Abstract

Phase-sensitive optical parametric amplifiers (PSAs) can provide low-noise optical amplification while simultaneously mitigating nonlinear distortions caused by the Kerr effect. However, nonlinearity mitigation using PSAs is affected by link parameters, and imperfect link design results in residual nonlinear distortions. In this paper, we use first-order perturbation theory to describe these residual nonlinear distortions, and develop a way to mitigate them using a modified third-order Volterra nonlinear equalizer (VNLE) in the receiver. Using numerical simulations, we show that our proposed VNLE reduces the residual nonlinear distortions in links using in-line PSAs for several combinations of symbol rates and modulation formats, and can increase the maximum transmission distance by up to 80%. We also perform a proof-of-concept experiment and confirm that our modified VNLE can mitigate the residual nonlinear distortions on a 10-Gbaud 16QAM signal after transmission through a 10$\times$80-km link with in-line PSAs.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

2018 (3)

2017 (4)

2016 (2)

2015 (1)

2014 (4)

2013 (2)

F. P. Guiomar and A. N. Pinto, “Simplified Volterra series nonlinear equalizer for polarization-multiplexed coherent optical systems,” J. Lightwave Technol. 31(23), 3879–3891 (2013).
[Crossref]

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

2012 (1)

2011 (2)

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[Crossref]

S. Kumar and D. Yang, “Optical backpropagation for fiber-optic communications using highly nonlinear fibers,” Opt. Lett. 36(7), 1038–1040 (2011).
[Crossref]

2010 (5)

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightwave Technol. 28(6), 939–951 (2010).
[Crossref]

A. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. 28(4), 423–433 (2010).
[Crossref]

Z. Tong, A. Bogris, M. Karlsson, and P. A. Andrekson, “Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers,” Opt. Express 18(3), 2884–2893 (2010).
[Crossref]

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental demonstration of intra-channel nonlinearity mitigation in coherent QPSK systems with nonlinear electrical equaliser,” Electron. Lett. 46(5), 353–355 (2010).
[Crossref]

2009 (1)

2008 (1)

R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101(16), 163901 (2008).
[Crossref]

2005 (3)

2004 (1)

2002 (1)

2001 (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001).
[Crossref]

1997 (1)

K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers,” J. Lightwave Technol. 15(12), 2232–2241 (1997).
[Crossref]

1983 (1)

1982 (2)

R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[Crossref]

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D: Part. Fields 26(8), 1817–1839 (1982).
[Crossref]

1948 (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27(3), 379–423 (1948).
[Crossref]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic, 2013).

Andrekson, P.

B. Corcoran, M. Karlsson, C. Lundström, S. Olsson, and P. Andrekson, “Mitigation of nonlinear impairments on QPSK data in phase-sensitive amplified links,” in 39th European Conference and Exhibition on Optical Communication (ECOC 2013), (Institution of Engineering and Technology, 2013), pp. 1–3.

Andrekson, P. A.

E. Astra, H. Eliasson, T. Ruuben, and P. A. Andrekson, “Improved mitigation of self-phase modulation induced impairments in 28 GBaud phase-sensitive amplified links,” Opt. Express 27(4), 4304–4316 (2019).
[Crossref]

H. Eliasson, K. Vijayan, B. Foo, S. L. I. Olsson, E. Astra, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplifier link with distributed Raman amplification,” Opt. Express 26(16), 19854–19863 (2018).
[Crossref]

S. L. I. Olsson, H. Eliasson, E. Astra, M. Karlsson, and P. A. Andrekson, “Long-haul optical transmission link using low-noise phase-sensitive amplifiers,” Nat. Commun. 9(1), 2513 (2018).
[Crossref]

H. Eliasson, S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Mitigation of nonlinear distortion in hybrid Raman/phase-sensitive amplifier links,” Opt. Express 24(2), 888–900 (2016).
[Crossref]

S. L. I. Olsson, B. Corcoran, C. Lundström, T. A. Eriksson, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplified transmission links for improved sensitivity and nonlinearity tolerance,” J. Lightwave Technol. 33(3), 710–721 (2015).
[Crossref]

B. Corcoran, R. Malik, S. L. I. Olsson, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise beating in hybrid phase-sensitive amplifier systems,” Opt. Express 22(5), 5762–5771 (2014).
[Crossref]

A. Lorences-Riesgo, L. Liu, S. L. I. Olsson, R. Malik, A. Kumpera, C. Lundström, S. Radic, M. Karlsson, and P. A. Andrekson, “Quadrature demultiplexing using a degenerate vector parametric amplifier,” Opt. Express 22(24), 29424–29434 (2014).
[Crossref]

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[Crossref]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Z. Tong, A. Bogris, M. Karlsson, and P. A. Andrekson, “Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers,” Opt. Express 18(3), 2884–2893 (2010).
[Crossref]

B. Foo, M. Karlsson, K. Vijayan, M. Mazur, and P. A. Andrekson, “Combining phase-sensitive amplifiers with DSP for enhanced nonlinearity mitigation,” in 2019 European Conference on Optical Communications, (Institution of Engineering and Technology, 2019), pp. 1–3. (to be published).

S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Long-haul optical transmission of 16-QAM signal with in-line phase-sensitive amplifiers,” in 2017 European Conference on Optical Communication (ECOC), (IEEE, 2017), pp. 1–3.

K. Vijayan, H. Eliasson, B. Foo, S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Optical bandwidth dependency of nonlinearity mitigation in phase-sensitive amplifier links,” in European Conference on Optical Communications 2018, (2018), pp. 1–3.

Asobe, M.

Astra, E.

Bayvel, P.

Bjorkholm, J.

R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[Crossref]

Blessing, D. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[Crossref]

Bogris, A.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Z. Tong, A. Bogris, M. Karlsson, and P. A. Andrekson, “Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers,” Opt. Express 18(3), 2884–2893 (2010).
[Crossref]

Bononi, A.

Brandt-Pearce, M.

K. Peddanarappagari and M. Brandt-Pearce, “Volterra series transfer function of single-mode fibers,” J. Lightwave Technol. 15(12), 2232–2241 (1997).
[Crossref]

Cartledge, J. C.

Caves, C. M.

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D: Part. Fields 26(8), 1817–1839 (1982).
[Crossref]

Chandrasekhar, S.

X. Liu, S. Chandrasekhar, P. J. Winzer, R. W. Tkach, and A. R. Chraplyvy, “Fiber-nonlinearity-tolerant superchannel transmission via nonlinear noise squeezing and generalized phase-conjugated twin waves,” J. Lightwave Technol. 32(4), 766–775 (2014).
[Crossref]

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Chen, Z.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental demonstration of intra-channel nonlinearity mitigation in coherent QPSK systems with nonlinear electrical equaliser,” Electron. Lett. 46(5), 353–355 (2010).
[Crossref]

Chraplyvy, A. R.

X. Liu, S. Chandrasekhar, P. J. Winzer, R. W. Tkach, and A. R. Chraplyvy, “Fiber-nonlinearity-tolerant superchannel transmission via nonlinear noise squeezing and generalized phase-conjugated twin waves,” J. Lightwave Technol. 32(4), 766–775 (2014).
[Crossref]

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Corcoran, B.

Cotter, D.

Dar, R.

Dasgupta, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Devgan, P. S.

Du, L. B.

Eliasson, H.

E. Astra, H. Eliasson, T. Ruuben, and P. A. Andrekson, “Improved mitigation of self-phase modulation induced impairments in 28 GBaud phase-sensitive amplified links,” Opt. Express 27(4), 4304–4316 (2019).
[Crossref]

H. Eliasson, K. Vijayan, B. Foo, S. L. I. Olsson, E. Astra, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplifier link with distributed Raman amplification,” Opt. Express 26(16), 19854–19863 (2018).
[Crossref]

S. L. I. Olsson, H. Eliasson, E. Astra, M. Karlsson, and P. A. Andrekson, “Long-haul optical transmission link using low-noise phase-sensitive amplifiers,” Nat. Commun. 9(1), 2513 (2018).
[Crossref]

H. Eliasson, S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Mitigation of nonlinear distortion in hybrid Raman/phase-sensitive amplifier links,” Opt. Express 24(2), 888–900 (2016).
[Crossref]

K. Vijayan, H. Eliasson, B. Foo, S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Optical bandwidth dependency of nonlinearity mitigation in phase-sensitive amplifier links,” in European Conference on Optical Communications 2018, (2018), pp. 1–3.

Ellis, A.

Ellis, A. D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Epworth, R.

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Simple criterion for the characterization of nonlinear impairments in dispersion-managed optical transmission systems,” IEEE Photonics Technol. Lett. 17(10), 2089–2091 (2005).
[Crossref]

Eriksson, T. A.

Essiambre, R.-J.

R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101(16), 163901 (2008).
[Crossref]

Faruk, M. S.

Fisher, R. A.

Foo, B.

H. Eliasson, K. Vijayan, B. Foo, S. L. I. Olsson, E. Astra, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplifier link with distributed Raman amplification,” Opt. Express 26(16), 19854–19863 (2018).
[Crossref]

B. Foo, B. Corcoran, and A. J. Lowery, “Distributed nonlinear compensation using optoelectronic circuits,” J. Lightwave Technol. 36(6), 1326–1339 (2018).
[Crossref]

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[Crossref]

B. Foo, M. Karlsson, K. Vijayan, M. Mazur, and P. A. Andrekson, “Combining phase-sensitive amplifiers with DSP for enhanced nonlinearity mitigation,” in 2019 European Conference on Optical Communications, (Institution of Engineering and Technology, 2019), pp. 1–3. (to be published).

K. Vijayan, H. Eliasson, B. Foo, S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Optical bandwidth dependency of nonlinearity mitigation in phase-sensitive amplifier links,” in European Conference on Optical Communications 2018, (2018), pp. 1–3.

Foschini, G. J.

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F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental demonstration of intra-channel nonlinearity mitigation in coherent QPSK systems with nonlinear electrical equaliser,” Electron. Lett. 46(5), 353–355 (2010).
[Crossref]

Grigoryan, V.

Grüner-Nielsen, L.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[Crossref]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Guiomar, F. P.

Herstrøm, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Simple criterion for the characterization of nonlinear impairments in dispersion-managed optical transmission systems,” IEEE Photonics Technol. Lett. 17(10), 2089–2091 (2005).
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Jakobsen, D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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H. Eliasson, K. Vijayan, B. Foo, S. L. I. Olsson, E. Astra, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplifier link with distributed Raman amplification,” Opt. Express 26(16), 19854–19863 (2018).
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M. Karlsson, “Transmission systems with low noise phase-sensitive parametric amplifiers,” J. Lightwave Technol. 34(5), 1411–1423 (2016).
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H. Eliasson, S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Mitigation of nonlinear distortion in hybrid Raman/phase-sensitive amplifier links,” Opt. Express 24(2), 888–900 (2016).
[Crossref]

S. L. I. Olsson, B. Corcoran, C. Lundström, T. A. Eriksson, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplified transmission links for improved sensitivity and nonlinearity tolerance,” J. Lightwave Technol. 33(3), 710–721 (2015).
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A. Lorences-Riesgo, L. Liu, S. L. I. Olsson, R. Malik, A. Kumpera, C. Lundström, S. Radic, M. Karlsson, and P. A. Andrekson, “Quadrature demultiplexing using a degenerate vector parametric amplifier,” Opt. Express 22(24), 29424–29434 (2014).
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B. Corcoran, R. Malik, S. L. I. Olsson, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise beating in hybrid phase-sensitive amplifier systems,” Opt. Express 22(5), 5762–5771 (2014).
[Crossref]

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[Crossref]

Z. Tong, A. Bogris, M. Karlsson, and P. A. Andrekson, “Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers,” Opt. Express 18(3), 2884–2893 (2010).
[Crossref]

K. Vijayan, H. Eliasson, B. Foo, S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Optical bandwidth dependency of nonlinearity mitigation in phase-sensitive amplifier links,” in European Conference on Optical Communications 2018, (2018), pp. 1–3.

S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Long-haul optical transmission of 16-QAM signal with in-line phase-sensitive amplifiers,” in 2017 European Conference on Optical Communication (ECOC), (IEEE, 2017), pp. 1–3.

B. Corcoran, M. Karlsson, C. Lundström, S. Olsson, and P. Andrekson, “Mitigation of nonlinear impairments on QPSK data in phase-sensitive amplified links,” in 39th European Conference and Exhibition on Optical Communication (ECOC 2013), (Institution of Engineering and Technology, 2013), pp. 1–3.

B. Foo, M. Karlsson, K. Vijayan, M. Mazur, and P. A. Andrekson, “Combining phase-sensitive amplifiers with DSP for enhanced nonlinearity mitigation,” in 2019 European Conference on Optical Communications, (Institution of Engineering and Technology, 2019), pp. 1–3. (to be published).

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F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental demonstration of intra-channel nonlinearity mitigation in coherent QPSK systems with nonlinear electrical equaliser,” Electron. Lett. 46(5), 353–355 (2010).
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F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental demonstration of intra-channel nonlinearity mitigation in coherent QPSK systems with nonlinear electrical equaliser,” Electron. Lett. 46(5), 353–355 (2010).
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Liu, L.

Liu, X.

X. Liu, S. Chandrasekhar, P. J. Winzer, R. W. Tkach, and A. R. Chraplyvy, “Fiber-nonlinearity-tolerant superchannel transmission via nonlinear noise squeezing and generalized phase-conjugated twin waves,” J. Lightwave Technol. 32(4), 766–775 (2014).
[Crossref]

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
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Louchet, H.

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[Crossref]

Lowery, A. J.

Lundström, C.

S. L. I. Olsson, B. Corcoran, C. Lundström, T. A. Eriksson, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplified transmission links for improved sensitivity and nonlinearity tolerance,” J. Lightwave Technol. 33(3), 710–721 (2015).
[Crossref]

B. Corcoran, R. Malik, S. L. I. Olsson, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise beating in hybrid phase-sensitive amplifier systems,” Opt. Express 22(5), 5762–5771 (2014).
[Crossref]

A. Lorences-Riesgo, L. Liu, S. L. I. Olsson, R. Malik, A. Kumpera, C. Lundström, S. Radic, M. Karlsson, and P. A. Andrekson, “Quadrature demultiplexing using a degenerate vector parametric amplifier,” Opt. Express 22(24), 29424–29434 (2014).
[Crossref]

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[Crossref]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

B. Corcoran, M. Karlsson, C. Lundström, S. Olsson, and P. Andrekson, “Mitigation of nonlinear impairments on QPSK data in phase-sensitive amplified links,” in 39th European Conference and Exhibition on Optical Communication (ECOC 2013), (Institution of Engineering and Technology, 2013), pp. 1–3.

Luo, Y.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental demonstration of intra-channel nonlinearity mitigation in coherent QPSK systems with nonlinear electrical equaliser,” Electron. Lett. 46(5), 353–355 (2010).
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Mazur, M.

J. Schröder and M. Mazur, “QAMPy a DSP chain for optical communications,” (2018). DOI: 10.5281/zenodo.1195720.

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Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
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Noé, R.

O’Gorman, J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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B. Corcoran, M. Karlsson, C. Lundström, S. Olsson, and P. Andrekson, “Mitigation of nonlinear impairments on QPSK data in phase-sensitive amplified links,” in 39th European Conference and Exhibition on Optical Communication (ECOC 2013), (Institution of Engineering and Technology, 2013), pp. 1–3.

Olsson, S. L. I.

S. L. I. Olsson, H. Eliasson, E. Astra, M. Karlsson, and P. A. Andrekson, “Long-haul optical transmission link using low-noise phase-sensitive amplifiers,” Nat. Commun. 9(1), 2513 (2018).
[Crossref]

H. Eliasson, K. Vijayan, B. Foo, S. L. I. Olsson, E. Astra, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplifier link with distributed Raman amplification,” Opt. Express 26(16), 19854–19863 (2018).
[Crossref]

H. Eliasson, S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Mitigation of nonlinear distortion in hybrid Raman/phase-sensitive amplifier links,” Opt. Express 24(2), 888–900 (2016).
[Crossref]

S. L. I. Olsson, B. Corcoran, C. Lundström, T. A. Eriksson, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplified transmission links for improved sensitivity and nonlinearity tolerance,” J. Lightwave Technol. 33(3), 710–721 (2015).
[Crossref]

A. Lorences-Riesgo, L. Liu, S. L. I. Olsson, R. Malik, A. Kumpera, C. Lundström, S. Radic, M. Karlsson, and P. A. Andrekson, “Quadrature demultiplexing using a degenerate vector parametric amplifier,” Opt. Express 22(24), 29424–29434 (2014).
[Crossref]

B. Corcoran, R. Malik, S. L. I. Olsson, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise beating in hybrid phase-sensitive amplifier systems,” Opt. Express 22(5), 5762–5771 (2014).
[Crossref]

S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Long-haul optical transmission of 16-QAM signal with in-line phase-sensitive amplifiers,” in 2017 European Conference on Optical Communication (ECOC), (IEEE, 2017), pp. 1–3.

K. Vijayan, H. Eliasson, B. Foo, S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Optical bandwidth dependency of nonlinearity mitigation in phase-sensitive amplifier links,” in European Conference on Optical Communications 2018, (2018), pp. 1–3.

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R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
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Richardson, D. J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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H. Louchet, A. Hodzic, K. Petermann, A. Robinson, and R. Epworth, “Simple criterion for the characterization of nonlinear impairments in dispersion-managed optical transmission systems,” IEEE Photonics Technol. Lett. 17(10), 2089–2091 (2005).
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Shafik, R. A.

R. A. Shafik, M. S. Rahman, and A. R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics,” in 2006 International Conference on Electrical and Computer Engineering, (IEEE, 2006), pp. 408–411.

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R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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Syvridis, D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
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X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
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Toda, H.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
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Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
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Z. Tong, A. Bogris, M. Karlsson, and P. A. Andrekson, “Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers,” Opt. Express 18(3), 2884–2893 (2010).
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Vannucci, A.

Vasilyev, M.

Vijayan, K.

H. Eliasson, K. Vijayan, B. Foo, S. L. I. Olsson, E. Astra, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplifier link with distributed Raman amplification,” Opt. Express 26(16), 19854–19863 (2018).
[Crossref]

K. Vijayan, H. Eliasson, B. Foo, S. L. I. Olsson, M. Karlsson, and P. A. Andrekson, “Optical bandwidth dependency of nonlinearity mitigation in phase-sensitive amplifier links,” in European Conference on Optical Communications 2018, (2018), pp. 1–3.

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Figures (7)

Fig. 1.
Fig. 1. Illustration of a copier-PSA link with the signal and idler fields marked at several points. We assume that the PSA perfectly compensates the span loss and that the effect of the Kerr nonlinearity is described as a small perturbation to the output of a linear channel. Abbreviations are explained in the text.
Fig. 2.
Fig. 2. The magnitude of $\delta _{\textrm {NL, res}}(0, L_{\textrm {span}})$ vs. dispersion pre-compensation for 10- (squares), 28- (circles), and 50-Gbaud (diamonds) signals. Curves are normalized to the maximum residual distortion for each symbol rate.
Fig. 3.
Fig. 3. (a) Block diagram of the numerical simulation for long-haul transmission using a copier-PSA scheme with in-line PSAs. (b) Block diagram of a simplified PSA, assuming high parametric gain and an undepleted pump. (c) Block diagram of the numerical simulation for long-haul transmission using in-line PIAs.
Fig. 4.
Fig. 4. Simulated $Q_{\textrm {EVM}}$ vs. dispersion pre-compensation after three spans for QPSK and 16QAM signals at 10-, 28-, and 50-Gbaud, for links employing PIAs, PSAs, and PSAs with a VNLE. $P_{\textrm {IN}}$ was fixed at 6 dBm
Fig. 5.
Fig. 5. Simulated maximum transmission distance (for BER $\leq$ $10^{-3}$) vs. launch power for QPSK (left) and 16QAM (right) at 10- (top), 28- (center), and 50-Gbaud (bottom) signals.
Fig. 6.
Fig. 6. Block diagram of experimental setup for re-circulating loop experiment using copier-PSA scheme. Inset: Receiver DSP flow-chart. Abbreviations are explained in the text.
Fig. 7.
Fig. 7. (a) Experimental measurement of $Q_{\textrm {BER}}$ vs. dispersion pre-compensation for a 10-Gbaud 16QAM signal after 10 spans with and without the VNLE. Inset: Measured constellations with and without the VNLE with 100% pre-compensation. (b) $Q_{\textrm {BER}}$ vs. $P_{\textrm {IN}}$ for: 323 ps/nm (Case 1), 170 ps/nm (Case 2), or 1280 ps/nm (Case 3) dispersion pre-compensation, with and without the VNLE.

Equations (16)

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[ B s ( ω ) B i ( ω ) ] = [ μ ν ν μ ] [ A s ( ω ) A i ( ω ) ]
B PI, s ( ω ) = μ A s ( ω ) , and B PI, i ( ω ) = ν A s ( ω ) ,
B PS, s ( ω ) = μ A s ( ω ) + ν A i ( ω ) and B PS, i ( ω ) = μ A i ( ω ) + ν A s ( ω ) ,
G PS ( θ rel ) = | μ | 2 + | ν | 2 + 2 | μ | | ν | cos ( θ rel ) ,
B PS, s ( ω ) | μ | ( A s ( ω ) + A i ( ω ) ) and B PS, i ( ω ) | μ | ( A i ( ω ) + A s ( ω ) ) ,
E s / i ( ω ) = E s / i ( ω ) + δ NL , s / i ( ω ) ,
E PSA , s ( ω ) = | μ | ( E s ( ω ) 2 | μ | + E i ( ω ) 2 | μ | ) = E s ( ω ) + 0.5 ( δ NL , s ( ω ) + δ NL , i ( ω ) ) .
δ NL ( ω , L span ) = j γ η ( Δ Ω , L span ) E ( ω 1 , 0 ) E ( ω 2 , 0 ) E ( ω ω 1 + ω 2 , 0 ) d ω 1 d ω 2 ,
η ( Δ Ω , L span ) = 0 L span exp ( G ( z ) + j Δ Ω D ( z ) ) d z ,
η ( Δ Ω , L span ) = 0 L span exp ( α z + j Δ Ω ( β 2 z D 0 ) ) d z , = 1 exp ( α L span + j Δ Ω β 2 L span ) α j Δ Ω β 2 exp ( j Δ Ω D 0 ) ,
δ NL,res ( ω , L span ) = 0.5 j γ ( η ( Δ Ω , L span ) E s ( ω 1 , 0 ) E s ( ω 2 , 0 ) E s ( ω ω 1 + ω 2 , 0 ) d ω 1 d ω 2 η ( Δ Ω , L span ) E i ( ω 1 , 0 ) E i ( ω 2 , 0 ) E i ( ω 1 ω 2 ω , 0 ) d ω 1 d ω 2 ) = j γ η res ( Δ Ω , L span ) E s ( ω 1 , 0 ) E s ( ω 2 , 0 ) E s ( ω ω 1 + ω 2 , 0 ) d ω 1 d ω 2 ,
η res ( Δ Ω , L span ) = 0.5 ( η ( Δ Ω , L span ) η ( Δ Ω , L span ) ) = j Im { 1 exp ( α L span + j Δ Ω β 2 L span ) α j Δ Ω β 2 exp ( j Δ Ω D 0 ) } ,
E s ( ω , N span L span ) = E s ( ω , 0 ) + N span δ NL,res ( ω , L span ) .
E s ( ω k , z L link ) = E s ( ω k , z ) + A NL ( ω k , z L link )
A NL ( ω k , z L link ) = j γ N span K 3 , PSA E s ( ω 1 , z ) E s ( ω 2 , z ) E s ( ω ω 1 + ω 2 , z ) d ω 1 d ω 2 ,
Q EVM [ dB ] = 10 log 10 n = 1 N | S TX [ n ] | 2 n = 1 N | S TX [ n ] S RX [ n ] | 2 ,

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