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.     

Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion

We study the frequency autocorrelation of the differential group delay (DGD) in fibers with polarization mode dispersion (PMD). We show that the correlation bandwidth of the DGD is comparable with that of the orientation of the PMD vector. Furthermore, we show that all the most general statistical properties of polarization mode dispersion in long fibers are uniquely determined by the mean DGD. An estimate of the accuracy of measurements in which the mean DGD is extracted by frequency averaging in a single fiber is obtained as a function of the measured bandwidth.     

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.     

三类偏振模色散模拟器的多阶特性和频率统计相关性分析

对现有三类偏振模色散模拟器：旋转晶体型、偏振控制器型和加热器型模拟器，进行了详尽的相关群时延、高阶偏振模色散的统计分布和频率自相关函数三大统计特性的数值模拟和性能比较.以级联段数作为主要参量的分析结果表明：相关群时延分布的产生准确度，旋转晶体型模拟器略优于偏振控制器型，而加热型模拟器相对最差；在产生精确的高阶偏振模色散分布方面，偏振控制器型模拟器最为优越，加热型模拟器略优于旋转晶体型；而对于产生较低的频率自相关本底水准方面，加热型模拟器则优于偏振控制器型和旋转晶体型.综合而言，偏振控制器型模拟器的性能最为优越；十段左右的偏振控制器型模拟器就可以产生合格的模拟效果，其效果等价于十五段以上旋转晶体型，或二十段以上加热型模拟器.     

用庞加莱球法测量二阶偏振模色散

用庞加莱球法测量单模光纤中的二阶偏振模色散，并对二阶偏振模色散的各个分量的统计特性及其影响进行了分析。对75km的G．652普通单模光纤的二阶偏振模色散进行了测量，并对二阶偏振模色散的平行分量、垂直分量、偏振相关色散和消偏振项进行了详细的分析．得到了二阶偏振模色散随波长的分布情况、统计特性以及偏振主态随波长的变化情况。从统计结果可以得到．与偏振相关色散项相比，消偏振项在二阶偏振模色散中起主要作用。该研究对二阶偏振模色散的补偿有一定的指导意义。     

Compensating large PMD by a fiber grating

In this paper, the first- and second-order polarization mode dispersion (PMD) with the amount of 132.994-ps differential group-delay (DGD) and maximum 476.129-ps/nm second-order PMD can be compensated by a two-stages PMD compensator at a 40-Gb/s optical fiber communication system. The first stage has one free degree that is used for first order and high orders PMD compensations by rotating the state of polarization. The second-stage is used for remainder PMD compensations. After compensation, the average DGD and the maximum second-order PMD are reduced to 345.310 fs and 3.102 ps/nm, respectively.     

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.     

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.     

40 Gb/s光时分复用系统中两级偏振模色散自适应补偿实验研究

偏振模色散效应严重制约着长距离高速光纤通信的发展,偏振模色散的自适应补偿成为光通信领域研究的焦点。利用两阶段偏振模色散补偿器,采用6个自由度的粒子群优化算法(PSO),通过在线监测搜索光纤链路信号的偏振度极值作为反馈控制信息,在40Gb／s归零码高速光纤传输链路中成功实现了ms量级的偏振模色散自适应补偿。补偿前后采用庞加莱球法测量光纤链路中偏振模色散量,测量结果表明在信号中心波长1560．5nm处,差分群时延补偿前后测量值分别为21ps和1．3ps,而二阶偏振模色散补偿前后测量值分别为266ps^2和43．5ps^2。补偿后实验链路中的一阶和二阶的偏振模色散同时得到不同程度的补偿,并且系统的总的功率代价在误码率为10^-9时小于1dB。     

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.     

二阶偏振模色散矢量致脉冲展宽的理论分析

我们首次提出了消偏矢量的概念，并用它来描述二阶偏振模色散中偏振模色散矢量方向的变化。本文导出了由于二阶偏振模色散所引起的脉冲展宽的解析表达式，结论指出，偏振相关的本征色散总是使脉冲展宽加剧；而偏振模色散矢量方向的变化（消偏矢量），却是使脉冲展宽减弱。二阶偏振模色散对脉冲的展宽，不仅与偏振相关的本征色散和消偏矢量有关，而且还与信号的传输速率以及初始一阶偏振模色散的大小有关。信号速率的提高，将明显的使二阶偏振模色散的影响增强。在偏振相关的本征色散不为零的情况下，通过调整初始偏振态矢量、初始一阶偏振模色散矢量以及消偏矢量三者的方向，使它们互相平行，可以获得最佳的色散补偿。但是却不能获得完全的色散补偿。在最佳色散补偿时的最小脉冲展宽为σ= (2^1/2/4)( DCF/T₀).     

Compensating Large PMD by Four Free degrees in an OTDM System

In this paper, by introducing a two-stages polarization mode dispersion (PMD) compensator after a optical fiber link with a large PMD, we compensated over 270ps first-order and 2000ps2 high-order PMD in a optical fiber link with super high PMD. Our experimental results shows that, the compensators based on the two-stages of compensator can be used to PMD compensation in a 20Gb/s OTDM system with 60 km high PMD fiber. Before compensation,270ps DGD is became into max. 7ps after compensation. At simultaneity, the tunable FBG have a function of dispersion compensation.     

偏振模色散模拟器的特性

通过对微分群时延差(DGD)统计特性和偏振模色散(PMD)矢量自相关函数的数值模拟，分析比较了目前常用的三种PMD模拟器的性能. 结果表明：在DGD分布方面，由DGD发生器构成的模拟器，一个DGD发生器就可与实际光纤PMD的统计特性相符合，而由保偏光纤和可旋转的连接器构成的模拟器则至少需要15段. 在自相关函数方面，基于保偏光纤的模拟器取决于各段光纤的延时量，而基于DGD发生器的模拟器在中心频带外的自相关值很平稳，可视为常数. 关键词： 光纤通信 偏振模色散 偏振模色散模拟器 自相关函数     

10 Gb/s光通信传输系统中一阶PMD自适应补偿实验

在10 Gb/s归零码(RZ)光通信传输链路中成功地搭建一阶PMD自适应补偿的实验系统,补偿量29 ps,跟踪补偿时间在1 s以内,补偿效果明显.     

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.     

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.     

Synthesis of optical PMD compensating filter using FIR lattice structure

We investigate the potential of n-stage optical finite impulse response (FIR) lattice filter for compensating first order polarization mode dispersion (PMD). This compensation is based on minimizing the differential group delay (DGD) between the two principal state of polarization (PSP) within a given frequency range. The filter is realized by concatenating optical delay lines, directional couplers, and phase shifters in a lattice architecture. A numerical simulation is performed for an 8th and 12th order filters to demonstrate the impact of using higher order filters. The results show that DGD can be reduced significantly as we increase the order of the filter.     

PMD compensation using a fuzzy automatic polarization controller

A new first-order polarization mode dispersion (PMD) compensation technique is experimentally demonstrated in a 2.5 Gbit/s optical transmission system. It achieves adaptive compensation over a wide range of differential group delay (DGD) values, since it does not try to compensate it, but to eliminate one of the principal states of polarization by means of a liquid crystal polarization controller and a polarizer. The PMD parameters of the received signal are measured in real time through its spectrum analysis, and used as the feedback signal in a fuzzy logic algorithm controlling the liquid crystal device. The algorithm achieves a response time faster than the PMD variations in real links, also featuring endless operation. Moreover, a deterministic compact PMD emulator has been implemented in order to test the PMD compensator system.     

一种测量偏振模色散的新方法

提出利用检偏器和光谱仪同时测量单模光纤各个波长的输出偏振态，从而测量出偏振横色散群时延差，这种方法和传统方法相比，测量时间大为节省，降低了偏振模色散随时间变化而引起的测量误差，提高了测量精度。     

Adaptive PMD compensation in 10-Gb/s RZ optical communication system

We report an experiment of adaptive compensation for first-order polarization mode dispersion (PMD) in 10-Gb/s return zero (RZ) optical communication system. The compensated differential group delay (DGD) is up to 30 ps. The quasi-real-time, less than one second, PMD compensation is realized. In the experiment, for the first time, the algorithm so-called particle swarm optimization (PSO) is used to control feedback compensation system.