Transmission of many WDM channels through a cascade of EDFA's inlong-distance links and ring networks

We analyze the transmission of many wavelength-division-multiplexed (WDM) channels through a cascade of erbium-doped fiber amplifiers (EDFA) in both long-distance links and ring-based networks. For a megameter long-distance system, optimal operating conditions are found for achieving a high signal-to-noise ratio (SNR) per channel with as small an SNR differential as possible between 20 WDM channels spaced 0.5 nm apart. Critical issues addressed in this paper include: (a) the non-uniformity of the EDFA gain with wavelength: (b) the link loss between amplifiers; (c) the small-signal gain per amplifier; and (d) the input signal power     

Passive equalization of nonuniform EDFA gain by optical filteringfor megameter transmission of 20 WDM channels through a cascade ofEDFA's

Through the incorporation of optical filters in a cascade of erbium-doped fiber amplifiers (EDFA's), with each amplifier exhibiting nonuniform gain, we determine the optimal conditions for passively equalizing many wavelength division multiplexed (WDM) channels while maintaining a high SNR. For 20 WDM channels spaced 0.5 nm apart, it is found that 3-dB, 2-nm-wide notch filters with center wavelength at 1.560 μm will provide sufficient SNR equalization for potential megameter transmission when located after every 20 EDFA's. This performance is achieved with no a priori knowledge of the input or output signals     

波分复用系统中四波混频引入光信噪比的恶化及其抑制

本文对陆上级联接掺铒光纤放大器（ＥＤＰＡ）波分复用光纤通信系统中国波混频所造成的各个光信道光信噪比的恶化提出了一套计算方法，并结合常规单模光纤及一种特殊设计的色散位移光纤进行了分析计算。结果表明：在四波混频所引入的光信噪比恶化中，因新生频率分量导致的噪声增加一般远大于光信号功率的减弱。不等信道间隔划分能有效地避免四波混频的影响，而光滤波器的带宽应在允许范围内尽量压窄。对采用色散补偿技术的级联ＥＤＦＡ波分复用系统，在同一光中继段内，使常规单模光纤置于特殊设计的色散位移光纤之前，能进一步减少四波混频带来的光信噪比的恶化。     

A generalized suboptimum unequally spaced channel allocationtechnique. I. In IM/DD WDM systems

Four-wave mixing (FWM) is the most serious fiber nonlinearity associated with low-input optical power levels in long-haul multichannel optical systems employing dispersion-shifted fiber. To reduce the crosstalk due to FWM, a generalized suboptimum unequally spaced channel allocation (S-USCA) technique is proposed and investigated. Even though the developed technique is useful in combating FWM crosstalk in wavelength division multiplexing (WDM) lightwave systems with up to 12 channels, its main virtue is in designing multichannel WDM lightwave systems with more than 12 channels. Comparisons of power penalty due to FWM between equal channel spacing (ECS) systems and the S-USCA systems are presented. It is shown that for an intensity modulation/direct detection (IM/DD) transmission system operating in an optical bandwidth of 16 nm with 0 dBm (1 mW) peak optical input power per channel, while a conventional ECS WDM system with 0.84-nm channel spacing cannot even achieve a bit-error rate (BER)=10^-9, the suboptimum technique developed in this paper, for the same minimum channel spacing, can achieve a BER=10^-9 with an FWM crosstalk power of less than 1 dB at the worst channel in a 20-channel WDM system     

Analysis of repeated unequally spaced channels for FDM lightwavesystems

In long-haul optical frequency-division-multiplexing (FDM) systems, transmission characteristics are degraded by four-wave mixing (FWM). To overcome this problem, repeated unequally spaced (RUS) channels have been recently proposed as a new frequency allocation. In this paper, frequency distribution and intensity of generated FWM lights, and a total bandwidth of signal lights of RUS channels are compared with those of already known equally spaced (ES) and unequally spaced (US) channels. It is found that intensities of generated FWM lights of RUS are less than those of ES when the number of channels and a total bandwidth of signals are common in both channels. It is also revealed that RUS has a narrower total bandwidth than US when the number of channels and the minimum channel spacing are common in both channels. Since RUS simultaneously satisfies a low FWM light intensity and a narrow signal bandwidth, it is considered that RUS is suitable for FDM lightwave transmission systems     

Long-distance WDM transmission experiments using the dispersionslope compensator

Recently, long-haul transmission experiments of more than 100-Gbit/s capacity were reported. Wavelength-division multiplexing (WDM) is a key technology to achieve this kind of high-capacity transmission. One technical problem of the long distance WDM transmission is the dispersion slope of the transmission fiber. It causes the difference of the chromatic dispersion accumulation upon the WDM channels, and it will lead to transmission performance degradation. In order to solve the problem, equalization of the dispersion slope should be quite effective. This paper describes the results of the long-distance transmission experiments using the dispersion slope equalization. Both IM-DD WDM and optical soliton WDM are discussed     

Four-wave mixing suppression effect of dispersion distributedfibers

The four-wave mixing (FWM) suppression effect of dispersion distributed fibers (DDF's), which have a nonuniform chromatic dispersion along their length, has been investigated experimentally and theoretically. We fabricated two different kinds of DDF by the vapor-phase axial deposition (VAD) method to clarify the FWM suppression effect. Moreover, we investigated experimentally the effect of our fabricated DDF's on the transmission characteristics of 4×10 Gb/s wavelength division multiplexing (WDM) systems. We confirmed that the proposed DDF's can not only suppress PWM but also improve the input power limitation for WDM systems     

波分复用系统中偏振模色散特性的研究

推导了双折射光纤中两个波长的光波所满足的耦合非线性薛定谔方程。建立了研究两信道波分复用(WDM)系统中偏振模色散效应的模型。基于这一模型,在考虑偏振模色散情况下,数值模拟了在两信道WDM系统中光信号的传输变化,并且分析了在此系统中偏振模色散的影响     

Effect of the cross-phase modulation on WDM optical systems:analysis of fiber propagation

In wavelength-division-multiplexed (WDM) optical systems, cross-phase modulation induced by Kerr effect gives rise to nonlinear phase modulation of each channel, which depends on the overall power in all the other channels. In this letter, the fiber propagation of WDM optical signals affected by cross-phase modulation is analyzed. In particular, the effect due to fiber chromatic dispersion is evaluated after that cross-phase modulation has arisen and stabilized     

Long-haul WDM transmission using higher order fiber dispersionmanagement

We propose a fiber dispersion management scheme for large-capacity long-haul wavelength division multiplexing (WDM) transmission systems that considers not only second- but also third-order dispersion characteristics using transmission fibers with opposite dispersion signs. It eliminates the waveform distortion of WDM signals that originates from the existence of third-order dispersion, which is a constraint placed on WDM capacity in conventional dispersion management, while reducing the interchannel interaction caused by the interplay of fiber nonlinearity and second-order dispersion. Design concept of the scheme is discussed to show the feasibility of using actual fiber parameters. An experimental investigation on transmission performance regarding the signal pulse format, nonreturn-to-zero (NRZ) and return-to-zero (RZ), and interchannel interaction caused by four-wave mixing (FWM) and cross-phase modulation (XPM) is described for optimizing WDM system performance. It is experimentally shown that RZ pulse transmission is possible without significant spectral broadening over a wide wavelength range in dispersion managed fiber spans. Using these results together with a wideband optical amplifier gain-bandwidth management technique, yields long-distance WDM transmission with the capacity of 25×10 Gb/s over 9288 km     

WDM系统中的非线①性研究及仿真实验

利用分离信道的分步傅立叶法对信道间距为0.8nm的8路10 Gbit/s波分复用色散补偿系统进行仿真实验，分析了在具有级联光放大器系统中光纤色散和各种非线性效应（自相位调制SPM、交叉相位调制XPM、四波混频FWM）对系统传输的影响。仿真结果表明，在色散补偿WDM通信系统中，SPW对系统传输造成的损伤最大。并且由于非线性效应、传输损耗及噪声的综合影响，应当选取合适的系统输入功率。     

WDM systems with unequally spaced channels

Crosstalk due to four-wave mixing (FWM) is the dominant nonlinear effect in long-haul multichannel optical communication systems employing dispersion-shifted fiber. A method is discussed to find non-uniform channel separations for which no four-wave mixing product is superimposed on any of the transmitted channels, therefore suppressing FWM crosstalk. The residual crosstalk, due to channel power depletion only, is analytically evaluated for intensity-modulated repeaterless wavelength-division-multiplexed (WDM) systems and compared to experimental results. The theory includes the effect of the channel depletion on the amplitude of each phase-matched FWM wave. The probability of error is evaluated including the statistics of the pattern dependent channel depletion. The BER curve computed for an 8-channel WDM system is found to be in good agreement with experimental results. In the experiment, repeaterless transmission of eight 10 Gb/s WDM channels over 137 km (11 Tb/s-km) of dispersion-shifted fiber was demonstrated and error-free operation was achieved over a wide range of input powers using unequally spaced channels. The same system with equally spaced channels could not achieve a probability of error lower than 10^-6. The use of unequal channel spacing allowed fiber input power to be increased by as much as 7 dB, which could be translated into a fivefold increase of the bit rate per channel (and therefore of the system capacity), or to an increase in the system length of about 30 km     

Mean Field Method with Different Dispersion Maps for WDM Systems

Using mean field method proposed in Ref. [4], the 40 Gb/s multi--channel WDM optical fiber transmission systems with different dispersion maps are simulated. By this method, the computation time can be greatly reduced since following only the full time evolution of a limited number of channels while treating the other ehannels as continuous wave. But since dispersion plays an important role in the process of FWM and XPM,different dispersion maps will affect the application of the method. The dependence of the method on dispersion maps is investigated. The results not only confirm the mean field method,but also give useful approach for system design.     

Demonstration of timing skew compensation for bit-parallel WDM datatransmission with picosecond precision

We demonstrate transmission of seven wavelength-division-multiplexed (WDM) bit-parallel channels with a total of 15-nm spectral span over a 2.5-km standard single-mode fiber/dispersion-compensating fiber link with less than 3-ps timing skew. The synchronized WDM channels are generated by spectrally slicing pulses from a single femtosecond fiber laser using a femtosecond pulse shaper. The small residual timing skew arises from the residual dispersion slope of the link. We measure a dispersion slope of D'=0.017 ps/km/mn², which is roughly four times less than for an equivalent length of dispersion-shifted fiber. Our work shows that the dispersion-compensating fiber technique could significantly reduce the timing skew for WDM bit-parallel transmission over a several-kilometer fiber link     

Performance Comparison of Duobinary Formats for 40-Gb/s and Mixed 10/40-Gb/s Long-Haul WDM Transmission on SSMF and LEAF Fibers

Duobinary formats are today considered as being one of the most promising cost-effective solutions for the deployment of 40-Gb/s technology on existing 10-Gb/s WDM long-haul transmission infrastructures. Various methods for generating duobinary formats have been developed in the past few years but to our knowledge their respective performances for 40-Gb/s WDM transmission have never been really compared. In this paper, we made an extensive numerical evaluation of the robustness of these different types of duobinary transmitter to accumulation of ASE noise, chromatic dispersion, PMD but also to single-channel and WDM 40-Gb/s transmission impairments on standard single-mode fiber. A numerical evaluation of the ability of duobinary format for mixed 10/40-Gb/s WDM long-haul transmission with 50-GHz channel spacing is also led, on both standard single-mode and LEAF fibers, and compared to DQPSK format. In order to clearly identify the limiting transmission effects on each of these two fiber types, the assessment of the performance of a 50-GHz spaced WDM 40-Gb/s long-haul transmission using either duobinary or DQPSK channels only is implemented at last.      

Four-wave-mixing suppression effect of dispersion varying fiber

This letter describes the four-wave-mixing (FWM) suppression effect of dispersion varying fiber (DVF) whose chromatic dispersion increases (or decreases) along its length. The FWM suppression performance is investigated for the dispersion variation rate and its cycle number in the DVF. Moreover, it is clarified experimentally that the DVF functions efficiently in wavelength division multiplexing (WDM) systems with an input power of more than 10 dBm/ch     

波分复用系统的四波混频特性研究

本文对波分复用（WDM）光纤通信系统中的四波混频（FWM）特性进行了研究，得到了WDM可用于由多段不同长度，不同色散值的光纤组成的多级放大WDM系统FWM效应的计算方法，进而分析了单级、多级放大和色散补偿这3种特例的FWM特性，研究结果表明，标准单模光纤与高负色散值色散移位光纤的组合可以有效地抑制FWM混频效应。     

Demonstration of RSOA‐Based 20 Gb/s Linear Bus WDM‐PON with Simple Optical Add‐Drop Node Structure

We demonstrate a linear bus wavelength‐reused gigabit wavelength‐division multiplexing passive optical network (WDM‐PON) with multiple optical add‐drop nodes. A commercially available reflective semiconductor optical amplifier‐based WDM‐PON has a sufficient power budget to provide multiple optical add/drop nodes in 16 WDM channels. Sixteen 1.25 Gb/s WDM channels are successfully transmitted over 20 km of single‐mode fiber with four optical add/drop multiplexers, even with 32 dB reflection and chromatic dispersion in the link.     

Polarization evolution due to the Kerr nonlinearity and chromaticdispersion

This paper numerically investigated the evolution of the degree of polarization of individual channels and their Stokes parameters in a wavelength division multiplexed (WDM) system in which Kerr nonlinearity and chromatic dispersion are taken into account but in which polarization mode dispersion as well as polarization-dependent loss and gain are neglected. We compared the results to a mean field model which assumes that the channels are strongly dispersion-managed so that each channel is only affected by the Stokes parameters of the others. This model predicts no change in the degree of polarization of each of the channels so that an initially polarization-scrambled channel does not repolarize. The full simulations showed that the repolarization of a polarization-scrambled signal is small for parameters corresponding to realistic communication systems, validating the use of the mean field model. However, we also found that the repolarization can become significant for low data rates and a small number of channels in a dispersion-managed system with a short length map, thus setting limits on the model's validity and indicating operating regimes that should be avoided in real communication systems     

Multicanonical Monte Carlo Modeling of Wavelength Division Multiplexed Differential Phase Shift Keying Systems

Differential phase shift keying (DPSK) modulation is being considered as a possible candidate for future optical wavelength division multiplexed (WDM) transmission systems. In a single channel link, the balanced interferometric DPSK receiver exhibits increased tolerance against amplified spontaneous emitting (ASE) noise and fiber nonlinear effects. In this paper, a model is presented that can be used to estimate the performance of a multichannel DPSK system taking into account the influence of interchannel phenomena, namely cross-phase modulation (XPM) and four wave mixing (FWM), in the phase noise statistics. The model is based on an approximate solution of the fiber propagation equation and the multicanonical Monte Carlo (MCMC) method. It provides an efficient tool that can be used to investigate the influence of many link design parameters such as channel spacing, launch power, and fiber dispersion. The model is illustrated in the comparison of the performance of multichannel DPSK to on-off keying (OOK) systems. It is verified that, even in the presence of interchannel effects, DPSK modulation greatly enhances the system performance compared to OOK.