掺铒聚合物光波导放大器的数值分析

针对掺铒聚合物光波导放大器(EDWA),提出了一种基于Douglas离散格式改进的有限差光束传播法(FD-BPM)的数值计算方法。对每一传输步长结合多能级速率方程计算出EDWA中光场传输强度分布,及掺铒光波导放大器的增益传输特性。设计并研究了掺铒聚合物通道波导和Y形分束器的放大增益特性。在掺铒聚合物直波导中,Er3 浓度为9.0×1025ions·m-3,输入信号和泵浦光功率分别为1μW和2mW,其增益为1.6dB/cm;在掺铒聚合物Y形分束器中,输出信号光分束比相等,并能实现无损耗分束。     

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     

掺铒磷酸盐玻璃波导放大器的特性研究

研究了掺铒磷酸盐玻璃波导放大器的特性。利用重叠因子将980nm光抽运的掺铒玻璃波导放大器四能级模型的速率-传输方程进行化简,在考虑上转换效应和放大自发发射的情况下．利用数值模拟的方法,得到了掺铒玻璃波导放大器的增益与Er^3 离子浓度、抽运功率、波导长度等参量之间的关系曲线;同时模拟出放大自发发射曲线并与实验测量结果进行比较。结果表明在考虑上转换效应和放大自发发射的情况下,理论结果和实验测量结果是一致的。同时看到,选择合适的铒离子浓度是制作掺铒玻璃波导放大器的关键;并且为了全面发挥掺铒玻璃波导放大器的性能,需要抽运功率、波导长度等各个参量配合起来。     

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.     

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     

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.     

油酸修饰的LaF_3:Er,Yb纳米颗粒的光学特性及有机-无机复合型光波导放大器

采用微乳液法制备了LaF3:Er,Yb纳米颗粒,在有机-无机杂化材料中有良好的溶解性,掺杂质量比可达到50%。通过TEM观察到纳米颗粒的粒径为6~10 nm;XRD的测试结果表明材料中形成了LaF3六方晶体结构;荧光发射谱的测试表明纳米颗粒的荧光半峰全宽为79 nm;通过时间相关单光子计数法测得铒离子4I13/2能级的寿命为100μs。结合半导体工艺,制备了嵌入条形结构的平面光波导放大器,在信号光(1 550nm)功率为0.2 mW,泵浦光(980 nm)功率为188 mW的条件下,在1.9 cm的样品上得到了3.2 dB的相对增益;同时分析了散射损耗随颗粒大小的变化关系。     

Er与Yb共掺波导放大器的ADI-FDTD数值模拟

提出了一种新的简单的数值计算方法模拟Er与Yb共掺磷酸盐玻璃波导放大器(EYCDWA)的增益特性.该方法是基于交变隐式差分方向的时域有限差分法(ADI-FDTD)的迭代方法,用ADI-FDTD计算波导中的光场强度分布,用迭代法研究光波的传输方程.数值结果表明,增加光波导长度和提高Er³⁺浓度是提高EYCD WA增益的两种重要途径,Yb³⁺起能量传递的作用,Er/Yb的比率取1~4较好.     

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.     

掺铒玻璃波导放大器中抽运光信号光重叠因子分析

通过分析掺铒(Er3 )玻璃波导放大器(EDWA)的放大增益机理,提出抽运光与信号光光模场分布之间的归一化重叠积分因子(Γ),并引入到掺铒波导放大器增益模拟计算中,使理论模型更切合实际。以Ag -Na 二次离子交换工艺制作的具有埋入型渐变折射率分布的掺铒波导放大器为例,采用数值方法模拟了条形波导截面上的二维折射率分布及抽运光、信号光的光模场分布。计算了不同工艺参量设置下的Γ大小,讨论Γ对放大器增益的影响。结果显示,在二次离子交换制作过程中设置适当工艺参量优化折射率分布,能有效改善波导中抽运光与信号光光模场分布之间的重叠因子,提高掺铒波导放大器的增益。计算结果显示,在一定条件下,Γ从0.5增至0.8,每厘米长度掺铒波导放大器的放大增益可提高近1.5 dB。     

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.     

Amplifying Characteristics of Er3+/Yb3+ Co-Doped Parallel-Cascaded Double Microring Resonators

Abstract

In terms of the coupled mode theory, formulas of the transfer function and the output power gain are presented for an Er³⁺/Yb³⁺ co-doped parallel-cascaded double microring resonator. Around the pump wavelength of 0.98 μm and the central signal wavelength of 1.55 μm, analysis is performed for the dependence of the output power gain on the pump power, signal power, dopant concentration, amplitude coupling ratio, and ring spacing. The results show that the output power gain of this device is much larger than that of the Er³⁺/Yb³⁺ co-doped waveguide amplifier with identical waveguide lengths. In the case of the amplitude coupling ratio κ = 0.064, ring spacing L₂ = 10π R, pump power P_p0 = 8 mW, signal power P_s0 = 37.2 μW, Er³⁺ ion concentration N_Er = 1 × 26 m^?3, and Yb³⁺ ion concentration N_Yb = 3 × 27 m^?3, the device can produce higher signal power gain from 11.9 dB even up to 70 dB.     

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.     

Analysis for amplifying characteristics of Er-Yb-co-doped microring resonators

Formulas of the transfer functions and the output power gains are presented, amplifying characteristics are analyzed, and simulation is performed for an Er³⁺-Yb³⁺-co-doped microring resonator. Under the pump wavelength of 980 nm and the central signal wavelength of 1550 nm, the dependence of the output power gain on the amplitude coupling ratio, pump power, signal power, and the dopant concentration is investigated, the output spectra are presented, and the optimization of the device is carried out. Simulated results show that the output power gain of this device is much larger than that of the Er³⁺-Yb³⁺-co-doped straight waveguide amplifier (EYCDWA) with the same waveguide parameters.     

Modeling and Simulation of Saturation Gain of IR Integrated Photonic Amplifiers

IR integrated photonic amplifiers at 1.55m operation will have good foreground in optical phasedarray radars for splitters and signal processing. The saturation gain characteristics of IR integrated photonic waveguide amplifiers (taken Er³⁺Yb³⁺ co-doped phosphate glass waveguide amplifiers as an example) are studied theoretically. For the homemade laser glass materials the calculated saturation intensities are 2.22kw /cm² for signal and 10.15kw/cm² for pump. The effects of absorption saturation of signal and pump lights on the gain of amplifiers are discussed.     

High index contrast Er:Ta2O5 waveguide amplifier on oxidised silicon

We report a high index contrast erbium doped tantalum pentoxide waveguide amplifier. 2.3 cm long waveguides with erbium concentration of 2.7 × 10²⁰ cm^? 3 were fabricated by magnetron sputtering of Er-doped tantalum pentoxide on oxidised silicon substrates and Ar-ion milling with photolithographically defined mask. A net on-chip optical gain of ~ 2.25 dB/cm at 1531.5 nm was achieved with 20 mW of pump power at 977 nm launched into the waveguide. The pump threshold for transparency was 4.5 mW.     

Numerical analysis of amplification characteristics of ErxY2 − xSiO5

The gain characteristics of Er_xY_2 − xSiO₅ waveguide amplifiers have been investigated by solving rate equations and propagation equations. The gain at 1.53 μm as a function of waveguide length, Er³⁺ concentration and pump power is studied pumping at three different wavelengths of 654 nm, 980 nm and 1480 nm, respectively. The optimum Er³⁺ concentrations of 1 × 10²¹ cm^− 3-2 × 10²¹ cm^− 3 with the high gain are obtained for all three pump wavelengths. Pumping at 654 nm wavelength is shown to be the most efficient one due to weak cooperative upconversion. A maximum 16 dB gain at 1 mm waveguide length under a 30 mW pump with Er³⁺ concentration of 1 × 10²¹ cm^− 3 is demonstrated pumping at 654 nm wavelength.     

Optical phase conjugation and waveguide coupling by cascading transverse second-harmonic and difference-frequency generation in a vertical cavity

We propose a novel scheme for implementing optical phase conjugation (OPC) by cascading transverse second-harmonic and difference-frequency generation in a vertical cavity. We propose to achieve phase conjugation in the pump and input-output two-waveguide structure. For a symmetric waveguide structure, the structure can be used as an optical phase conjugate mirror. For a realistic structure based on III–V semiconductor materials, a pump power per unit waveguide of 0.74 W m^-1 is required to reach a conversion efficiency of 9.4%. Combined with another phase-conjugate mirror, the reflectivity of the proposed phase-conjugate mirror can be efficiently modulated by control of the pump power. For an asymmetric waveguide structure, a gain is predicted. In addition, by cascading second-harmonic generation (SHG) and parametric oscillation, we propose to use the same structure as a waveguide coupler. There is a threshold to achieve coupling.     

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.     

Correct determination of net gain in Er-doped optical waveguide amplifier from pump-on/off measurement

Starting with evolution equation of signal optical power in an Er-doped channel waveguide, rigorous theoretical expressions used for correct determination of net gain from signal enhancement measured by using pump-on/off method are derived. These expressions allow to clarify the argument on relationships between net gain, internal gain and signal enhancement in some earlier literatures. Physical implications of net gain, internal gain and signal enhancement expressions are analyzed. Standardized definitions for the three physical quantities are proposed. The definition for net gain is proposed on the basis of practical application of an EDWA in optical fiber communication and the definitions for the latter two are suggested based on the physical implication analysis of their expressions.