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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 19, Iss. 7 — Mar. 28, 2011
  • pp: 6790–6796
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Statistics of polarization dependent loss in an installed long-haul WDM system

Lynn E. Nelson, Cristian Antonelli, Antonio Mecozzi, Martin Birk, Peter Magill, Anton Schex, and Lutz Rapp  »View Author Affiliations


Optics Express, Vol. 19, Issue 7, pp. 6790-6796 (2011)
http://dx.doi.org/10.1364/OE.19.006790


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Abstract

We have made continual, multiple-day measurements of the polarization dependent loss of multiple C-band channels in an installed 1800 km terrestrial link. The PDLs of individual channels varied on the time-scale of hours, while the temporal variations of the PDLs of adjacent channels often tracked. The probability densities of the field measurements of PDL were not Maxwellian and instead were truncated, consistent with the limited number of elements in the link having appreciable PDL. A new model for the statistics of PDL in systems with few PDL elements is proposed, where a lower bound of the distribution exists if there is a dominant PDL element. The probability distributions from measurement and theory show good agreement.

© 2011 OSA

1. Introduction

Recent research and development has focused on coherent detection and digital signal processing (DSP), particularly for the polarization-division-multiplexed (PDM) quadrature-phase-shift-keyed modulation format [1

1. H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16(2), 873–879 (2008). [CrossRef] [PubMed]

], to meet the demands for 40 Gb/s and 100 Gb/s line rates. In addition to the promise of high spectral efficiency, coherent transponders using DSP offer several advantages to carriers, including high tolerance to chromatic dispersion [1

1. H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16(2), 873–879 (2008). [CrossRef] [PubMed]

] and polarization mode dispersion (PMD) [2

2. L. E. Nelson, S. L. Woodward, S. Foo, X. Zhou, M. D. Feuer, D. Hanson, D. McGhan, H. Sun, M. Moyer, M. O. Sullivan, and P. D. Magill, “Performance of a 46-Gbps dual-polarization QPSK transceiver with real-time coherent equalization over high PMD fiber,” J. Lightwave Technol. 27(3), 158–167 (2009). [CrossRef]

], permitting operation over a variety of fiber types, vintages, and ranges of fiber parameters.

Polarization dependent loss (PDL), on the other hand, is proving to be a more challenging impairment for coherent systems, particularly those employing numerous reconfigurable add-drop multiplexers (ROADMs), since the DSP cannot completely compensate the effects of PDL on a PDM signal. Prior measurements [3

3. T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent PolMux-NRZ-DQPSK,” in Proc. OFC-NFOEC 2008, Feb. 24–28, 2008, San Diego, CA, paper OThU5.

,4

4. O. Vassilieva, T. Hoshida, X. Wang, J. Rasmussen, H. Miyata, and T. Naito, “Impact of polarization dependent loss and cross-phase modulation on polarization-multiplexed DQPSK signals,” in Proc. OFC-NFOEC 2008, Feb. 24–28, 2008, San Diego, CA, paper OThU6.

], simulations [5

5. C. Xie, “Polarization-dependent loss induced penalties in PDM-QPSK coherent optical communication systems,” in Proc. OFC-NFOEC 2010, March 21–25, 2010, San Diego, CA, paper OWE6.

], and theoretical studies [6

6. M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008). [CrossRef] [PubMed]

] have elucidated the effects of PDL on PDM signals: a single PDL element causes a power/optical signal-to-noise ratio (OSNR) difference of the two polarization tributaries and/or non-orthogonality of the (originally orthogonal) polarization tributaries, depending on the relative orientation of the polarization tributaries to the PDL axis. A PDM signal in a system with multiple amplified spans and multiple, randomly oriented PDL elements will incur both impairments. Although DSP can effectively separate the tributaries even in the presence of non-orthogonality [1

1. H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16(2), 873–879 (2008). [CrossRef] [PubMed]

], DSP is not able to compensate the degraded OSNR of one of the polarization tributaries.

2. Measurements of PDL in the field

2.1 Measurement procedure

2.2 Measurement results

Figure 3
Fig. 3 Normalized autocorrelations of the PDL – <PDL> for the four channels shown in Fig. 2 as a function of time delay. Solid curve is the average of the normalized autocorrelations for all 12 channels included in the histograms in Fig. 4 and is also shown in the inset.
shows normalized autocorrelations as a function of time delay for the PDL measurements shown in Fig. 2. Measurements of the other channels showed similar correlation times. Also shown is the average of the normalized autocorrelations of the PDLs of all twelve channels considered in this paper. The average autocorrelation drops to 1/e at τcorr ≈3 hours. Assuming an exponential decay of the correlation function, over the T = 15 days of measurements in Fig. 2, the number of independent samples in each PDL time series is therefore the observation time divided by the width of the two-sided correlation function, that is T/(2 τcorr) ~60.

3. Model of truncated PDL

The hinge model for PMD [13

13. M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, “Persistence of spectral variations in DGD statistics,” Opt. Express 13(11), 4090–4095 (2005). [CrossRef] [PubMed]

] assumes that the PMDs of the buried sections of installed fibers are frequency dependent yet fixed (over some time scale), and the hinges, which model the components (jumpers, etc.) at the amplifier huts, randomly vary in time in response to environmental perturbations. The analysis of this model reveals that the temporal statistics of the differential group delay (DGD) is characterized by a truncated distribution [14

14. A. Mecozzi, C. Antonelli, M. Boroditsky, and M. Brodsky, “Characterization of the time dependence of polarization mode dispersion,” Opt. Lett. 29(22), 2599–2601 (2004). [CrossRef] [PubMed]

], although the full theoretical characterization of the temporal statistics is limited by the fact that the hinge rotation statistics are in general anisotropic [15

15. M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, “Polarization mode dispersion of installed fibers,” J. Lightwave Technol. 24(12), 4584–4599 (2006). [CrossRef]

].

Here we extend the hinge model to PDL, assuming that at a given time the amplifier huts are the locations of the fixed, frequency independent PDL elements, and the transmission fibers connecting amplifier huts act as frequency-dependent rotators. A similar model, restricted to the case of identical PDL elements, was considered in [16

16. Y. Fukada, “Probability density function of polarization dependent loss (PDL) in optical transmission systems composed of passive devices and connecting fibers,” J. Lightwave Technol. 20(6), 953–964 (2002). [CrossRef]

]. In this situation, at a given time, different channels experience different fiber rotations but the same PDL elements and thus are equivalent to different realizations of the same PDL statistics. A single histogram of the data measured over many channels should hence provide the statistics of PDL over an ensemble of realizations obtained with concatenated PDL elements of fixed magnitudes and isotropically distributed axes. In addition, the PDL of each channel still experiences a random variation in time caused by the jumpers at amplifiers huts, which act as time dependent and frequency independent (in general anisotropic) rotators. In this framework, measuring the PDLs of multiple channels over a time interval longer than the PDL correlation time, gives access to different sets of independent realizations of the same ensemble statistics.

If instead of considering the time-frequency statistics of PDL, one considers the time-frequency statistics of the DGD, the result would be a Maxwellian distribution, because the individual PMD elements are frequency dependent and their DGDs span a Maxwellian distribution when frequency varies. An important difference between the temporal statistics of PMD and the time-frequency statistics of PDL is that the time-frequency statistics of PDL may be accurately predicted, because the rotations performed by the fiber sections are isotropic when frequency varies over a range much wider than the correlation bandwidth of the PMD vector. As noted previously, hinge rotations are generally anisotropic for PMD [15

15. M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, “Polarization mode dispersion of installed fibers,” J. Lightwave Technol. 24(12), 4584–4599 (2006). [CrossRef]

].

It is apparent that the PDFs are truncated from both ends. The upper bound is a general feature of the hinge model [14

14. A. Mecozzi, C. Antonelli, M. Boroditsky, and M. Brodsky, “Characterization of the time dependence of polarization mode dispersion,” Opt. Lett. 29(22), 2599–2601 (2004). [CrossRef] [PubMed]

]. The lower bound indicates that one PDL element, which we speculate to correspond to the directly-connected ROADMs, predominates over the others. Note that the lower bounds to the histograms greatly exceed 0.25 dB, which as mentioned was the minimum PDL that could be measured.

Assuming isotropy of the PDL vector, the observed data of the PDL magnitude allow us to extract the distribution of the component of the PDL vector along a generic direction u, which is the quantity measured in [7

7. J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, “Non-intrusive polarization dependent loss monitoring in fiber-optic transmission systems,” Opt. Commun. 281(18), 4631–4633 (2008). [CrossRef]

,8

8. J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, “PMD and PDL monitoring of traffic-carrying transatlantic fibre-optic system,” Electron. Lett. 45(2), 123–124 (2009). [CrossRef]

]. The PDF of such a component (expressed in dB), which we denote by PDLu, is plotted in Fig. 4(e). The presence of a lower bound in the PDF of the PDL is reflected as a flat-topped distribution near zero for PDLu. Note however that if PDLu is directly measured with a set-up of the kind of [7

7. J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, “Non-intrusive polarization dependent loss monitoring in fiber-optic transmission systems,” Opt. Commun. 281(18), 4631–4633 (2008). [CrossRef]

,8

8. J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, “PMD and PDL monitoring of traffic-carrying transatlantic fibre-optic system,” Electron. Lett. 45(2), 123–124 (2009). [CrossRef]

], this feature may be hidden by the limited statistics of the measurement, and the presence of the PDL’s lower bound can be overlooked.

4. Conclusion

Acknowledgments

The authors gratefully acknowledge helpful discussions with Paul Wysocki and Jon Nagel.

References and links

1.

H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16(2), 873–879 (2008). [CrossRef] [PubMed]

2.

L. E. Nelson, S. L. Woodward, S. Foo, X. Zhou, M. D. Feuer, D. Hanson, D. McGhan, H. Sun, M. Moyer, M. O. Sullivan, and P. D. Magill, “Performance of a 46-Gbps dual-polarization QPSK transceiver with real-time coherent equalization over high PMD fiber,” J. Lightwave Technol. 27(3), 158–167 (2009). [CrossRef]

3.

T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent PolMux-NRZ-DQPSK,” in Proc. OFC-NFOEC 2008, Feb. 24–28, 2008, San Diego, CA, paper OThU5.

4.

O. Vassilieva, T. Hoshida, X. Wang, J. Rasmussen, H. Miyata, and T. Naito, “Impact of polarization dependent loss and cross-phase modulation on polarization-multiplexed DQPSK signals,” in Proc. OFC-NFOEC 2008, Feb. 24–28, 2008, San Diego, CA, paper OThU6.

5.

C. Xie, “Polarization-dependent loss induced penalties in PDM-QPSK coherent optical communication systems,” in Proc. OFC-NFOEC 2010, March 21–25, 2010, San Diego, CA, paper OWE6.

6.

M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008). [CrossRef] [PubMed]

7.

J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, “Non-intrusive polarization dependent loss monitoring in fiber-optic transmission systems,” Opt. Commun. 281(18), 4631–4633 (2008). [CrossRef]

8.

J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, “PMD and PDL monitoring of traffic-carrying transatlantic fibre-optic system,” Electron. Lett. 45(2), 123–124 (2009). [CrossRef]

9.

L. E. Nelson, M. Birk, P. Magill, A. Schex, and L. Rapp, “Measurements of the polarization dependent loss of multiple WDM channels in an installed, long-haul terrestrial link,” in IEEE Photonics Society Summer Topical2010, 19–21 July 2010, Playa del Carmen, Mexico, paper MA3.4.

10.

A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14(3), 313–315 (2002). [CrossRef]

11.

C. Hentschel and D. Derickson, in Fiber Optic Test and Measurement, (Prentice Hall, 1998), p. 355.

12.

N. Bergano, in Optical Fiber Telecommunications IVB (Academic Press, 2002), p. 183.

13.

M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, “Persistence of spectral variations in DGD statistics,” Opt. Express 13(11), 4090–4095 (2005). [CrossRef] [PubMed]

14.

A. Mecozzi, C. Antonelli, M. Boroditsky, and M. Brodsky, “Characterization of the time dependence of polarization mode dispersion,” Opt. Lett. 29(22), 2599–2601 (2004). [CrossRef] [PubMed]

15.

M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, “Polarization mode dispersion of installed fibers,” J. Lightwave Technol. 24(12), 4584–4599 (2006). [CrossRef]

16.

Y. Fukada, “Probability density function of polarization dependent loss (PDL) in optical transmission systems composed of passive devices and connecting fibers,” J. Lightwave Technol. 20(6), 953–964 (2002). [CrossRef]

17.

C. Antonelli and A. Mecozzi, “Statistics of the DGD in PMD emulators,” IEEE Photon. Technol. Lett. 16(8), 1840–1842 (2004). [CrossRef]

18.

N. Gisin, “Statistics of polarization dependent losses,” Opt. Commun. 114(5-6), 399–405 (1995). [CrossRef]

19.

M. Shtaif and A. Mecozzi, “Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion,” Opt. Lett. 25(10), 707–709 (2000). [CrossRef]

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(260.5430) Physical optics : Polarization

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 4, 2011
Revised Manuscript: March 16, 2011
Manuscript Accepted: March 16, 2011
Published: March 24, 2011

Citation
Lynn E. Nelson, Cristian Antonelli, Antonio Mecozzi, Martin Birk, Peter Magill, Anton Schex, and Lutz Rapp, "Statistics of polarization dependent loss in an installed long-haul WDM system," Opt. Express 19, 6790-6796 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-6790


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References

  1. H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16(2), 873–879 (2008). [CrossRef] [PubMed]
  2. L. E. Nelson, S. L. Woodward, S. Foo, X. Zhou, M. D. Feuer, D. Hanson, D. McGhan, H. Sun, M. Moyer, M. O. Sullivan, and P. D. Magill, “Performance of a 46-Gbps dual-polarization QPSK transceiver with real-time coherent equalization over high PMD fiber,” J. Lightwave Technol. 27(3), 158–167 (2009). [CrossRef]
  3. T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, “Impact of polarisation dependent loss on coherent PolMux-NRZ-DQPSK,” in Proc. OFC-NFOEC 2008, Feb. 24–28, 2008, San Diego, CA, paper OThU5.
  4. O. Vassilieva, T. Hoshida, X. Wang, J. Rasmussen, H. Miyata, and T. Naito, “Impact of polarization dependent loss and cross-phase modulation on polarization-multiplexed DQPSK signals,” in Proc. OFC-NFOEC 2008, Feb. 24–28, 2008, San Diego, CA, paper OThU6.
  5. C. Xie, “Polarization-dependent loss induced penalties in PDM-QPSK coherent optical communication systems,” in Proc. OFC-NFOEC 2010, March 21–25, 2010, San Diego, CA, paper OWE6.
  6. M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008). [CrossRef] [PubMed]
  7. J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, “Non-intrusive polarization dependent loss monitoring in fiber-optic transmission systems,” Opt. Commun. 281(18), 4631–4633 (2008). [CrossRef]
  8. J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, “PMD and PDL monitoring of traffic-carrying transatlantic fibre-optic system,” Electron. Lett. 45(2), 123–124 (2009). [CrossRef]
  9. L. E. Nelson, M. Birk, P. Magill, A. Schex, and L. Rapp, “Measurements of the polarization dependent loss of multiple WDM channels in an installed, long-haul terrestrial link,” in IEEE Photonics Society Summer Topical2010, 19–21 July 2010, Playa del Carmen, Mexico, paper MA3.4.
  10. A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14(3), 313–315 (2002). [CrossRef]
  11. C. Hentschel and D. Derickson, in Fiber Optic Test and Measurement, (Prentice Hall, 1998), p. 355.
  12. N. Bergano, in Optical Fiber Telecommunications IVB (Academic Press, 2002), p. 183.
  13. M. Brodsky, M. Boroditsky, P. Magill, N. J. Frigo, and M. Tur, “Persistence of spectral variations in DGD statistics,” Opt. Express 13(11), 4090–4095 (2005). [CrossRef] [PubMed]
  14. A. Mecozzi, C. Antonelli, M. Boroditsky, and M. Brodsky, “Characterization of the time dependence of polarization mode dispersion,” Opt. Lett. 29(22), 2599–2601 (2004). [CrossRef] [PubMed]
  15. M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, “Polarization mode dispersion of installed fibers,” J. Lightwave Technol. 24(12), 4584–4599 (2006). [CrossRef]
  16. Y. Fukada, “Probability density function of polarization dependent loss (PDL) in optical transmission systems composed of passive devices and connecting fibers,” J. Lightwave Technol. 20(6), 953–964 (2002). [CrossRef]
  17. C. Antonelli and A. Mecozzi, “Statistics of the DGD in PMD emulators,” IEEE Photon. Technol. Lett. 16(8), 1840–1842 (2004). [CrossRef]
  18. N. Gisin, “Statistics of polarization dependent losses,” Opt. Commun. 114(5-6), 399–405 (1995). [CrossRef]
  19. M. Shtaif and A. Mecozzi, “Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion,” Opt. Lett. 25(10), 707–709 (2000). [CrossRef]

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