Analysis of the Crosstalk in WDM Systems Caused by Cross-phase Modulation in Erbium-doped Fiber Amplifiers

The crosstalk in WDM systems caused by cross-phase modulation (XPM) in erbium-doped fiber amplifiers(EDFA) was studied analytically. The results confirm that the EDFA induced phase shift does cause crosstalk in WDM systems. The crosstalk between two channels both with modulated pulse signals is studied for the first time. It was found that the EDFA induced phase shift will cause serious deterioration of the eye diagram when the optical signals continue to travel in the normal-dispersion regime of the transmission fiber, while in the anomalous-dispersion regime this phase shift will not cause much deterioration of the eye diagram.     

An ASE Reduction Filter Using Cascaded Optical Fiber Grating Couplers in EDFA Repeater

A new configuration for an ASE reduction filter in EDFA repeaters for WDM optical transmission systems using optical fiber grating couplers (FGCs) was proposed and first demonstrated. The filtering characteristics of the proposed filter for amplified single wavelength signal and 2-channel WDM signals using EDFA were identified. It was found that the filter was effective to improve SNR in optical domain by reducing ASE noise. The required FGC characteristics for the filter were theoretically predicted under the condition that the total filter loss did not exceed 3 dB. More than 70% of drop efficiency was required in each FGC for the application of the proposed filter to an 8-channel WDM system using EDFA repeaters.     

Analytical investigations on crosstalk in fiber Raman amplification for WDM systems

In this paper, the analytical investigations for the crosstalk in fiber amplification for WDM channels have been reported. The crosstalk between WDM channels with external Raman amplification including second-order dispersion terms has been investigated. It has been shown that the higher-order dispersion severely degrades the performance of optical communication systems. To ensure small crosstalk, the signal gain and the injected pump power should be limited to the value well below the threshold of Raman amplification. Analytical formula for signal interference ratio (SIR) and gain in fiber Raman amplifier including the impact of second-order dispersion terms for WDM systems has been derived at different wavelengths. It has also been shown that there is increase in crosstalk due to second-order dispersion.     

利用色散管理抑制半导体光放大器引起的信道间串扰

理论研究了半导体光放大器增益饱和效应引起的信道间串扰,数值模拟了多路信道复用时系统的误码率随复用信道数和光功率的变化情况,发现随着复用信道数的增加,半导体光放大器增益饱和引起的信道间串扰越来越严重.对利用色散管理技术抑制半导体光放大器引起的信道间串扰进行了实验研究,实验验证了信号色散补偿之前用半导体光放大器放大可以抑制半导体光放大器引起的信道间串扰.结果表明,采用先放大后色散补偿这种新的色散补偿方案,可以有效抑制半导体光放大器引起的信道间串扰.     

Optimum algorithm for WDM channel allocation for reducing four-wave mixing effects

A novel channel allocation method, based on optical Golomb ruler (OGR), that allows reduction of the FWM effect while maintaining bandwidth efficiency along with the algorithms has been presented in this paper. Very high-capacity, long-haul optical communication systems can be designed by wavelength division multiplexing (WDM) of high-bit-rate channels and by using erbium-doped fiber amplifiers (EDFAs) to periodically compensate the fiber loss. In such all-optical systems, the effects of chromatic dispersion and nonlinearities accumulate during light propagation, imposing limits on the achievable performance. Chromatic dispersion at 1.55 pm can be effectively reduced by using dispersion-shifted fiber (DSF). The use of very-low-dispersion fiber, however, enhances the efficiency of generation of four-wave mixing (FWM) waves by reducing the phase mismatch naturally provided by the fiber dispersion. For this reason, crosstalk due to FWM is the dominant nonlinear effect in long-haul WDM systems using DSFs. To reduce four-wave-mixing crosstalk in high capacity long-haul repeater less WDM light wave systems, the use of the channel allocation method that involves unequal spaced channels has been proposed.     

一种适于高速,多路通信系统的小色散单模光纤

给出了色散系数分别为（±２ｐｓ／ｋｍ／ｎｍ的小色散单模光纤一种可能的折射率分布及主要的设计参数，并讨论了此光纤在系统中的应用。结果表明小色散单模光纤具有的适当色散，既可有效抑制四波混频，又不致造成严重的色散限制，故适于高速、多路光纤通信系统采用。在系统中同时使用色散补偿技术时，在相邻在线放大器间采用ＩＴＵ－ＴＧ．６５２常规单模光纤结合负小色散单模光纤的方案不仅可有效地抑制四波混频并减小光纤色散限制，使１０×１０Ｇｂ／ｓ、１０级掺铒光纤放大器系统占用带宽从１６．２ｎｍ压缩到９．４ｎｍ；甚至可能实现等间距信道传输，从而大大简化了此类系统的设计     

Space radiation effect on EDFA for inter-satellite optical communication

The erbium-doped fiber (EDF) has been irradiated by electron with a dose of 1000 krad to analyse the space radiation effect on EDF amplifier (EDFA) in inter-satellite optical communication. This is the first work to analyse the effect on actually applied systems. Three critical parameters of EDFA, most important for external module subsystems, have been tested. The output power comes down to −57.21 dBm and the noise figure (NF) climbs up to 18.14 dB at dose 1000 krad, when the input power is −2.00 dBm. Although there is a strong ability to recover after the radiation experiment, EDFA deterioration is really huge. Apart from that, the central wavelength of EDFA never changes. To guarantee the accuracy of analysis of the radiation effect on EDFA, WDM coupler and isolator are also irradiated with the EDF at the same time. According to the results of all the tests, the EDFA could be directly used in the low-radiation dose orbits if doses are less than 20 krad. And the radiation experiment data will also be a good reference for the design of the actual systems in inter-satellite optical communication with different dose orbits.     

Suppression of Output Power and NF Excursions in Cascades of Highly Inverted EDFAs with Packet-Switched Traffic

Significant output power excursions in cascades of erbium-doped fiber amplifiers (EDFAs) can cause serious problems in wavelength division multilexing (WDM) packet-switched burst-mode networks. Signal power excursions more serious than those induced by channel addition/removal in circuit switched networks can arise when data on the WDM channels is highly variable in nature. Self-similar traffic can be subject to large variation in EDFA gain. In order to prevent unacceptable error bursts, due, for example, to channel power becoming too low to preserve adequate eye opening or exceeding thresholds for optical nonlinearities, the channel power should be maintained constant. In this letter, it is shown that the sizable power and noise figure swings arising in a cascade of EDFAs with WDM burst-mode packet-switched networks with self-similar traffic can be effectively suppressed when highly inverted amplifiers are employed. The analysis is based on the application of a numerical model, which solves the transcendental equation for length averaged metastable level population of an EDFA.     

Suppression of Output Power and NF Excursions in Cascades of Highly Inverted EDFAs with Packet-Switched Traffic

Significant output power excursions in cascades of erbium-doped fiber amplifiers (EDFAs) can cause serious problems in wavelength division multilexing (WDM) packet-switched burst-mode networks. Signal power excursions more serious than those induced by channel addition/removal in circuit switched networks can arise when data on the WDM channels is highly variable in nature. Self-similar traffic can be subject to large variation in EDFA gain. In order to prevent unacceptable error bursts, due, for example, to channel power becoming too low to preserve adequate eye opening or exceeding thresholds for optical nonlinearities, the channel power should be maintained constant. In this letter, it is shown that the sizable power and noise figure swings arising in a cascade of EDFAs with WDM burst-mode packet-switched networks with self-similar traffic can be effectively suppressed when highly inverted amplifiers are employed. The analysis is based on the application of a numerical model, which solves the transcendental equation for length averaged metastable level population of an EDFA.     

交叉相位调制对非线性光纤环镜中光脉冲传输的影响

基于耦合非线性薛定谔方程，采用分步傅里叶方法分析了在单波长信道和WDM（波分复用）4波长信道中XPM（交叉相位调制）对高速NOLM（非线性光纤环镜）光开关中脉冲传输的影响.数值计算表明：XPM造成NOLM中信号脉冲串扰与畸变，并造成NOLM开关性能的下降.WDM系统NOLM光纤环中的同向传播的各波长之间的XPM串扰比相向脉冲之间的XPM效应的影响更大，并且波长越短输出功率越低，中间信道受XPM的影响所导致的脉座现象和走离效应比两侧波长信道严重.     

Performance comparison between digital back propagation (DBP) and pilot-aided method for fiber nonlinearity compensation in different fiber links

We numerically investigate and compare the performance of fiber nonlinearity compensation using digital back propagation (DBP) method and pilot-aided method in coherent optical transmission systems using different fiber links. Simulations for wavelength division multiplexed (WDM) 112 Gb/s polarization division multiplexed quadrature phase shift keying (PDM-QPSK) systems with dispersion unmanaged (no DM) and dispersion managed (DM) fiber links are implemented. System Q-factor and maximum transmission distance at bit error rate (BER) of 3.8 ÿ 10^?3 are calculated for performance comparison. The results show that, for system with no DM fiber link, DBP method outperforms pilot-aided method, because DBP method has better performance for intra-channel fiber nonlinearity compensation. However, for system with DM fiber link where inter-channel fiber nonlinearity plays an important role, pilot-aided method performs better than DBP method, because of its ability for inter-channel fiber nonlinearity compensation.     

Impacts of dispersion maps on nonlinear distortion in distributed Raman amplified multi-span systems

The influences of dispersion maps on three major nonlinear effects (SPM, XPM and SRS) in distributed Raman amplified fiber transmission systems with periodic dispersion compensation are numerically investigated at identical nonlinear phase shift. The results show that compared with lumped amplification, distributed amplification tends to enhance the SPM/XPM induced penalties provided per span complete DC is used. However, these performance differences can be canceled out by means of optimal dispersion managements. Moreover, distributed Raman amplification can change the optimal dispersion maps for XPM effects. On the other hand, the impacts of SRS crosstalk are mainly determined by wavelength spacing and walk-off parameter, and the effects of dispersion management are quite limited. For a system with properly designed fiber dispersion characteristics, SRS induced waveform distortion can be well suppressed.     

A Novel Gain-Clamped Erbium Doped Fiber Amplifier for Wavelength Division Multiplexed Systems

Amplification of multiwavelength signals by an erbium-doped fiber amplifier (EDFA) is becoming critical, due to the proliferation of wavelength division multiplexed systems. However, when a standard EDFA is employed, the dissimilarities among the signals’ gain may prove unacceptable. Thus, a novel gain-clamped EDFA is proposed here to tackle the issue of gain tilt. The suitability of the configuration is then investigated through a numerical model, which is developed based on the standard EDFA and fiber laser models.     

Limitation in the intrinsic method of EDFA gain optimization for 32 × 40 Gbit/s WDM systems

The gain flattening of the erbium doped fiber amplifier (EDFA) is one of the most important aspects in the EDFA which the gain is wavelength dependent. For the first time the limitation of EDFA gain optimizing for a 32-channel wavelength division multiplexing (WDM) systems is investigated and reported in this paper. In a 32-channel WDM system the most favorable flatness gain achieved was 23.16 ± 1.51 dB with an average noise figure of 5.70 dB. This outcome proposes that the method does not achieve a uniform spectral gain in a 32-channel WDM system that incorporates a bandwidth of around 25 nm. Based on the simulation results the intrinsic optimization of EDFA causes the poor SNR and peak signal power with great variation over a transmission distance of 480 km single mode fiber.     

THE NONLINEAR SCHR?DINGER EQUATION AND THE CROSS-PHASE MODULATION IN ERBIUM-DOPED FIBER AMPLIFIERS

The nonlinear Schr$\ddot{o}$dinger equation(NLSE) in erbium-doped fiber(EDF) was obtained. The cross-phase modulation (XPM) in the erbium-doped fiber amplifiers (EDFA) was studied based on this NLSE and the rate equations. A more generalized form of the propagation equation in EDFA was obtained which included the phase shifts the EDFA induced. An analytical expression was given to the XPM in the EDFA. It was found that the XPM in the EDFA dose not change very much with the wavelength except at the neighboring wavelengths (around 1531 nm) where the absorption and emission cross-sections of the erbium ions reach their maxima, and the XPMs have opposite signs on the two sides around 1531 nm. Furthermore, it was found that the XPM increases with the increase of the length of EDF.     

色散控制光孤子系统性能分析

研究色散控制光孤子系统中的放大器的自发辐射噪声与交叉相位调制对孤子传输特性的影响，采用变分法分析了色散控制孤子的均方频移、定时抖动和误码特性，从降低自发辐射噪声和交叉相位调制扰动引起的均方频移出发，确定了补偿段的特性参量，给出了三种传输控制方案，分析了各方案中色散控制孤子的传输特性，其结果对色散控制孤子系统的设计具有参考价值。     

Impact of ASE noise in WDM systems

The small signal analysis method is presented for the discussion of amplified spontaneous emission (ASE) noise in dispersion and nonlinear transmission fibers in wavelength division multiplex (WDM) systems. Based on it, the complete ASE noise spectra (include the ASE noise, the ASE noise enhanced by parametric gain and the crosstalk caused by ASE noise and parametric gain) are described and the factors impacting on them are discussed. The crosstalk caused by ASE noise and parametric gain in single mode fibers, non-zero dispersion shift fibers and dispersion compensation fibers are analyzed. Taking into account the dispersion effect in the transmission fibers, the three types of ASE noise may decrease.     

Cross-phase modulation induced phase fluctuations in optical RZ pulse propagating in dispersion compensated WDM transmission systems

The basic mechanism of cross-phase modulation induced phase fluctuations in optical RZ pulse propagating in a periodically dispersion compensated transmission line has been investigated. Ordinary differential equations have been derived using variational analysis to estimate the phase fluctuation and the analytical result is verified by numerical simulations based on split-step Fourier method. We therefore explore the impact of different dispersion compensation maps on phase fluctuation for 10 Gb/s and 40 Gb/s WDM transmission systems. The effects of initial pulse spacing between channels, channel spacing and residual dispersion on phase shift have been studied. We find that cross-phase modulation induced phase fluctuation can be mitigated by proper adjustment of channel spacing and/or residual dispersion.     

光孤子传输演化的分步傅里叶法研究

光孤子传输的数值仿真研究对其实用化及系统设计具有重要意义。本文详细介绍了分步傅里叶法的基本原理和仿真步骤，并用Matlab语言对光孤子在光纤中的传输演化进行了仿真。讨论了光纤损耗对光孤子传输的影响,并说明当光孤子对在光纤中传播时，距离太近将会产生强烈的相互作用，导致孤子形状发生畸变。最后对掺铒光纤放大器对孤子能量补偿作用做了探讨，指出光孤子通信中主要是色散受限，采用980 nm光源泵浦的EDFA具有较好的效果。     

Effects of polarization mode dispersion on cross-phase modulation in a WDM optical transmission system

The cross-phase modulation (XPM) changes the state-of-polarization (SOP) of various channels and leads to amplitude modulation of the propagating waves in a WDM system. Due to the presence of polarization mode dispersion (PMD), the angles between the SOP of the channels change randomly and cause the modulation amplitude fluctuation random in the perturbed channel. We analytically derive the dynamic equation of the perturbed channel, determine the combined probability density function of the random angle between the SOP of pumps and probe channel and evaluate the effects of PMD on XPM for a 4-channel IM-DD WDM system in terms of BER at bit rate of 10 Gb/s per channel. We also simulate the impact PMD on XPM for a 4-channel WDM system in terms of eye diagram and found that eye opening penalty is 1.85 dB higher when the fiber PMD coefficient increases from 0.5 to 1.5 ps/√km.