Simultaneously compensating tunable CD and adaptive PMD using two different nonlinearly chirped fiber Bragg gratings

Experimental research of simultaneous tunable chromatic dispersion(CD)and adaptive polarization mode dispersion(PMD)compensations in optical fiber communication system was reported.Two different nonlinearly chirped fiber Bragg gratings fabricated through the equivalent chirp technology were adopted in the experiment.One of the gratings was used as CD compensator,with a tunable dispersion range from 300 to 600 ps/nm.The other made of photosensitive polarization maintaining fiber was used as a tunable delay line of PMD compensator,which provided a varying amount of differential group delay(DGD)from 40 to 110 ps.Our experiment was operated at 10-Gb/s non-return-to-zero(NRZ)system and the results showed that the eye pattern recovery is excellent after both PMD and CD are compensated.Especially,the power penalty at a bit error rate(BER)of 10-9 is about 1 dB.     

A deeper analysis of the second order polarization mode dispersion in optical communications systems

This article presents a new approach to the combined analysis of the first and second-order polarization mode dispersion (SOPMD) and shows their importance in optical communication systems performance. How it affects the relation between second-order polarization mode dispersion (PMD) and the differential group delay (DGD) in a single mode fiber is discussed. The analysis is based on time or wavelength and temperature variations changing/impacting PMD and DGD measured values. We present long term statistical characteristics of second-order PMD over a PMD emulator, and investigate the correlation between SOPMD, depolarization (DEP) and polarization dependent chromatic dispersion (PCD). Some authors calculate these modes from measurements obtained from the first order polarization mode dispersion, assuming a positive correlation between these effects, but this not the real relationship between them. A new interpretation of SOPMD was used to analyze the problem of the spectral stability in terms of the temperature. Actual techniques for determination SOPMD, consequently DEP and PCD, use the variation in time and/or wavelength. In some studies the results obtained for SOPMD are correlated to first-order PMD (FOPMD). This paper shows, based on measurements, that the correlation between first and second order Polarization Mode Dispersion (PMD) in the case where the last one is a function of the temperature can assume positive or negative values.     

Performance comparison between sampling methods using DOP as feedback signal for higher-order PMD compensator

We numerically analyzed the performance of the two polarization-mode dispersion (PMD) compensation methods of the single degree of polarization (DOP) sampling and DOP ellipsoid sampling methods. The numerical results show that the single DOP sampling method can generate the maximum DOP, and may result in a small overall differential group delay (DGD) or the principal state of polarization (PSP)launching. By the PSP launching, just the first-order PMD is compensated while second-order PMD not.When the DOP ellipsoid sampling method is used the performance is evidently better, because the effect of high-order PMD on PMD compensation is reduced.     

Dynamic PMD compensation in 40-Gb/s optical communication system

A 40-Gb/s optical time division multiplexing (OTDM) return-to-zero (RZ) transmission experiments in cluding a dynamic polarization mode dispersion (PMD) compensation was reported. The dynamic PMD compensator is made up of two-stage four degrees of freedom (DOF). The first stage adopts polarization controller and fixed time-delayed line. The second stage is variable differential group delay (DGD) element. The PMD monitoring technique is based on degree of polarization (DOP) as error signal. A novel practical adaptive optimization algorithm was introduced in dynamic adaptive PMD compensation. The experimental results show that the performance of the PMD compensator is excellent for 40-Gb/s RZ transmission systems with the large DGD. With this compensator, a significant improvement of system performance can be achieved in the eye pattern of a received signal. The first-order compensating ability of the compensator is greater than 30 ps. The second-order compensating ability is greater than 200 ps2.The first-order optimum compensating time is within 10 ms. The second-order optimum compensating time is within 24 ms.     

The Statistical Analysis of Polarziation Mode Dispersion and Filter Control on Dispersion Managed Soliton Links

In this paper, the statistical distributing and magnitude of the first and the second-order PMD (polarization mode dispersion) vectors are evaluated and the filters control PMD effects also are analyzed on DMS (dispersion-managed soliton) links. Firstly, the so-called coarse-step approach is applied to the DMS links. The PMD statistical characteristics of the first and the second-order are simulated and the evolutions of energy and mean square of time displacement of DMS two polarization modes are gotten. Secondly, The DMS transmission of filter control with the conventional model of PMD is analyzed by Varitional method, from which the evolving rules of characteristically DMS parameters are obtained and the stability of filter control the DMS transmission are investigated. The results are not only very useful to simplify the measurement of the second-order PMD and instructively reveal degree of PMD effects in DMS systems, but also give that condition of stability of filter control PMD in DMS systems.     

高阶PMD统计特性研究

讨论了三阶偏振模色散(PMD)的统计特性及其对于高阶PMD补偿系统的影响.数值模拟结果表明,随着即时差分群时延(DGD)的增加,二阶PMD单位矢量旋转速率的统计覆盖范围的变化趋势与主偏振态(PSP)旋转斜率的相应变化正好相反.此外,随着即时DGD的增加,二阶PMD模值的统计覆盖范围不断增加,使得高速光通信系统中高阶PMD补偿的实现将更加困难.     

基于偏振度的偏振模色散补偿中检测信号对不同归零码型的响应研究

从理论上数值分析和比较了一阶和二阶偏振模色散对各种光调制码型（RZ、CSRZ、RZ-DPSK、CSRZ-DPSK）的偏振模色散的影响,结果表明:不同码型的偏振度大不相同,RZ码受偏振度影响最大,CSRZ-DPSK码受二阶偏振模色散的影响最小,在补偿系统中更适合缓解偏振模色散.     

光纤偏振模色散对信号偏振度的影响

采用一种简化的线路传输模型，详细讨论了在高速光纤通信系统中，线路偏振模色散（PMD ），尤其是二阶PMD、输入信号偏振态等对信号偏振度（DOP）的影响，并指出以信号DOP做 反馈控制信号适合于一阶PMD优化补偿系统，但在较大二阶PMD的影响下，将增加控制算法的 复杂性，使系统可能陷入局部最优解. 关键词： 信号偏振度 偏振模色散 信号偏振态     

Two-stage adaptive PMD compensation experiment for 10-Gb/s optical communication system

We report the adaptive compensation experiment of polarization mode dispersion (PMD) for 10-Gb/s non return-to-zero (NRZ) and return-to-zero (RZ) optical communication systems using a two-stage PMD compensator and the monitoring technique based on degree of polarization (DOP) feedback-signals. The DOP monitor has its advantages of bit-rate independent and modulation format independent. The two-stage compensator has the capacity of compensation for the first- and second-order PMD. The compensated differential group delay (DGD) is up to 80 ps, and compensated principal state of polarization rotation rate is 20 ps. The time used for compensation is less than 1 second.     

单模光纤偏振模色散统计特性的分析

用琼斯矩阵本征分析法对偏振模色散各参量的统计特性进行了分析 ,得到了一阶和二阶偏振模色散的统计规律 ,并给出了二阶偏振模色散各参量与一阶偏振模色散各参量之间的比例关系 ,对二阶偏振模色散的获取、补偿和系统设计均有指导意义。     

单模光纤二阶偏振模色散的Jones矩阵

利用单模光纤PMD矢量与Jones矩阵之间的关系,推导了由该矢量表示的光纤二阶PMD的Jones矩阵解析表达式,利用该矩阵可以确定输出端时域脉冲在二阶PMD近似下的表达式,并由此仿真二阶PMD对信号传输质量的影响.通过比较输入与输出信号脉冲波形和眼图发现,随着传输速率和传输距离的增加输出信号劣化.最后结果表明,当主偏振态的旋转速率为零时,二阶PMD的影响可以忽略;但当其值增大时,输出信号劣化严重.在光纤通信系统设计时,需要考虑偏振模色散影响分析结果,可提供参考依据.     

PMD Characterization of a Dispersion Managed Link up to the Second-order with High Accuracy

We report an algorithm on the characterization up to second-order polarization mode dispersion (PMD). Our algorithm is able to characterize very short link with low PMD coefficient (less than 0.04 ps/ ). The link includes dispersion compensating fiber modules and loss compensating optical amplifiers. The estimation for first- and second-order PMD is successfully performed for dispersion-managed links of 85 and 265 km using the Jones matrix eigen-analysis (JME). The algorithm was developed to detect the evolution of the principal state of polarization (PSP) and subsequent calculation of second-order PMD components such as polarization-dependence, chromatic dispersion (PDCD) and depolarization.     

Jones matrix of polarization mode dispersion

We describe how to calculate the Jones matrix transfer function of a fiber if its principal states of polarization and its differential group delay as functions of frequency are known. Using two counterexamples related to second-order polarization mode dispersion (PMD), we also show that a previous method used for the same purpose induces overestimation of second-order PMD effects by a factor of 2. Our new method is used to solve the problem for both counterexamples.     

基于偏振度椭球的PMD补偿的前馈信息提取方法

通过建立一个简单的模型推导了偏振模色散与偏振度椭球的关系式,可以直接从偏振度椭球的长轴和短轴得到偏振模色散的大小.将得到的一阶偏振模色散大小与理论上从琼斯矩阵中计算的结果进行比较,发现在差分群时延小于20 ps时,模拟结果与理论计算值较好相符.分析了如何从偏振度椭球的长轴判断偏振模色散矢量的方向.因此,从得到的偏振模色散矢量的大小和方向信息可以为一阶偏振模色散补偿提供前馈信息.     

Schemes for complete compensation for polarization mode dispersion up to second order

The required structure and elements of polarization mode dispersion (PMD) compensators for complete second-order compensation are investigated by use of a general PMD vector formalism of concatenated PMD elements based on Mueller matrices and Stokes vectors. The investigation shows that two- and three-stage compensators with five independent parameters can compensate for polarization-dependent chromatic dispersion as well as the depolarization component of second-order PMD.     

Wideband all-order polarization mode dispersion compensation via pulse shaping

We demonstrate the application of ultrafast pulse-shaping techniques for experimental wideband all-order polarization mode dispersion (PMD) compensation, for the first time to our knowledge. PMD is treated as arbitrary variations of state of polarization and phase versus wavelength, in an all-order sense. Consequently, two pulse shapers are implemented in a serial manner to compensate for the polarization and the phase spectra independently. We report compensation of subpicosecond pulses (14 nm bandwidth around 1550 nm) that are anomalously spread to more than 2 ps as a result of PMD. This PMD compensation scheme can potentially be a powerful and cost-effective solution for fiber optic telecommunication networks.     

Extended Jones matrix for first-order polarization mode dispersion

I present numerical simulations of the average transfer function of polarization mode dispersion (PMD) in optical fibers conditioned on various given values of the differential group delay (DGD). I find that even fibers with relatively small mean DGD can exhibit significant coupling between the two principal states of polarization. The average frequency dependence of this coupling can be approximated by a generic analytic function that deviates substantially from the quadratic frequency dependence that is often assumed in second-order PMD models. Finally, I define an extended transfer matrix for first-order PMD that describes the average frequency dependence of all PMD-induced distortions as a function of the DGD and show that this matrix is much better suited for optical PMD compensation than that of a conventional first- and second-order PMD model.     

Tuneable polarization mode dispersion emulator: Fixed polarization maintaining fibre sections and rotatable polarization orientations

We design a polarization mode dispersion (PMD) emulator capable of adjusting first-order (FO-) and second-order (SO-) PMD statistics, making it capable to mimick differerent fibre links or fibre plants. The emulator can adjust PMD statistics by controlling mode coupling angles between polarization maintaining fibres (PMFs) of fixed length using its seven rotatable electro-optic polarization rotators which act as half waveplates (HWPs). The stability and repeatability of the emulator under a stable laboratory environment makes PMD statistics reproducible. The control mechanism of the emulator is in real-time.     

Two-stage adaptive PMD compensation in 40 Gb/s OTDM optical communication system using PSO algorithm

An experiment of two-stage adaptive compensation for polarization mode dispersion (PMD) in a 40 Gb/s optical time-division multiplexed (OTDM) communication system is reported. The PMD monitoring technique based on degree of polarization (DOP) was adopted. The Particle Swarm Optimization (PSO) algorithm was introduced in adaptive PMD compensation. The comparison was made to estimate the effectiveness between PSO algorithms with global neighborhood structure (GPSO) and with local neighborhood structure (LPSO). The LPSO algorithm is shown to be more effective to search global optimum for PMD compensation than GPSO algorithm. The ability of tracking changed PMD using PSO algorithm was also investigated. The two-stage PMD compensator is shown to be effective for both first- and second-order PMD, and the compensator is shown to be bit rate independent. The optimum searching time is within several hundreds of milliseconds. The response time for recovery from a sharp disturbance is about 11 ms.     

旋转光纤对二阶偏振模色散的影响

论述了单模光纤生产过程中旋转光纤对二阶偏振模色散的影响. 从理论上指出虽然旋转光纤 有助于减小一阶偏振模色散，但是同时会使二阶偏振模色散增大，这对10 Gb/s以上速率的 光纤通信系统是个重要的问题. 关键词： 二阶偏振模色散 旋转光纤 动态方程