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.     

A simple and useful model for Jones matrix to evaluate higher orderpolarization-mode dispersion effects

Starting from the differential equation that relates the Jones matrix of a polarization-mode dispersion (PMD) fiber to its output dispersion vector, the analytical expressions of the matrix coefficients are determined in the case of a dispersion vector rotating on a circumference in the Stokes space. This model, that needs only few parameters with known statistics, is applied to evaluate the performance of an optical system. The results obtained with it and with other models proposed in literature are compared to those evaluated by numerical simulations with all-order PMD effects, showing that our model gives an accurate representation of real system performances     

Multiple importance sampling for first- and second-order polarization-mode dispersion

A simulation method that targets all possible combinations of first- and second-order polarization-mode dispersion (PMD) is described. Use of this method in importance-sampled Monte Carlo simulations yields a more comprehensive determination of PMD-induced system penalties than first-order biasing alone and significantly speeds up the calculation of outage probabilities, particularly when PMD compensation is employed. The technique is demonstrated by using it to calculate the probability distribution function (pdf) of second-order PMD and the joint pdf of the magnitude of first- and second-order PMD.     

Statistical correlation between first and second-order PMD

We investigate the statistical correlation between first- and second-order polarization mode dispersion (PMD) effects, which is important for PMD mitigation. The theoretical results are compared to numerical simulations and experimental data from a real high-PMD fiber. A new dependence between first- and second-order PMD is found. We show that the root mean square (RMS) value of the second-order PMD component, perpendicular to the PMD vector, increases with the length of the PMD vector     

Method to measure and estimate total outage probability for PMD-impaired systems

A programmable polarization-mode-dispersion (PMD) source is used to measure receiver performance in the presence of first- and second-order PMD. Combined with scalable joint probability-distribution functions of PMD statistics, total outage probability can be estimated.     

System Penalty From Second-Order PMD Approximation: Reference Frame Implication

In this paper, we show that second-order PMD approximations, when derived using the input frame and output frame of an optical link, result in two different PMD systems represented by two distinct Jones matrices. In contrast to an all-order representation of a system, which is independent of reference frame, it is found that a finite second-order approximation cannot be obtained simultaneously in both input and output reference frames, except in some limited special cases. The consequences of this are illustrated by analyzing the difference between these two approximations in pulsewidth distortion. It is shown that the second-order PMD approximation in the input frame corresponds to a truncated second-order expansion of the pulse distortion, whereas the second-order PMD approximation in the output frame leads to an infinite-order pulse distortion     

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.      

Comparison of system penalties from first- and multiorder polarization-mode dispersion

We experimentally investigate the polarization-mode dispersion (PMD)-induced system penalty arising from first-order and all-order PMD. We use a measurable quantity, "string" length, to parameterize the penalty, find a deterministic correction to the accepted first-order PMD-induced system penalty approximation, and discuss the implications for system outages. Further, we show that higher orders of PMD introduce an additional penalty scatter that is nearly independent of "string" length, and correlated to the magnitude of the 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.     

PMD second-order effects on pulse propagation in single-modeoptical fibers

The time-space varying birefringence in single-mode optical fibers causes the polarization mode dispersion (PMD) to be a serious problem in high bit-rate transmissions. The PMD first- and second-order statistics are well known in the literature, but second-order PMD-induced pulse distortions have still to be clarified for sequences of pulses of arbitrary shape. We give, for the first time, the exact PMD time impulse response, up to second order. We show, both numerically and experimentally, that the effect of the rotation of the principal states of polarization (PSP) is to generate power overshoots on the “1” and “0” bit sequences     

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.     

First- and second-order PMD statistical properties of constantly spun randomly birefringent fibers

Polarization-mode dispersion (PMD) causes significant impairment for high bit-rate optical telecommunications systems. It is known that PMD can be strongly reduced by spinning the fiber as it is drawn. In this paper, we focus on the case of randomly birefringent fibers spun at a constant rate, providing analytical expressions for the asymptotic statistical properties of PMD. In particular, we investigate the behavior of the first- and second-order PMD, demonstrating that a constantly spun fiber behaves asymptotically as an unspun fiber. Conversely, we show that the distance at which the PMD reaches its asymptotic trend increases with the spin rate up to lengths of several kilometers.     

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…     

Experimental comparison of PMD-induced system penalty models

We present experimental investigations of polarization-mode dispersion (PMD)-induced system penalties arising from an all-order PMD source, for amplified spontaneous emission and thermally limited systems. Further, we compare the experimental first-order PMD-induced penalties with predictions from both the string length model and the modified quadratic model. We show that the both models are in good agreement with the experimental data. The major difference between the two models is in the measurement requirements, which are less stringent for the string length method.     

Methods to construct programmable PMD Sources. II. Instrument demonstrations

Demonstrations of several four-stage programmable polarization-mode-dispersion sources are compared with theoretical predictions. The instruments can independently control first- and second-order polarization-mode dispersion (PMD). Birefringent phase is used to continuously frequency-shift the PMD spectrum, and used to show the difference between a coherent and incoherent spectra.     

DOP ellipsoids for systems with frequency-dependent principalstates

The effects of polarization mode dispersion (PMD) in optical communication systems limit the practical length of fiber optic links. Characterization of the PMD of an optical system can be performed by observing the surface obtained from the vector whose length is the degree of polarization and direction is defined by the output state of polarization for a randomly varying input polarization. An analytical solution to the ellipsoid is derived for a simple higher order PMD system that is composed of two polarization-maintaining fibers. An approximate inverse relationship between the ellipsoid radii and the first- and second-order components of the PMD vector is also derived     

A deterministically controlled four-segment polarization-mode dispersion emulator

In this paper, we propose a novel design of a first- and second-order polarization-mode dispersion (PMD) emulator based on four concatenated first-order PMD segments. Instead of polarization scrambling at each junction, we set these polarization rotators according to a statistical schedule, so as to produce a realistic probability density function of the first- and second-order PMD presented in long-haul transmission fiber.     

二阶偏振模色散自适应补偿的关键技术

对自行研制的能同时补偿一阶和二阶偏振模色散的自适应补偿器作了详细介绍。以光波偏振度(DOP)为监控信号,用局部邻居结构的粒子群优化算法(LPSO)为逻辑控制算法,使搜索时间低于100ms,跟踪过程响应时间为16ms,基本实现了实时跟踪补偿。     

偏振模色散对光纤系统的影响及补偿方案研究

PMD是对高速长距离光纤传输系统影响较大的一个因素。描述了一阶PMD补偿的基本原理及其局限性,给出PMD补偿系统的一般模型,对各个模块和关键技术进行较为详细的讨论。对高阶PMD及其补偿问题进行分析与讨论,并实现了一种二阶PMD补偿器的具体设计与实验研究。