PMD effect on pulse shapes and power penalty in optical communication systems

We present an analytical expression relating the output state of polarization and the first-order polarization mode dispersion (PMD) vector in terms of the angle of precession of the output state of polarization around the PMD vector. We derive, incorporating for the first time this angle of precession, a general relation to study the effect of first-order PMD on pulses of arbitrary shapes, and expressions for pulse shape, pulse broadening and power penalty taking into account both PMD and chromatic dispersion. Measured experiment results are presented for NRZ, RZ, NRZ-DPSK, and RZ-DPSK modulation formats.     

Analytical theory for pulse broadening induced by all-order polarization mode dispersion combined with frequency chirp and group-velocity dispersion

We derive an analytical expression for the expected root-mean-square (rms) pulse broadening with considering the combined effects of all-order polarization mode dispersion (PMD), group velocity dispersion (GVD) and frequency chirp. It is shown that two commonly used first-order PMD compensators lose their efficiency quickly with chirp parameter increasing if GVD is ignored. When GVD is added, prechirp technique is helpful for the enhancement of PMD tolerance for both uncompensated case and first-order compensators when GVD and PMD coefficient satisfy some special relationship.     

Dispersion induced power fading for radio frequency signals and its application for fast online PMD and CD monitoring

We derive the expressions for the power fading including first-order polarization mode dispersion (PMD), chromatic dispersion, chirp parameter as well as polarization-dependent chromatic dispersion (PCD), which is dependent on the angle of precession of output state of polarization around the PMD vector. From the expression for radio frequency (RF) signals power fading, we get the average power fading for chromatic dispersion, chirp parameter, first-order PMD and PCD for both double sideband (DSB) modulation and single sideband (SSB) modulation. We also demonstrate a fast PMD and chromatic dispersion monitoring technology with reduced polarization-dependent gain. The measured results agree well with theoretical analysis. PACS 42.81.-i; 42.81.Gs; 42.30.Lr     

Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems

We demonstrate both numerically and experimentally that the phase-change due to fiber nonlinearities induces a bit-pattern-dependent rotation of the state-of-polarization which translates to uncertainty in the principal states of polarization. This effect severely limits the performance of the first-order PMD post-compensation and suggests the use of in-line compensators. Our simulation shows that fiber nonlinearities cause significant distortion (more than 4-dBm Q-penalty after 600-km transmission at 10 Gbit/s) after first-order PMD compensation. For optical powers as low as 3 dBm/channel in systems where PMD is not uniformly distributed along the transmission link, first-order PMD compensation may be ineffective.     

Comparison of penalties resulting from first-order and all-order polarization mode dispersion distortions in optical fiber transmission systems

We compare the eye-opening penalty from a first-order polarization mode dispersion (PMD) model with that from an all-order PMD model in optical fiber transmission systems. Evaluating the performance by taking into account only first-order PMD produces a good approximation of the true eye-opening penalty of uncompensated systems when the penalty is low. However, when the penalties are high, this model overestimates the penalty for outage probabilities in the range of interest for systems designers, which is typically approximately 10(-5) to 10(-6).     

Comparison of soliton robustness with respect to polarization-mode dispersion with first-order polarization-mode dispersion compensated linear systems

Soliton robustness to polarization-mode dispersion (PMD) is compared, both analytically and numerically, with that of linear pulses that use first-order PMD compensation. It is found that soliton robustness to PMD is comparable with first-order PMD compensation and in some cases is even better. The effects of soliton control methods on soliton robustness to PMD were also investigated, and it was found that soliton control methods can significantly improve the soliton's robustness to PMD, particularly for long-distance systems.     

Generation of DQPSK format and its performance against polarization mode dispersion

We propose a novel transmitter and receiver for differential quadrature phase-shift keying （DQPSK） format. The impact of the first-order polarization mode dispersion （PMD） on systems using DQPSK with 100- Gb/s non-return-to-zero （NRZ） or return-to-zero （RZ） format is investigated. Through computing the eye openings of DQPSK formats under different PMD conditions, it is found that NRZ DQPSK, as compared with RZ DQPSK, incurs smaller eye opening due to PMD. Carrier-suppressed return-to-zero （CSRZ） DQPSK format has better tolerance than RZ DQPSK format to PMD for a given bit rate.     

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     

Emulator with inverse trend in first-order and second-order polarisation mode dispersion

We design a polarisation mode dispersion (PMD) emulator through subdividing a polarisation maintaining fibre (PMF) of 22 m in length. The aim of this emulator design is to show that first-order and second-order PMD can be inversely proportional to each other. Furthermore, the emulator is also used to show that the magnitude of PMD is independent to whether its statistics approach theoretical distributions or not, of most importance is the degree of mode coupling. The same (as former) applies to its autocorrelation function (ACF). The PMD control mechanism for the emulator is not in real time.     

40 Gb/s差分相移键控格式抗偏振模色散的性能研究

研究了40Gb/s非归零或归零格式下,差分相移键控和开关键控信号对一阶偏振模色散的影响.比较分析了不同偏振模色散影响下的各种调制格式的眼开度.结果表明:使用非归零和归零格式,在一阶偏振模色散情况下,差分相移键控信号均比开关键控信号有更高的眼开度;与归零差分相移键控格式相比,非归零差分相移键控格式受偏振模色散影响眼开度要小;对于给定的比特率,载波抑制归零差分相移键控格式比归零差分相移键控格式有更好的抗偏振模色散能力.     

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.     

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.     

Impacts of polarization mode dispersion on the pulse-width with considering initial pulse chirp and fiber GVD

The impacts of polarization mode dispersion (PMD) on the pulse-width in linear systems have been investigated. The analytical solutions, including the effects of initial frequency chirp and group velocity dispersion (GVD), are derived. Analyses show that the pulse broadening effects induced by the second-order PMD depend on GVD and chirp parameter, which are different from those induced by the first-order PMD. An initially chirped Gaussian pulse is taken as an example, upon which analytical solutions of rms pulse-width are derived before and after the first-order PMD compensation. The first-order PMD compensator is also evaluated based on these solutions. The results show that the pulse broadening effects will be resisted efficiently by choosing appropriate GVD and chirp parameter; in general, the post-transmission compensation method will be less efficient than the PSP-transmission method.     

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.     

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。     

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.     

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.     

40Gb/s差分相移键控格式抗偏振模色散的性能研究

研究了40Gb／s非归零或归零格式下,差分相移键控和开关键控信号对一阶偏振模色散的影响．比较分析了不同偏振模色散影响下的各种调制格式的眼开度．结果表明：使用非归零和归零格式,在一阶偏振模色散情况下,差分相移键控信号均比开关键控信号有更高的眼开度;与归零差分相移键控格式相比,非归零差分相移键控格式受偏振模色散影响眼开度要小;对于给定的比特率,载波抑制归零差分相移键控格式比归零差分相移键控格式有更好的抗偏振模色散能力．     

粒子群优化算法在自适应偏振模色散补偿中的性能研究

反馈控制算法是偏振模色散的自适应补偿器的关键组成部分,将粒子群优化算法(PSO)引入到偏振模色散自适应补偿系统中。该算法的优点是具有快速收敛到全局最佳值的能力、避免搜索陷入局部极值的能力、抗噪声能力和多自由度控制能力。理论上分析了粒子群优化算法的两个分类———全局邻居结构粒子群优化(GPSO)和局部邻居结构粒子群优化(LPSO)在搜索全局最佳值方面的能力优劣,给出了局部邻居结构粒子群优化算法成功率达100%的三种邻居拓扑结构。实验表明:在补偿一阶偏振模色散时,全局邻居结构和局部邻居结构搜索全局最佳的成功率都能满足要求,全局邻居结构算法收敛速度快。而在补偿二阶偏振模色散时,全局邻居结构成功率降低,而局部邻居结构仍可以满足要求。     

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.