Polarization Mode Dispersion Statistics Research Articles

Polarization dependent loss complications on polarization mode dispersion emulation

Polarization dependent loss (PDL) and polarization mode dispersion (PMD) coexist in an optical network system. So, PMD emulation is normally complicated by PDL. In this paper, an analysis of the implications of PDL on PMD statistics is done using a 35-PMF section emulator. The first order PMD (FO-PMD) and second order PMD (SO-PMD) statistics of the emulator with a PDL value of 0.06dB approached the theoretical Maxwellian and Foschini et al. distributions respectively. On increasing the PDL value to 4.59dB, both FO-PMD and SO-PMD statistics were distorted away from the above theoretical distributions even with presence of high number of random mode coupling sites.

Insight into PMD Regimes: An Analysis on Buried Optical Fibres

Polarization mode dispersion (PMD) field measurements on deployed buried fibres showed that the PMD variation over the 1520 to 1570 nm wavelength was stochastic. The PMD variation over the 98-hour period for each wavelength was directional and limited; they are due to the presence of random mode coupling along the fibre length and limited influence from extrinsic perturbations over time, respectively. PMD variation in the wavelength domain showed that the mean first-order PMD (FO-PMD) value is independent of whether the FO-PMD statistics of a fibre link approaches the Maxwellian theoretical distribution; the key factor is sufficient random mode coupling. The accompanying second-order PMD (SO-PMD) statistics, with FO-PMD statistics approaching Maxwellian, followed the PDF given by Foschini et al. (1999). The FO- and SO-PMD statistics at a given wavelength gave nonstochastic PMD distributions with time.

The Development of PMD and its Compensation Method

With the quickly development of fiber communication, PMD(Polarization mode dispersion) has became one of the key factor which limit high-bit rate system performance. In 1986, C.D.Poole[1] and other people found that if do not consider loss of SOP, two upright PSP will change along certain length SMF. In 1987, D.Andresciani and N.S.Bergano validate the theory of C.D.Poole each either. Late ninety of last century, statistical theory forming[2]. In the paper, we discuss the study of PMD, including statistics of PMD, measure technology, the affect of system by PMD, and PMD Compensation Method.

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.

Polarization mode dispersion emulation using polarization maintaining fibers: Fixed root-mean-square differential group delay but varying second-order polarization mode dispersion

We report on a polarization mode dispersion (PMD) emulator with a fixed root-mean-square differential group delay (RMS-DGD) but varying second-order PMD (SO-PMD) using only a combination of polarization maintaining fibers and a polarization controller. The SO-PMD control mechanism is not completely in real time. Besides controlling the mean PMD values of the emulator, simultaneous adjustments in the maximum and minimum values of PMD statistics can be performed. We therefore illustrate irregular fluctuations that occur around the RMS-DGD due to SO-PMD. This novel design can be used to further show the impact of a high first-order PMD segment on the DGD and SO-PMD statistical distributions that might occur in an optical network system.

Polarization Mode Dispersion of Installed Fibers

Polarization mode dispersion (PMD), a potentially limiting impairment in high-speed long-distance fiber-optic communication systems, refers to the distortion of propagating optical pulses due to random birefringences in an optical system. Because these perturbations (which can be introduced through manufacturing imperfections, cabling stresses, installation procedures, and environmental sensitivities of fiber and other in-line components) are unknowable and continually changing, PMD is unique among optical impairments. This makes PMD both a fascinating research subject and potentially one of the most challenging technical obstacles for future optoelectronic transmission. Mitigation and compensation techniques, proper emulation, and accurate prediction of PMD-induced outage probabilities critically depend on the understanding and modeling of the statistics of PMD in installed links. Using extensive data on buried fibers used in long-haul high-speed links, the authors discuss the proposition that most of the temporal PMD changes that are observed in installed routes arise primarily from a relatively small number of "hot spots" along the route that are exposed to the ambient environment, whereas the buried shielded sections remain largely stable for month-long time periods. It follows that the temporal variations of the differential group delay for any given channel constitute a distinct statistical distribution with its own channel-specific mean value. The impact of these observations on outage statistics is analyzed, and the implications for future optoelectronic fiber-based transmission are discussed

Enabling "Hinge" model in polarization-mode-dispersion statistics using variable differential-group-delay-based emulator

By slow polarization coupling and reorganizing applied differential group delay (DGD) to each section of a variable DGD-based polarization-mode-dispersion (PMD) emulator, we realize slow dynamics with negligible distortion of generated PMD statistics to enable a "hinge" model for system evaluation.

Statistical properties of polarization mode dispersion

Polarization mode dispersion (PMD) is one of the effects which limit bit rates in optical communications systems. The statistics of PMD is complicated because it is multi-dimensional, however, many useful results have been obtained. Much work has been done, but the subject is not yet closed, as witnessed by the existence of this conference. In this talk I will review the way some statistical equations are treated. I will briefly discuss the methods of Ito and Lax, and their application to the PMD problem.

Polarization-Mode Dispersion Emulation With Maxwellian Lengths and Importance Sampling

We describe an efficient polarization-mode dispersion (PMD) emulation method that combines a concatenation of birefringent sections having Maxwellian-distributed lengths with importance sampling. The method generates PMD statistics with accurate tail distributions using relatively few sections and reasonable numbers of samples, and allows the targeting of specific, arbitrarily large, first- and second-order PMD values.

A fast and accurate method for evaluating joint second-order PMD statistics

A fast and efficient way for evaluating the joint probability density function of the polarization-mode dispersion (PMD) vector derivative components parallel and orthogonal to the PMD vector itself is presented. This allows for a fully analytical evaluation of outage probabilities, overcoming thus the limitation of the Monte Carlo method, which do not allow for reliable evaluation of probabilities smaller than about 10/sup -4/.

Comparison of the jones matrix analytical models applied to optical system affected by high-order pmd

The analytical models for the Jones matrix of an optical fiber affected by high-order polarization-mode dispersion (PMD) are studied in an original comparative analysis with the purpose of finding a useful, precise, and stable tool for the system performance evaluation. First, a preliminary deterministic study is done to explain how the conceptual difference among the models reflects onto their representation of the fiber PMD effects in terms of Jones matrix coefficients and dispersion vector. Then, the analytical models with PMD up to third order are exploited for the calculation of the outage probability on the sensitivity penalty at the receiver, and the results obtained are compared with those of the discrete random wave-plate numerical model, assumed as a faithful description of the real fiber. Two different approaches are used for the outage probability evaluation: an analytical method, which is precise and faster but can only be used with PMD parameters up to second order, and a semi-analytical method that allows a comparison of the numerical and analytical results with homogeneity, when the statistics of high-order PMD are not known. The analytical model, which describes the dispersion vector as rotating on a circumference in the Stokes space, is found to be the most accurate in the system performance computation.

A deterministic emulator for the statistical reproduction of a real fiber with accurate PMD statistics up to the third order

A novel deterministic polarization-mode dispersion (PMD) emulator, consisting of delay-sections coupled by rotators is proposed. By opportunely choosing the rotation angles, this device is shown to correctly reproduce the higher order PMD statistics with a reduced number of sections.

Interferometer measurement of polarization-mode dispersion statistics

A new relationship between polarimeter and interferometer measurements of polarization mode dispersion is proposed. This model bridges the gap between interferometer patterns and probability density function of the principal states of polarization group delay. Experimental results supporting the theory are presented.

Pulsewidth distortion monitoring in a 40-Gb/s optical system affected by PMD

A novel technique for monitoring the pulse broadening due to polarization-mode dispersion (PMD) in optical systems is described. The technique is based on the measurement of the Stokes vectors at different frequencies over the spectrum of the received optical pulse find does not require a priori knowledge of the fiber PMD statistics or details of the optical path. The validity of our technique has been demonstrated by both simulation and experimental results.

Statistics of polarization mode dispersion in presence of the polarization dependent loss in single mode fibers

The authors present a simulation result for the statistics of the polarization mode dispersion (PMD) in the presence of the polarization dependent loss (PDL) in a single mode fiber. It is shown, in the presence of strong PDL fluctuations, that the PMD probability density distribution function can deviate significantly from the well-known Maxwell distribution function.