Variable differential-group-delay module without second-order PMD

We propose a design for a variable differential-group-delay (DGD), formed by concatenation of four identical fixed DGD segments. Due to the symmetry involved, it produces zero second-order polarization mode dispersion (PMD). The generated third-order PMD is half the value of the conventional two-segment concatenation for variable DGD.     

Statistical analysis of the performance of PMD compensators using multiple importance sampling

In this letter, we evaluate the performance of fixed and variable differential group delay (DGD) polarization-mode dispersion (PMD) compensators as the first- and second-order PMD varies using multiple importance sampling. We show that importance sampling yields estimates of the average penalty with low variance over the entire region of interest of first- and second-order PMD. We also show that there is little advantage in using a compensator with a variable-DGD element and that the performance of a compensator that minimizes the residual DGD at the central frequency of the channel is considerably worse than a compensator that maximizes the eye opening.     

Independently tunable first- and second-order polarization-mode dispersion emulator

By solving the equation set for the first- and second-order polarization-mode dispersion (PMD) in retro-verse manner, we show that the independent control of first- and second-order PMD is possible, with only two control parameters. The analysis on the emulation algorithm as well as the operation range/resolution shows excellent agreement with the experimental demonstration operated with a sample emulator constructed of a fixed differential group delay (DGD), a polarization rotator, and a variable-DGD element.     

Theoretical and experimental analysis of the dependence of a signal's degree of polarization on the optical data spectrum

We show theoretically and experimentally the relationship between a signal's degree of polarization (DOP), all-order polarization mode dispersion (PMD), and the optical spectrum (and hence the data modulation format and pulse width), and that these effects must be taken into account when using the DOP for differential group delay (DGD) monitoring. We explain the theory behind how all-order PMD affects a signal's DOP, and observe the pulse-width dependence for 10-, 20-, and 40-Gb/s return-to-zero (RZ) systems as the duty cycle changes. We then analyze and show (via simulation and experimentation) the effects of different data modulation formats (RZ, carrier-suppressed RZ, alternate-chirped RZ, and differential phase-shift keying) on the DOP in a DGD monitor. We conclude that the measurable DGD range and DOP sensitivity in DOP-based DGD monitors are dependent on a signal's pulse width and the data modulation format. We also show the theory behind the effects of first- and second-order PMD on the maximum and minimum DOP.     

Frequency and Duration of Communication System Outages Resulting From Polarization Mode Dispersion

In this paper, we employ measurements of transponder tolerance to both differential group delay (DGD) and second-order polarization mode dispersion (SOPMD) and of the temporal evolution of DGD and SOPMD in installed transmission systems to predict the influence of PMD on the rate and duration of PMD-induced system outages. An empirical 2-D random-walk model predicts that the outage rate and duration depends solely on the mean fiber DGD. We find that the step size of the random walk is nearly uncorrelated with the instantaneous value of the PMD. We then justify the assumptions of this procedure with a full numerical simulation and employ a biased Markov chain algorithm to generate highly accurate results for system outages where simplified models fail.      

Average frequency dependence of polarization-mode dispersion

We present a numerical analysis of the average frequency dependence of a Jones matrix describing polarization-mode dispersion (PMD) with arbitrarily large differential group delay (DGD). Using a properly oriented autocorrelation matrix, we calculate the relative frequency dependence of the phase delays in the principal states of polarization (PSP) and of the cross coupling between the PSPs. Our results show that the averaged frequency dependence of these components scales with the product of the relative optical frequency times the average DGD. We also find a previously unknown correlation between the third-order PMD vector and the cross product of the first- and second-order PMD vector.     

Automatic compensation of polarization-mode dispersion for 40 Gb/s transmission systems

We present an automatic compensator that effectively mitigates signal distortion due to polarization-mode dispersion (PMD). Accurate compensation is achieved by utilizing a degree of polarization (DOP) monitor with a measurement uncertainty of better than 1% achieved by applying a self-dependent precalibration procedure. The compensation performance at 43 Gb/s was evaluated systematically with respect to both first- and second-order PMD by using a crystal-optical PMD emulator. The compensator extended the tolerable differential group-delay (DGD) limit from 8 to 28 ps, while maintaining the Q penalty below 1 dB. In terms of the average of a Maxwellian-distributed DGD, the PMD compensator enabled transmission for up to 8 ps, or about three times higher than the level tolerated in the uncompensated case. In addition to the compensation performance, we demonstrate successful operation, even for distorted signals with high chromatic dispersion. We believe this capability will be a key enabler for a combined operation with adaptive chromatic dispersion compensators.     

Degree-of-polarization-based PMD monitoring for subcarrier-multiplexed signals via equalized carrier/sideband filtering

We demonstrate a method for differential-group-delay (DGD) and polarization-mode-dispersion (PMD) monitoring using the degree-of-polarization (DOP) in subcarrier-multiplexed (SCM) systems. Traditional SCM signal show very little DOP sensitivity to DGD/PMD due to the low modulation depth used for generating SCM signals. We use a narrow-band optical filter to equalize the power of the carrier and one of the sidebands by offsetting the filter from the carrier, enabling PMD and DGD monitoring and more than tripling the DOP sensitivity to DGD/PMD. Our technique is simple, uses only a single optical filter, and can be applied to both single- and double-sideband (SSB and DSB) SCM signals as well as single and multisubcarrier systems. Additionally, we show that our monitoring technique is robust to the chromatic dispersion-induced radio-frequency (RF) power fading effect seen in DSB SCM signals. Using this technique to enhance the DOP sensitivity to DGD/PMD and generate a feedback signal to a PMD compensator (PMDC), we obtain an 11-dB improvement in the 5% RF power tail.     

40 Gb/s光纤通信系统中一阶PMD对信号频谱的影响

首先给出了受一阶偏振模色散(PMD)影响的40 Gbit/s高斯脉冲信号功率谱的数学表达式,并分析了脉冲波形、分光比、监测频率以及差分群延时(DGD)对接收信号功率谱的影响.实验测量了在分光比为0.5时的40 Gbit/s归零(RZ)码伪随机信号在接收频率为12 GHz处的电功率谱密度随DGD变化的关系,实验结果与理论计算一致.这表明,对于40 Gb/s的光纤通信系统,可以通过简单地检测某一特定频率的电信号功率,动态跟踪系统中PMD的变化情况,从而为补偿一阶PMD提供了重要依据.     

Statistical characteristics and effects of polarization mode dispersion in dispersion managed soliton systems

Recently,the dispersion-managed solitons(DMS) areof great interest in soliton communication systems .Be-cause of some prior advantages compared with conven-tional solitons ,such as higher pulse energy and signalnoise ratio,lower averaged dispersionline an…     

Practical Solutions to Polarization-Mode-Dispersion Emulation and Compensation

Polarization-mode dispersion (PMD) still remains a challenge for high-data-rate optical-communication systems. Practical solutions are desirable for PMD emulation, monitoring, and compensation. The authors review and compare various techniques for PMD emulation and compensation, with an emphasis on the application of programmable differential-group-delay (DGD) elements for manipulating PMD effects. The authors pay special attention to advanced emulation techniques, such as importance sampling and the hinge model, for practical applications. The tunability of programmable DGD elements proves to be attractive for both system performance evaluation and overall optimization     

Dynamic PMD Mitigation at 10 Gb/s Using Viterbi Equalization in DPSK Systems

Compensating dynamically changing polarization- mode dispersion (PMD) is important for optical fiber transmission systems. We present simulations of a Viterbi equalization for dynamic PMD mitigation in 10-Gb/s nonreturn-to-zero differential phase-shift keying systems. The equalizer can dynamically track fast varying differential group delay (DGD) and achieve similar performance to static DGD.      

A comparative study of single-section polarization-mode dispersion compensators

This paper shows how to use multiple importance sampling to study the performance of polarization-mode dispersion (PMD) compensators with a single differential group delay (DGD) element. We compute the eye opening penalty margin for compensated and uncompensated systems with outage probabilities of 10/sup -5/ or less with a fraction of the computational cost required by standard Monte Carlo methods. This paper shows that the performance of an optimized compensator with a fixed DGD element is comparable to that of a compensator with a variable DGD element. It also shows that the optimal value of the DGD compensator is two to three times larger than the mean DGD of the transmission line averaged over fiber realizations. This technique can be applied to the optimization of any PMD compensator whose dominant sources of residual penalty are both the DGD and the length of the frequency derivative of the polarization-dispersion vector.     

Comparison of different feedback signals used in one stage PMD compensators for different modulation formats

As PMD compensation has become a very intense subject of research in recent years, the achievement of simple PMD compensators based on a feedback signal is a key issue. As PMD compensation uses a feedback indicator for system performance evaluation, such feedback signals must reproduce the DGD variations with time. In this paper, the correlation between DGD and different feedback signals is studied with a new method. This method is applied for various modulation schemes, leading to well-known results. By applying the method to the electrical and optical duobinary formats, it is shown that for duobinary signals, the DOP feedback signal shows the best correlation with instantaneous DGD value. Such a behavior of duobinary format is very interesting since duobinary modulation schemes are now considered for systems upgrades or mixed architectures (10 Gbit/s-40 Gbit/s on the same link). In such systems, PMD compensation has to be bit-rate independent which is available with the DOP as feedback indicator.     

Performance of a 46-Gbps Dual-Polarization QPSK Transceiver With Real-Time Coherent Equalization Over High PMD Fiber

We report experimental results on the transmission performance of a coherent dual-polarization quadrature phase-shift-keyed (DP-QPSK) transceiver with real-time electronic equalization over fiber having 50-ps mean polarization mode dispersion (PMD). Both single-channel, single-span and multi-channel, multi-span measurements were performed over the high PMD fiber, which has near Maxwellian statistics for the differential group delay (DGD) as well as higher order PMD as expected for a long, mode-coupled fiber. Transmission of eighty channels was achieved over 8$, times ,$100 km of TrueWave Reduced Slope fiber plus distributed high PMD fiber, where individual channels had instantaneous DGD as high as 127 ps. The dependence of the OSNR penalty on the launch state of polarization was evaluated and found to be minimal, and the contribution of fiber nonlinearities to the transmission penalty was evaluated for two different per-channel launch powers. Finally, using a transceiver equipped with forward-error-correction, error-free transmission over the 800-km link was demonstrated over a 10-day period; during this time the DGD of the measured channel varied from 13 to 116 ps.      

Polarization mode dispersion compensation at 10, 20, and 40 Gb/swith various optical equalizers

Polarization mode dispersion (PMD), especially in “old” fibers, is considered harmful for installation and upgrading of trunk lines. An optical PMD equalizer should have several or many differential group delay (DGD) sections with polarization transformers in between which can endlessly transform any input polarization into a principal state of the following DGD section. The sections must practically have fixed DGDs unless there is only one section. The small-signal baseband transfer function for PMD, higher order PMD, and the necessary number of sections as well as their control by the output signals of an electrical filter bank in the receiver are also discussed in this context. Several PMD equalizers have been realized and successfully tested in transmission systems with bit rates of 10, 20, and 40 Gb/s. The systems operated stably with well-opened eye diagrams for DGDs ranging between 0 and 1.7 bit durations. Best performance is obtained from a distributed PMD equalizer with one piece of polarization-maintaining fiber twisted by 64 stepper motors. The principle can also be realized in LiNbO₃     

Polarization-mode-dispersion emulator using variable differential-Group-delay (DGD) elements and its use for experimental importance sampling

We demonstrate a practical polarization-mode-dispersion (PMD) emulator using programmable differential-group-delay (DGD) elements. The output PMD statistics of the emulator can be chosen by varying the average of the Maxwellian DGD distribution applied to each element. The emulator exhibits good stability and repeatability in a laboratory environment. In addition, we demonstrate how this emulator may be used to experimentally employ the powerful technique of importance sampling to quickly generate extremely low probability events. This technique is used to measure the Q-factor degradation due to both average and rare PMD values in a 10-Gb/s transmission system.     

基于偏振度的差分群时延检测的理论分析

文章从理论上分析了信号偏振度(DOP)和各阶偏振模色散(PMD)、光脉冲宽度的关系,当DOP用于差分群时延(DGD)检测并作为PMD补偿的控制信号时,必须综合考虑这些因素;说明了DGD、一阶和二阶PMD对最大和最小DOP的影响,以及光脉冲宽度对DOP检测范围的影响。     

基于脉冲位置调制系统的偏振模色散监测方案

为了实现对脉冲位置调制传输系统光纤信道中偏振模色散的动态监测,提出了一种新型偏振膜色散监测方案,并基于监测原理构建了数学模型。该方案基于单边带内不同偏振信号相位差实现,具有结构简单、易于实现、成本低等优点。结果表明,本方案可以实现对光信号的差分群延时与偏振态的动态监测,即当差分群延时在0ps~100ps范围内时,可准确监测;同时证实了其与信号速率关系较小,能够适应不同速率的系统,且可对脉冲位置调制传输系统的偏振模色散进行实时动态监测。该方案是一个高效可行的偏振模色散监测方案。     

Polarization mode dispersion detected by arrival time measurementof polarization-scrambled light

Polarization mode dispersion (PMD) limits optical fiber capacity. PMD compensators usually minimize the associated eye closure. This measure scales with the square of the differential group delay (DGD) and makes it difficult to detect low DGDs. However, light with a low-speed polarization modulation suffers arrival time variations, in the presence of PMD, that are proportional to the DGD. These are detected by integrating the voltage-controlled oscillator (VCO) input signal of the clock recovery phase-locked loop (PLL). This novel method has been demonstrated for 40 Gb/s nonreturn-to-zero (NRZ) and for 2×40 Gb/s return-to-zero (RZ) polarization division multiplex transmission. PMD detection sensitivities range between 2 ps and 84 fs