Spectrally resolved reflectometric measurement of polarization mode dispersion in an optical fiber link with polarization-dependent loss

In an optical fiber link with polarization-dependent loss (PDL), we demonstrate that although the complex polarization mode dispersion vector cannot be fully obtained by the reflectometric measurement, the spectrally resolved differential group delay (DGD) and differential attenuation slope (DAS) can be explicitly determined by such measurements performed simultaneously in the optical frequency domain and the fiber length domain. In principle, this technique can be used to realize the spectrally resolved and spatially resolved measurement of DGD and DAS in an optical fiber link having PDL based on distributed Rayleigh backscattering. We report the experimental result based on the far-end Fresnel reflection to confirm the validity of the proposed method.     

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.     

20Gb/s系统中偏振模色散的偏振度反馈控制分析

基于主偏振态理论和一阶偏振模色散近似,推导出光信号偏振度的一个简洁解析表达式。并利用该解析表达式和快速傅里叶变换,对20Gb／s系统的偏振模色散补偿中,偏振度监测法的灵敏度和跟踪范围受多种因素(如脉冲啁啾、占空比、消光比、放大自发辐射噪声、自相位调制等)的影响程度进行了数值模拟分析。发现利用偏振度监测法反馈控制偏振模色散补偿时,监测灵敏度和跟踪范围是折中的,较小的占空比有利于提高偏振度监测法的灵敏度,而且总可以对高达1．5个位周期(75ps)的差分群延时进行跟踪,但当占空比低于0．5时,跟踪范围迅速缩小,消光比和放大自发辐射噪声不会明显改变偏振度监测法的跟踪范围,自相位调制效应显著地影响偏振度监测法的性能。     

Simultaneous strain and temperature measurement with a single fiber Bragg grating based on the polarization properties analysis

In this paper, a new technique for discrimination of temperature and strain exploiting the polarization properties of a single normal fiber Bragg grating (FBG) is firstly proposed and experimentally demonstrated. The spectral characterization of the differential group delay (DGD) of the FBG is studied. The evolution of the DGD response of the FBG as a function of temperature and strain is analyzed. The numerical simulations and experimental results suggest that implementing two independent measurements of the resonance wavelength shift and the changes of the DGD can discriminate the temperature and strain effects.     

Characterization of Birefringence and Dispersion Properties in an Arrayed Waveguide Grating

We have characterized polarization dependent loss(PDL), differential group delay(DGD), and chromatic dispersion of an AWG and a simple method was proposed to estimate the chromatic dispersion from the measured DGD of the device.     

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     

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.     

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.     

Quantum Statistical Theory of Polarization Mode Dispersion

Polarization mode dispersion is modelled as decoherence of polarization under the disturbance of environment and the coupling with frequency. This model is described by the quantum master equation and the Langevin equation. It can be predicted that the optical beam is depolarized exponentially in a fibre and the differential group delay （DGD） is proportional to the square root of the propagation distance. The distribution of the DGD can also be calculated.     

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.     

Polarization mode dispersion probability distribution for arbitrary distances

The probability distribution of the differential group delay (DGD) at any fiber length is determined by use of a physically reasonable model of the fiber birefringence. We show that if the fiber correlation length is of the same order as or larger than the beat length, the DGD distribution approaches a Maxwellian in roughly 30 fiber correlation lengths, corresponding to a couple of kilometers in realistic cases. We also find that the probability distribution function of the polarization dispersion vector at the output of the fiber depends on the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances.     

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.     

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.     

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.     

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.     

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.     

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.     

偏振模色散补偿中偏振度与差分群延时关系的理论分析和实验

偏振模色散是高速光纤通信系统的主要问题之一。在用偏振度作为反馈信号的动态偏振模色散补偿系统中，偏振度与差分群延时的关系对于准确快速的动态偏振模色散补偿很重要。推导出了准单色光波情况下任意波形和高斯脉冲的偏振度的数学表达式，理论分析了高斯脉冲情况下分光比、脉冲宽度和连续脉冲个数分别对偏振度与差分群延时关系的影响，并用10Gbit／s归零／不归零伪随机码序列进行了实验，实验证明了理论推导和理论分析的正确性。实验还表明偏振度的大小与脉冲啁啾和光纤色散无关，从而肯定了将实际光脉冲化简为准单色光波分析的可行性。     

一种可编程PMD模拟器

为了研究光纤通信中的偏振模色散(PMD)及其对高速光通信系统的影响和补偿技术,研制了一种可编程控制的PMD模拟器,它由6组双折射晶体和磁光晶体组成,群时延差(DGD)变化范围为±(0.3~35) ps,可设为不同平均值的Maxwell统计分布随机变化,也可以设为其它要求的数学分布.实验证明,该模拟器测量值与理论符合得很好,且具有较高的重复性和稳定性,响应时间小于1 ms.这种模拟器可用于10 Gb/s和40 Gb/s光传输系统PMD问题的研究.     

偏振复用光纤通信系统色散均衡器及算法的研究

设计了一种适用于偏振复用相干解调光纤通信系统的色散均衡器,用于补偿信道传输的色散损伤。该均衡器采用半码元间隔的蝶形有限脉冲响应滤波器结构,与此结构配合的自适应算法分别采用最小均方算法和递归最小二乘算法。通过仿真实验,分析了两种算法对残留色度色散和偏振模色散的补偿容限。仿真结果表明,递归最小二乘算法的补偿效果优于最小均方算法,它可以同时补偿1760ps/nm的残留色度色散和104.9ps偏振模色散引起的差分群时延,比同等条件的最小均方算法提升性能2.23dB。