Cross-phase modulation in intensity modulation-direct detection WDMsystems with multiple optical amplifiers and dispersioncompensators

The cross-phase modulation (XPM) effect in intensity modulation-direct-detection (IM)-(DD) optical fiber links with multiple fiber segments with different characteristics and optical amplifiers is investigated theoretically and numerically. A generalized model of the IM induced by an arbitrary number of channels through XPM is derived, compared to simulation results and its validity range is presented. Results show that the XPM-induced IM can be modeled as an intensity modulator driven by the intensity of copropagating waves. The frequency response of the intensity modulator corresponding to each copropagating wave is mainly affected by the walk-off parameter and fiber dispersion. When the walk-off effect is weak the XPM-induced IM is approximately proportional to the square frequency. In single-segment fiber links when the walk-off effect is strong the XPM-induced IM is approximately linearly proportional to the frequency and inversely proportional to the wavelength separation. Both theory and simulation show that the XPM-induced IM in fiber links with multiple optical amplifiers can be enhanced or reduced by properly arranging the dispersion characteristics in each fiber segment. In a nondispersion compensated amplified link and for weak walk-off effect, the total XPM-induced IM increases approximately with the square of the number of fiber segments and of modulation frequency. However, if the dispersion is compensated for within each fiber segment the total XPM-induced IM increases proportionally to the number of fiber segments and to the square frequency. Furthermore, it is shown that in fiber links with a large number of segments placing a single dispersion compensator in the last segment of the link leads to almost the same performance as for non dispersion compensated fiber link and is significantly worse than placing one dispersion compensator in each fiber segment as far as the XPM-induced IM reduction is concerned     

Cross-phase modulation in multispan WDM optical fiber systems

The spectral characteristics of cross-phase modulation (XPM) in multispan intensity-modulation direct-detection (IM-DD) optical systems are investigated, both experimentally and theoretically. XPM crosstalk levels and its spectral features are found to be strongly dependent on fiber dispersion and optical signal channel spacing. Interference between XPM-induced crosstalk effects created in different amplified fiber spans is also found to be important to determine the overall frequency response of XPM crosstalk effects. XPM crosstalk between channels with different data rates is evaluated. The crosstalk level between higher and lower bit rate channels is found to be similar to that between two lower bit rate channels. The effect of dispersion compensation on XPM crosstalk in multispan optical systems is discussed and per span dispersion compensation was found to be the most effective way to minimize the effect of XPM crosstalk     

Frequency response of cross-phase modulation in multispan WDMoptical fiber systems

The spectral characteristics of cross-phase modulation (XPM) in multispan intensity-modulation direct-detection optical systems were investigated both experimentally and theoretically. XPM crosstalk levels and its spectral features were found to be strongly dependent on fiber dispersion and optical signal channel spacing. Interference between XPM-induced crosstalk effects created in different amplified fiber spans is also found to be important to determine the overall frequency response of XPM crosstalk effects     

Effects of polarization-mode dispersion on cross-phase modulation in dispersion-managed wavelength-division-multiplexed systems

This paper develops a vector theory of cross-phase modulation (XPM) in optical fibers and use it to investigate the impact of polarization-mode dispersion (PMD) on the crosstalk induced by XPM in wavelength-division multiplexed lightwave systems. Under certain reasonable approximations, the theory permits us to obtain an analytic expression for the amplitude of probe fluctuations induced by a copropagating pump channel through XPM. We use this expression to calculate the average level of XPM-induced crosstalk together with its variance for several dispersion maps. We show that PMD not only reduces the crosstalk on average, but also impacts the efficiency of a commonly used polarization-interleaving technique.     

多周期色散管理系统中交叉相位调制产生的相移研究

以泵浦探测波结构为例,针对多周期色散管理系统,研究了色散作用下交叉相位调制产生的相位移动,推导了多段放大线路中色散作用下交叉相位调制产生的相移表达式,对该表达式进行简化得到了特定线路中色散作用下交叉相位调制所致的相移表达式。研究表明,线路总相移正比于传输线路中的光纤段数,随着调制频率的提高,相移量总体趋势逐渐减小,局部出现极大极小波动,且波动周期随走离参量增大逐渐减小,在高频段色散对交叉相位调制产生的相移产生显著影响,随着调制频率的提高,色散对相移的贡献正负交替变化,解析和仿真结论能较好吻合。     

Second-order theory for self-phase modulation and cross-phase modulation in optical fibers

The authors develop a second-order perturbation technique for the study of self-phase modulation (SPM) and cross-phase modulation (XPM) effects in optical fibers. When the dispersion distance is much shorter than the nonlinear length, it is found that the difference between the first- and second-order solution is negligible. However, as the dispersion distance increases, nonlinearity becomes a stronger perturbation, and the first-order theory is not adequate to describe the SPM effects. However, the results obtained using the second-order perturbation technique is in good agreement with numerical simulations even when the dispersion distance is longer than the nonlinear length. When pulses of different channels are copropagating in a fiber, they undergo amplitude distortion and timing shift due to XPM. The perturbation technique presented in this paper accounts for both amplitude distortion and timing shift of a pulse due to XPM.     

Analysis of cross-phase modulation (XPM) effect on WDM transmissionperformance

The authors analyse the effect of cross-phase modulation (XPM) on wavelength division multiplexing (WDM) transmissions by experiments and numerical simulations, and provide the XPM limitation in a normalised and closed form formula. They also investigate the effect of XPM on dispersion compensated transmissions. It is shown that the location of dispersion compensators and the amount of compensation should be determined by considering the XPM effect     

Cross-phase modulation in dispersive fibers: theoretical andexperimental investigation of the impact of modulation frequency

We investigated, theoretically and experimentally, the impact of modulation frequency on cross-phase modulation (XPM) in dispersive fibers. A simple expression for the XPM index has been derived and verified by experiment. The XPM index is found to depend on fiber length, fiber chromatic dispersion, wavelength separation between the signal and the pump, and the intensity modulation frequency. At high modulation frequencies, the XPM index is inversely proportional to the product of the modulation frequency and wavelength separation     

Impact of modulation frequency on cross-phase modulation effect inintensity modulation-direct detection WDM systems

The impact of modulation frequency on the crossphase modulation (XPM) effect in intensity modulation (IM)-direct detection wavelength-division multiplexing systems is investigated theoretically and numerically. A simple expression for IM is derived, verified by simulation and its validity is presented. The dependence of XPM-induced IM on the fiber length, fiber dispersion, channel separation and pump modulation frequency is assessed. It is shown that at very low frequency the walkoff effect has almost no influence on the XPM-induced IM efficiency which increases with the square of the frequency; at higher frequency the IM efficiency can be reduced significantly by the walkoff and scales linearly with modulation frequency     

Analysis of interchannel crosstalk in a dispersion-managed analog transmission link

A technique for computing the effect of cross-phase modulation (XPM) on two copropagating analog channels in an optical fiber link is presented. In this approach, the interaction between the two channels is linearized by keeping the self-phase modulation (SPM) and XPM interactions in the strong optical carrier components only at lowest order and then at the next order, deriving the effect on the modulation components of both channels when the optical carrier is strong relative to the other components of the channel. In contrast to some previously suggested approaches, it is not assumed that the pump is undistorted, and therefore, this method accurately describes distortions due to SPM, XPM, and dispersion management in both channels. This method is easily applied to systems with multiple spans employing dispersion management with loss and gain. The expressions for the received radio frequency power and crosstalk between the two channels when direct detection is used are then provided. Using this approach, new expressions for the amplitude modulation and phase modulation modes of the two channels are derived, and the way they exchange energy when SPM, XPM, and dispersion are all considered is explained. This method yields excellent agreement between theory and experimental data.     

Nonlinear crosstalk and two countermeasures in SCM-WDM opticalcommunication systems

We investigate, theoretically and experimentally, crosstalk between wavelengths in subcarrier-multiplexed (SCM) wavelength-division multiplexed (WDM) optical communication systems. Crosstalk arises mainly from interactions between subcarriers on one wavelength and the optical carrier of another wavelength. In a dispersive fiber, crosstalk can be attributed to stimulated Raman scattering (SRS) and cross-phase modulation (XPM) combined with group velocity dispersion (GVD). We investigate the phase relationship between SRS-induced and XPM-induced crosstalks. Crosstalks induced by SRS and XPM add in the electrical domain and can interfere constructively or destructively. Experimental results show that the combined crosstalk level can be as high as 40 dBc after 25 km of SMF with two wavelengths and 18 dBm per wavelength of transmitted power. We propose two crosstalk countermeasures. The first countermeasure uses parallel fiber transmission. We show theoretically that both SRS-induced and XPM-induced crosstalks can be cancelled to the first order. We present an experimental demonstration of concept which has achieved 15 dB of crosstalk cancellation over 200 MHz. The second countermeasure uses optical carrier suppression. We show, theoretically and experimentally, that by suppressing the optical carrier, we can significantly reduce crosstalk while maintaining the same link budget and carrier-to-noise ratio (CNR) at the receiver, 20 dB of crosstalk reduction over 2 GHz has been demonstrated experimentally     

Degree of polarization degradation due to cross-phase modulation and its impact on polarization-mode dispersion compensators

A novel analytical model is proposed to predict the cross-phase modulation (XPM)-induced depolarization in a two-channel transmission system, in which the Stokes' vector of each channel rotates around a space-invariant pivot by a time-varying angle which depends on the total instantaneous optical power in the fiber, on the angle between pump and probe input Stokes' vectors, and on the walk-off between channels. The model leads to a simple formula of the probe degree of polarization (DOP) which is validated both by simulation and experiment. The model helps identify the key physical factors that determine the XPM-induced performance degradation of DOP-based first-order polarization-mode dispersion compensators, and experiments that quantify such degradation are presented.     

色散缓变光纤中交叉相位调制不稳定增益谱

从非线性薛定谔方程出发得到了色散缓变光纤中交叉相位调制(XPM)不稳定性的增益谱。结果表明,XPM产生的调制不稳定性既可以在光纤反常色散区产生,也可在正常色散区产生,反常色散区的增益谱宽比正常色散区宽,且色散缓变光纤中XPM不稳定增益谱宽比普通光纤中XPM不稳定增益谱宽宽,增益峰值高。色散缓变光纤是XPM调制不稳定性的较好色散介质。     

损耗作用下混频时调制不稳定性耦合模分析法

在考虑光纤损耗的情况下，以两载频以及混频过程中产生的边带频率成分为研究对象，给出了研究群速度色散（GVD）、自相位调制（SPM）、交叉相位调制（XPM）综合作用下混频过程中调制不稳定性（MI）的耦合模分析法。导出了当某一相位匹配较好、其他相位失配严重时，两载频自相位调制或交叉相位调制引起的调制不稳定性增益的解析表达式。分析发现，当调制不稳定性主要由自相位调制或交叉相位调制引起时，增益的最大值与色散无关，交叉相位调制在各边带引起的调制不稳定性最大增益相等，同时，考虑损耗后，幅度增益减小的大小受功率、非线性系数、色散情况、损耗系数和传输距离等因素共同影响，调制小稳定性产生的增益只有当频率偏移量足够大时才会出现，载频自相位调制引起的最大增益对应的频率偏移量减小。     

基于光纤差分相移键控的色散补偿方案的研究

为了研究光差分相移键控(DPSK)调制格式在光纤高速传输系统中的色散补偿, 利用色散补偿光纤(DCF)的色散补偿原理, 对40Gbit/s光纤传输系统进行色散补偿, 分析了40Gbit/s单通道光纤传输系统中3种DPSK调制格式信号的频谱特性; 仿真了3种码型的色散容忍度以及3种调制格式在考虑光纤的非线性下的色散补偿方案。结果表明, 光非归零码差分相移键控(NRZ-DPSK)信号具有最好的色散容忍度, 但其受非线性的影响比较大; 33%归零码差分相移键控(33%RZ-DPSK)信号的色散容忍度差, 但其色散补偿后的效果优于NRZ-DPSK; 而载波抑制归零码差分相移键控信号对色散和非线性效应都有较好的抑制; 3种DPSK调制格式均在对称补偿2方案中色散补偿的效果最佳。此仿真研究对光DPSK信号在光纤中的色散补偿具有参考意义。     

多信道IM—DD密集波分复用光纤传输系统中的交叉相位调制效应

本文研究了交叉相位调制（XPM）对DWDM数字基带主干传输网性的影响,建立了表征XPM效应对任意调制信号在色散信道中传输的指标损伤的等效系统函数模型,并据此推导出了不同系统参数条件下（基带信号速率,波长信道间隔,复用信道数）计算XPM导致和系统光功率代价的计算公式,通过数值模拟计算证明了在基带信号速率高（＞2.5Gbit/s),波长信道间隔窄（－1nm),复用信道数多（＞8）的条件下XPM效应将成为限制系统性能的主要非线性因素。     

Improved phase delays for optical compensation of polarization-mode dispersion

We present numerical simulations of the average frequency dependence of the differential phase delays (DPDs) that are introduced by polarization-mode dispersion (PMD) between the signal components transmitted in the two principal states of polarization of the fiber. Our study confirms that the first-order approximation of frequency-independent DPDs is valid for fibers that normally do not require PMD compensation. However, for fibers with larger mean differential group delays (DGDs), the first-order approximation tends to overestimate the mean DPDs for any given DGD. Based on our numerical results, we derive closed-form approximations for the frequency and group-delay dependence of the mean DPD conditioned on a given DGD and show that these more accurate DPDs may significantly improve the performance of optical PMD compensators.     

A new method for fiber chromatic dispersion measurement with microwave interference effect

The chromatic dispersion (CD) is a key parameter for optical fibers. Based on the microwave interference effect, a new method for CD measurement of optical fibers is proposed. The radio frequency (RF) signals carried by two light-waves with different wavelengths transmit through the dispersive optical fiber under test. After photo-detector they interfere with each other due to the different phase shifts induced by the CD of fiber. The CD can be obtained by monitoring the changing interference RF power with scanning the wavelength of tunable laser source. The CD values of single mode fiber and dispersion compensating fiber are measured within the wavelength range from 1525 to 1605 nm. The common phase shift method is used to measure the CDs of the two types of fiber, which demonstrates the feasibility and veracity of the proposed method.     

WDM+EDFA+DCF光纤传输系统中色散补偿方案的分析

由于在ＷＤＭ＋ＥＤＦＡ光纤传输系统中使用常规单模光纤（ＳＭＦ）在１５５０ｎｍ窗口的大色散限制了传输距离,采用色散补偿光纤（ＤＣＦ）进行色散补偿是上前一种较为理想的方法。本文基于光纤ＷＤＭ＋ＥＤＦＡ＋ＤＣＦ的长距离传输系统,讨论了ＤＣＦ色散补偿对光纤非线性效应交叉相位调制和四波混频（ＦＷＭ）的影响,提出了采用ＤＣＦ集总、后置、非完全补偿的色散补偿方案,这种方案可合系统具有更佳的传输性能。     

Cross-phase modulation in short-period dispersion managed fiber

Reports on the theoretical investigation of the cross-phase modulation (XPM) in a short-period dispersion managed fiber (SPDMF) system. The results show, that to minimize the XPM-induced intensity interference in an SPDMF, the dispersion of the negative section should be less than -14 ps/nm/km, assuming that the dispersion of the positive section was 17 ps/nm/km (as for a conventional single-mode fiber). Together with the design criteria for the suppression of four-wave mixing, this result could be used to optimize an SPDMF for use in high-speed wavelength-division multiplexing systems