Modeling of gain in erbium-doped fiber amplifiers

An analytic method is described for fully characterizing the gain of an erbium-doped fiber amplifier (EDFA) that is based on easily measured monochromatic absorption data. The analytic expressions presented, which involve the solution of one transcendental equation, can predict signal gains and pump absorptions in an amplifier containing an arbitrary number of pumps and signals from arbitrary directions. The gain of an amplifier was measured over a range of more than 20 dB in both pump and signal powers. The measured theoretical results agreed to within 0.5 dB. Although the results described apply explicitly to EDFAs pumped in the 1480-nm region, they are also applicable to EDFAs pumped in the 980-nm region. The method is valid whenever the gain saturation by amplified spontaneous-emission noise can be neglected, which is typically the case for amplifiers with less than about 20 dB of gain     

Modeling of noise in erbium-doped fiber amplifiers in the saturatedregime

We have made a theoretical study of the noise figure of erbium-doped fiber amplifiers in the saturated regime. The noise figures of amplifiers subjected to specific gain and gain compression requirements were calculated for various amplifier lengths. The resulting noise figures together with the required pump and input signal powers map out all possible solutions given constraints on gain, compression, pump power, output signal power, and noise figure. In some cases, requirements on the output signal power prohibit any solutions. A way to solve this problem is the introduction of a post-amplifier loss. For this configuration, two possible solutions exist, which collapse into one solution at a certain critical loss, under which there exist no solutions. When the impact of amplified spontaneous emission is neglected in the model, only one solution is obtained, and the critical loss is much smaller than when the amplified spontaneous emission is included in the model. We conclude that amplified spontaneous emission generally has to be taken into account, even when the gain is as low as 10 dB, to accurately predict the noise performance of erbium-doped fiber amplifiers     

Novel fiber sensor arrays using erbium-doped fiber amplifiers

We examine the signal-to-noise ratio (SNR) performance of a novel type of time domain multiplexed sensor arrays in which low gain (1-10 dB) fiber amplifiers are incorporated to compensate for splitting losses between sensors. The system noise figure for passive and amplified sensor arrays is presented, along with expressions to optimize the array parameters for high SNRs. We show that practical amplified sensor arrays exhibit low system noise figures that allow much larger arrays (hundreds of sensors) than passive arrays     

Performance of high-concentration erbium-doped fiber amplifiers

The full characteristics for two high-concentration erbium-doped fibers are reported. The comparison of the fibers characteristics indicates that design of fiber geometry can be used to partially compensate for the degradation of the amplifiers performance due to upconversion processes. For high NA fiber the 22-dB small-signal gain, and 3.5-dB noise figure are obtained from a 24-cm length of fiber. We report a photon quantum conversion efficiency of 28%, which corresponds to the highest efficiency obtained in heavily doped fibers     

Transient analysis of erbium-doped fiber amplifiers

The transient response of an erbium-doped fiber amplifier (EDFA) pumped at 1.48 μm, taking into account the gain-saturation effects due to the amplified spontaneous emission (ASE), is studied theoretically and experimentally. The theoretical model is used to predict the gain saturation and recovery times of an EDFA and its effects to the amplification of optical pulses     

Modulation instability in erbium-doped fiber amplifiers

The onset of modulation instability in erbium-doped fiber amplifiers (EDFAs) is studied through a stability analysis of the underlying nonlinear Schrodinger equation. The existence of gain in EDFAs lowers the threshold for modulation instability considerably compared with the case of undoped fibers. Modulation instability generates multiple pulses when a single pulse is amplified. It can also create multiple subpulses in mode-locked fiber lasers, a feature observed experimentally. Numerical simulations show that EDFAs can convert a continuous-wave optical signal into a train of high-repetition rate femtosecond pulses     

Design optimization for efficient erbium-doped fiber amplifiers

The gain and pumping efficiency of aluminosilicate erbium-doped fiber amplifiers (EDFAs) are analyzed as a function of guiding parameters and Er-doping profile for two pump wavelengths of λ _p=980 nm and λ_p=1.47 μm. Three designs of fiber-amplifier waveguides are considered: one with the same mode size as standard 1.5-μm communication fibers (type 1); one with the same mode size as standard 1.5-μm dispersion-shifted fibers (type 2); and one with mode size smaller than those of communication fibers (type 3). For the 1.47-μm pump, fundamental LP₀₁ mode excitation is assumed, while for the λ_p=980-nm pump, concurrent excitation of LP₁₁ modes is considered. It is shown that excitation of higher-order pump modes at 980 nm does not significantly affect the amplifier gain performance. The effect of concentrating the Er³⁺ doping near the center of the fiber core is shown to increase the amplifier gain coefficients by a factor of 1.5 to 2     

Efficient erbium-doped fiber amplifiers incorporating an opticalisolator

A composite-EDFA configuration which incorporates an optical isolator has been investigated theoretically and experimentally. The isolator prevents the build-up of the backward-ASE and results in an amplifier with high gain and near-quantum-limited noise figure (NF). The optimum position of the isolator has been calculated as a function of the pump power so that minimum NF and maximum gain are achieved simultaneously. It is shown that under practical pump powers, the optimized composite EDFA exhibits a gain improvement of about 5 dB and a NF reduction in excess of 1.5 dB when compared with an optimized conventional EDFA. It is also shown that with further optimization the composite EDFA can be employed in a practical fiber link as a pre-amplifier without the use of an input isolator. Finally, a high-gain composite EDFA has been experimentally demonstrated which exhibits a gain of 51 dB (54 dB) and NF of 3.1 dB for only 435 mW (93 mW) of pump power     

Spectral hole burning in erbium-doped fiber amplifiers

A new theoretical/numerical model of the spectral hole burning (SHB) effect in erbium-doped fiber amplifiers (EDFAs) is suggested. A new measurement technique for SHB measurement is developed. Experiments are conducted to identify the particular mechanism of SHB. A computer simulation program is developed using this approach. The shape and depth of the spectral hole are in accordance with the suggested theory.     

Detailed design analysis of erbium-doped fiber amplifiers

When pumping the erbium-doped fiber amplifier at 0.98 and 1.48 mu m, the optimum cutoff wavelength for step profiles with arbitrary numerical aperture is shown to be 0.80 and 0.90 mu m, respectively. The use of a confined erbium profile can improve the gain coefficient up to 45%. The index raising co-dopant is shown to be very significant for the gain coefficient when pumping at 0.98 mu m.<>     

Distributed temperature sensing with erbium-doped fiber amplifiers

The experimental verification of a novel fiber-optic sensor which performs distributed measurement of temperature by using a distributed erbium-doped fiber amplifier (EDFA) is presented. The sensor configuration is similar to that of a conventional optical time-domain reflectometer and detects the Rayleigh backscattered portion of a pulsed optical signal which is amplified by the EDFA, along with the backward amplified spontaneous emission (ASE) generated by the EDFA. The sensor utilizes the temperature dependence of the gain in an EDFA. The amplification provided by the erbium-doped fiber, which is pumped at 1.48 μm, significantly increases the magnitude of the optical signal reaching the receiver, thus leading to a simplified configuration and a potentially superior performance as compared to other types of distributed fiber-optic temperature sensors     

掺铒光纤放大器的速率方程研究

在引入光场与掺杂分布的重迭因子后,对1.48μm波段泵浦的掺饵光纤放大器的速率方程组进行了解析求解,并利用有关的表达式对放大器的重要特性进行了讨论和分析。     

Average power analysis technique for erbium-doped fiber amplifiers

It is shown that an average power analysis technique similar to that used for semiconductor optical amplifiers can be used to analyze both the discrete and the distributed fiber amplifier for multiwavelength operation without the need for numerical integration. It is also shown to give results that are in excellent agreement with those from other studies. This approach gives performance insights that are not otherwise readily available     

Analysis of distributed erbium-doped fiber amplifiers with fiber background loss

An accurate model for erbium-doped fiber amplifiers with fiber background loss applicable to the unsaturated gain regime is presented. Exact analytical solutions are derived for the output pump power, gain, and amplified spontaneous noise as a function of input pump power in the cases of unidirectional or bidirectional pumping. An exact relation is also derived between the pump threshold and the pump required for fiber transparency. Such expressions are particularly useful to model distributed fiber amplifiers and to determine the optimal fiber parameters corresponding to a given pumping scheme. As an example, the analytical solutions are used to study the pump power requirement for distributed fiber amplifiers unidirectionally pumped at 1.48 mu m, and to determine an optimum Er/sup 3+/ absorption coefficient.<>     

Dynamic gain compensation in saturated erbium-doped fiber amplifiers

Dynamic compensation of low-frequency gain fluctuations in saturated erbium-doped fiber amplifiers is demonstrated. This compensation, based on a simple feedback-loop scheme makes it possible to reduce transient gain fluctuations efficiently across the whole amplifier bandwidth using only a low-power optical feedback signal. Such an, automatic gain control technique could be applied to suppress data packet interference due to traffic bursts in multiple-access networks, as well as in the implementation of long-haul fiber systems using erbium fiber amplifiers.<>     

Noise figure of erbium-doped fiber amplifiers in saturatedoperation

We have developed a simple electrical noise figure measurement technique for the characterization of optical amplifiers. By subtracting the results of noise measurements at identical detected power levels made with and without the amplifier present, we are able to achieve an accuracy of ±0.3 dB in measured noise figure. Using this technique we obtain an excellent agreement between electrically and optically measured noise figures for two 98O-nm-pumped, copropagating erbium-doped fiber amplifiers (EDFA's) operating in saturation     

多波长掺铒光纤激光放大器的放大特性研究

为了研究多波长掺铒光纤激光放大器的放大特性,在单频放大器的基础上,忽略放大自发辐射,推导了描述多波长掺铒双包层光纤放大器的稳态速率方程组,建立了多波长掺铒光纤放大器的理论模型。利用该模型对单波长放大、双波长放大、四波长放大的特性,进行了数值模拟和理论分析;以四波长的激光信号放大为例,对多波长掺铒光纤放大器的放大特性,均衡增益特性进行了研究。结果表明,在单波长注入情况下,光纤放大器的掺杂光纤存在最佳光纤长度为8m;与小信号放大不同,大功率掺铒光纤放大器在1530nm~1560nm之间增益谱趋于平坦;双波长放大输出功率差随着波长间隔的增加线性增大波长间隔为20nm时,通过调节输入信号功率比可以实现最大功率差6.855W的功率均衡补偿;四波长放大时,通过信号功率配比之后的四波长激光输出功率最大偏差为0.28W,在一定范围内实现了均衡增益。这一结果对于掺铒光纤激光的多波长激光输出以及在激光多普勒测风雷达中的应用具有一定帮助。     

On the non-Gaussian noise in erbium-doped fiber amplifiers

The non-Gaussian character of the probability density functions (PDFs) of binary signals dominated by signal-spontaneous and spontaneous-spontaneous beat noise in erbium-doped fiber amplifiers (EDFAs) is experimentally verified and their impact on the operation of decision circuits in optically preamplified digital receivers discussed     

Second-order harmonic distortion and optimal fiber length in erbium-doped fiber amplifiers

The gain of an erbium-doped fiber amplifier (EDFA) operating in the kHz regimes and its second-order harmonic distortion (SBD) are studied. Using the rate and beam-propagation equations, we have shown the dependences of the distortion on the pump power, the modulation frequency, and the position along the fiber. Moreover, it is found that the SHD is the smallest when the fiber has an optimal length for the maximum gain. A relation between the optimal length and fiber parameters is presented for calculating easily the optimal fiber length in an EDFA.