Abstract

In this paper, we highlight that it is inadequate to describe the rotation of the state of polarization (RSOP) in a fiber channel with the 2-parameter description model, which was mostly used in the literature. This inadequate model may result in problems in polarization demultiplexing (PolDemux) because the RSOP in a fiber channel is actually a 3-parameter issue that will influence the state of polarization (SOP) of the optical signal propagating in the fiber and is different from the 2-parameter SOP itself. Considering three examples of the 2-parameter RSOP models typically used in the literature, we provide an in-depth analysis of the reasons why the 2-parameter RSOP model cannot represent the RSOP in the fiber channel and the problems that arise for PolDemux in the coherent optical receiver. We present a 3-parameter solution for the RSOP in the fiber channel. Based on this solution, we propose a DSP tracking and equalization scheme for the fast time-varying RSOP using the extended Kalman filter (EKF). The proposed scheme is proved to be universal and can solve all the PolDemux problems based on the 2- or 3-parameter RSOP model and exhibits good performance in the time-varying RSOP scenarios.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Window-split structured frequency domain Kalman equalization scheme for large PMD and ultra-fast RSOP in an optical coherent PDM-QPSK system

Zibo Zheng, Nan Cui, Hengying Xu, Xiaoguang Zhang, Wenbo Zhang, Lixia Xi, Yuanyuan Fang, and Liangchuan Li
Opt. Express 26(6) 7211-7226 (2018)

Joint equalization scheme of ultra-fast RSOP and large PMD compensation in presence of residual chromatic dispersion

Wei Yi, Zibo Zheng, Nan Cui, Xiaoguang Zhang, Liyuan Qiu, Nannan Zhang, Lixia Xi, Wenbo Zhang, and Xianfeng Tang
Opt. Express 27(15) 21896-21913 (2019)

Joint tracking and equalization scheme for multi-polarization effects in coherent optical communication systems

Yiqiao Feng, Linqian Li, Jiachuan Lin, Hengying Xu, Wenbo Zhang, Xianfeng Tang, Lixia Xi, and Xiaoguang Zhang
Opt. Express 24(22) 25491-25501 (2016)

References

  • View by:
  • |
  • |
  • |

  1. M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, R. Saunders, G. Nicholl, M. Nowell, and F. Forghieri, “Real-time single-carrier coherent 100 Gb/s PM-QPSK field trial,” J. Lightwave Technol. 29(4), 417–425 (2011).
    [Crossref]
  2. P. Winzer, “High-spectral-efficiency optical modulation formats,” J. Lightwave Technol. 30(24), 3824–3835 (2012).
    [Crossref]
  3. G. Raybon, “High symbol rate transmission systems for data rates from 400 Gb/s to 1Tb/s,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper M3G.1.
    [Crossref]
  4. J. N. Damask, Polarization Optics in Telecommunications (Springer,2005).
  5. Y. Feng, L. Li, J. Lin, H. Xu, W. Zhang, X. Tang, L. Xi, and X. Zhang, “Joint tracking and equalization scheme for multi-polarization effects in coherent optical communication systems,” Opt. Express 24(22), 25491–25501 (2016).
    [Crossref] [PubMed]
  6. M. Kuscherov and M. Herrmann, “Lightning affects coherent optical transmission in aerial fiber,” (lightwave, 2016), http://www.lightwaveonline.com/articles/2016/03/lightning-affects-coherent-optical-transmission-in-aerial-fiber.html .
  7. H. Yaffe, “Are ultrafast SOP events affecting your coherent receivers?” https://newridgetech.com/are-ultrafast-sop-events-affecting-your-receivers .
  8. D. Charlton, S. Clarke, D. Doucet, M. O’Sullivan, D. L. Peterson, D. Wilson, G. Wellbrock, and M. Bélanger, “Field measurements of SOP transients in OPGW, with time and location correlation to lightning strikes,” Opt. Express 25(9), 9689–9696 (2017).
    [Crossref] [PubMed]
  9. B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
    [Crossref] [PubMed]
  10. B. Szafraniec, T. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Lightwave Technol. 31(4), 648–663 (2013).
    [Crossref]
  11. N. Muga and A. Pinto, “Adaptive 3-D stokes space-based polarization demultiplexing algorithm,” J. Lightwave Technol. 32(19), 3290–3298 (2014).
    [Crossref]
  12. N. Muga and A. Pinto, “Extended Kalman filter vs. geometrical approach for Stokes space-based polarization demultiplexing,” J. Lightwave Technol. 33(23), 4826–4833 (2015).
    [Crossref]
  13. Z. Yu, X. Yi, Q. Yang, M. Luo, J. Zhang, L. Chen, and K. Qiu, “Polarization demultiplexing in stokes space for coherent optical PDM-OFDM,” Opt. Express 21(3), 3885–3890 (2013).
    [Crossref] [PubMed]
  14. Z. Yu, X. Yi, J. Zhang, D. Zhao, and K. Qiu, “Experimental demonstration of polarization-dependent loss monitoring and compensation in Stokes space for coherent optical PDM-OFDM,” J. Lightwave Technol. 32(23), 3926–3931 (2014).
  15. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
    [Crossref] [PubMed]
  16. E. Collett, Polarized Light in Fiber Optics (SPIE,2003).
  17. A. Kumar and A. Ghatak, Polarization of Light with Applications in Optical Fibers (SPIE,2011).
  18. R. Noé, Essentials of Modern Optical Fiber Communication (Springer,2016).
  19. J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
    [Crossref] [PubMed]
  20. X. Zhang and Y. Zheng, “The number of least degrees of freedom required for a polarization controller to transform any state of polarization to any other output covering the entire Poincaré sphere,” Chin. Phys. B 17(7), 2509–2513 (2008).
    [Crossref]
  21. S. S. Haykin, Adaptive Filter Theory, 4th ed. (Pearson Education India, 2008).
  22. H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 7204615 (2017).
    [Crossref]

2017 (2)

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 7204615 (2017).
[Crossref]

D. Charlton, S. Clarke, D. Doucet, M. O’Sullivan, D. L. Peterson, D. Wilson, G. Wellbrock, and M. Bélanger, “Field measurements of SOP transients in OPGW, with time and location correlation to lightning strikes,” Opt. Express 25(9), 9689–9696 (2017).
[Crossref] [PubMed]

2016 (1)

2015 (1)

2014 (2)

2013 (2)

2012 (1)

2011 (1)

2010 (1)

2008 (2)

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
[Crossref] [PubMed]

X. Zhang and Y. Zheng, “The number of least degrees of freedom required for a polarization controller to transform any state of polarization to any other output covering the entire Poincaré sphere,” Chin. Phys. B 17(7), 2509–2513 (2008).
[Crossref]

2000 (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

Bai, C.

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 7204615 (2017).
[Crossref]

Bélanger, M.

Birk, M.

Charlton, D.

Chen, L.

Clarke, S.

Curto, R.

Doucet, D.

Feng, Y.

Forghieri, F.

Gerard, P.

Glavanovic, M.

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

Ibragimov, E.

Khatana, S.

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

Li, L.

Lin, J.

Lofland, R.

Luo, M.

Magill, P.

Malouin, C.

Marcoccia, R.

Marshall, T.

Muga, N.

Nebendahl, B.

Nelson, L.

Nicholl, G.

Nowell, M.

O’Sullivan, M.

Peterson, D. L.

Pinto, A.

Qiu, K.

Saunders, R.

Savory, S. J.

Schmidt, T.

Szafraniec, B.

Tang, X.

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 7204615 (2017).
[Crossref]

Y. Feng, L. Li, J. Lin, H. Xu, W. Zhang, X. Tang, L. Xi, and X. Zhang, “Joint tracking and equalization scheme for multi-polarization effects in coherent optical communication systems,” Opt. Express 24(22), 25491–25501 (2016).
[Crossref] [PubMed]

Wellbrock, G.

Wilson, D.

Winzer, P.

Xi, L.

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 7204615 (2017).
[Crossref]

Y. Feng, L. Li, J. Lin, H. Xu, W. Zhang, X. Tang, L. Xi, and X. Zhang, “Joint tracking and equalization scheme for multi-polarization effects in coherent optical communication systems,” Opt. Express 24(22), 25491–25501 (2016).
[Crossref] [PubMed]

Xu, H.

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 7204615 (2017).
[Crossref]

Y. Feng, L. Li, J. Lin, H. Xu, W. Zhang, X. Tang, L. Xi, and X. Zhang, “Joint tracking and equalization scheme for multi-polarization effects in coherent optical communication systems,” Opt. Express 24(22), 25491–25501 (2016).
[Crossref] [PubMed]

Yang, Q.

Yi, X.

Yu, Z.

Zhang, B.

Zhang, J.

Zhang, W.

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 7204615 (2017).
[Crossref]

Y. Feng, L. Li, J. Lin, H. Xu, W. Zhang, X. Tang, L. Xi, and X. Zhang, “Joint tracking and equalization scheme for multi-polarization effects in coherent optical communication systems,” Opt. Express 24(22), 25491–25501 (2016).
[Crossref] [PubMed]

Zhang, X.

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 7204615 (2017).
[Crossref]

Y. Feng, L. Li, J. Lin, H. Xu, W. Zhang, X. Tang, L. Xi, and X. Zhang, “Joint tracking and equalization scheme for multi-polarization effects in coherent optical communication systems,” Opt. Express 24(22), 25491–25501 (2016).
[Crossref] [PubMed]

X. Zhang and Y. Zheng, “The number of least degrees of freedom required for a polarization controller to transform any state of polarization to any other output covering the entire Poincaré sphere,” Chin. Phys. B 17(7), 2509–2513 (2008).
[Crossref]

Zhao, D.

Zheng, H.

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 7204615 (2017).
[Crossref]

Zheng, Y.

X. Zhang and Y. Zheng, “The number of least degrees of freedom required for a polarization controller to transform any state of polarization to any other output covering the entire Poincaré sphere,” Chin. Phys. B 17(7), 2509–2513 (2008).
[Crossref]

Zhou, X.

Chin. Phys. B (1)

X. Zhang and Y. Zheng, “The number of least degrees of freedom required for a polarization controller to transform any state of polarization to any other output covering the entire Poincaré sphere,” Chin. Phys. B 17(7), 2509–2513 (2008).
[Crossref]

IEEE Photonics J. (1)

H. Xu, X. Zhang, X. Tang, C. Bai, L. Xi, W. Zhang, and H. Zheng, “Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second-order for flexible receivers,” IEEE Photonics J. 9(6), 7204615 (2017).
[Crossref]

J. Lightwave Technol. (6)

Opt. Express (5)

Proc. Natl. Acad. Sci. U.S.A. (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[Crossref] [PubMed]

Other (8)

S. S. Haykin, Adaptive Filter Theory, 4th ed. (Pearson Education India, 2008).

M. Kuscherov and M. Herrmann, “Lightning affects coherent optical transmission in aerial fiber,” (lightwave, 2016), http://www.lightwaveonline.com/articles/2016/03/lightning-affects-coherent-optical-transmission-in-aerial-fiber.html .

H. Yaffe, “Are ultrafast SOP events affecting your coherent receivers?” https://newridgetech.com/are-ultrafast-sop-events-affecting-your-receivers .

G. Raybon, “High symbol rate transmission systems for data rates from 400 Gb/s to 1Tb/s,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper M3G.1.
[Crossref]

J. N. Damask, Polarization Optics in Telecommunications (Springer,2005).

E. Collett, Polarized Light in Fiber Optics (SPIE,2003).

A. Kumar and A. Ghatak, Polarization of Light with Applications in Optical Fibers (SPIE,2011).

R. Noé, Essentials of Modern Optical Fiber Communication (Springer,2016).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1 An arbitrary elliptical polarization can be represented by either | E( α,δ )or | E( θ,β ), which are two SOP representations, one in the laboratory x-y coordinate system and the other in the principal ξ-η coordinate system.
Fig. 2
Fig. 2 The polarization states represented (a) on the observable polarization sphere and (b) on the Poincaré sphere corresponding to the laboratory x-y coordinate system and the principal ξ-η coordinate system.
Fig. 3
Fig. 3 The flow process for establishing the (α,δ)-two-step RSOP model.
Fig. 4
Fig. 4 The flow process for establishing the (α,δ)-one-step RSOP model.
Fig. 5
Fig. 5 The flow process for establishing the (θ,β) RSOP model.
Fig. 6
Fig. 6 For each subfigure, the left column shows Stokes space representation for the PDM-QPSK signal, and the right column represents its x-polarization corresponding constellation diagrams. The signal suffers a static RSOP rotation by {α=pi/6;δ=pi/3} for (a) the J 1 -model and (b) the J 2 -model, and {θ=arctan( 3 /2)/2;β=arcsin(4/3)/2} for (c) the J 3 -model. The signal suffers a time-varying RSOP rotation by (d) the J 1 -model, (e) the J 2 -model and (f) the J 3 -model.
Fig. 7
Fig. 7 Stokes space representations of the sample SOP: (a) back-to-back scenario; (b) signal before SOP compensation; (c) signal after SOP compensation using J 1 1 ( α,δ ); (d) signal after SOP compensation using J 3 1 ( θ,β ).
Fig. 8
Fig. 8 Schematic diagram of DSP module.
Fig. 9
Fig. 9 BER as the functions of the speed of the RSOP under (a) the J 1 -model, (b) the J 2 -model, (c) the J 3 -model and (d) the U-model.
Fig. 10
Fig. 10 Speed of convergence of (a) the proposed EKF method, (b) CMA, (c) the Stokes method.

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

| x-polarizaed=( 1 0 ) and | y-polarizaed=( 0 1 )
| E 1 ( α,δ )=( cosα sinα e jδ ) and | E 2 ( α,δ )=( sinα e jδ cosα )
or | E 1 ( α,δ )=( cosα e jδ/2 sinα e jδ/2 ) and | E 2 ( α,δ )=( sinα e jδ/2 cosα e jδ/2 )
| E 1 ( θ,β )=( cosθcosβjsinθsinβ sinθcosβ+jcosθsinβ ) and | E 2 ( θ,β )=( cosθsinβ+jsinθcosβ sinθsinβjcosθcosβ )
S 2 = S 0 sin2αcosδ S 3 = S 0 sin2αsinδ S 1 = S 0 cos2α and S 1 = S 0 cos2θcos2β S 2 = S 0 sin2θcos2β S 3 = S 0 sin2β
J 1 (α,δ)=( e jδ/2 0 0 e jδ/2 )( cosα sinα sinα cosα )=( cosα e jδ/2 sinα e jδ/2 sinα e jδ/2 cosα e jδ/2 )
J 2 (α,δ)=( cosα sinα e jδ sinα e jδ cosα )
J 3 ( θ,β )=( cosθ sinθ sinθ cosθ )( cosβ jsinβ jsinβ cosβ ) =( cosθcosβjsinθsinβ sinθcosβ+jcosθsinβ sinθcosβ+jcosθsinβ cosθcosβjsinθsinβ )
U=( a+jb c+jd c+jd ajb ) with a 2 + b 2 + c 2 + d 2 =1
U=Icos( φ/2 )j r ^ σ sin( φ/2 )
| r Rx =J| r Tx
| r Eq = J 1 | r Rx
| r Rx = J i | r Tx and | r Eq = J j 1 | r Rx with ji.
cos2α= a a 2 + b 2 + c 2 and tanδ= c b
tan2θ= b a and sin2β= c a 2 + b 2 + c 2 .
e k =( 0 1 )( a k s 1,k + b k s 2,k + c k s 3,k a k 2 + b k 2 + c k 2 )
U Eq ( ξ,η,κ )= U 1 ( ξ,η,κ )= ( cosκ e jξ sinκ e jη sinκ e jη cosκ e jξ ) 1
| r Eq = U Eq ( ξ,η,κ )| r Rx
x k = ( ξ k , η k , κ k ) T
e k = z k h( x k )=( 0 0 )( s 1,k ( s 2,k 2 s 0,k 2 )( s 3,k 2 s 0,k 2 ) )
x ^ k = x ^ k1
P k = P k1 +Q
Gk= P k H *T ( H P k H *T +R ) 1
x ^ k= x ^ k +Gk( z k h( x ^ k ))
P k =( I G k H ) P k

Metrics