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.     

Analysis of PMD compensators with fixed DGD using importancesampling

In this letter, we use importance sampling to analyze polarization-mode dispersion compensators with a constant differential group delay (DGD) element. We optimize the value of the fixed DGD element of the compensator with respect to the outage probability. We show that the optimum value of the fixed DGD element of the compensator can reduce the outage probability by several orders of magnitude, even though it does not provide a substantial reduction of the average penalty due to polarization-mode dispersion in the cases that we studied. By contrast, choosing the fixed DGD element to maximally reduce the average penalty may lead to an outage probability that is orders of magnitude larger than the optimal choice     

Importance sampling for polarization-mode dispersion

We describe the application of importance sampling to Monte-Carlo simulations of polarization-mode dispersion (PMD) in optical fibers. The method allows rare differential group delay (DGD) events to be simulated much more efficiently than with standard Monte-Carlo methods and, thus, it can be used to assess PMD-induced system outage probabilities at realistic bit-error rates. We demonstrate the technique by accurately calculating the tails of the DGD probability distribution with a relatively small number of Monte-Carlo trials     

Measurement of Q degradation due to polarisation mode dispersion using multiple importance sampling

Multiple importance-sampling (IS) is used to measure the Q degradation due to the polarisation mode dispersion generated by three programmable DGD elements with uniform polarisation coupling between sections. The measured Q-penalty probability distribution extends to <10/sup -17/ with only 1800 experimental samples.     

偏振模色散统计特性的研究

利用动态方程研究了偏振模色散矢量的统计特性 ,分别用统计系综和频率系综两种方法进行数值模拟。数值结果表明 ,统计系综和频率系综两种方法的结果一致。在大归一化距离条件下 ,均方根时延的平方随归一化距离线性变化 ;偏振模色散矢量的各个分量服从高斯分布 ,差分群时延服从麦克斯韦分布 ;偏振模色散矢量弥散于整个邦加球     

光纤偏振模散随波长变化特性的研究

目前,偏振模散已经成为高速光纤通信系统发展的主要障碍,本文用琼斯传输矩阵法研究了偏振模散,通过数值模拟给出其统计特性,差分群时延服从麦克斯韦分布;PMD各阶项随波长随机变化;偏振主态在邦加球上的变化走向说明出现了PMD高阶项。     

Time evolution of polarization mode dispersion in long terrestriallinks

Although polarization mode dispersion is well characterized in terms of principal states of polarization (PSP) and of their differential group delay (DGD), both analytically and experimentally, very few data have been published on their time evolution in terrestrial links, where temperature fluctuations are larger than in undersea links. The authors demonstrate strong correlation between temperature fluctuations and evolution of DGD and PSP. Correlation is even stronger in links which include connectors. Also, they report that DGD, as a random function of time, has a Maxwellian distribution and thus shows that it is an ergodic process     

The Brownian-bridge method for simulating polarization mode dispersion in optical communications systems

We propose a technique that allows efficient simulation of fibers with a specific value of instantaneous polarization mode dispersion (PMD) at a given optical frequency. The proposed technique is rigorously indistinguishable in the statistical sense from applying the brute-force Monte Carlo method and then selecting the fibers whose PMD vector has the desired value. To demonstrate the capabilities of the proposed method, we calculate the probability density function of the differential group delay (DGD) conditioned on the value of the DGD at an offset frequency.     

Statistical treatment of the evolution of the principal states ofpolarization in single-mode fibers

A simple relationship is found for the evolution of the principal states of polarization (PSPs) and their differential group delay in fiber links. A simple expression is found, using the relationship, for the probability of the differential group delay (DGD), considering the evolution of the PSPs as a Brownian motion. The theory has been verified experimentally on an optical cable composed of 12 single-mode, shifted-dispersion fibers 2.2-km long. The results show that the DGD grows as the square root of the length when the length of the fiber is far larger than the correlation length of the perturbation. The measured value of DGD can vary substantially in two fibers belonging to the same ensemble, and in the same fiber, considering two frequencies differing by more than 5 nm     

Statistics of Polarization-Induced Loss Ripples

The interaction of polarization mode dispersion and polarization dependent loss is shown to cause significant loss ripples (LRs) over the signal bandwidth. Polarization-induced LR is a random process; an analytical expression for its probability density function is found, and expressions for its cumulative density function and outage values are derived. Finally, the impact on system design of time varying LR is discussed in the light of the joint statistics of LR and differential group delay (DGD) and of LR and differential attenuation slope. The authors find that this effect cannot be neglected and should be accounted for within the filter cascade budget and that margin trade is possible as simultaneous occurrence of large DGD and large LR events is unlikely     

Noncompliant Capacity Ratio for Systems With an Arbitrary Number of Polarization Hinges

We study the statistics of transmission impairments due to polarization-mode dispersion in systems characterized by the hinge model. In particular, we validate the use of a computationally efficient expression for the probability density function (PDF) of the differential group delay (DGD) of systems with an arbitrary number of hinges. We then combine this expression for the PDF of the DGD with the outage map approach to compute outage probabilities and noncompliant capacity ratios for transmission links with varying numbers of sections (from 4 up to 20), each for several values of mean DGD and different system parameters.      

光纤链路偏振模色散统计特性的数值仿真

对多段保偏光纤（PMF）组成的光纤链路的偏振模色散（PMD）统计特性进行了数值仿真，分析比较了光纤段的长度、段数和级联角度不同的条件下，链路的群时延差（DGD）分布特性。仿真结果表明，在相同的条件下，级联的PMF段数越多，仿真得到的DGD分布就越趋向麦克斯维分布；随机变化的物理量越多，使DGD分布趋向于麦克斯维分布所需要的光纤段数就越小。     

PMD outage probabilities of optical fiber transmission systems employing bit-to-bit alternate polarization

The impact of differential group delay (DGD), induced by polarization-mode dispersion, on the performance of differential phase-shift keyed and on-off keyed modulation formats employing bit-to-bit alternate polarization (APol) is investigated by means of numerical simulation. Thereby, it is observed that the optical signal-to-noise ratio (OSNR) penalty due to DGD is almost independent of the power splitting ratio between the principal states of polarization (PSP) of a DGD emulator, when APol modulation formats are employed. Although this leads to a higher mean OSNR penalty for a given DGD value compared to conventional modulation formats, it is shown that the allowed mean DGD for required low system outage probabilities does not change significantly.     

Analysis of Degree of Polarization as a Control Signal in PMD Compensation Systems Aided by Polarization Scrambling

The performance of degree of polarization (DOP) is investigated as a control signal in polarization-mode dispersion (PMD) compensation systems aided by polarization scrambling. The relation between the input and output polarization states of a signal propagating through a polarization scrambler and a PMD-induced optical fiber is described by a 3 $,times,$3 Stokes transfer matrix. The average DOP of the output signal over a period of polarization scrambling is derived as an alternative to the conventional DOP-based control signal, i.e., minimum DOP. In the presence of first- and all-order PMDs, the performance of the average and minimum DOPs in monitoring of differential group delay (DGD) for different data formats (i.e., RZ and NRZ) is evaluated. The performance of the two control signals are further investigated by calculating the outage probability of a feedforward first-order PMD compensation system. The results show that the average DOP outperforms the minimum DOP and also gives a wider DGD monitoring range.      

一种重要抽样仿真方法的研究及应用

介绍了蒙特-卡洛仿真原理,分析了改进型的蒙特-卡洛仿真即重要抽样(IS)的原理及其在通信中的应用,特别是在高速光纤通信的偏振模色散(PMD)仿真中的应用价值.实验证明,采用重要抽样的仿真方法可以得到大差分群时延(DGD)值的小概率事件,并且系统配置比用蒙特-卡洛的仿真方法简单得多.     

Multichannel Differential Group Delay Emulation and Compensation via a Phase Pulse Shaper

We developed a differential group delay (DGD) emulator which is based on a high spectral resolution phase pulse shaper. DGD generation has been demonstrated for up to four wavelength channels independently and simultaneously, with DGD accuracy of approximately 1 ps for up to 400-ps DGD range. For each channel, DGD versus frequency profiles can be arbitrarily programmed to user specifications. Multichannel DGD compensation has also been demonstrated using the same setup.     

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.     

Narrow-band measurement of differential group delay by a six-state RF phase-shift technique: 40 fs single-measurement uncertainty

We describe in detail our implementation of a modulation phase shift (MPS) technique for narrow-bandwidth measurement of differential group delay (DGD) and the principal states of polarization (PSP) in optical fibers and components. Our MPS technique involves launching six orthogonal polarization states (as opposed to the four states typically launched) to achieve improved measurement stability. The measurement bandwidth is 4.92 GHz (twice the 2.46 GHz RF modulation frequency), the measurement time is 13 s per point, and the single-measurement uncertainty is better than 40 fs (/spl sim/95% confidence interval) for DGD values from 10 to 1000 fs. We demonstrate that this uncertainty can be greatly improved by averaging, yielding a 9.7 fs uncertainty (95% confidence interval) on a device with 315 fs of DGD. Sources of uncertainty are detailed, including a DGD contribution from the detector itself. Simulations illustrate the uncertainty contribution of multiple DGD elements in series.     

Enhancing the dynamic range and DGD monitoring windows in DOP-based DGD monitors using symmetric and asymmetric partial optical filtering

We propose and demonstrate a new type of degree-of-polarization (DOP)-based differential-group-delay (DGD) monitor using an optical filter such that the DGD monitoring range and DOP dynamic range are dramatically increased. We apply this technique to varying pulsewidth return-to-zero (RZ), carrier-suppressed RZ (CSRZ), and alternate-chirped RZ (ACRZ) signals and show that by optimally setting the position, bandwidth, and shape of a filter, we can double the DGD monitoring range compared to traditional DOP-based DGD monitors. Using our technique, the DGD monitoring ranges for 10, 20, and 40 Gb/s /spl sim/12.5-ps pulsewidth RZ signals are increased by 32, 33, and 12 ps, respectively. We also show that a narrow-band optical filter, offset from the center of the optical spectrum by the bit-rate frequency, can double the dynamic range of DOP-based DGD monitors for non-RZ (NRZ) signals.