Abstract

A Gaussian noise (GN) model, precisely accounting for an arbitrary frequency dependent signal power profile along the link, is presented. This allows accurate evaluation of the impact of inter-channel stimulated Raman scattering (ISRS) on the optical Kerr nonlinearity. Additionally, the frequency dependent fiber attenuation can be taken into account and transmission systems that use hybrid amplification schemes can be modeled, where distributed Raman amplification is partly applied over the optical spectrum. For the latter two cases, a set of coupled ordinary differential equations must be numerically solved to obtain the signal power profile yielding a semianalytical model. However for lumped amplification and negligible variation in fiber attenuation, a less complex and fully analytical model is presented denoted as the analytical ISRS GN model. The derived model is exact to first-order for Gaussian modulated signals and extensively validated by numerical split-step simulations. A maximum deviation of only 0.1 dB in nonlinear interference power between simulations and the ISRS GN model is reported. The model is applied to a transmission system that occupies the entire C + L band (10 THz optical bandwidth). At optimum launch power, changes of up to 2 dB in nonlinear interference power due to ISRS are reported. The ISRS GN model is quantitatively compared with other models published in the literature and found to be significantly more accurate.

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2018 (2)

I. Roberts, J. M. Kahn, J. Harley, and D. Boertjes, “Corrections to “Channel power optimization of WDM systems following Gaussian noise nonlinearity model in presence of stimulated Raman scattering”,” J. Lightw. Technol., vol. 36, no. 11, pp. 2309–2309,  2018.

M. Tanet al., “RIN mitigation and transmission performance enhancement with forward broadband pump,” IEEE Photon. Technol. Lett., vol. 30, no. 3, pp. 254–257,  2018.

2017 (9)

D. Semrau and P. Bayvel, “The Gaussian noise model in the presence of inter-channel stimulated Raman scattering,” arXiv:1801.02460, 2017.

T. Hasegawa, Y. Yamamoto, and M. Hirano, “Optimal fiber design for large capacity long haul coherent transmission,” Opt. Express, vol. 25, no. 2, pp. 706–712,  2017.

G. Saavedraet al., “Experimental analysis of nonlinear impairments in fibre optic transmission systems up to 7.3 THz,” J. Lightw. Technol., vol. 35, no. 21, pp. 4809–4816,  2017.

D. Semrau, G. Saavedra, D. Lavery, R. I. Killey, and P. Bayvel, “A closed-form expression to evaluate nonlinear interference in Raman-amplified links,” J. Lightw. Technol., vol. 35, no. 19, pp. 4316–4328,  2017.

A. Ghazisaeidi, “A theory of nonlinear interactions between signal and amplified spontaneous emission noise in coherent wavelength division multiplexed systems,” J. Lightw. Technol., vol. 35, no. 23, pp. 5150–5175,  2017.

P. Poggiolini and Y. Jiang, “Recent advances in the modeling of the impact of nonlinear fiber propagation effects on uncompensated coherent transmission systems,” J. Lightw. Technol., vol. 35, no. 3, pp. 458–480,  2017.

D. Semrau, R. Killey, and P. Bayvel, “Achievable rate degradation of ultra-wideband coherent fiber communication systems due to stimulated Raman scattering,” Opt. Express, vol. 25, no. 12, pp. 13 024–13 034,  2017.

I. Roberts, J. M. Kahn, J. Harley, and D. W. Boertjes, “Channel power optimization of WDM systems following Gaussian noise nonlinearity model in presence of stimulated Raman scattering,” J. Lightw. Technol., vol. 35, no. 23, pp. 5237–5249,  2017.

M. Cantono, D. Pilori, A. Ferrari, and V. Curri, “Introducing the generalized GN-model for nonlinear interference generation including space/frequency variations of loss/gain,” ArXiv e-prints, 2017.

2016 (5)

T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On probabilistic shaping of quadrature amplitude modulation for the nonlinear fiber channel,” J. Lightw. Technol., vol. 34, no. 21, pp. 5063–5073,  2016.

P. Poggioliniet al., “Analytical and experimental results on system maximum reach increase through symbol rate optimization,” J. Lightw. Technol., vol. 34, no. 8, pp. 1872–1885,  2016.

D. Semrauet al., “Achievable information rates estimates in optically amplified transmission systems using nonlinearity compensation and probabilistic shaping,” Opt. Lett., vol. 42, no. 1, pp. 121–124,  2016.

O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the bit-error-rate performance of nonlinear fiber-optic systems,” J. Lightw. Technol., vol. 34, no. 15, pp. 3482–3489,  2016.

E. Agrellet al., “Roadmap of optical communications,” J. Opt., vol. 18, no. 6, 2016, Art no. .

2015 (4)

P. Serena and A. Bononi, “A time-domain extended Gaussian noise model,” J. Lightw. Technol., vol. 33, no. 7, pp. 1459–1472,  2015.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A simple and effective closed-form GN model correction formula accounting for signal non-Gaussian distribution,” J. Lightw. Technol., vol. 33, no. 2, pp. 459–473,  2015.

J. X. Caiet al., “49.3 Tb/s transmission over 9100 km using C + L EDFA and 54 Tb/s transmission over 9150 km using hybrid-Raman EDFA,” J. Lightw. Technol., vol. 33, no. 13, pp. 2724–2734,  2015.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Inter-channel nonlinear interference noise in WDM systems: Modeling and mitigation,” J. Lightw. Technol., vol. 33, no. 5, pp. 1044–1053,  2015.

2014 (4)

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Accumulation of nonlinear interference noise in fiber-optic systems,” Opt. Express, vol. 22, no. 12, pp. 14 199–14 211,  2014.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory,” J. Lightw. Technol., vol. 32, no. 16, pp. 2862–2876,  2014.

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Express, vol. 22, no. 13, pp. 16335–16362,  2014.

A. Nespolaet al., “GN-Model validation over seven fiber types in uncompensated PM-16QAM Nyquist-WDM links,” IEEE Photon. Technol. Lett., vol. 26, no. 2, pp. 206–209,  2014.

2013 (3)

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Express, vol. 21, no. 22, p. 25685,  2013.

P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightw. Technol., vol. 31, no. 8, pp. 1273–1282,  2013.

E. M. Dianov, “Amplification in extended transmission bands using bismuth-doped optical fibers,” J. Lightw. Technol., vol. 31, no. 4, pp. 681–688,  2013.

2012 (5)

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightw. Technol., vol. 30, no. 10, pp. 1524–1539,  2012.

A. Mecozzi and R.-J. Essiambre, “Nonlinear shannon limit in pseudolinear coherent systems,” J. Lightw. Technol., vol. 30, no. 12, pp. 2011–2024,  2012.

M. Secondini and E. Forestieri, “Analytical fiber-optic channel model in the presence of cross-phase modulation,” IEEE Photon. Technol. Lett., vol. 24, no. 22, pp. 2016–2019,  2012.

P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightw. Technol., vol. 30, no. 24, pp. 3857–3879,  2012.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” ArXiv e-prints, 2012.

2011 (3)

2010 (1)

X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express, vol. 18, no. 18, pp. 19 039–19 054,  2010.

2008 (1)

2007 (1)

V. Anagnostopoulos, C. T. Politi, C. Matrakidis, and A. Stavdas, “Physical layer impairment aware wavelength routing algorithms based on analytically calculated constraints,” Opt. Commun., vol. 270, no. 2, pp. 247–254, 2007.

2006 (1)

A. N. Pilipetskii, “High-capacity undersea long-haul systems,” J. Sel. Topics Quantum Electron., vol. 12, no. 4, pp. 484–496,  2006.

2004 (1)

J. Bromage, “Raman amplification for fiber communications systems,” J. Lightw. Technol., vol. 22, no. 1, pp. 79–93,  2004.

2002 (2)

V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightw. Technol., vol. 20, no. 2, pp. 250–254,  2002.

J. Tang, “The channel capacity of a multispan DWDM system employing dispersive nonlinear optical fibers and an ideal coherent optical receiver,” J. Lightw. Technol., vol. 20, no. 7, pp. 1095–1101,  2002.

2001 (1)

S. Norimatsu and T. Yamamoto, “Waveform distortion due to stimulated Raman scattering in wide-band WDM transmission systems,” J. Lightw. Technol., vol. 19, no. 2, pp. 159–171,  2001.

2000 (1)

K.-P. Ho, “Statistical properties of stimulated Raman crosstalk in WDM systems,” J. Lightw. Technol., vol. 18, no. 7, pp. 915–921,  2000.

1998 (1)

M. Zirngibl, “Analytical model of Raman gain effects in massive wavelength division multiplexed transmission systems,” Electron. Lett., vol. 34, no. 8, pp. 789–790,  1998.

1995 (1)

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Effect of modulation statistics on Raman crosstalk in WDM systems,” IEEE Photon. Technol. Lett., vol. 7, no. 1, pp. 101–103,  1995.

1993 (1)

S. Tariq and J. C. Palais, “A computer model of non-dispersion-limited stimulated Raman scattering in optical fiber multiple-channel communications,” J. Lightw. Technol., vol. 11, no. 12, pp. 1914–1924,  1993.

1973 (1)

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” App. Phys. Lett., vol. 22, no. 6, pp. 276–278, 1973.

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics. Amsterdam, The Netherlands: Elsevier, 2012.

Agrell, E.

E. Agrellet al., “Roadmap of optical communications,” J. Opt., vol. 18, no. 6, 2016, Art no. .

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory,” J. Lightw. Technol., vol. 32, no. 16, pp. 2862–2876,  2014.

Alvarado, A.

T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On probabilistic shaping of quadrature amplitude modulation for the nonlinear fiber channel,” J. Lightw. Technol., vol. 34, no. 21, pp. 5063–5073,  2016.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory,” J. Lightw. Technol., vol. 32, no. 16, pp. 2862–2876,  2014.

Anagnostopoulos, V.

V. Anagnostopoulos, C. T. Politi, C. Matrakidis, and A. Stavdas, “Physical layer impairment aware wavelength routing algorithms based on analytically calculated constraints,” Opt. Commun., vol. 270, no. 2, pp. 247–254, 2007.

Auge, J. L.

M. Cantono, J. L. Auge, and V. Curri, “Modelling the impact of SRS on NLI generation in commercial equipment: an experimental investigation,” in Proc. Opt. Fiber Commun. Conf. Opt. Soc. Amer., 2018, p. M1D.2.

Bao, H.

Bayvel, P.

D. Semrau, G. Saavedra, D. Lavery, R. I. Killey, and P. Bayvel, “A closed-form expression to evaluate nonlinear interference in Raman-amplified links,” J. Lightw. Technol., vol. 35, no. 19, pp. 4316–4328,  2017.

D. Semrau, R. Killey, and P. Bayvel, “Achievable rate degradation of ultra-wideband coherent fiber communication systems due to stimulated Raman scattering,” Opt. Express, vol. 25, no. 12, pp. 13 024–13 034,  2017.

D. Semrau and P. Bayvel, “The Gaussian noise model in the presence of inter-channel stimulated Raman scattering,” arXiv:1801.02460, 2017.

Böcherer, G.

T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On probabilistic shaping of quadrature amplitude modulation for the nonlinear fiber channel,” J. Lightw. Technol., vol. 34, no. 21, pp. 5063–5073,  2016.

Boertjes, D.

I. Roberts, J. M. Kahn, J. Harley, and D. Boertjes, “Corrections to “Channel power optimization of WDM systems following Gaussian noise nonlinearity model in presence of stimulated Raman scattering”,” J. Lightw. Technol., vol. 36, no. 11, pp. 2309–2309,  2018.

Boertjes, D. W.

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