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.     

掺铒聚合物狭缝波导放大器的增益特性研究

设计了一种高浓度稀土铒掺杂聚合物填充硅狭缝结构的平面光波导放大器（工作波长1 550 nm,泵浦波长1 480 nm）,能够在低泵浦下获得高增益,可以应用于硅基光互联的损耗补偿。通过扫描电镜照片观察发现,合成的铒掺杂聚合物材料具有良好的纳米狭缝填充能力。考虑铒离子的合作上转换和激发态吸收,利用铒离子四能级跃迁模型,建立原子速率方程和光功率传输方程,数值仿真分析了聚合物光学性质、狭缝波导结构参数及信号光泵浦光功率等放大器增益特性的影响因素。这种具有纳米截面尺寸的光波导放大器,获得4.5 dB的信号光相对增益仅需要1.5 mW的泵浦光,展现了良好的集成光学应用前景。为了进一步提高增益,引入了多层狭缝结构,四层狭缝波导的重叠积分因子比一层狭缝的高42%。     

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.     

Optical properties of ErFOD-doped polymers and fabrication of channel waveguides

ErFOD-doped P(MMA-co-GMA) (poly-methyl-methacrylate-co-glycidyl-methacrylate) polymer film was synthesized. The NIR photoluminescence (PL) spectrum of the material showed strong characteristic emission of Er³⁺ ions with broad full width at half-maximum (FWHM) of 55 nm. The rib channel waveguide using ErFOD-doped P(MMA-co-GMA) was designed and fabricated. The loss and gain measurements of the waveguides were also characterized. Further theoretical analysis on Er³⁺ ions in P(MMA-co-GMA) was performed using Judd-Ofelt theory. The results showed that it is a promising material for the elaboration of laser or optical amplifier.     

A Novel Erbium-Doped Fiber Amplifier Simulator for Gain Excursion Estimation in Multi-Channel Dynamic Optical Network

Abstract

A novel erbium-doped fiber amplifier simulator designed using the SIMULINK toolbox of MATLAB 7.0 (The MathWorks, Natick, MA, USA) is reported in this article. The present simulator has an ability to incorporate multi-channel amplification simultaneously in both the C- and L-bands. It is realized by defining new FUNCTION block sets and replacing the MATLAB FUNCTION block set reported earlier for multi-channel amplification. Spectral variation of gain for an erbium-doped fiber amplifier simulator is first verified in both the C- and L-bands. Next, the simulator is employed to study gain excursion in a multi-channel dynamic optical network, where the change in the gain excursion by varying the pump power has also been estimated. The present approach to estimate the gain excursion will find applications in quantifying inter-channel cross-talk due to cross-gain saturation among co-propagating multi-channels in a dynamic optical network.     

基于硅波导的喇曼光放大器

在硅波导上添加反向偏压的PIN结构,当波导产生受激喇曼散射时,可以将波导中双光子吸收(TPA)产生的光生自由载流子扫出波导,降低了波导的非线性损失,极大地提高了硅波导中泵浦光对信号光的喇曼增益。为了应用已经非常成熟的硅工艺,并且应用硅波导使器件小型化,根据法布里-帕罗(F-P)腔和行波放大器理论,在硅波导两端的解理面蒸镀增透膜,应用这种波导的喇曼效应设计了一种光放大器,即基于硅波导的喇曼光放大器。建立了计算放大器增益的方程,给出了不同波导长度和输入功率情况下的放大器增益,得出适当增加波导长度和泵浦光功率可以得到较高喇曼增益的结论。基于硅的光放大器有较高的饱和功率且没有泵浦源的限制,通过调整泵浦激光的波长可以放大不同波长的信号光。     

Modelling of 980 nm pumped EDWAs: Spectroscopic variations associated to fabrication process

In this work the optical amplification, in the small signal regime, at 1.5 m in Zn-diffused, proton exchange and reverse proton exchange Er³⁺-doped waveguide amplifiers (EDWAs) based on LiNbO₃ under 980 nm excitation has been modelled, including the dominant up-conversion channel activated by this pumping wavelength. The overlapping integrals method has been used to investigate how the spectroscopic changes, induced by the waveguide fabrication technique, affect the optical amplifier performance. In particular, it has been found that either the amplifier threshold and the maximum gain achievable are spectroscopy-dependent and therefore fabrication-dependent.     

Numerical analysis of amplification characteristic of erbium-doped waveguide amplifiers by FD-BPM

An efficient analysis method for erbium-doped optical waveguide amplifiers (EDWA) is presented. By solving the rate equation, the propagation in EDWA is stimulated using the finite difference beam propagation method (FD-BPM). The dependence of the gain of EDWA is investigated on the waveguide length, erbium concentration, and signal and pump power. The analysis shows that considerable gain levels, 3.35 dB/cm can be achieved in 10 cm-long EDWA with an erbium concentration of 2.0 × 10²⁶ ions/m³, signal power 1 W and pump power 100 mW at 980 nm.     

Design of 1480-nm diode-pumped Er3+-doped integrated optical amplifiers

Abstact Erbium-doped Y₂O₃ integrated optical amplifiers are designed for low-threshold operation and 3 dB amplification. The most important design parameter for minimal threshold, the erbium concentration, is found to have an optimum value of 0.35 at% for a given waveguide structure with 1.0 dB cm^-1 background loss. The corresponding threshold power is 7 mW. The pump power to obtain 3 dB gain is found to be 22 mW for an amplifier with an optimum erbium concentration of 0.6 at% and 2.8 cm length. At 30 mW pump power the maximum gain is shown to be 5 dB.Designing is done using a comprehensive numerical model of an erbium-doped integrated optical amplifier. In the model two-dimensional intensity-dependent overlap integrals are used, which allow arbitrary erbium dopant profiles and waveguide crosssections. Concentration-dependent effects such as quenching and upconversion are also included in the model.Input parameters for the model are determined from measurements on an unoptimized Er: Y₂O₃ optical waveguide amplifier. Amplification simulations and gain measurements of the unoptimized waveguides are found to be in close agreement, providing a sound basis for the design calculations.     

Gain-Flattened Optical Limiting Amplifier Modules for Wavelength Division Multiplexing Transmission

By integration of a bidirectional erbium-doped fiber amplifier and a three-port optical circulator with several fiber Bragg gratings (FBGs), two gain-flattened optical limiting amplifier (OLA) modules are proposed and experimentally demonstrated. They rely on the use of central wavelength misalignment and bending loss methods, respectively. They can effectively cover the whole useful 1.55-mum band. Both modules can provide gain-flattening characteristics over a large input dynamic range. The FBGs integrated OLA configuration has potential application in wavelength division multiplexing lightwave communication systems.     

抽运光与信号光的光强重叠因子和掺铒玻璃波导放大器的增益特性

在掺铒玻璃波导放大器（EDWA）的三能级速率-传输方程中,考虑两次离子交换工艺中波导掩模窗口宽度w不同所导致的抽运光、信号光模场与光强分布的不同,讨论不同w对EDWA增益特性的影响,得到光强分布的数值解.引入描述波导中抽运光和信号光的归一化光强重叠因子,对EDWA的传统近似解提出修正,得到了修正解,使其更加接近光强分布的数值解.模拟结果表明,在条波导长度为4 cm、抽运光波长为980 nm、功率为80 mW、信号光波长为1534 nm、功率为-10 dBm条件下,不同w所导致EDWA的增益差别可达297 dB.修正解的结果比传统近似解更加接近光强分布的数值解.修正解对于EDWA的理论研究、器件设计具有指导作用. 关键词： 集成光学 掺铒玻璃波导放大器 重叠积分因子 增益     

Simultaneously gain-flattened and gain-clamped erbium fiber amplifier

In this paper, we propose and demonstrate a simple erbium amplifier module based on an erbium-doped fiber amplifier (EDFA) and an erbium-doped waveguide amplifier (EDWA) in serial, having gain-flatted (GF) and gain-clamped (GC) functions simultaneously. In first proposed GF amplifier scheme, the maximum gain variation of 2.5 dB can be observed in the effective range of 1528 to 1562 nm and the entire gains are above 35 dB with the input signal power of ?30 dBm. Hence, we investigate second scheme by optical feedback method in the proposed fiber amplifier achieving gain-flattened (GF) and gain-clamped (GC) efficiencies simultaneously. Thus, the maximum gain variations of ±0.8 and ±1.8 dB can be obtained in the operating range of 1530 to 1564 nm, when the input signal powers are ?16 and ?40 dBm, respectively. Moreover, the dynamic gain profile can be adjusted and dynamic input power range is also measured based on the proposed GF and GC fiber amplifier.     

Gain evaluation of compact designing on Er/Yb codoped germanate glass channel waveguide

Bent waveguide structures (U- and F-bend) based on UV-sensitive Er³⁺/Yb³⁺ codoped germanate glass substrates have been designed to achieve high-gain C-band amplification. Using simulated-bend method, the optimal radius for curved structure is offered to be 1.90 cm with loss coefficient of 0.0015 dB/cm, as the substrate size is minimally schemed. In the wavelength range of 1528–1559 nm, obvious gain enhancement for the bent structure waveguides is anticipated, while, for the F-bend waveguide, the internal gain at 1533.8 nm wavelength is derived to be 22.55 dB, which is much higher than the value of 14.06 dB in the U-bend waveguide, and over three times higher than that of the straight one, after compensating both the bend loss and the transition loss. The simulation results indicate that the bent structure designing is beneficial in attaining high optical gain in Er³⁺/Yb³⁺ codoped germanate glass substrates, which assures that long-period grating can be applied to implement practical C-band gain-flattened amplification.     

Modeling of graded index waveguide fabricated by ion exchange on Er3+ doped glass

A general numerical tool,based on thermal diffusion equation and full-vectorial eigen-mode equation,has been presented for the systematic analysis of graded index channel waveguide fabricated by ion exchange on Er3+ doped glass.Finite difference method with full-vectorial formulation(FV-FDM) is applied to solving the full-vectorial modes of graded index channel waveguide for the first time.The coupled difference equations based on magnetic fields in FV-FDM are derived from the Taylor series expansion and accurate formulation of boundary conditions.Hybrid nature of vectorial guided modes for both pump(980 nm) and signal light(1550 nm) are demonstrated by the simulation.Results show that the fabrication parameters of ion exchange,such as channel opening width and time ratio of second step to first step in ion exchange,have large influence on the properties of waveguide.By optimizing the fabrication parameters,maintenance of monomode for signal light and improvement of the gain dynamics can be achieved in Er3+ doped waveguide amplifier(EDWA) fabricated by ion exchange technique.This theoretical model is significant for the design and fabrication of EDWA with ion exchange technique.Furthermore,a single polarization EDWA,which operates at wavelength from 1528 nm to 1541 nm for HE polarization,is numerically designed.     

Side-polished fiber based gain-flattening filter for erbium doped fiber amplifiers

A simple and accurate novel normal mode analysis has been developed to take into account the effect of the non-uniform depth of polishing in the study of the transmission characteristics of optical waveguide devices based on loading of a side-polished fiber half-coupler with a multimode planar waveguide. We apply the same to design and fabricate a gain-flattening filter suitable for fiber amplifiers. The wavelength dependent filtering action of the overall device could demonstrate flattening of an EDFA gain spectrum within ±0.7 dB over a bandwidth of 30 nm in the C-band. Results obtained by the present analysis agree very well with our experimental results. This present analysis should be very useful in the accurate design and analysis of any SPF-MMOW device/component including side-polished fiber based sensors.     

Apodized fibre Bragg grating with modulated refractive index change for transmissive gain equalization

This paper presents a new enhanced design of fibre Bragg grating for flattening the gain profile of an erbium-doped fibre amplifier in transmission configuration. This grating has modulation of refractive index change and constant chirp rate, wherein both profiles of the parameters are properly apodized. The design utilizes an alternative approach to the renowned inverse scattering method, yet produces a similar spectral response quality and conceptually simpler. Moreover, it offers precise control over all parameters of the grating structure. It is shown that the design approach could produce gain-flattening filters of satisfactory quality through simulations using the accurate transfer matrix method.     

Optimization of erbium-doped waveguide amplifier

Based on the combined model of erbium-doped waveguide amplifier with high erbium ion concentration, the rate equation and evolution equation is solved numerically. The waveguide parameters such as doping concentration, waveguide length are optimized in this paper. With pumping power of 150 mW, the optimal erbium doping concentration and waveguide length is 6×10²⁶ m⁻³, 15 cm or so, respectively. The amplifier with these optimal parameters may reach gain more than 35 dB.     

基于KMnF_3∶Yb~(3+),Er~(3+)纳米晶的红光聚合物平面光波导放大器

制作了基于KMnF_3∶Yb~(3+),Er~(3+)纳米晶材料的工作波长655 nm的聚合物平面光波导放大器。材料的吸收光谱表明,KMnF_3∶Yb~(3+),Er~(3+)纳米晶在980 nm附近有很强的吸收。在980 nm激光的激发下,由于Er~(3+)和Mn2+能级之间的能量传递,KMnF_3∶Yb~(3+),Er~(3+)纳米晶产生了很强的红色上转换发光。根据KMnF_3∶Yb~(3+),Er~(3+)纳米粒子的发光特性,制备了KMnF_3∶Yb~(3+),Er~(3+)NCs-PMMA复合材料,用其作为芯层设计了掩埋形结构光波导放大器,利用传统的半导体工艺完成器件制备。器件测试结果表明,当655 nm信号光功率为0.1 m W、980 nm泵浦功率为260 m W时,器件获得了2.7 d B的相对增益。     

制备工艺对掺杂NaYF4:Er3+,Yb3+发光纳米晶的聚合物光波导放大器性能的影响

制备了NaYF₄：Er³⁺,Yb³⁺纳米晶,表征了纳米晶的形貌,通过物理掺杂的方式将纳米粒子掺杂到SU-8中作为光波导放大器的芯层材料,优化了波导放大器的尺寸,利用旋涂、刻蚀等工艺,在二氧化硅衬底上制备了光波导放大器。实验中用光漂白法和湿法刻蚀两种方法制备光波导放大器,分别给出了两种方法制备的器件的结构、工艺流程、光场模拟结果,并对两种方法制备的器件的放大特性进行了测试。测试结果表明,当980 nm波长的泵浦光功率为241 mW且1 550 nm波长的信号光功率为0.1 mW时,使用湿法刻蚀法制备的放大器得到2.7 dB的相对增益。当980 nm波长的泵浦光功率为235 mW且1 550 nm波长的信号光功率为0.1 mW时,使用光漂白法制备的放大器得到4.5 dB的相对增益。根据以上测试结果,分析了两种工艺对器件性能的影响。     

Stabilization of a multiwavelength erbium-doped fiber laser using a nonlinear silicon waveguide

We propose and demonstrate a multiwavelength erbium-doped fiber laser stabilized by four-wave mixing (FWM) in a nonlinear silicon-on-insulator (SOI) waveguide. The optical gain was provided by an erbium-doped fiber amplifier, and the wavelength selectivity was achieved by a Fabry–Pérot comb filter in the ring cavity. The FWM in the SOI waveguide was enhanced by applying a reverse-biased p-i-n diode structure to reduce free-carrier absorption. Making use of the nonlinearity of the SOI waveguide, a multiwavelength laser with six output wavelengths at 0.8 nm spacing was achieved. The power difference among modes was equalized within a range of 1.8 dB. The power fluctuation of each mode was stabilized to <0.65 dB during 20 min observation at room temperature.