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.     

A Novel Approach for the Temperature Dependence of the Saturated Signal Power in EDFAs

The temperature dependence of the saturated signal power for the ⁴I_13/2 → ⁴I_15/2 transition in erbium-doped fiber amplifiers (EDFAs) pumped at 980 nm and 1480 nm pumping wavelengths within a temperature range from −20 to 60°C are investigated by a novel approach. This approach is based on the temperature dependence of the saturated signal power. The influence of pump excited-state absorption (ESA) is inserted into the rate equations so as to investigate a generally situation. For 1480 nm pumping regime, it is seen that the saturated signal power increases more quickly than that of 980 nm pumping regime, with the increasing temperature. The variation in the saturated signal power with temperature is nearly constant at 980 nm pumping regime. In addition, the population inversion with respect to the increasing normalized signal power is examined and it is seen that it is independent temperature for 980 nm but it strongly depends on temperature for 1480 nm especially at lower normalized signal powers.     

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.     

High-gain Al2O3:Nd3+ channel waveguide amplifiers at 880 nm, 1060 nm, and 1330 nm

Neodymium-doped aluminum oxide films with a range of Nd³⁺ concentrations are deposited on silicon wafers by reactive co-sputtering, and single-mode channel waveguides with various lengths are fabricated by reactive ion etching. Photoluminescence at 880, 1060, and 1330 nm from the Nd³⁺ ions with a lifetime of 325 μs is observed. Internal net gain at 845–945 nm, 1064, and 1330 nm is experimentally and theoretically investigated under continuous-wave excitation at 802 nm. Net optical gain of 6.3 dB/cm at 1064 nm and 1.93 dB/cm at 1330 nm is obtained in a 1.4-cm-long waveguide with a Nd³⁺ concentration of 1.68×10²⁰ cm^?3 when launching 45 mW of pump power. In longer waveguides a maximum gain of 14.4 dB and 5.1 dB is obtained at these wavelengths, respectively. Net optical gain is also observed in the range 865–930 nm and a peak gain of 1.57 dB/cm in a short and 3.0 dB in a 4.1-cm-long waveguide is obtained at 880 nm with a Nd³⁺ concentration of 0.65×10²⁰ cm^?3. By use of a rate-equation model, the gain on these three transitions is calculated, and the macroscopic parameter of energy-transfer upconversion as a function of Nd³⁺ concentration is derived. The high internal net gain indicates that Al₂O₃:Nd³⁺ channel waveguide amplifiers are suitable for providing gain in many integrated optical devices.     

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     

Broadband photoluminescence from pulsed laser deposited Er2O3 films

Photoluminescence (PL) with the bandwidth of 45 nm (1523-1568 nm at the level of 3 dB) was observed in amorphous Er₂O₃ films grown on to the quartz substrate by pulsed laser ablation of erbium oxide stoichiometric target. Optical transmission spectrum has been fitted to Swanepoel formula to determine the dispersion of refractive index and to extract resonance absorption peaks at 980 and 1535 nm. The maximum gain coefficient of 800 dB/cm at 1535 nm was estimated using McCumber theory and experimental spectrum of the resonance absorption. In 5.7 mm-long waveguide amplifier a theory predicts the spectral gain of 20 dB with 1.4 dB peak-to-peak flatness in the bandwidth of 31 nm (1532-1563 nm) when 73% of Er³⁺ ions are excited from the ground state to the ⁴I_13/2 laser level. Strong broadband PL at room temperature and inherently flat spectral gain promise Er₂O₃ films for ultra-short high-gain optical waveguide amplifiers and integrated light circuits.     

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.     

Numerical investigation of gain characteristics of Er3+/Yb3+ co-doped fiber amplifiers

In this work, a model for analyzing the gain characteristics of heavily Er³⁺/Yb³⁺ co-doped compact fiber amplifier is presented. Four-level rate equations and finite-difference beam propagation method are applied to simulate the optical field evolution along the active fiber. Based on this model, the influences of ion concentration, fiber length and pump power on the gain characteristics of Er³⁺/Yb³⁺ co-doped phosphate glass fiber amplifiers are theoretically investigated. Numerical results show that for a fiber length of 3.6 cm the internal gain can reach 27.2 dB with N _Er = 2.6 × 10²⁶ ions/m³ and N _Yb = 1.2 × 10²⁷ ions/m³ when pumped with 224 mW at 980 nm. The gain per centimeter is 7.56 dB/cm. The results can provide useful information to optimize the gain performance of these compact fiber amplifiers.     

Waveguiding and photoluminescence in Er-doped Ta2O5 planar waveguides

The optimization of erbium-doped Ta₂O₅ thin film waveguides deposited by magnetron sputtering onto thermally oxidized silicon wafer is described. Optical constants of the film were determined by ellipsometry. For the slab waveguides, background losses below 0.4 dB/cm at 633 nm have been obtained before post-annealing. The samples, when pumped at 980 nm yielded a broad photoluminescence spectrum (FWHM∼50 nm) centred at 1534 nm, corresponding to ⁴I_13/2-⁴I_15/2 transition of Er³⁺ ion. The samples were annealed up to 600 °C and both photoluminescence power and fluorescence lifetime increase with post-annealing temperature and a fluorescence lifetime of 2.4 ms was achieved, yielding promising results for compact waveguide amplifiers.     

The temperature dependency of EDFAs in the 1480 nm pumping configuration

A theoretical study of the temperature-dependent gain and noise figure effects on erbium-doped fiber amplifiers (EDFAs) pumped at 1480 nm is investigated, solving the propagation equations related to two level systems. The solution of these equations is based on the population and temperature difference among amplification levels. The temperature-dependent propagation equation considered is used to determine the gain and noise figure effects on EDFAs. The population difference depends on pump and signal powers, Boltzmann factor K_B, cross-sections, noise figure (NF) and Er³⁺ concentration. The temperature-dependent gain and noise figure effect the EDFA length are numerically obtained for the temperature range of −20 °C to +60 °C. All of the analyses consist of the amplified spontaneous emission (ASE) effect.     

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.     

Bismuth-based erbium-doped fiber as a gain medium for L-band amplification and Brillouin fiber laser

Bismuth-based erbium-doped fiber (Bi-EDF) is demonstrated as an alternative medium for optical amplification and nonlinear applications. The bismuth glass host provides the opportunity to be doped heavily with erbium ions to allow a compact optical amplifier design. The bismuth-based erbium-doped fiber amplifier (Bi-EDFA) is demonstrated to operate at wavelength region from 1570 to 1620 nm using only a 215 cm long of gain medium. The maximum gain of 15.8 dB is obtained at signal wavelength of 1610 nm with the corresponding noise figure of about 6.3 dB. A multi-wavelength laser comb is also demonstrated using a stimulated Brillouin scattering in the 215 cm long Bi-EDF assisted by the 1480 nm pumping. The laser generates more than 40 lines of optical comb with a line spacing of approximately 0.08 at 1612.5 nm region using 152 mW of 1480 nm pump power.     

Er3+-Yb3+共掺磷酸盐玻璃(LGS-L)波导放大器设计

就作者自行研制的Er3 + Yb3 + 共掺磷酸盐玻璃 (LGS L) ,用重叠积分方法进行放大器设计。在Er3 + 、Yb3 + 掺杂浓度分别为 1.5 1× 10 2 6ions/m3 、19.1× 10 2 6ions/m3 的情况下可获得 2 .6dB/cm的增益 ;Er3 + 掺杂浓度为2× 10 2 6ions/m3 时 ,在 4cm的器件上可获得超过 15dB的增益。此外 ,讨论了信号光和抽运光光场强度的横向分布与Er3 + 、Yb3 + 横向掺杂浓度分布之间的重叠对放大器增益的影响 ,放大器的最佳长度 ,以及在 980nm抽运下 ,Yb3 + 、Er3 + 掺杂浓度比对放大器增益的影响。     

长波段掺铒光纤放大器用掺铒光纤的设计考虑

本文分析了长波段掺铒光纤放大器(EDFA)的增益系数与Er³⁺离子浓度的关系.研制了铝共掺杂的高浓度掺铒光纤,以缩短长波段掺铒光纤的长度.用两级泵浦实现了L-波段EDFA.光纤放大器的掺铒光纤总长18m,在1570nm波长处的小信号增益为42.26dB,输出功率为17.5dBm.我们认为,较低的浓度淬灭效应归因于光纤中较高的A1掺杂浓度.当总的输入信号功率为-3dBm时,在1570至1600nm间的7路WDM信号的增益不平坦度仅为0.68dB..     

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.     

Spectral gain characteristics induced by 980 nm pumping band in a gain-flattened EDFA

We demonstrate the effect of inversion population ratio mediated by 980 nm pumping band on the gain spectra of a gain-flattened Erbium-doped fiber amplifier. The gain equalizing filter was designed at 977 nm and the amplifier was built in the four-stage arrangement. In the pumping structure, the 1480 nm lasers were maintained in the final gain block while the 980 nm band lasers were utilized in the first three blocks. These laser sources were arranged at several combinations of 977 and 980 nm wavelengths. Within these 3 nm spectrum, an absorption cross-section difference around 0.32 × 10⁻²⁵ m² contributed to a dispensable gain variation up to 3-dB. These inequalities were the results of variations in population inversion induced by the pump wavelength discrepancy. The findings show the importance of designing a filter at the specific absorption wavelength to allow the operation of consistent gain level.     

基于Bi3+Ga3+Al3+共掺高掺铒光纤的短线腔激光器

短线腔掺铒光纤激光器由环形器(OC)、自制的Bi3+Ga3+Al3+共掺高浓度掺铒光纤(BiGaAl-EDF)、均匀光纤布拉格光栅(UFBG)和波分复用器(WDM)组成.以OC作为全反射腔镜,UFBG为波长选择性部分反射腔镜,利用1 530 nm处吸收系数为84.253 dB/m的BiGaAl-EDF为增益介质,室温下...     

Theoretical and experimental investigations on erbium-doped fiber amplifiers

A comprehensive model of erbium-doped fiber amplifiers (EDFA) is proposed in this paper, taking exited-state absorption (ESA), amplified spontaneous emission (ASE), background absorption, mode field, and Erbium ion radial distribution into account. Computer programs capable of handling forward, backward, and different wavelength bidirectional pumping are developed. Among other things, it is found that under typical conditions, Gaussian field approximations may cause considerable errors. The optimum V-value for small signal gain is much smaller than that for minimum Gaussian or Desurvire spot size; ASE propagating opposite to the pimp beam can be several times higher than at propagating along the pump beam, resulting in a faster-than-linear decrease of the pump power at its beginning portion. Experimental results of domestic-made erbium-doped fibers pumped by 980 nm and 1480 nm laser diodes are also given.     

Yb3+sensitized Er3+-doped waveguide amplifiers: a theoretical approach

Silicate and phosphate glass waveguide amplifiers doped with Er³⁺, and co-doped with Er³⁺/Yb³⁺ are theoretically studied. Configurations for core and core–cladding doped waveguide amplifiers are considered. It is shown that gain in the core–cladding doped amplifiers is considerably higher than core doped amplifiers. It is also shown that with input signal power up to 1 and 200mW pump power, a 12.5dB gain can be achieved in a 3cm long waveguide amplifier, with a noise figure of 3dB.