Polarization Effects in Lightwave Systems

Poole, C. D.; Nagel, J.A.

doi:10.1016/b978-0-08-051316-4.50010-2

Cited by 115 publications

(66 citation statements)

References 78 publications

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“…Poole et al (2,3), in effect, noted that if ͉t͘ is either of the two orthogonal eigenstates of the operator jU U † , then t ϭ 0, and so ͉t͘ should be expressible in the form…”

Section: Pmd Vectorsmentioning

confidence: 99%

“…This birefringence changes randomly along the fiber length (3,4). It stems from asymmetries in the fiber stress and geometry, such as elliptical cross sections, microbends, or microtwists.…”

Section: Pmd Vectorsmentioning

confidence: 99%

“…With current practical transmission technology the resulting PMD phenomena lead to pulse distortion and system impairments that limit the transmission capacity of the fiber. Excellent reviews are available (3,4), covering the practical aspects and applications of PMD concepts to fiber transmission systems and the effects of PMD on nonlinear fiber transmission (5). In this review we aim to complement these surveys and to collect and synthesize the fundamental concepts and theory of PMD, interweaving and linking the principal laws and key formulas that appear scattered in various places in the literature.…”

mentioning

confidence: 99%

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PMD fundamentals: Polarization mode dispersion in optical fibers

Gordon¹,

Kogelnik²

2000

Proc. Natl. Acad. Sci. U.S.A.

698

414

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This paper reviews the fundamental concepts and basic theory of polarization mode dispersion (PMD) in optical fibers. It introduces a unified notation and methodology to link the various views and concepts in Jones space and Stokes space. The discussion includes the relation between Jones vectors and Stokes vectors, rotation matrices, the definition and representation of PMD vectors, the laws of infinitesimal rotation, and the rules for PMD vector concatenation.

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“…Poole et al (2,3), in effect, noted that if ͉t͘ is either of the two orthogonal eigenstates of the operator jU U † , then t ϭ 0, and so ͉t͘ should be expressible in the form…”

Section: Pmd Vectorsmentioning

confidence: 99%

Section: Pmd Vectorsmentioning

confidence: 99%

mentioning

confidence: 99%

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PMD fundamentals: Polarization mode dispersion in optical fibers

Gordon¹,

Kogelnik²

2000

Proc. Natl. Acad. Sci. U.S.A.

698

414

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show abstract

“…Birefringence is practically frozen, i.e. the typical time scale of the birefringence variations is long compared to the time it takes for a pulse to pass the entire fiber line [3]. Therefore, birefringence can be treated as time-independent disorder, short-correlated in space.…”

mentioning

confidence: 99%

Outage probability for soliton transmission

Chernyak¹,

Chertkov²,

Kolokolov³

et al. 2004

Europhys. Lett.

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Abstract. -We study the interplay between amplifier noise and birefringent disorder in the case of strongly nonlinear (soliton) type of transmission in optical fibers. Assuming both noise and disorder to be weak, we evaluate the probability distribution function (PDF) of the Bit-Error-Rate (BER) for the values of BER that are much larger than the typical (average) value. The PDF tail that describes probability of the system outage shows log-normal shape, strongly dependent on the fiber length. We also discuss a simple timing shift technique capable of the outage compensation.Nonlinear information transmission in optical fibers when elementary bits are represented by optical solitons constitutes a promising technology that has been a subject of intensive research over the past decades [1,2]. In ideal fibers, the information carried by the solitons would be transmitted without any loss. In practice, however, various impairments lead to information loss. Amplifier noise and birefringent disorder represent the two major impairments in both linear and nonlinear transmission regimes. The noise generated by spontaneous emission in optical amplifiers is, therefore, short-correlated both in space and time. Birefringence that stems from variations of the optical fiber core degree of ellipticity is sensitive to external stresses and temperature changes, which leads to its substantial changes along the fiber line. Birefringence is practically frozen, i.e. the typical time scale of the birefringence variations is long compared to the time it takes for a pulse to pass the entire fiber line [3]. Therefore, birefringence can be treated as time-independent disorder, short-correlated in space. The optical communication system performance is usually measured by Bit-Error-Rate (BER) that represents the probability of an incorrect bit identification at the system output. However, because of the quasi-static nature of the birefringent disorder, the system performance may not be characterized in terms of a single number, e.g. some BER averaged over disorder realizations. BER should be rather considered as a number, dependent on a given realization of birefringent disorder, whereas the system performance should be characterized in terms of the Probability Distribution Function (PDF) of BER, with the statistics being collected by averaging over a large number of birefringent-disorder realizations. Note that the co-existence of two very different randomness sources constitutes a common feature of many problems in c EDP Sciences

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“…Polarization Mode Dispersion (PMD) is an essential impairment for modern optical fiber systems [1], [2], [3]. Therefore, dynamical PMD compensation became an important subject in modern communication technology [4], [5], [6], [7].…”

mentioning

confidence: 99%

Periodic and quasi-periodic compensation strategies of extreme outages caused by polarization mode dispersion and amplifier noise

et al. 2003

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Abstract-Effect of birefringent disorder on the Bit Error Rate (BER) in an optical fiber telecommunication system subject to amplifier noise may lead to extreme outages, related to anomalously large values of BER. We analyze the Probability Distribution Function (PDF) of BER for various strategies of Polarization Mode Dispersion (PMD) compensation. A compensation method is proposed that is capable of more efficient extreme outages suppression, which leads to substantial improvement of the fiber system performance. [7]. Optical noise generated in optical amplifiers represents another impairment that may not be reduced/compensated and, therefore, should be also considered in any evaluation of a fiber system performance [8]. BER calculated for a given realization of birefringent disorder by means of averaging over the amplifier noise statistics constitutes an appropriate object to characterize joint effect of the two impairments. In two preceding papers [9], [10] we have demonstrated that the probability of extreme outages (values of BER much higher than typical) is substantially larger than one could expect from naive Gaussian estimates singling out effects of either of the two impairments. The natural object of interest is the PDF of BER and, specifically, the PDF tail corresponding to anomalously large BER. In [9] we have developed a consistent theoretical approach to calculating this tail. The case when no compensation is applied and also the effect of the simplest "setting the clock" compensation on the PDF tail suppression have been discussed in [9]. Then our investigation was extended to study effects of the standard first-and higherorder compensations on extreme outages [10]. In the present letter we propose a compensation scheme that appears to be more efficient in reducing the extreme outages compared to the traditional high-order compensation scheme with the same number of the compensating degrees of freedom. Index Terms-We consider the return-to-zero (RZ) modulation format, when optical pulses are well separated in time t, and thus can be analyzed as individual objects. We represent the pulse intensity measured at the system output aswhere G(t) is a convolution of the electrical (current) filter function with the sampling window function. The twocomponent complex field Ψ (t) describes the output optical signal (the components correspond to two polarization states of the signal). The linear operator K in Eq. (1) represents optical filtering, it may also account for a compensating device. The compensating part of the linear operator, K c , is applied first, i.e. before filtering described by K f , resulting inIdeally, I takes two distinct values depending on whether the information slot is vacant or filled. However, the impairments enforce deviations of I from those fixed values. If the output signal intensity exceeds the decision level I d , then "1" is associated with the slot, otherwise the slot is labeled by "0". Sometimes the information is lost, i.e. the initial "1" is detected as "0" at the output...

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Polarization Effects in Lightwave Systems

Cited by 115 publications

References 78 publications

PMD fundamentals: Polarization mode dispersion in optical fibers

PMD fundamentals: Polarization mode dispersion in optical fibers

Outage probability for soliton transmission

Periodic and quasi-periodic compensation strategies of extreme outages caused by polarization mode dispersion and amplifier noise

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