直接检测光OFDM系统中的偏振相关损耗研究

对于高速光传输,直接检测的光正交频分复用系统（direct detection optical orthogonal frequency division multiplexing, DDO-OFDM）中的偏振相关损耗（polarization dependent loss, PDL）与偏振模色散相互作用,对系统传输带来较大影响。对DDO-OFDM系统中PDL与一阶PMD作用机理和数学模型进行了分析,并通过数字仿真加以验证。结果表明:在PDL与PMD联合作用下,对OFDM信号幅度及相位均产生影响,通过发送导频序列可有效实现信号均衡;由于输出偏振态随频率产生旋转,PMD效应一定程度上缓解PDL所致系统损伤,差分群时延为50 ps条件下,以10 Gb/s的速率在单模光纤传输480 km,DDO-OFDM系统Q值提高约0.8 dB。     

A model to characterize the effect of cross phase modulation on polarization in an optical fiber transmission system

This paper presents a model that described the process of inter-influence between cross phase modulation (XPM) and polarization effects such as polarization mode dispersion (PMD) and polarization dependant loss (PDL) in an optical fiber communication system. Previous papers have discussed PMD-PDL and PMD-XPM effects in separate models, but in this work we developed a model that is capable of characterizing and evaluating PMD, PDL and XPM simultaneously. From the model, we found that PMD and PDL can be affected by XPM. The presence of XPM changed the vector directions of PMD and PDL in Stokes space.     

光纤偏振效应导致脉冲展宽的解析模型

在10Gb／s,尤其是40Gb／s以上高速光纤通信系统中,光纤的偏振特性已成为限制系统传输距离的主要因素之一。光纤的偏振效应主要包括偏振模色散和偏振依赖损耗。而脉冲均方根展宽是判断信号传输性能的一个主要物理量。本文讨论了光纤线路偏振模色散与偏振相关损耗的相互作用及对信号脉宽的影响。给出了线路偏振模色散矢量和偏振相关损耗矢量之间的关系式,并基于严格的数学方法,导出了在光纤偏振模色散和偏振相关损耗共同作用下的信号均方根脉宽变化的解析形式,同时考虑了光纤色散,啁啾等。该模型可用于分析高阶偏振模色散和偏振相关损耗,任意线性光纤通信系统脉冲展宽分析。     

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.     

Statistical PMD and PDL effects emulator based on polarization maintaining optical fiber segments

Low cost statistical PMD/PDL emulator is presented. The emulator was initially designed as a classical PMD emulator. But PDL measurements of the designed emulator show that it can be also used as statistical PDL emulator. The emulator was constructed by concatenating 15 highly birefringence optical fiber segments and randomly varying the mode coupling between them, by rotating the polarization state between them. The achieved numerical and experimental results show that the designed emulator can mimic the polarization effects (PMD and PDL) of a real modern optical fiber link.     

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.     

Impact of polarization dependent loss on degree of polarization as feedback signal of polarization mode dispersion

Polarization dependent loss (PDL) has been recognized as a critical issue because various inline optical components may have nonnegligible PDL effect that interacts with polarization mode dispersion (PMD).We investigated the impact of PMD-PDL interaction on degree of polarization (DOP), which is the most commonly used feedback signal in PMD compensation. The simulation results of a 40-Gb/s NRZ code optical transmission system show that the maximum PMD increases from approximately 40 ps to more than 45 ps, while minimum DOP declines from approximately 0.6 to approximately 0.2. The interaction of PMD and PDL also induces residual PMD underestimation of 5-8 ps, which causes degradation of PMD compensation performance.     

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.     

偏分复用系统中偏振模色散补偿与偏分解复用一体化方案

本文建立了偏分复用系统中偏振模色散与信号偏振态变化引起信道串扰的数学模型, 分析了偏振模色散对偏分复用信道射频功率的影响, 并提出了适用于偏分复用系统的光域偏振模色散补偿与偏分解复用同时进行的方案: 用信道的射频功率作为反馈控制信号, 监测链路中偏振模色散和偏振态变化引起的信道串扰的大小, 用改进的粒子群优化算法对偏振控制器进行自适应控制, 同时完成偏振模色散补偿与偏分解复用. 在112 Gb/s偏分复用-差分正交相移键控(PDM-DQPSK)传输系统中仿真验证了该方案的有效性. 结果表明该方案可以使112 Gb/s-PDM-DQPSK传输系统完成自适应偏分解复用的同时, 在1 dB的光信噪比代价下, 使系统对偏振模色散的容忍度提高20 ps. 关键词： 偏分复用系统 信道串扰 偏振模色散 偏分解复用     

The Effects of Polarization and Non-Linearity on the Performance of WDM System with Optical Cross-Connects

The performance of a wavelength division multiplexing (WDM) system with optical cross-connects (OXCs) and in the presence of polarization and nonlinear effects was analyzed. We determined the effect of PMD and PDL; nonlinearity such as XPM, SPM, and FWM; and CD on the system performance. We found that the system outage probability is highest at DGD threshold for the respective maximum eye closure (EC). We showed that the allowable DGD depends on the time slot for one bit T, which is the inverse of the network bit rate. Wider T is more immune to large PMD with the EC still maintained at the same level since DGD/T is unchanged. Our analysis also indicated that as DGD increases, BER increases. The BER also increases with increase in PDL and further increases with the presence of XPM, SPM, FWM, and CD.     

Study of the stability of polarization mode dispersion in fibre

Polarization mode dispersion (PMD) is the ultimate limitation to high bit-rate fibre communication system. The stability of PMD is very important to its measurement and compensation. This paper puts forward a method to measure the stability of PMD by measuring the stability of the state of polarization (SOP) and introduces the conception of time evolution vector (TEV) of SOP. We observe the fact that the regularity of the principal state of polarization changing with time is the same as other SOPs‘‘, if we neglect the dependence of TEV on wavelength. We also measure the SOP‘‘s stability of some fibres with different lengths, and obtain results of PMD changing with time.     

偏振模色散矢量的研究

研究了无损光纤的密勒矩阵,进而得出了偏振模色散矢量的解析表达式、主偏振态对应的斯托克斯矢量的解析表达式,以及高阶偏振模色散矢量的解析表达式.这些解析表达式是由光纤参数决定的.讨论了局部偏振模色散矢量与整体偏振模色散矢量的关系,讨论了利用偏振模色散矢量进行偏振模色散补偿的原理.引入了偏振模色散补偿元件的偏振模色散补偿矢量C,具体计算了正规的非圆光波导类的补偿元件的C.从理论上证明了仅仅利用一个正规的非圆光波导类的补偿元件,例如一根保偏光纤或是一个双折射晶体,是不能实现偏振模色散补偿 关键词： 偏振模色散 密勒矩阵 色散补偿 主偏振态斯托克斯矢量     

Reflections from polished single mode fiber ends

Abstract

The performance of a wavelength division multiplexing (WDM) system with optical cross-connects (OXCs) and in the presence of polarization and nonlinear effects was analyzed. We determined the effect of PMD and PDL; nonlinearity such as XPM, SPM, and FWM; and CD on the system performance. We found that the system outage probability is highest at DGD threshold for the respective maximum eye closure (EC). We showed that the allowable DGD depends on the time slot for one bit T, which is the inverse of the network bit rate. Wider T is more immune to large PMD with the EC still maintained at the same level since DGD/T is unchanged. Our analysis also indicated that as DGD increases, BER increases. The BER also increases with increase in PDL and further increases with the presence of XPM, SPM, FWM, and CD.     

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.     

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     

偏振模色散补偿控制中偏振度技术的性能

基于主偏振态理论，导出了光信号偏振度的解析表达式.并对40 Gb/s光传输系统中的信号偏振度受各种因素的影响进行了数值模拟，包括啁啾、脉冲形状、脉冲宽度、自发辐射噪声以及消光比等.结果表明，偏振度技术能有效地监测和控制40 Gb/s系统中小于37.5 ps的偏振模色散.而且发现就最大化偏振度技术对差分群延时的容许范围而言，脉冲的1/e强度半宽取0.45个位宽（11.25 ps）是最优的.     

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.     

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.     

Effects of polarization mode dispersion on cross-phase modulation in a WDM optical transmission system

The cross-phase modulation (XPM) changes the state-of-polarization (SOP) of various channels and leads to amplitude modulation of the propagating waves in a WDM system. Due to the presence of polarization mode dispersion (PMD), the angles between the SOP of the channels change randomly and cause the modulation amplitude fluctuation random in the perturbed channel. We analytically derive the dynamic equation of the perturbed channel, determine the combined probability density function of the random angle between the SOP of pumps and probe channel and evaluate the effects of PMD on XPM for a 4-channel IM-DD WDM system in terms of BER at bit rate of 10 Gb/s per channel. We also simulate the impact PMD on XPM for a 4-channel WDM system in terms of eye diagram and found that eye opening penalty is 1.85 dB higher when the fiber PMD coefficient increases from 0.5 to 1.5 ps/√km.     

Nonlinear repolarization in optical fibers: polarization attraction with copropagating beams

We propose a type of lossless nonlinear polarizer, novel to our knowledge, a device that transforms any input state of polarization (SOP) of a signal beam into one and the same well-defined SOP toward the output, and perform this without any polarization-dependent losses. At the polarizer output end, the signal SOP appears to be locked to the input pump SOP. The polarizer is based on the nonlinear Kerr interaction of copropagating signal and pump beams in a telecom or randomly birefringent optical fiber.