Abstract

This paper investigates the use of optoelectronic subsystems placed all the way along a fiber link to provide distributed mitigation of the distortion caused by the Kerr nonlinearity. These subsystems use power-dependent phase modulation to mitigate the low-frequency ( $<$ 1 GHz) components of the self-phase modulation and cross-phase modulation (XPM) distortion experienced by several wavelength channels simultaneously. Furthermore, this technique compensates the nonlinear distortion on a per-span basis, and so can mitigate XPM in optically routed links, unlike transmitter- or receiver-side nonlinearity compensation techniques. We present proof-of-concept results from both experimental and numerical studies that show our optoelectronic technique can effectively mitigate the distortion caused by fiber nonlinearity. Additional simulations study the impact of various link parameters on the effectiveness of this scheme.

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2017 (7)

S. T. Le and H. Buelow, “64 $\times$ 0.5 Gbaud nonlinear frequency division multiplexed transmissions with high order modulation formats,” J. Lightw. Technol., vol. 35, no. 17, pp. 3692–3698,  2017.

A. Ellis, M. Al-Khateeb, and M. McCarthy, “Impact of optical phase conjugation on the nonlinear Shannon limit,” J. Lightw. Technol., vol. 35, no. 4, pp. 792–798,  2017.

S. Namiki, K. Solis-Trapala, H. N. Tan, M. Pelusi, and T. Inoue, “Multi-channel cascadable parametric signal processing for wavelength conversion and nonlinearity compensation,” J. Lightw. Technol., vol. 35, no. 4, pp. 815–823,  2017.

H. Hu, R. M. Jopson, A. H. Gnauck, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity mitigation of WDM-PDM QPSK/16-QAM signals using fiber-optic parametric amplifiers based multiple optical phase conjugations,” Opt. Express, vol. 25, no. 3, pp. 1618–1628,  2017.

X. Liang and S. Kumar, “Optical back propagation for fiber optic networks with hybrid EDFA Raman amplification,” Opt. Express, vol. 25, no. 5, pp. 5031–5043,  2017.

R. Dar and P. J. Winzer, “Nonlinear interference mitigation: Methods and potential gain,” J. Lightw. Technol., vol. 35, no. 4, pp. 903–930, 2017.

B. Foo, B. Corcoran, and A. Lowery, “Compensating XPM using a low-bandwidth phase modulator,” IEEE Photon. Technol. Lett., vol. 29, no. 9, pp. 699–702,  2017.

2016 (9)

B. Foo, B. Corcoran, C. Zhu, and A. J. Lowery, “Distributed nonlinearity compensation of dual-polarization signals using optoelectronics,” IEEE Photon. Technol. Lett., vol. 28, no. 20, pp. 2141–2144,  2016.

M. E. McCarthy, M. A. Z. A. Kahteeb, F. M. Ferreira, and A. D. Ellis, “PMD tolerant nonlinear compensation using in-line phase conjugation,” Opt. Express, vol. 24, no. 4, pp. 3385–3392,  2016.

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, vol. 24, no. 2, pp. 888–900,  2016.

X. Liang and S. Kumar, “Optical back propagation for compensating nonlinear impairments in fiber optic links with ROADMs,” Opt. Express, vol. 24, no. 20, pp. 22 682–22 692,  2016.

A. Ghazisaeidiet al., “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol., vol. 34, no. 8, pp. 1886–1895,  2016.

K. Solis-Trapala, M. Pelusi, H. N. Tan, T. Inoue, and S. Namiki, “Optimized WDM transmission impairment mitigation by multiple phase conjugations,” J. Lightw. Technol., vol. 34, no. 2, pp. 431–440,  2016.

A. D. Elliset al., “4 Tb/s transmission reach enhancement using 10 $\times$ 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightw. Technol., vol. 34, no. 8, pp. 1717–1723,  2016.

S. T. Le, I. D. Philips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightw. Technol., vol. 34, no. 10, pp. 2459–2466,  2016.

S. T. Le, J. E. Prilepsky, P. Rosa, J. D. Ania-Castan, and S. K. Turitsyn, “Nonlinear inverse synthesis for optical links with distributed Raman amplification,” J. Lightw. Technol., vol. 34, no. 8, pp. 1778–1786,  2016.

2015 (8)

X. Liang and S. Kumar, “Correlated digital back propagation based on perturbation theory,” Opt. Express, vol. 23, no. 11, pp. 14655–14665,  2015.

E. Tempranaet al., “Overcoming Kerr-induced capacity limit in optical fiber transmission,” Science, vol. 348, no. 6242, pp. 1445–1448, 2015.

E. Tempranaet al., “Two-fold transmission reach enhancement enabled by transmitter-side digital backpropagation and optical frequency comb-derived information carriers,” Opt. Express, vol. 23, no. 16, pp. 20774–20783, 2015.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugators,” Opt. Express, vol. 23, no. 16, pp. 20381–20393, 2015.

S. L. I. Olsson, B. Corcoran, C. Lundstrm, T. A. Eriksson, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplified transmission links for improved sensitivity and nonlinearity tolerance,” J. Lightw. Technol., vol. 33, no. 3, pp. 710–721,  2015.

N. Rossi, P. Serena, and A. Bononi, “Symbol-rate dependence of dominant nonlinearity and reach in coherent WDM links,” J. Lightw. Technol., vol. 33, no. 14, pp. 3132–3143,  2015.

F. Zhang, Q. Zhuge, M. Qiu, W. Wang, M. Chagnon, and D. V. Plant, “XPM model-based digital backpropagation for subcarrier-multiplexing systems,” J. Lightw. Technol., vol. 33, no. 24, pp. 5140–5150,  2015.

B. Foo, B. Corcoran, and A. Lowery, “Optoelectronic method for inline compensation of XPM in long-haul optical links,” Opt. Express, vol. 23, no. 2, pp. 859–872, 2015.

2014 (6)

X. Liang and S. Kumar, “Analytical modeling of XPM in dispersion-managed coherent fiber-optic systems,” Opt. Express, vol. 22, no. 9, pp. 10579–10592,  2014.

M. Morshed, L. B. Du, B. Foo, M. D. Pelusi, B. Corcoran, and A. J. Lowery, “Experimental demonstrations of dual polarization CO-OFDM using mid-span spectral inversion for nonlinearity compensation,” Opt. Express, vol. 22, no. 9, pp. 10455–10466, 2014.

M. H. Shoreh, “Compensation of nonlinearity impairments in coherent optical OFDM systems using multiple optical phase conjugate modules,” IEEE/OSA J. Opt. Commun. Netw., vol. 6, no. 6, pp. 549–558,  2014.

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. Lightw. Technol., vol. 32, no. 4, pp. 766–775,  2014.

X. Liang and S. Kumar, “Multi-stage perturbation theory for compensating intra-channel nonlinear impairments in fiber-optic links,” Opt. Express, vol. 22, no. 24, pp. 29733–29745, 2014.

X. Liang, S. Kumar, J. Shao, M. Malekiha, and D. V. Plant, “Digital compensation of cross-phase modulation distortions using perturbation technique for dispersion-managed fiber-optic systems,” Opt. Express, vol. 22, no. 17, pp. 20 634–20 645,  2014.

2013 (2)

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,” Nature Photon., vol. 7, no. 7, pp. 560–568, 2013.

X. Liang, S. Kumar, and J. Shao, “Ideal optical backpropagation of scalar NLSE using dispersion-decreasing fibers for WDM transmission,” Opt. Express, vol. 21, no. 23, pp. 28668–28675, 2013.

2012 (3)

2011 (7)

2010 (4)

E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightw. Technol., vol. 28, no. 6, pp. 939–951,  2010.

L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express, vol. 18, no. 16, pp. 17075–17088, 2010.

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightw. Technol., vol. 28, no. 4, pp. 423–433,  2010.

L. B. Du and A. J. Lowery, “Practical XPM compensation method for coherent optical OFDM systems,” IEEE Photon. Technol. Lett., vol. 22, no. 5, pp. 320–322,  2010.

2008 (5)

2007 (2)

A. J. Lowery, “Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation,” IEEE Photon. Technol. Lett., vol. 19, no. 19, pp. 1556–1558, 2007.

A. J. Lowery, “Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM,” Opt. Express, vol. 15, no. 20, pp. 12965–12970,  2007.

2006 (1)

C. R. Menyuk and B. S. Marks, “Interaction of polarization mode dispersion and nonlinearity in optical fiber transmission systems,” J. Lightw. Technol., vol. 24, no. 7, pp. 2806–2826,  2006.

2004 (1)

S. L. Jansenet al., “16 $\times$ 40 Gb/s over 800 km of SSMF using mid-link spectral inversion,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1763–1765,  2004.

2002 (1)

2001 (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature, vol. 411, no. 6841, pp. 1027–1030, 2001.

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. Lightw. Technol., vol. 15, no. 9, pp. 1735–1746,  1997.

1996 (1)

T.-K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightw. Technol., vol. 14, no. 3, pp. 249–260,  1996.

1994 (2)

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Dependence of cross-phase modulation on channel number in fiber WDM systems,” J. Lightw. Technol., vol. 12, no. 5, pp. 885–890,  1994.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: Theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photon. Technol. Lett., vol. 6, no. 6, pp. 733–736,  1994.

1987 (1)

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron., vol. QE-23, no. 7, pp. 1205–1210,  1987.

1974 (1)

F. Tappert, “Numerical solutions of the Korteweg-de Vries equation and its generalizations by the split-step Fourier method,” Nonlinear Wave Motion, vol. 15, pp. 215–216, 1974.

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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, vol. 24, no. 2, pp. 888–900,  2016.

S. L. I. Olsson, B. Corcoran, C. Lundstrm, T. A. Eriksson, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplified transmission links for improved sensitivity and nonlinearity tolerance,” J. Lightw. Technol., vol. 33, no. 3, pp. 710–721,  2015.

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S. T. Le, J. E. Prilepsky, P. Rosa, J. D. Ania-Castan, and S. K. Turitsyn, “Nonlinear inverse synthesis for optical links with distributed Raman amplification,” J. Lightw. Technol., vol. 34, no. 8, pp. 1778–1786,  2016.

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N. Rossi, P. Serena, and A. Bononi, “Symbol-rate dependence of dominant nonlinearity and reach in coherent WDM links,” J. Lightw. Technol., vol. 33, no. 14, pp. 3132–3143,  2015.

A. Bononi, N. Rossi, and P. Serena, “Transmission limitations due to fiber nonlinearity,” in Proc. Opt. Fiber Commun. Conf. Expo./Nat. Fiber Opt. Eng. Conf.,  2011, Paper OWO7.

Braun, R.

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron., vol. QE-23, no. 7, pp. 1205–1210,  1987.

Buelow, S. T. Le and H.

S. T. Le and H. Buelow, “64 $\times$ 0.5 Gbaud nonlinear frequency division multiplexed transmissions with high order modulation formats,” J. Lightw. Technol., vol. 35, no. 17, pp. 3692–3698,  2017.

Chagnon, M.

F. Zhang, Q. Zhuge, M. Qiu, W. Wang, M. Chagnon, and D. V. Plant, “XPM model-based digital backpropagation for subcarrier-multiplexing systems,” J. Lightw. Technol., vol. 33, no. 24, pp. 5140–5150,  2015.

Chandrasekhar, S.

H. Hu, R. M. Jopson, A. H. Gnauck, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity mitigation of WDM-PDM QPSK/16-QAM signals using fiber-optic parametric amplifiers based multiple optical phase conjugations,” Opt. Express, vol. 25, no. 3, pp. 1618–1628,  2017.

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. Lightw. Technol., vol. 32, no. 4, pp. 766–775,  2014.

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,” Nature Photon., vol. 7, no. 7, pp. 560–568, 2013.

H. Hu, R. M. Jopson, A. H. Gnauck, D. Pilori, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity compensation by repeated phase conjugation in 2.048-Tbit/s WDM transmission of PDM 16-QAM channels,” in Proc. Opt. Fiber Commun. Conf. Exhib.,  2016, Paper Th4F.3.

Charlet, G.

I. F. d. J. Ruiz, A. Ghazisaeidi, and G. Charlet, “Optimization rules and performance analysis of filtered digital backpropagation,” in Proc. Eur. Conf. Exhib. Opt. Commun., 2015, pp. 1–3.

Chen, X.

Chiang, T.-K.

T.-K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightw. Technol., vol. 14, no. 3, pp. 249–260,  1996.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: Theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photon. Technol. Lett., vol. 6, no. 6, pp. 733–736,  1994.

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. Lightw. Technol., vol. 32, no. 4, pp. 766–775,  2014.

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,” Nature Photon., vol. 7, no. 7, pp. 560–568, 2013.

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Dependence of cross-phase modulation on channel number in fiber WDM systems,” J. Lightw. Technol., vol. 12, no. 5, pp. 885–890,  1994.

Chugtai, M. N.

Corcoran, B.

B. Foo, B. Corcoran, and A. Lowery, “Compensating XPM using a low-bandwidth phase modulator,” IEEE Photon. Technol. Lett., vol. 29, no. 9, pp. 699–702,  2017.

B. Foo, B. Corcoran, C. Zhu, and A. J. Lowery, “Distributed nonlinearity compensation of dual-polarization signals using optoelectronics,” IEEE Photon. Technol. Lett., vol. 28, no. 20, pp. 2141–2144,  2016.

S. L. I. Olsson, B. Corcoran, C. Lundstrm, T. A. Eriksson, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplified transmission links for improved sensitivity and nonlinearity tolerance,” J. Lightw. Technol., vol. 33, no. 3, pp. 710–721,  2015.

B. Foo, B. Corcoran, and A. Lowery, “Optoelectronic method for inline compensation of XPM in long-haul optical links,” Opt. Express, vol. 23, no. 2, pp. 859–872, 2015.

M. Morshed, L. B. Du, B. Foo, M. D. Pelusi, B. Corcoran, and A. J. Lowery, “Experimental demonstrations of dual polarization CO-OFDM using mid-span spectral inversion for nonlinearity compensation,” Opt. Express, vol. 22, no. 9, pp. 10455–10466, 2014.

B. Foo, B. Corcoran, and A. Lowery, “Demonstration of DP-16QAM WDM link with in-line nonlinearity compensation,” in Proc. Opto-Electron. Commun. Conf. Photonics Global Conf.,  2017, pp. 1–3.

Cotter, D.

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightw. Technol., vol. 28, no. 4, pp. 423–433,  2010.

Dar, R.

R. Dar and P. J. Winzer, “Nonlinear interference mitigation: Methods and potential gain,” J. Lightw. Technol., vol. 35, no. 4, pp. 903–930, 2017.

Diaz, A.

A. Diazet al., “Analysis of back-propagation and RF pilot-tone based nonlinearity compensation for a 9 $\times$ 224 Gb/s POLMUX-16QAM system,” in Proc. Opt. Fiber Commun. Conf. Expo./Nat. Fiber Opt. Eng. Conf., 2012, Paper OTh3C.5.

Dou, L.

Y. Fan, L. Dou, Z. Tao, T. Hoshida, and J. C. Rasmussen, “A high performance nonlinear compensation algorithm with reduced complexity based on XPM model,” in Proc. Opt. Fiber Commun. Conf. Exhib.,  2014, Paper Th2A.8.

Du, L.

L. Du, M. M. Morshed, and A. J. Lowery, “Fiber nonlinearity compensation for OFDM super-channels using optical phase conjugation,” Opt. Express, vol. 20, no. 18, pp. 19921–19927, 2012.

L. Du and A. Lowery, “Experimental demonstration of XPM compensation for CO-OFDM systems with periodic dispersion maps,” in Proc. Opt. Fiber Commun. Conf. Expo./Nat. Fiber Opt. Eng. Conf.,  2011, Paper OWW2.

Du, L. B.

Eliasson, H.

Ellis, A.

A. Ellis, M. Al-Khateeb, and M. McCarthy, “Impact of optical phase conjugation on the nonlinear Shannon limit,” J. Lightw. Technol., vol. 35, no. 4, pp. 792–798,  2017.

Ellis, A. D.

S. T. Le, I. D. Philips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightw. Technol., vol. 34, no. 10, pp. 2459–2466,  2016.

A. D. Elliset al., “4 Tb/s transmission reach enhancement using 10 $\times$ 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation,” J. Lightw. Technol., vol. 34, no. 8, pp. 1717–1723,  2016.

M. E. McCarthy, M. A. Z. A. Kahteeb, F. M. Ferreira, and A. D. Ellis, “PMD tolerant nonlinear compensation using in-line phase conjugation,” Opt. Express, vol. 24, no. 4, pp. 3385–3392,  2016.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugators,” Opt. Express, vol. 23, no. 16, pp. 20381–20393, 2015.

D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express, vol. 19, no. 4, pp. 3449–3454, 2011.

D. Rafique, M. Mussolin, M. Forzati, J. Martensson, M. N. Chugtai, and A. D. Ellis, “Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm,” Opt. Express, vol. 19, no. 10, pp. 9453–9460, 2011.

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightw. Technol., vol. 28, no. 4, pp. 423–433,  2010.

Eriksson, T. A.

S. L. I. Olsson, B. Corcoran, C. Lundstrm, T. A. Eriksson, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplified transmission links for improved sensitivity and nonlinearity tolerance,” J. Lightw. Technol., vol. 33, no. 3, pp. 710–721,  2015.

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., vol. 101, no. 16, 2008, Art. no. .

Fan, Y.

Y. Fan, L. Dou, Z. Tao, T. Hoshida, and J. C. Rasmussen, “A high performance nonlinear compensation algorithm with reduced complexity based on XPM model,” in Proc. Opt. Fiber Commun. Conf. Exhib.,  2014, Paper Th2A.8.

Ferreira, F. M.

Fong, T. K.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: Theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photon. Technol. Lett., vol. 6, no. 6, pp. 733–736,  1994.

Foo, B.

B. Foo, B. Corcoran, and A. Lowery, “Compensating XPM using a low-bandwidth phase modulator,” IEEE Photon. Technol. Lett., vol. 29, no. 9, pp. 699–702,  2017.

B. Foo, B. Corcoran, C. Zhu, and A. J. Lowery, “Distributed nonlinearity compensation of dual-polarization signals using optoelectronics,” IEEE Photon. Technol. Lett., vol. 28, no. 20, pp. 2141–2144,  2016.

B. Foo, B. Corcoran, and A. Lowery, “Optoelectronic method for inline compensation of XPM in long-haul optical links,” Opt. Express, vol. 23, no. 2, pp. 859–872, 2015.

M. Morshed, L. B. Du, B. Foo, M. D. Pelusi, B. Corcoran, and A. J. Lowery, “Experimental demonstrations of dual polarization CO-OFDM using mid-span spectral inversion for nonlinearity compensation,” Opt. Express, vol. 22, no. 9, pp. 10455–10466, 2014.

A. Lowery and B. Foo, “Distributed nonlinear compensation using optoelectronic circuits,” in Proc. Eur. Conf. Exhib. Opt. Commun.,  2017, Paper W.2.E.2.

B. Foo, B. Corcoran, and A. Lowery, “Demonstration of DP-16QAM WDM link with in-line nonlinearity compensation,” in Proc. Opto-Electron. Commun. Conf. Photonics Global Conf.,  2017, pp. 1–3.

Forzati, M.

Foschini, G. 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., vol. 101, no. 16, 2008, Art. no. .

Gao, G.

Ghazisaeidi, A.

A. Ghazisaeidiet al., “Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction,” J. Lightw. Technol., vol. 34, no. 8, pp. 1886–1895,  2016.

I. F. d. J. Ruiz, A. Ghazisaeidi, and G. Charlet, “Optimization rules and performance analysis of filtered digital backpropagation,” in Proc. Eur. Conf. Exhib. Opt. Commun., 2015, pp. 1–3.

Gnauck, A. H.

H. Hu, R. M. Jopson, A. H. Gnauck, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity mitigation of WDM-PDM QPSK/16-QAM signals using fiber-optic parametric amplifiers based multiple optical phase conjugations,” Opt. Express, vol. 25, no. 3, pp. 1618–1628,  2017.

H. Hu, R. M. Jopson, A. H. Gnauck, D. Pilori, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity compensation by repeated phase conjugation in 2.048-Tbit/s WDM transmission of PDM 16-QAM channels,” in Proc. Opt. Fiber Commun. Conf. Exhib.,  2016, Paper Th4F.3.

Hanik, N.

B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, “Pilot-tone-based nonlinearity compensation for optical OFDM systems,” in Proc. 36th Eur. Conf. Exhib. Opt. Commun., 2010, Paper Tu.4.A.6.

Harper, P.

S. T. Le, I. D. Philips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightw. Technol., vol. 34, no. 10, pp. 2459–2466,  2016.

Hoshida, T.

Y. Fan, L. Dou, Z. Tao, T. Hoshida, and J. C. Rasmussen, “A high performance nonlinear compensation algorithm with reduced complexity based on XPM model,” in Proc. Opt. Fiber Commun. Conf. Exhib.,  2014, Paper Th2A.8.

Hu, H.

H. Hu, R. M. Jopson, A. H. Gnauck, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity mitigation of WDM-PDM QPSK/16-QAM signals using fiber-optic parametric amplifiers based multiple optical phase conjugations,” Opt. Express, vol. 25, no. 3, pp. 1618–1628,  2017.

H. Huet al., “Fiber nonlinearity compensation of an 8-channel WDM PDM-QPSK signal using multiple phase conjugations,” in Proc. Opt. Fiber Commun. Conf. Exhib., 2014, Paper M2C.2.

H. Hu, R. M. Jopson, A. H. Gnauck, D. Pilori, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity compensation by repeated phase conjugation in 2.048-Tbit/s WDM transmission of PDM 16-QAM channels,” in Proc. Opt. Fiber Commun. Conf. Exhib.,  2016, Paper Th4F.3.

Inan, B.

B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, “Pilot-tone-based nonlinearity compensation for optical OFDM systems,” in Proc. 36th Eur. Conf. Exhib. Opt. Commun., 2010, Paper Tu.4.A.6.

Inoue, T.

S. Namiki, K. Solis-Trapala, H. N. Tan, M. Pelusi, and T. Inoue, “Multi-channel cascadable parametric signal processing for wavelength conversion and nonlinearity compensation,” J. Lightw. Technol., vol. 35, no. 4, pp. 815–823,  2017.

K. Solis-Trapala, M. Pelusi, H. N. Tan, T. Inoue, and S. Namiki, “Optimized WDM transmission impairment mitigation by multiple phase conjugations,” J. Lightw. Technol., vol. 34, no. 2, pp. 431–440,  2016.

K. Solis-Trapala, T. Inoue, and S. Namiki, “Signal power asymmetry tolerance of an optical phase conjugation-based nonlinear compensation system,” in Proc. Eur. Conf. Exhib. Opt. Commun.,  2014, Paper We.2.5.4.

K. Solis-Trapala, T. Inoue, and S. Namiki, “Nearly-ideal optical phase conjugation based nonlinear compensation system,” in Proc. Opt. Fiber Commun. Conf. Exhib.,  2014, Paper W3F.8.

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E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightw. Technol., vol. 28, no. 6, pp. 939–951,  2010.

E. Ip and J. M. Khan, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol., vol. 26, no. 20, pp. 3416–3425,  2008.

Jansen, S. L.

S. L. Jansenet al., “16 $\times$ 40 Gb/s over 800 km of SSMF using mid-link spectral inversion,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1763–1765,  2004.

B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, “Pilot-tone-based nonlinearity compensation for optical OFDM systems,” in Proc. 36th Eur. Conf. Exhib. Opt. Commun., 2010, Paper Tu.4.A.6.

Jopson, R. M.

H. Hu, R. M. Jopson, A. H. Gnauck, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity mitigation of WDM-PDM QPSK/16-QAM signals using fiber-optic parametric amplifiers based multiple optical phase conjugations,” Opt. Express, vol. 25, no. 3, pp. 1618–1628,  2017.

H. Hu, R. M. Jopson, A. H. Gnauck, D. Pilori, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity compensation by repeated phase conjugation in 2.048-Tbit/s WDM transmission of PDM 16-QAM channels,” in Proc. Opt. Fiber Commun. Conf. Exhib.,  2016, Paper Th4F.3.

Kagi, N.

T.-K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightw. Technol., vol. 14, no. 3, pp. 249–260,  1996.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: Theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photon. Technol. Lett., vol. 6, no. 6, pp. 733–736,  1994.

Kahteeb, M. A. Z. A.

Karlsson, M.

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, vol. 24, no. 2, pp. 888–900,  2016.

S. L. I. Olsson, B. Corcoran, C. Lundstrm, T. A. Eriksson, M. Karlsson, and P. A. Andrekson, “Phase-sensitive amplified transmission links for improved sensitivity and nonlinearity tolerance,” J. Lightw. Technol., vol. 33, no. 3, pp. 710–721,  2015.

Kazovsky, L. G.

T.-K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightw. Technol., vol. 14, no. 3, pp. 249–260,  1996.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: Theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photon. Technol. Lett., vol. 6, no. 6, pp. 733–736,  1994.

Khan, J. M.

E. Ip and J. M. Khan, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol., vol. 26, no. 20, pp. 3416–3425,  2008.

Kikuchi, K.

Kramer, G.

R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett., vol. 101, no. 16, 2008, Art. no. .

Kumar, S.

X. Liang and S. Kumar, “Optical back propagation for fiber optic networks with hybrid EDFA Raman amplification,” Opt. Express, vol. 25, no. 5, pp. 5031–5043,  2017.

X. Liang and S. Kumar, “Optical back propagation for compensating nonlinear impairments in fiber optic links with ROADMs,” Opt. Express, vol. 24, no. 20, pp. 22 682–22 692,  2016.

X. Liang and S. Kumar, “Correlated digital back propagation based on perturbation theory,” Opt. Express, vol. 23, no. 11, pp. 14655–14665,  2015.

X. Liang and S. Kumar, “Multi-stage perturbation theory for compensating intra-channel nonlinear impairments in fiber-optic links,” Opt. Express, vol. 22, no. 24, pp. 29733–29745, 2014.

X. Liang and S. Kumar, “Analytical modeling of XPM in dispersion-managed coherent fiber-optic systems,” Opt. Express, vol. 22, no. 9, pp. 10579–10592,  2014.

X. Liang, S. Kumar, J. Shao, M. Malekiha, and D. V. Plant, “Digital compensation of cross-phase modulation distortions using perturbation technique for dispersion-managed fiber-optic systems,” Opt. Express, vol. 22, no. 17, pp. 20 634–20 645,  2014.

X. Liang, S. Kumar, and J. Shao, “Ideal optical backpropagation of scalar NLSE using dispersion-decreasing fibers for WDM transmission,” Opt. Express, vol. 21, no. 23, pp. 28668–28675, 2013.

J. Shao and S. Kumar, “Optical backpropagation for fiber-optic communications using optical phase conjugation at the receiver,” Opt. Lett., vol. 37, no. 15, pp. 3012–3014, 2012.

Le, S. T.

S. T. Le, I. D. Philips, J. E. Prilepsky, P. Harper, A. D. Ellis, and S. K. Turitsyn, “Demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” J. Lightw. Technol., vol. 34, no. 10, pp. 2459–2466,  2016.

S. T. Le, J. E. Prilepsky, P. Rosa, J. D. Ania-Castan, and S. K. Turitsyn, “Nonlinear inverse synthesis for optical links with distributed Raman amplification,” J. Lightw. Technol., vol. 34, no. 8, pp. 1778–1786,  2016.

Li, G.

Li, X.

Liang, X.

Liu, X.

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IEEE J. Quantum Electron. (1)

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IEEE Photon. Technol. Lett. (6)

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IEEE/OSA J. Opt. Commun. Netw. (1)

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J. Lightw. Technol. (21)

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T.-K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightw. Technol., vol. 14, no. 3, pp. 249–260,  1996.

Z. Taoet al., “Simple fiber model for determination of XPM effects,” J. Lightw. Technol., vol. 29, no. 7, pp. 974–986,  2011.

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Dependence of cross-phase modulation on channel number in fiber WDM systems,” J. Lightw. Technol., vol. 12, no. 5, pp. 885–890,  1994.

F. Zhang, Q. Zhuge, M. Qiu, W. Wang, M. Chagnon, and D. V. Plant, “XPM model-based digital backpropagation for subcarrier-multiplexing systems,” J. Lightw. Technol., vol. 33, no. 24, pp. 5140–5150,  2015.

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