关键词： 镱铒共掺光纤放大器 速率方程 传输方程 高浓度     

Performance of optical amplifier employing silica host magnesium-aluminum-germanium co-doped erbium-doped fiber

Two silica host magnesium(Mg)-aluminum(Al)-germanium(Ge) co-doped erbium-doped fibers (EDFs)have been fabricated, which have different Mg concentrations. The concentration of all the compositions in the preform is measured through electronics probe micro analysis (EPMA). The maximum Mg concentrations of fibers A and B are 3.98 and 1.28 mol%, respectively. The performance characteristics including absorption spectrum and gain are measured and analyzed. The absorption coefficients of fibers A and B are 13.3 and 14.3 dB/m respectively at wavelength of 1532 nm. The max gains of these two erbium-doped fiber amplifiers (EDFAs) are 30.1 and 35.9 dB with input signal power of -30 dBm and pump power of 100 mW at 980 nm. Fiber B with maximum Mg concentration 1.28 mol% has better performance than fiber A. Fiber B has high absorption coefficient and high gain characteristics. The optimum fiber B length of C-band EDFA is 7 m and that of L-Band EDFA is about 30 m, which is much shorter than standard commercial EDFAs. The result of experiments showed that a few Mg added to silica host EDF can increase the concentration of erbium ions, which will shorten the EDF length much, but not degrade the performance characteristics.     

A numerical analysis of gain characteristics of Er-doped Al2O3 waveguide amplifiers

The gain characteristics of erbium-doped Al₂O₃ waveguide amplifiers are investigated by solving numerically rate equations with upconversion effects and propagation equations. We obtained the dependence of gain of erbium-doped Al₂O₃ waveguide amplifiers on the waveguide length, erbium concentration and pump power at different pumping wavelengths (980 and 1480 nm). The performance of amplifiers pumping at 1480 and 980 nm are compared. It is shown that 980 nm pumping has higher gain and higher pumping efficiency. The parameters of waveguide amplifiers have been optimized. A optical gain of 43 dB can be achieved for a optimum waveguide length of 8.25 cm and 5.8 × 10²⁰ cm^–3 Er concentration pumped with 100 mW at 980 nm, that is a gain of 5.2 dB/cm.     

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.     

Spectral luminescence and information characteristics of transparent lead fluoride nano-glass-ceramics doped with erbium ions

Spectral luminescence properties of synthesized transparent nano-glass-ceramics doped with erbium ions are studied. It is shown that, as a result of the secondary heat treatment of nano-glass-ceramics, the width of the luminescence spectrum at half maximum increases more than by 15 nm. Luminescence life-time dependences of erbium ions in studied samples are measured, their absorption cross-sections are determined, and their emission cross-sections are calculated by the McCumber method. Spectral and ultimate information characteristics of erbium-doped fiber amplifiers based on synthesized nano-glass-ceramics are numerically simulated. It is shown that, in the unsaturated gain regime, a substantial ripple of the absorption and emission cross-section spectra and shorter lifetime of the metastable level of the erbium ion reduce the pumping radiation power that is required for obtaining the given peak gain, narrow the gain spectra, and lower the transmission capacity of devices based on nano-glass-ceramics compared to the initial glass. Conversely, fiber amplifiers based on calcium fluoride glass-ceramics, for which the lifetime of the metastable level increases with increasing annealing temperature, have an advantage in the transmission capacity over devices based on the primary glass.     

Modeling erbium–thulium-co-doped fiber amplifier for 1400–1650 nm band

We present numerical models of tri-valence erbium ion and thulium ion-co-doped fiber amplifiers pumped by 800-nm and 980-nm lasers. The rate and power propagation equations of the models are numerically solved to analyze the gain as a function of co-doping concentrations, fiber length and signal wavelength. The results reveal that with 800-nm or 980-nm pump, gain competition exists between 1470- and 1530-nm bands, which may arise from the pump absorption competition and complicated energy transfer between the two types of active ions, and the results further show that the gain spectra may cover 305 nm (1375–1680 nm) for 800-nm pump and 160 nm (1400–1560 nm) for 980-nm pump. The doping concentrations and fiber length may be tuned to reduce the ripple of the gain spectra.     

WDM系统中碲基掺铒光纤放大器泵浦问题的理论研究

依据均匀加宽四能级结构速率方程组和光功率传输方程组, 对WDM系统中碲基掺铒光纤放大器（EDTFA）的泵浦问题进行了理论研究,给出了三种泵浦方式小信号和大信号状态下EDTFA信号增益分布曲线和放大的自发辐射（ASE）噪声功率谱,在此基础上探讨了EDTFA泵浦方式与信号增益、ASE噪声的关系.     

Simulation Performance of Erbium-Doped Fiber Amplifiers

In this paper, a simple approach is introduced to simulate the main performance of erbium-doped fiber amplifiers by using two empirical formulas to calculate saturated gain and corresponding noise figure. Then conflict equations are presented to improve this approach. At the end of the paper the comparison of calculation results before and after improvement is given. It has been shown to be more accurate.     

掺铒光纤激光放大的研究

本文研究了描述掺铒光纤激光放大的速率方程解,分析了光纤中几种场分布和铒离子横向分布时的解析解,并进行了数值计算.得到了任意信号强度(包括大信号)时的增益以及影响信号增益的主要参数,利用532nm激光泵浦掺铒光纤,得到信号的最大增益为29.5dB.     

基于环形芯光纤的超低差分模式增益涡旋光纤放大器

提出了一种基于环形芯铒离子部分掺杂光纤的涡旋光纤放大器。针对该掺铒光纤的放大特性,研究了光纤长度、掺铒浓度与抽运功率对信号模式增益特性的影响。研究结果表明,该光纤放大器能够支持22个轨道角动量模式稳定传输,且C波段(1530~1565 nm)所有信号模式增益大于23 dB,信噪比高于27 dB,差分模式增益小于0.015 dB。所提出的基于环形芯光纤的涡旋光纤放大器具有支持轨道角动量模式数量多、差分模式增益低、信噪比高的优势,对于OAM复用长距离传输系统中的在线放大具有重要参考价值。     

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。     

Erbium-doped fiber laser passively Q-switched by an InGaAs/InP multiple quantum well saturable absorber

We report on the behavior of an erbium-doped fiber laser passively Q-switched by an InGaAs/InP multiple quantum well semiconductor saturable absorber. The fiber is moderately doped in erbium ions. The saturable absorber consists of 40 periods of InGaAs (8.5 nm)/InP (10 nm) grown on an InP substrate. The laser efficiency is nonlinear under Q-switch regime and unusual temporal pulse shapes with rising times lower than decay times are observed around threshold. Pulse duration is around the microsecond range. Simple arguments based on a rate-equations approach are proposed in order to explain our results. They are justified a posteriori via numerical integration of the equations. The variation of threshold level versus spectroscopic parameters has been determined and that makes a guideline for generalizing our discussion.     

A theoretical analysis of the effects of erbium ion pair on the dynamics of an optical gain stabilized fiber amplifier

In this paper, the effects of ion-pair formation on the gain dynamics of multi cavity optical automatic gain control erbium doped fiber amplifier is modelled. The inhomogeneous Cabezas simple model is used to write the rate and propagation equations for the active medium. The solution of the governing equations shows that in high concentration of the erbium ions, depending on the pumping rate, the relaxation oscillations are converted to nT-Periodic or even to chaotic behavior. Although the high concentration erbium ion in the optical amplifiers decreases the conversion efficiency and increases the threshold pump power, amplitude of the transient effects is reduced in the multi feedback-loop WDM amplifiers relative to the low concentration erbium ions multi feedback-loop optical amplifiers and ion-pairs, which act as a saturable absorber to compensate the gain tilt caused by the OAGC laser spectral hole burning. The theoretical results are in complete agreement with the previous published experimental results.     

碲基掺铒光纤放大器增益饱和特性的数值模拟

依据均匀加宽四能级结构速率方程组和光功率传输方程组,数值模拟了1520～1620nm波段范围内碲基掺铒光纤放大器(EDTFA)增益谱特性,以及EDTFA增益谱特性与输入信号光功率的关系.模拟结果显示:随着输入信号光功率的增大,EDTFA增益谱由于饱和效应而呈现平坦化特征.模拟结果与报道的实验测量结果达到了很好的一致.     

Evaluation of Theoretical Model for Erbium-Doped Silica Fiber Amplifiers

AAmplified spontaneous emission measurements for three types of erbium-doped silica ffibers are presented. The characteristic parameters of these fibers was previously oobtained employing gain and pump power measurements. A theoretical model for eerbium-doped silica fiber amplifiers is evaluated and its scarcities are analyzed bby mmeans of a comparison between experimental and theoretical results for gain and ccopropagating amplified spontaneous emission.     

Evaluation of Theoretical Model for Erbium-Doped Silica Fiber Amplifiers

AAmplified spontaneous emission measurements for three types of erbium-doped silica ffibers are presented. The characteristic parameters of these fibers was previously oobtained employing gain and pump power measurements. A theoretical model for eerbium-doped silica fiber amplifiers is evaluated and its scarcities are analyzed bby mmeans of a comparison between experimental and theoretical results for gain and ccopropagating amplified spontaneous emission.     

Dynamic Gain-Clamped Amplifier with Backward-Injection of a Fabry-Perot Laser

We have been experimentally demonstrated an active control technique of dynamic gain-clamped spectra for the erbium-doped fiber amplifiers (EDFA's) by a backward-injected Fabry-Perot (F-P) laser into this EDFA. In addition, employing a short length erbium-doped fiber (EDF) that not cause any gain saturation for preamplification in front of this amplifier module, it can reduce the noise figure degradation and simultaneously achieve gain variation from 11.1 dB to 0.5 dB for 10 dB input power level change.