Performance of All-optical WDM Network in Presence of Four-wave Mixing, Optical Amplifier Noise, and Wavelength Converter Noise

The article investigates the effect of four-wave mixing (FWM), amplified spontaneous emission (ASE) noise, and wavelength converter noise on the performance of WDM all-optical networks. Analysis for the evaluation of probability of error has been carried out (a) when only thermal and shot noise are present; (b) when thermal, shot, FWM, and ASE noise are present; and (c) when thermal, shot, FWM, ASE, and wavelength converter noise are present. Numerical results are presented in the graphical forms for the practical values of parameters.     

Effect of Four-Wave Mixing on Optimal Placement of Optical Amplifier in WDM Star Networks

In this article, the effect of four-wave mixing (FWM) and amplified spontaneous emission (ASE) noise on WDM optical star networks has been investigated. Analysis for the evaluation of probability of error has been carried out (a) when only FWM is present and (b) when both FWM and ASE noise are present. Numerical results are presented in the graphical and tabular forms for the practical values of parameters. Finally, optimal location of the amplifier in the network has been identified as being before the star coupler preceding the receiver.     

Impact of fibre nonlinearities in optical DWDM transmission systems at different data rates

The impact of major fibre nonlinearities, like stimulated Raman scattering (SRS) and four wave mixing (FWM), in cascaded amplifier dense wavelength division multiplexing (DWDM) transmission system, has been studied at different data rates. SRS has been calculated considering pulse walk off effect. Analysis has been carried out to evaluate signal to noise ratio (SNR) considering the combined effect of SRS and FWM in the presence of amplified spontaneous emission (ASE) noise to achieve minimum noise at different data rates.     

Effect of four-wave mixing in WDM optical fibre systems

Wavelength division multiplexing (WDM) can both significantly enhance transmission capacity and provide more flexibility in optical network design. Through the use of erbium-doped fibre amplifiers (EDFAs), it is possible to build long-distance transparent optical transmission links without electrical regenerators. In such systems, fibre nonlinearities are likely to impose a transmission limit due to increased total interaction length. There are a number of optical nonlinear effects in optical fibres, such as stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), carrier-induced phase modulation and four-wave mixing (FWM). Out of these SRS and FWM are the dominant effects. In this paper, an algorithm has been suggested to study the effect of FWM in the total system noise considering the combined effect of SRS and FWM in the presence of amplified spontaneous noise (ASE). It has been found from the study that to maximize the signal-to-noise ratio of the transmitted signal in a WDM system FWM noise needs to be reduced as this is the dominant noise factor.     

基于小波变换的长距离光正交频分复用系统中四波混频引起的相位噪声分析

四波混频（FWM）效应是相干光正交频分复用（CO-OFDM）系统中最主要的非线性作用。分析基于小波变换的相干光正交频分（WT-OOFDM）系统原理,研究小波变换对FWM效应和光放大器自发辐射（ASE）引起的相位噪声的改善效果。数值结果表明,在采用常规G. 652光纤,100 Gbit/s的WT-OOFDM传输1500 km时,非线性相位噪声降低20%,总相位噪声降低15%。     

A novel method degrading the combined effect of FWM and ASE noise in WDM systems containing in-line optical amplifiers

In this paper, a novel method degrading the combined effect of four-wave mixing (FWM) and amplified spontaneous emission (ASE) noise of the amplifier on the most heavily affected channel in an equally channel spaced wavelength division multiplexing (WDM) system containing in-line optical amplifiers is proposed. FWM effect is directly related to input powers of channels. So, FWM effect can be degraded by controlling channel input powers. In the proposed method, varying the input power of each channel in an optical fiber, the output optical signal to noise ratio (OSNR) values are evaluated and input powers of all channels are optimized in order to maximize the OSNR value of the channel having the lowest OSNR. To interpret the results obtained, output OSNR values for the minimum optical input power launched to the system by each channel are also computed. Being compared to the computed results for minimum optical input powers, the lowest output OSNR value among all channels for optimized input powers shows a 5.1867 dB increase in a 5-channel system, a 3.5988 dB increase in a 9-channel system, a 3.0855 dB increase in a 15-channel system and a 1.6795 dB increase for a 21-channel system. Furthermore, output OSNR values of all channels exhibit a significant increase.     

Novel Strategies for Reducing FWM Using Modified Repeated Unequally Spaced Channel Allocation

Four-wave mixing (FWM) is a dominant nonlinear effect present in optical wavelength division multiplexing (WDM) networks employing dispersion-shifted fiber. The method of placing the carrier at unequally spaced frequencies to reduce the FWM effect in these networks is known. A modification to this method with periodic unequally spaced channel allocation repeated base unit structures has been suggested that leads to a much better bandwidth utilization with lesser number of FWM components. A figure of merit, defined as the ratio of decrease in number of FWM components generated to increase in bandwidth, has been used as a metric of performance.     

小信号脉冲抽运时掺铒光纤自发辐射的研究

自发辐射(ASE)是掺铒光纤放大器(EDFA)的重要噪声源,对于由EDFA构成的光纤激光器有重要影响。理论与实践证明,它与抽运方式紧密相关,所以研究脉冲抽运时掺铒光纤(EDF)的自发辐射有重要的学术价值。同时,脉冲抽运对于EDFA锁模激光器的研究也有一定意义。从理论和实验两方面研究了小信号脉冲抽运时,抽运脉冲宽度和幅度对于EDF的自发辐射特性的影响,得到了小信号抽运时输出ASE噪声平均值的近似解析解。研究发现,小信号脉冲抽运时输出信号的幅度与抽运脉冲的宽度成正比。这个新现象可用于脉冲宽度的全光检测。     

DWDM系统非简并四波混频串扰的分析

考虑到DWDM系统中的比特序列的随机性、信道间脉冲走离效应等多种因素的影响,完善了归零调制格式下的四波混频效率的计算方法,给出了相应的非简并四波混频噪声标准差的计算公式,并利用该公式进行实例分析,计算结果表明,当占空比和信道间隔变小时,不同信道内的随机比特序列的相对初始时延及光纤色散值的取值组合对四波混频效率的影响变得更大,为保证系统的低色散和低四波混频串扰特性,必须对这些量取值组合进行优化. 关键词： 非简并四波混频 脉冲走离 密集波分复用     

A comparative study of modified PUSCA and paired PUSCA strategies in WDM system

In G.653 compliant fiber, four-wave mixing (FWM) is a dominant non-linear effect. Performance of optical wavelength division multiplexing (WDM) network based on G.653 fiber is affected by the generated FWM components. The paper aims to discuss the methods used to reduce the number of FWM components and make efficient utilization of bandwidth. We have earlier proposed two methods (a) modified periodically unequally spaced channel allocation (modified PUSCA) and (b) paired PUSCA. In this paper, we have compared both the methods by considering the ratio of increase in weighted average signal to FWM noise ratio to increase in bandwidth as a figure of merit. Further, the performance of paired PUSCA scheme on G.653 fiber has been compared with equally spaced channel allocation (ESCA) scheme on G.652 fiber in which FWM is not a dominant non-linear effect. We demonstrate that paired PUSCA on G.653 fiber performs better than ESCA on G.652 fiber when the number of channels is less than 30.     

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.     

Performance evaluation of path-averaged soliton pulses in loss-managed 10-Gbps soliton transmission link over a long haul

In this paper, the performance evaluation of path-averaged soliton transmission link for various performance measures viz. OSNR, optical power, extinction ratio, bit error rate (BER) and Q factor at different levels of noise figure and values of pulse width (FWHM) has been carried out. The performance of soliton transmission link is studied, taking into account soliton interaction, amplified spontaneous emission (ASE) noise and noise figure. The model presented considers interaction in a random sequence of solitons and the effect of the ASE noise added in each amplification stage. The influence of ASE noise, noise figure and pulse width with different amplifier spacing on the BER and quality factor has been investigated. It has been shown that these play dominant roles in degrading the performance measures. We have demonstrated the capability of path-averaged (guiding-centre) soliton for a long-haul distance of 17,000 km at a bit rate of 10 Gbps without ASE effect and noise figure in each amplifier span length of 500 km. The average value of quality factor is found to be 16.6 dB and the average BER is of the order of 10⁻¹² over the transmission distance of 17,000 km. Further, it has been investigated that a severe system penalty results on the inclusion of ASE effect and noise figure in order to achieve the same level of performance. Thus, the investigations ascertain that in order to maintain the same level of BER and Q factor, the amplifier spacing and total transmission distance reduce considerably.     

高功率光纤激光器中ASE噪声的测量方法（英）

高峰值功率脉冲光纤激光器在激光雷达系统中有着广泛的应用。然而,光纤激光器中放大自发辐射噪声（ASE）严重影响了系统的探测性能。提出一种测量高峰值功率脉冲光纤激光器中ASE噪声的方法。在该方法中,首先对高峰值功率的激光脉冲衰减,然后在时域分别测量和计算ASE噪声和激光脉冲的相对能量。给出了光纤激光器在驱动电流分别为6 A,7 A和8 A时衰减后的ASE噪声廓线以及ASE噪声占激光脉冲能量的比例。     

Effects of frequency and polarization allocations on FDM lightwave transmission systems

In long-haul frequency-division-multiplexing (FDM) lightwave transmission systems, transmission characteristics are degraded by four-wave mixing (FWM) generated in optical fibers. To overcome this problem in equally spaced (ES) allocation, modified repeated unequally spaced (RUS) allocations such as equally spaced RUS (ERUS) and unequally spaced RUS (URUS) allocations have been already examined. Also, it has been shown that FWM noises are decreased by arranging the polarization states of the channels. In this paper, dependence of FWM noises on frequency allocations and polarization allocations is investigated. It is revealed that FWM noises are decreased in ES, RUS, ERUS, and URUS with alternating polarization allocations of the channels, and FWM noises are drastically reduced when light polarizations are perpendicularly crossed at both sides of the zero dispersion frequency.     

Phase noise characteristics induced by stimulated Brillouin scattering in the presence of four-wave mixing in an interferometric fiber sensing system

Phase noise characteristics induced by stimulated Brillouin scattering (SBS) in the presence of four-wave mixing (FWM) in an interferometric fiber sensing system are investigated. It is found that the phase noise mainly results from SBS and the influence of FWM on the phase noise is negligible. It is due to that the channels are not perfectly equally spaced in the wavelength division multiplexing (WDM) system and the induced beat noise is filtered by the ??kHz/MHz photodetector. The phase noise caused by SBS rather than FWM should be focused on in the practical applications of interferometric fiber sensing systems.     

旋光纤喇曼放大器中ASE噪音模型及仿真计算

通过分析旋光纤喇曼放大器中信号光、抽运光的非线性薛定谔波动方程及放大自发辐射噪音特性,提出一种能同时在旋光纤喇曼放大器中产生预计波形放大自发辐射噪音,又方便计算的方法.根据放大自发辐射噪音时域特性,建立并在波动方程中加入放大自发辐射非高斯噪音模型.在考虑旋光纤双折射的非线性效应同时,通过分步傅里叶法对波动方程求解,计算了旋光纤喇曼放大器中的放大自发辐射噪音,并与实验结果吻合.     

Relative intensity noise induced by four-wave mixing in the case of two-wave transmission in an optical fiber

Four-wave mixing (FWM) is a significant nonlinear effect in wavelength division multiplexing (WDM) fiber-optic systems. For two-wave transmission, it is easily found that the FWM noise power decreases with frequency spacing and increases with signal power. However, the variation of relative intensity noise (RIN) with frequency spacing and signal power is only 2 dB at most. The intensity fluctuations induced by the energy exchange between the FWM generated new waves and the original ones are trivial and the influence of FWM on RIN can be neglected. It is also found that the increase of RIN with signal power is mainly attributed to stimulated Brillouin scattering (SBS) rather than FWM.     

A Formalism to Study the Propagation of the Four-Wave Mixing Signal in a Strongly Driven Two-Level System Immersed in a Thermal Reservoir

We analyze two analytical solutions for the study of the propagation of the four-wave mixing (FWM) signal in a strongly driven two-level system, when the stochastic effects of the solvent are explicitly considered. The first solution is valid only for a constant pump intensity, while the second solution considers pump propagation explicitly. In both cases, we were able to derive analytical expressions for the FWM nonlinear intensity signal in terms of the field amplitude and thermal noise parameters. Copyright 2000 Academic Press.     

Bit-pattern-dependent non-degenerate four-wave-mixing crosstalk in dispersion-managed DWDM systems including walk-off

In this work, through a detailed derivation process, we obtain a semi-analytic model to deterministically calculate the variance of non-degenerate four-wave-mixing (FWM) noise for return-to-zero (RZ) dispersion and loss-managed system with lumped amplifiers including walk-off between channels. We show that, in general, when the value of duty cycle becomes smaller, the values of variance are more influenced by many factors, such as channel separation, dispersion management scheme and especially relative initial time delays of all interacting channels. For a 17-channel such system, the variance of non-degenerate FWM noise falling on the central channel is given.     

Investigation on modified FWM suppression methods in DWDM optical communication system

The focus of this paper is to investigate the methods for Four Wave Mixing (FWM) suppression. Modified techniques equal and unequal-channel spacing with polarization, equal channel spacing with alternate channel delay, optical coupling and varied laser power have been proposed to reduce the impact of FWM on Dense Wave Length Division Multiplexing (DWDM) optical communication system. Further the comparison of reduction of FWM for existing and proposed techniques has been discussed by varying the dispersion of fiber from 0 to 16 ps/nm/km. It has been observed that the suggested techniques are simpler to design optical communication system and superior to the existing methods.