Abstract

Coherent detection with digital signal processing (DSP) significantly changes the ways impairments are managed in optical communication systems. In this paper, we review the recent advances in understanding the impact of fiber nonlinearities, polarization-mode dispersion (PMD), and polarization-dependent loss (PDL) in coherent optical communication systems. We first discuss nonlinear transmission performance of three coherent optical communication systems, homogeneous polarization-division-multiplexed (PDM) quadrature-phase-shift-keying (QPSK), hybrid PDM-QPSK and on/off keying (OOK), and PDM 16-ary quadrature-amplitude modulation (QAM) systems. We show that while the dominant nonlinear effects in coherent optical communication systems without optical dispersion compensators (ODCs) are intra-channel nonlinearities, the dominant nonlinear effects in dispersion-managed (DM) systems with inline dispersion compensation fiber (DCF) are different when different modulation formats are used. In DM coherent optical communication systems using modulation formats of constant amplitude, the dominant nonlinear effect is nonlinear polarization scattering induced by cross-polarization modulation (XPolM), whereas when modulation formats of non-constant amplitude are used, the impact of inter-channel cross-phase modulation (XPM) is much larger than XPolM. We then describe the effects of PMD and PDL in coherent systems. We show that although in principle PMD can be completely compensated in a coherent optical receiver, a real coherent receiver has limited tolerance to PMD due to hardware limitations. Two PDL models used to evaluate PDL impairments are discussed. We find that a simple lumped model significantly over-estimates PDL impairments and show that a distributed model has to be used in order to accurately evaluate PDL impairments. Finally, we apply system outage considerations to coherent systems, taking into account the statistics of polarization effects in fiber.

© 2011 OSA

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2010 (3)

P. J. Winzer, “Beyond 100G ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010).
[CrossRef]

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and Beyond with Digital Coherent Signal Processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[CrossRef]

2009 (5)

C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express 17(6), 4815–4823 (2009).
[CrossRef] [PubMed]

Z. Wang, C. Xie, and X. Ren, “PMD and PDL impairments in polarization division multiplexing signals with direct detection,” Opt. Express 17(10), 7993–8004 (2009).
[CrossRef] [PubMed]

I. Fatadin, D. Ives, and S. J. Savory, “Blind Equalization and Carrier Phase Recovery in a 16-QAM Optical Coherent System,” J. Lightwave Technol. 27(15), 3042–3049 (2009).
[CrossRef]

C. Xie, “Inter-channel nonlinearities in coherent polarization-division-multiplexed quadrature-phase-shift-keying systems,” IEEE Photon. Technol. Lett. 21(5), 274–276 (2009).
[CrossRef]

N. Kaneda and A. Leven, “Coherent polarization-division-multiplexed QPSK receiver with fractionally spaced CMA for PMD compensation,” IEEE Photon. Technol. Lett. 21(4), 203–205 (2009).
[CrossRef]

2008 (3)

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett. 20(17), 1473–1475 (2008).
[CrossRef]

O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, and S. Bigo, “Nonlinearity Limitations When Mixing 40-Gb/s Coherent PDM-QPSK Channels With Preexisting 10-Gb/s NRZ Channels,” IEEE Photon. Technol. Lett. 20(15), 1314–1316 (2008).
[CrossRef]

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]

2006 (1)

C. Xie and L. Möller, “The accuracy assessment of different polarization mode dispersion models,” Opt. Fiber Technol. 12(2), 101–109 (2006).
[CrossRef]

2004 (1)

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, “Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission,” IEEE Photon. Technol. Lett. 16(6), 1591–1593 (2004).
[CrossRef]

1999 (2)

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, “Intrachannel Cross-Phase Modulation and Four-Wave Mixing in High-Speed TDM Systems,” Electron. Lett. 35(18), 1576–1578 (1999).
[CrossRef]

P. V. Mamyshev and L. F. Mollenauer, “Soliton collisions in wavelength-division-multiplexed dispersion-managed systems,” Opt. Lett. 24(7), 448–450 (1999).
[CrossRef] [PubMed]

1997 (1)

D. Marcuse, C. R. Manyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15(9), 1735–1746 (1997).
[CrossRef]

1995 (1)

1987 (1)

T. Kimura, “Coherent Optical Fiber Transmission,” J. Lightwave Technol. 5(4), 414–428 (1987).
[CrossRef]

Beckett, D.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and Beyond with Digital Coherent Signal Processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

Berthold, J.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and Beyond with Digital Coherent Signal Processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

Bertran-Pardo, O.

O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, and S. Bigo, “Nonlinearity Limitations When Mixing 40-Gb/s Coherent PDM-QPSK Channels With Preexisting 10-Gb/s NRZ Channels,” IEEE Photon. Technol. Lett. 20(15), 1314–1316 (2008).
[CrossRef]

Bigo, S.

O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, and S. Bigo, “Nonlinearity Limitations When Mixing 40-Gb/s Coherent PDM-QPSK Channels With Preexisting 10-Gb/s NRZ Channels,” IEEE Photon. Technol. Lett. 20(15), 1314–1316 (2008).
[CrossRef]

Boertjes, D.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and Beyond with Digital Coherent Signal Processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

Carena, A.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett. 20(17), 1473–1475 (2008).
[CrossRef]

Charlet, G.

O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, and S. Bigo, “Nonlinearity Limitations When Mixing 40-Gb/s Coherent PDM-QPSK Channels With Preexisting 10-Gb/s NRZ Channels,” IEEE Photon. Technol. Lett. 20(15), 1314–1316 (2008).
[CrossRef]

Chraplyvy, A. R.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, “Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission,” IEEE Photon. Technol. Lett. 16(6), 1591–1593 (2004).
[CrossRef]

Curri, V.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett. 20(17), 1473–1475 (2008).
[CrossRef]

Essiambre, R.-J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[CrossRef]

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, “Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission,” IEEE Photon. Technol. Lett. 16(6), 1591–1593 (2004).
[CrossRef]

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, “Intrachannel Cross-Phase Modulation and Four-Wave Mixing in High-Speed TDM Systems,” Electron. Lett. 35(18), 1576–1578 (1999).
[CrossRef]

Fatadin, I.

Forghieri, F.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett. 20(17), 1473–1475 (2008).
[CrossRef]

Foschini, G. J.

Gnauck, A. H.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, “Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission,” IEEE Photon. Technol. Lett. 16(6), 1591–1593 (2004).
[CrossRef]

Goebel, B.

Gordon, J. P.

Heismann, F.

Ives, D.

Kaneda, N.

N. Kaneda and A. Leven, “Coherent polarization-division-multiplexed QPSK receiver with fractionally spaced CMA for PMD compensation,” IEEE Photon. Technol. Lett. 21(4), 203–205 (2009).
[CrossRef]

Kimura, T.

T. Kimura, “Coherent Optical Fiber Transmission,” J. Lightwave Technol. 5(4), 414–428 (1987).
[CrossRef]

Kramer, G.

Laperle, C.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and Beyond with Digital Coherent Signal Processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

Leven, A.

N. Kaneda and A. Leven, “Coherent polarization-division-multiplexed QPSK receiver with fractionally spaced CMA for PMD compensation,” IEEE Photon. Technol. Lett. 21(4), 203–205 (2009).
[CrossRef]

Mamyshev, P. V.

Manyuk, C. R.

D. Marcuse, C. R. Manyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15(9), 1735–1746 (1997).
[CrossRef]

Marcuse, D.

D. Marcuse, C. R. Manyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15(9), 1735–1746 (1997).
[CrossRef]

Mardoyan, H.

O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, and S. Bigo, “Nonlinearity Limitations When Mixing 40-Gb/s Coherent PDM-QPSK Channels With Preexisting 10-Gb/s NRZ Channels,” IEEE Photon. Technol. Lett. 20(15), 1314–1316 (2008).
[CrossRef]

Mikkelsen, B.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, “Intrachannel Cross-Phase Modulation and Four-Wave Mixing in High-Speed TDM Systems,” Electron. Lett. 35(18), 1576–1578 (1999).
[CrossRef]

Mollenauer, L. F.

Möller, L.

C. Xie and L. Möller, “The accuracy assessment of different polarization mode dispersion models,” Opt. Fiber Technol. 12(2), 101–109 (2006).
[CrossRef]

Poggiolini, P.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett. 20(17), 1473–1475 (2008).
[CrossRef]

Raybon, G.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, “Intrachannel Cross-Phase Modulation and Four-Wave Mixing in High-Speed TDM Systems,” Electron. Lett. 35(18), 1576–1578 (1999).
[CrossRef]

Ren, X.

Renaudier, J.

O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, and S. Bigo, “Nonlinearity Limitations When Mixing 40-Gb/s Coherent PDM-QPSK Channels With Preexisting 10-Gb/s NRZ Channels,” IEEE Photon. Technol. Lett. 20(15), 1314–1316 (2008).
[CrossRef]

Roberts, K.

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and Beyond with Digital Coherent Signal Processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

Savory, S. J.

Shtaif, M.

Tran, P.

O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, and S. Bigo, “Nonlinearity Limitations When Mixing 40-Gb/s Coherent PDM-QPSK Channels With Preexisting 10-Gb/s NRZ Channels,” IEEE Photon. Technol. Lett. 20(15), 1314–1316 (2008).
[CrossRef]

Wai, P. K. A.

D. Marcuse, C. R. Manyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15(9), 1735–1746 (1997).
[CrossRef]

Wang, Z.

Wickham, L. K.

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, “Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission,” IEEE Photon. Technol. Lett. 16(6), 1591–1593 (2004).
[CrossRef]

Winzer, P. J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[CrossRef]

P. J. Winzer, “Beyond 100G ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010).
[CrossRef]

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, “Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission,” IEEE Photon. Technol. Lett. 16(6), 1591–1593 (2004).
[CrossRef]

Xie, C.

C. Xie, “Inter-channel nonlinearities in coherent polarization-division-multiplexed quadrature-phase-shift-keying systems,” IEEE Photon. Technol. Lett. 21(5), 274–276 (2009).
[CrossRef]

Z. Wang, C. Xie, and X. Ren, “PMD and PDL impairments in polarization division multiplexing signals with direct detection,” Opt. Express 17(10), 7993–8004 (2009).
[CrossRef] [PubMed]

C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express 17(6), 4815–4823 (2009).
[CrossRef] [PubMed]

C. Xie and L. Möller, “The accuracy assessment of different polarization mode dispersion models,” Opt. Fiber Technol. 12(2), 101–109 (2006).
[CrossRef]

Electron. Lett. (1)

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, “Intrachannel Cross-Phase Modulation and Four-Wave Mixing in High-Speed TDM Systems,” Electron. Lett. 35(18), 1576–1578 (1999).
[CrossRef]

IEEE Commun. Mag. (2)

P. J. Winzer, “Beyond 100G ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010).
[CrossRef]

K. Roberts, D. Beckett, D. Boertjes, J. Berthold, and C. Laperle, “100G and Beyond with Digital Coherent Signal Processing,” IEEE Commun. Mag. 48(7), 62–69 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett. 20(17), 1473–1475 (2008).
[CrossRef]

C. Xie, “Inter-channel nonlinearities in coherent polarization-division-multiplexed quadrature-phase-shift-keying systems,” IEEE Photon. Technol. Lett. 21(5), 274–276 (2009).
[CrossRef]

N. Kaneda and A. Leven, “Coherent polarization-division-multiplexed QPSK receiver with fractionally spaced CMA for PMD compensation,” IEEE Photon. Technol. Lett. 21(4), 203–205 (2009).
[CrossRef]

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, and A. R. Chraplyvy, “Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission,” IEEE Photon. Technol. Lett. 16(6), 1591–1593 (2004).
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O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, P. Tran, and S. Bigo, “Nonlinearity Limitations When Mixing 40-Gb/s Coherent PDM-QPSK Channels With Preexisting 10-Gb/s NRZ Channels,” IEEE Photon. Technol. Lett. 20(15), 1314–1316 (2008).
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I. Fatadin, D. Ives, and S. J. Savory, “Blind Equalization and Carrier Phase Recovery in a 16-QAM Optical Coherent System,” J. Lightwave Technol. 27(15), 3042–3049 (2009).
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Other (22)

J. Renaudier, O. Bertran-Pardo, G. Charlet, M. Salsi, M. Bertolini, P. Tran, H. Mardoyan, and S. Bigo, “On the Required Number of WDM Channels When Assessing Performance of 100Gb/s Coherent PDM-QPSK Overlaying Legacy Systems,” in Proceedings of European Conference on Optical Communication (Vienna, Austria, 2009), paper 3.4.5.

C. Xia and D. van den Borne, “Impact of the Channel Count on the Nonlinear Tolerance in Coherently-detected POLMUX-QPSK modulation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2011), paper OWO1.

H. Kogelnik, R. M. Jopson, and L. E. Nelson, Optical Fiber Telecommunications IV B, I. Kaminov and T. Li, eds. (Academic Press, 2002), Chap. 15.

C. Xie, “Inter-channel nonlinearities in hybrid OOK and coherent PDM-QPSK transmission systems with dispersion management,” in Proceeding IEEE Photonic Society Summer Topicals (Cancun, Mexico, 2010), paper TuA.3.2.

D. van den Borne, C. R. S. Fludger, T. Duthel, T. Wuth, E. D. Schmidt, C. Schulien, E. Gottwald, G. D. Khoe, and H. de Waardt, “Carrier phase estimation for coherent equalization of 43-Gb/s POLMUXNRZ-DQPSK transmission with 10.7-Gb/s NRZ neighbours,” in Proceedings of European Conference on Optical Communication, (Berlin, Germany, 2007), paper 7.2.3, 2007.

C. Xie, “Fiber Nonlinearities in 16QAM Transmission Systems,” in Proceedings of European Conference on Optical Communication, (Geneva, Switzerland, 2011), paper We.7.B.6.

T. Duthel, C. R. S. Fludger, J. Geyer, and S. Schulien, “Impact of polarisation dependent loss on coherent POLMUX-NRZ-DQPSK,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper OThU5.

C. Xie, “Polarization-Dependent Loss Induced Penalties in PDM-QPSK Coherent Optical Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper OWE6.

A. H. Gnauck, G. Charlet, P. Tran, P. J. Winzer, C. R. Doerr, J. C. Centanni, E. C. Burrows, T. Kawanishi, T. Sakamoto, and K. Higuma, “25.6-Tb/s C+L-Band Transmission of Polarization-Multiplexed RZ-DQPSK Signals,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP19.

C. Xie, “Dispersion management in WDM coherent PDM-QPSK systems,” in Proceedings of European Conference on Optical Communication (Vienna, Austria, 2009), paper 9.4.3.

C. Xie, “Nonlinear Polarization Effects and Mitigation in Polarization Multiplexed Transmission,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper OWE1.

G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient Mitigation of Fiber Impairments in an Ultra-Long Haul Transmission of 40Gbit/s Polarization-Multiplexed Data by Digital Processing in a Coherent Receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17.

N. Mantzoukis, A. Vgenis, C. S. Petrou, I. Roudas, T. Kamalakis, and L. Raptis, “Design guidelines for electronic PMD equalizers used in coherent PDM QPSK systems,” in Proceedings of European Conference on Optical Communication, (Torino, Italy, 2010), paper P4.16.

C. Xie, “Polarization-Mode-Dispersion Impairments in 112-Gb/s PDM-QPSK Coherent Systems,” in Proceedings of European Conference on Optical Communication, (Torino, Italy, 2010), paper Th.10.E.6.

P. Serena, N. Rossi, and A. Bononi, “Nonlinear penalty reduction induced by PMD in 112 Gbit/s WDM PDM-QPSK coherent systems,” in Proceedings of European Conference on Optical Communication (Vienna, Austria, 2009), paper 10.4.3.

O. Bertran-Pardo, J. Renaudier, G. Charlet, P. Tran, H. Mardoyan, M. Bertolini, M. Salsi, and S. Bigo, “Demonstration of the benefits brought by PMD in polarization-multiplexed systems,” in Proceedings of European Conference on Optical Communication (Torino, Italy, 2010), paper Th.10.E.4.

C. Xia, J. F. da Silva Pina, A. Striegler, and D. van den Borne, “PMD-induced nonlinear penalty reduction in coherent polarization-multiplexed QPSK transmission,” in Proceedings of European Conference on Optical Communication (Torino, Italy, 2010), paper Th.10.E.5.

A. Bononi, N. Rossi, and P. Serena, “Transmission Limitations due to Fiber Nonlinearity,”, ” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2011), paper OWO7.

C. Xie, “Impact of nonlinear and polarization effects on coherent systems,” in Proceedings of European Conference on Optical Communication (Geneva, Switzerland, 2011), paper We.8.B.1.

C. Xie and R.-J. Essiambre, “Electronic Nonlinearity Compensation in 112-Gb/s PDM-QPSK Optical Coherent Transmission Systems,” in Proceedings of European Conference on Optical Communication (Torino, Italy, 2010), paper Mo.1.C.1.

G. Li, E. Mateo, and L. Zhu, “Compensation of Nonlinear Effects Using Digital Coherent Receivers,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2011), paper OWW1.

E. Yamazaki, A. Sano, T. Kobayashi, E. Yoshida, and Y. Miyamoto, “Mitigation of Nonlinearities in Optical Transmission Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2011), paper OThF1.

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Figures (16)

Fig. 1
Fig. 1

Block diagram of a digital coherent optical communication system. TX: transmitter, CW: continuous wave, PDM: polarization-division multiplexed, Mod: modulator, RX: receiver, LO: local oscillator, ADC: analog-to-digital convertor, PBC/S: polarization-beam combiner/splitter, ASIC: application-specific integrated circuit, FEC: forward-error correction.

Fig. 2
Fig. 2

Transmission system model. TX: transmitter, RX: receiver, MUX: multiplexer, DEMUX: demultiplexer, RPM: Raman pump module. The modules in dotted lines are used for some of the studied configurations, as indicated in the text.

Fig. 3
Fig. 3

Required OSNR at a BER of 10−3 after 1000-km transmission versus launch power per channel for the 42.8-Gb/s (a) and 112-Gb/s NRZ-PDM-QPSK (b) coherent systems with and without inline DCF. Solid lines are for the results when all the channels are PDM-QPSK channels and dotted lines are the results when the center PDM-QPSK channel is surrounded by six SP-QPSK channels.

Fig. 4
Fig. 4

SOP of PDM-QPSK on the Poincaré sphere. The symbols on x and y polarizations are aligned.

Fig. 5
Fig. 5

XPolM induced depolarization in the 42.8-Gb/s (a) and 112-Gb/s (b) PDM-QPSK systems with and without inline DCF after 1000-km transmission. DOP: degree of polarization.

Fig. 6
Fig. 6

Required OSNR at a BER of 10−3 after 1000-km transmission versus launch power per channel for 112-Gb/s NRZ-PDM-QPSK co-propagating with six 10-Gb/s OOK channels.

Fig. 7
Fig. 7

XPolM from 10-Gb/s OOK channels induced depolarization in the 112-Gb/s PDM-QPSK channel with and without inline DCF after 1000-km transmission. DOP: degree of polarization.

Fig. 8
Fig. 8

Signal constellations of 112-Gb/s PDM-QPSK after co-propagating with 10-Gb/s OOK channels over 1000-km SSMF with DCF at −1-dBm per channel launch power.

Fig. 9
Fig. 9

Required OSNR at a BER of 10−3 after 1000-km transmission versus launch power per channel for single channel and WDM 224-Gb/s iRZ-PDM-16QAM systems with and without DCF.

Fig. 10
Fig. 10

Signal constellations of one polarization for single-channel and WDM 224-Gb/s iRZ-PDM-16QAM after 1000-km transmission with and without DCF and at 3-dBm and 1-dBm per-channel launch powers for single-channel and WDM transmission, respectively.

Fig. 11
Fig. 11

XPolM induced depolarization in the 224-Gb/s iRZ-PDM-16QAM system with and without inline DCF after 1000-km transmission, and in the 112-Gb/s iRZ-PDM-QPSK system with DCF. DOP: degree of polarization.

Fig. 12
Fig. 12

PMD induced OPs for a 112-Gb/s NRZ-PDM-QPSK system with a 7-tap butterfly equalizer for different PMDEs. A 0.5-dB OSNR margin is used.

Fig. 13
Fig. 13

PMD induced OPs for a 112-Gb/s NRZ-PDM-QPSK system with the butterfly equalizer of different tap numbers A 0.5-dB OSNR margin and all-order PMDE are used.

Fig. 14
Fig. 14

PDL models. (a) lumped model, (b) distributed model. PC: polarization controller.

Fig. 15
Fig. 15

Simulated probability density function (PDF) of PDL induced OSNR variations in one polarization using the lumped model and the distributed model at an RMS PDL value of 3 dB.

Fig. 16
Fig. 16

PDL induced OPs at BER = 10−3 versus RMS PDL in a 112-Gb/s PDM-QPSK system using the distributed model (symbols and solid lines) and lumped model (dashed lines).

Equations (4)

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E z + i 2 β 2 2 E t 2 i 8 9 γ | E | 2 E =0
E a z + i 2 β 2 2 E a t 2 i 8 9 γ( | E a | 2 E a + | E b | 2 E a + E b + E a E b )=0
d S a dz = 8 9 γ( S a × S b ),
Ω ( ω 0 +Δω )= Ω 0 ( ω 0 )+ Ω ω ( ω 0 )Δω+ 1 2 Ω ωω ( ω 0 )Δ ω 2 +

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