Definition of polarization mode dispersion and first results of the COST 241 round-robin measurements

Gisin, Nicolas; Passy, R.; Blasco, Pilar Diarte; Deventer, M.O. van; Distl, R.; Gilgen, H. H.; Perny, B.; Keys, R.W.; Krause, Egon; Larsen, Casper; Möri, K.; Pelayo, J.; Vobian, J.

doi:10.1088/0963-9659/4/5/006

Cited by 30 publications

(16 citation statements)

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“…In this Letter we study the fundamental question of determining the probability distribution of the DGD that is due to PMD at any fiber length with general fiber correlation and beat-length parameters. The results of our analytical work indicate that current systems approach a Maxwellian distribution in just a few kilometers, confirming the experimental work of Gisin et al 3 and placing on a f irm theoretical foundation the widely used approach of calculating the penalties on transmission that are due to PMD by assuming that the distribution of the DGD is Maxwellian. Moreover, our results indicate when this assumption breaks down, which may be of use in future systems.…”

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confidence: 87%

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Polarization mode dispersion probability distribution for arbitrary distances

2001

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The probability distribution of the differential group delay (DGD) at any fiber length is determined by use of a physically reasonable model of the fiber birefringence. We show that if the fiber correlation length is of the same order as or larger than the beat length, the DGD distribution approaches a Maxwellian in roughly 30 fiber correlation lengths, corresponding to a couple of kilometers in realistic cases. We also find that the probability distribution function of the polarization dispersion vector at the output of the fiber depends on the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances. Polarization mode dispersion (PMD) is caused by the random birefringence that is present in optical f ibers. It can lead to pulse spreading and depolarization, and it is detrimental to system performance. As transmission rates continue to increase, the PMD has become an increasingly important fiber impairment, thus motivating extensive experimental and theoretical study over the past few years. PMD is characterized by a three-component dispersion vector, V. Its magnitude, jVj, gives the differential group delay (DGD) between the principal states, and its direction gives the orientation of the slow principal state of polarization at the output on the Poincaré sphere. 1 At short distances, PMD is deterministic, and the DGD probability distribution is a d function. At long distances, however, previous work in which a weak random birefringence model was used showed that the three components of V are independent and Gaussian distributed, so the DGD distribution is Maxwellian.1 Similar results are also obtained if one assumes that the fiber birefringence completely randomizes the polarization state over the Poincaré sphere.2 Both analysis and numerous numerical and experimental studies have lead to the generally accepted wisdom that the asymptotic (long-length limit) distribution function of the DGD resulting from PMD is Maxwellian. The transient behavior of the distribution, however, is not so well elucidated. In this Letter we study the fundamental question of determining the probability distribution of the DGD that is due to PMD at any fiber length with general fiber correlation and beat-length parameters. The results of our analytical work indicate that current systems approach a Maxwellian distribution in just a few kilometers, confirming the experimental work of Gisin et al. 3 and placing on a f irm theoretical foundation the widely used approach of calculating the penalties on transmission that are due to PMD by assuming that the distribution of the DGD is Maxwellian. Moreover, our results indicate when this assumption breaks down, which may be of use in future systems. In addition, we f ind, for what is to our knowledge the first time, that the probability distribution function of the polarization dispersion vector at the output of the fiber depends on the angle between ...

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confidence: 87%

“…This theoretical result is consistent with previous experiments. 3 It is noted that the DGD probability distribution at large DGD values (the tail region) is of particular interest to the prediction of outrage probabilities. Figure 1(g) indicates that this tail distribution takes much longer to approach Maxwellian.…”

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confidence: 99%

Polarization mode dispersion probability distribution for arbitrary distances

2001

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“…7 The results also show that the tail distribution takes much longer (tens of kilometers) to approach a Maxwellian. Thus the widely used approach of calculating the penalties due to PMD by assuming a Maxwellian DGD distribution should be applied with caution when the fiber length is not long enough to guarantee that the transient behavior has completely died out.…”

Section: Introductionmentioning

confidence: 84%

“…Models based upon an analogy with Brownian motion 4 or upon the assumption of random mode coupling 5 have produced distributions with average characteristics that are consistent with more detailed stochastic analysis, 1,6 but experimental results have shown that the actual transient probability distributions themselves do not necessarily follow such models. 7 In particular, if the total fiber length is of the same order as the fiber correlation length, the DGD distribution appears skewed toward larger DGD values. If the fiber length is ten times longer than the correlation length, however, the main part of the DGD distribution appears to be well approximated by a Maxwellian.…”

Section: Introductionmentioning

confidence: 99%

“…If the fiber length is ten times longer than the correlation length, however, the main part of the DGD distribution appears to be well approximated by a Maxwellian. 7 While these results are significant, there have been no careful studies of the length required for an asymptotically valid Maxwellian probability distribution to be reached. This question is especially relevant at large DGD values, in the tails of the distribution.…”

Section: Introductionmentioning

confidence: 99%

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Transient evolution of the polarization-dispersion vector's probability distribution

et al. 2002

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We determine the transient evolution of the probability distribution of the polarization dispersion vector both analytically and numerically, using a physically reasonable model of the fiber birefringence. We show that, for all practical birefringence parameters, the distribution of the differential group delay (DGD), which is the magnitude of the polarization dispersion vector, becomes Maxwellian in just a few kilometers, except in the tail region, where the DGD is large. In this limit, the approach to a Maxwellian distribution takes much longer, of the order of tens of kilometers. In addition, we show that in the transient regime the DGD distribution is very different from Maxwellian. We also find that the probability-distribution function for the polarizationdispersion vector at the output of the fiber depends upon the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances.

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