Abstract

An accurate, closed-form expression to evaluate the nonlinear interference (NLI) noise power in Nyquist-spaced, coherent optical communication systems using backward-pumped Raman amplification is presented. This enables rapid estimation of the signal-to-noise ratio (SNR) and avoids the need of integral evaluations and split-step simulations. The accuracy of the proposed formula is compared to numerical integration of the Gaussian noise (GN) model and split-step simulations over a wide range of parameters, including three different fiber types. Additionally, the impact of pump depletion on the NLI noise power is studied and the formula is applied to a second-order Raman-amplified system. In the case of first-order amplification and negligible pump depletion, a maximum deviation of 0.34 dB in NLI coefficient between the GN model and the closed-form formula is found, which corresponds to a maximum deviation of $\sim$0.1 dB in optimal SNR or similar figures of merit (e.g., maximum reach). When pump depletion is considered, it is shown that the NLI coefficient becomes a function of launch power and as a result the cubic power dependence of the NLI noise power is no longer valid in such regimes. Finally, for the second-order Raman-amplified system, a maximum deviation of 0.39 dB in NLI coefficient is reported.

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2017 (8)

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, 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.

M. P. Yankovet al., “Nonlinear phase noise compensation in experimental WDM systems with 256QAM,” J. Lightw. Technol., vol. 35, no 8, pp. 1438–1443,  2017.

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

J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities [Invited],” Opt. Express, vol. 25, no. 3, pp. 1916–1936, 2017.

D. Lavery, R. Maher, G. Liga, D. Semrau, L. Galdino, and P. Bayvel, “On the bandwidth dependent performance of split transmitter-receiver optical fiber nonlinearity compensation,” Opt. Express, vol. 25, no. 4, pp. 4554–4563, 2017.

L. Galdinoet al., “On the limits of digital back-propagation in the presence of transceiver noise,” Opt. Express, vol. 25, no. 4, pp. 4564–4578, 2017.

G. Saavedra, D. Semrau, L. Galdino, R. I. Killey, and P. Bayvel, “Digital back-propagation for nonlinearity mitigation in distributed Raman amplified links,” Opt. Express, vol. 25, no. 5, pp. 5431–5439, 2017.

2016 (8)

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Pulse collision picture of inter-channel nonlinear interference in fiber-optic communications,” J. Lightw. Technol., vol. 34, no 2, pp. 593–607,  2016.

M. Tan, P. Rosa, S. T. Le, Md. A. Iqbal, I. D. Phillips, and P. Harper, “Transmission performance improvement using random DFB laser based Raman amplification and bidirectional second-order pumping,” Opt. Express, vol. 24, no. 3, pp. 2215–2221, 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.

W. S. Pelouch, “Raman amplification: An enabling technology for long-haul coherent transmission systems,” J. Lightw. Technol., vol. 34, no. 1, pp. 6–19,  2016.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: A study of transceiver performance,” Sci. Rep., vol. 6, 2016, Art. no. .

B. Liet al., “The role of effective area in the design of weakly coupled MCF: Optimization guidance and OSNR improvement,” IEEE J. Sel. Topics Quantum Electron., vol. 22, no. 2, pp. 81–87,  2016.

V. Curri and A. Carena, “Merit of Raman pumping in uniform and uncompensated links supporting NyWDM transmission,” J. Lightw. Technol., vol. 34, no. 2, pp. 554–565,  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.

2015 (2)

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.

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 (3)

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,” Photon. Technol. Lett., vol. 26, no. 2, pp. 206–209, 2014.

2013 (3)

2012 (1)

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.

2011 (1)

2010 (1)

2006 (1)

V. Anagnostopoulos, C. 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, 2006.

2004 (2)

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

J. D. Ania-Castañón, “Quasi-lossless transmission using second-order Raman amplification and fibre Bragg gratings,” Opt. Express, vol. 12, no. 19, pp. 4372–4377, 2004.

Agrell, E.

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.

Al-Khateeb, M. A. Z.

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proc. 2016 IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 795–796.

Alvarado, A.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: A study of transceiver performance,” Sci. Rep., vol. 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.

Anagnostopoulos, V.

V. Anagnostopoulos, C. 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, 2006.

Ania-Castañón, J. D.

Bayvel, P.

Bosco, G.

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.

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.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Express, vol. 21, no. 3, pp. 3308–3317, 2013.

G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Analytical results on channel capacity in uncompensated optical links with coherent detection,” Opt. Express, vol. 19, no. 26, pp. B440–B451, 2011.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Evaluation of non-linear interference in uncompensated links using Raman amplification,” in Proc. Eur. Conf. Opt. Commun., 2012, pp. 1–3.

A. Carena, G. Bosco, V. Curri, P. Poggiolini, and F. Forghieri, “Impact of the transmitted signal initial dispersion transient on the accuracy of the GN model of non-linear propagation,” in Proc. Eur. Conf. Opt. Commun., 2013, pp. 1–3.

Bromage, J.

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

Carena, A.

V. Curri and A. Carena, “Merit of Raman pumping in uniform and uncompensated links supporting NyWDM transmission,” J. Lightw. Technol., vol. 34, no. 2, pp. 554–565,  2016.

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.

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.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Express, vol. 21, no. 3, pp. 3308–3317, 2013.

G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Analytical results on channel capacity in uncompensated optical links with coherent detection,” Opt. Express, vol. 19, no. 26, pp. B440–B451, 2011.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Evaluation of non-linear interference in uncompensated links using Raman amplification,” in Proc. Eur. Conf. Opt. Commun., 2012, pp. 1–3.

A. Carena, G. Bosco, V. Curri, P. Poggiolini, and F. Forghieri, “Impact of the transmitted signal initial dispersion transient on the accuracy of the GN model of non-linear propagation,” in Proc. Eur. Conf. Opt. Commun., 2013, pp. 1–3.

Cartledge, J. C.

Charlet, G.

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

Chen, X.

Curri, V.

V. Curri and A. Carena, “Merit of Raman pumping in uniform and uncompensated links supporting NyWDM transmission,” J. Lightw. Technol., vol. 34, no. 2, pp. 554–565,  2016.

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.

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.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Express, vol. 21, no. 3, pp. 3308–3317, 2013.

G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Analytical results on channel capacity in uncompensated optical links with coherent detection,” Opt. Express, vol. 19, no. 26, pp. B440–B451, 2011.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Evaluation of non-linear interference in uncompensated links using Raman amplification,” in Proc. Eur. Conf. Opt. Commun., 2012, pp. 1–3.

A. Carena, G. Bosco, V. Curri, P. Poggiolini, and F. Forghieri, “Impact of the transmitted signal initial dispersion transient on the accuracy of the GN model of non-linear propagation,” in Proc. Eur. Conf. Opt. Commun., 2013, pp. 1–3.

Dar, R.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Pulse collision picture of inter-channel nonlinear interference in fiber-optic communications,” J. Lightw. Technol., vol. 34, no 2, pp. 593–607,  2016.

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.

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, pp. 25685–25699, 2013.

de Jauregui Ruiz, I. F.

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

Durisi, G.

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.

Ellis, A. D.

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. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proc. 2016 IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 795–796.

Feder, M.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Pulse collision picture of inter-channel nonlinear interference in fiber-optic communications,” J. Lightw. Technol., vol. 34, no 2, pp. 593–607,  2016.

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.

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, pp. 25685–25699, 2013.

Forestieri, E.

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightw. Technol., vol. 31, no. 23, pp. 3839–3852,  2013.

Forghieri, F.

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.

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.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Express, vol. 21, no. 3, pp. 3308–3317, 2013.

G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Analytical results on channel capacity in uncompensated optical links with coherent detection,” Opt. Express, vol. 19, no. 26, pp. B440–B451, 2011.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Evaluation of non-linear interference in uncompensated links using Raman amplification,” in Proc. Eur. Conf. Opt. Commun., 2012, pp. 1–3.

A. Carena, G. Bosco, V. Curri, P. Poggiolini, and F. Forghieri, “Impact of the transmitted signal initial dispersion transient on the accuracy of the GN model of non-linear propagation,” in Proc. Eur. Conf. Opt. Commun., 2013, pp. 1–3.

Galdino, L.

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

Guiomar, F. P.

Harper, P.

M. Tan, P. Rosa, S. T. Le, Md. A. Iqbal, I. D. Phillips, and P. Harper, “Transmission performance improvement using random DFB laser based Raman amplification and bidirectional second-order pumping,” Opt. Express, vol. 24, no. 3, pp. 2215–2221, 2016.

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proc. 2016 IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 795–796.

Hasegawa, T.

Hirano, M.

Iqbal, M. A.

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proc. 2016 IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 795–796.

Iqbal, Md. A.

Jiang, Y.

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.

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.

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.

Karlsson, M.

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.

Killey, R. I.

Kschischang, F. R.

Kurtzke, C.

A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, pp. 1–3.

Lavery, D.

D. Lavery, R. Maher, G. Liga, D. Semrau, L. Galdino, and P. Bayvel, “On the bandwidth dependent performance of split transmitter-receiver optical fiber nonlinearity compensation,” Opt. Express, vol. 25, no. 4, pp. 4554–4563, 2017.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: A study of transceiver performance,” Sci. Rep., vol. 6, 2016, Art. no. .

Le, S. T.

Li, B.

B. Liet al., “The role of effective area in the design of weakly coupled MCF: Optimization guidance and OSNR improvement,” IEEE J. Sel. Topics Quantum Electron., vol. 22, no. 2, pp. 81–87,  2016.

Liga, G.

Maher, R.

D. Lavery, R. Maher, G. Liga, D. Semrau, L. Galdino, and P. Bayvel, “On the bandwidth dependent performance of split transmitter-receiver optical fiber nonlinearity compensation,” Opt. Express, vol. 25, no. 4, pp. 4554–4563, 2017.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: A study of transceiver performance,” Sci. Rep., vol. 6, 2016, Art. no. .

Matrakidis, C.

V. Anagnostopoulos, C. 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, 2006.

McCarthy, M.

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proc. 2016 IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 795–796.

Mecozzi, A.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Pulse collision picture of inter-channel nonlinear interference in fiber-optic communications,” J. Lightw. Technol., vol. 34, no 2, pp. 593–607,  2016.

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.

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, pp. 25685–25699, 2013.

Naito, T.

T. Naito, T. Tanaka, K. Torii, N. Shimojoh, H. Nakamoto, and M. Suyama, “A broadband distributed Raman amplifier for bandwidths beyond 100 nm,” in Proc. Opt. Fiber Commun. Conf., 2002, pp. 1–3.

Nakamoto, H.

T. Naito, T. Tanaka, K. Torii, N. Shimojoh, H. Nakamoto, and M. Suyama, “A broadband distributed Raman amplifier for bandwidths beyond 100 nm,” in Proc. Opt. Fiber Commun. Conf., 2002, pp. 1–3.

Nespola, A.

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

A. Nespolaet al., “Experimental validation of the EGN-model in uncompensated optical links,” in Proc. Opt. Fiber Commun. Conf., 2015, pp. 1–3.

Pelouch, W. S.

W. S. Pelouch, “Raman amplification: An enabling technology for long-haul coherent transmission systems,” J. Lightw. Technol., vol. 34, no. 1, pp. 6–19,  2016.

Petermann, K.

A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, pp. 1–3.

Phillips, I. D.

Poggiolini, P.

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.

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.

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.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Express, vol. 21, no. 3, pp. 3308–3317, 2013.

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.

G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Analytical results on channel capacity in uncompensated optical links with coherent detection,” Opt. Express, vol. 19, no. 26, pp. B440–B451, 2011.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Evaluation of non-linear interference in uncompensated links using Raman amplification,” in Proc. Eur. Conf. Opt. Commun., 2012, pp. 1–3.

A. Carena, G. Bosco, V. Curri, P. Poggiolini, and F. Forghieri, “Impact of the transmitted signal initial dispersion transient on the accuracy of the GN model of non-linear propagation,” in Proc. Eur. Conf. Opt. Commun., 2013, pp. 1–3.

Politi, C.

V. Anagnostopoulos, C. 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, 2006.

Prati, G.

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightw. Technol., vol. 31, no. 23, pp. 3839–3852,  2013.

Rosa, P.

Saavedra, G.

G. Saavedra, D. Semrau, L. Galdino, R. I. Killey, and P. Bayvel, “Digital back-propagation for nonlinearity mitigation in distributed Raman amplified links,” Opt. Express, vol. 25, no. 5, pp. 5431–5439, 2017.

G. Saavedraet al., “Experimental investigation of nonlinear signal distortions in ultra-wideband transmission systems,” in Proc. Opt. Fiber Commun. Conf., 2017, pp. 1–3.

Secondini, M.

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightw. Technol., vol. 31, no. 23, pp. 3839–3852,  2013.

Semrau, D.

Shevchenko, N. A.

N. A. Shevchenkoet al., “Achievable information rates estimation for 100-nm Raman-amplified optical transmission system,” in Proc. Eur. Conf. Opt. Commun., 2016, pp. 1–3.

Shieh, W.

Shimojoh, N.

T. Naito, T. Tanaka, K. Torii, N. Shimojoh, H. Nakamoto, and M. Suyama, “A broadband distributed Raman amplifier for bandwidths beyond 100 nm,” in Proc. Opt. Fiber Commun. Conf., 2002, pp. 1–3.

Shtaif, M.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Pulse collision picture of inter-channel nonlinear interference in fiber-optic communications,” J. Lightw. Technol., vol. 34, no 2, pp. 593–607,  2016.

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.

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, pp. 25685–25699, 2013.

Splett, A.

A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, pp. 1–3.

Stavdas, A.

V. Anagnostopoulos, C. 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, 2006.

Suyama, M.

T. Naito, T. Tanaka, K. Torii, N. Shimojoh, H. Nakamoto, and M. Suyama, “A broadband distributed Raman amplifier for bandwidths beyond 100 nm,” in Proc. Opt. Fiber Commun. Conf., 2002, pp. 1–3.

Tan, M.

M. Tan, P. Rosa, S. T. Le, Md. A. Iqbal, I. D. Phillips, and P. Harper, “Transmission performance improvement using random DFB laser based Raman amplification and bidirectional second-order pumping,” Opt. Express, vol. 24, no. 3, pp. 2215–2221, 2016.

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proc. 2016 IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 795–796.

Tanaka, T.

T. Naito, T. Tanaka, K. Torii, N. Shimojoh, H. Nakamoto, and M. Suyama, “A broadband distributed Raman amplifier for bandwidths beyond 100 nm,” in Proc. Opt. Fiber Commun. Conf., 2002, pp. 1–3.

Torii, K.

T. Naito, T. Tanaka, K. Torii, N. Shimojoh, H. Nakamoto, and M. Suyama, “A broadband distributed Raman amplifier for bandwidths beyond 100 nm,” in Proc. Opt. Fiber Commun. Conf., 2002, pp. 1–3.

Yamamoto, Y.

Yankov, M. P.

J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities [Invited],” Opt. Express, vol. 25, no. 3, pp. 1916–1936, 2017.

M. P. Yankovet al., “Nonlinear phase noise compensation in experimental WDM systems with 256QAM,” J. Lightw. Technol., vol. 35, no 8, pp. 1438–1443,  2017.

IEEE J. Sel. Topics Quantum Electron. (1)

B. Liet al., “The role of effective area in the design of weakly coupled MCF: Optimization guidance and OSNR improvement,” IEEE J. Sel. Topics Quantum Electron., vol. 22, no. 2, pp. 81–87,  2016.

J. Lightw. Technol. (13)

V. Curri and A. Carena, “Merit of Raman pumping in uniform and uncompensated links supporting NyWDM transmission,” J. Lightw. Technol., vol. 34, no. 2, pp. 554–565,  2016.

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightw. Technol., vol. 31, no. 23, pp. 3839–3852,  2013.

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.

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.

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.

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.

W. S. Pelouch, “Raman amplification: An enabling technology for long-haul coherent transmission systems,” J. Lightw. Technol., vol. 34, no. 1, pp. 6–19,  2016.

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

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.

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Pulse collision picture of inter-channel nonlinear interference in fiber-optic communications,” J. Lightw. Technol., vol. 34, no 2, pp. 593–607,  2016.

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.

M. P. Yankovet al., “Nonlinear phase noise compensation in experimental WDM systems with 256QAM,” J. Lightw. Technol., vol. 35, no 8, pp. 1438–1443,  2017.

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.

Opt. Commun. (1)

V. Anagnostopoulos, C. 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, 2006.

Opt. Express (12)

J. D. Ania-Castañón, “Quasi-lossless transmission using second-order Raman amplification and fibre Bragg gratings,” Opt. Express, vol. 12, no. 19, pp. 4372–4377, 2004.

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. 19039–19054, 2010.

G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Analytical results on channel capacity in uncompensated optical links with coherent detection,” Opt. Express, vol. 19, no. 26, pp. B440–B451, 2011.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Express, vol. 21, no. 3, pp. 3308–3317, 2013.

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, pp. 25685–25699, 2013.

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.

M. Tan, P. Rosa, S. T. Le, Md. A. Iqbal, I. D. Phillips, and P. Harper, “Transmission performance improvement using random DFB laser based Raman amplification and bidirectional second-order pumping,” Opt. Express, vol. 24, no. 3, pp. 2215–2221, 2016.

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

J. C. Cartledge, F. P. Guiomar, F. R. Kschischang, G. Liga, and M. P. Yankov, “Digital signal processing for fiber nonlinearities [Invited],” Opt. Express, vol. 25, no. 3, pp. 1916–1936, 2017.

D. Lavery, R. Maher, G. Liga, D. Semrau, L. Galdino, and P. Bayvel, “On the bandwidth dependent performance of split transmitter-receiver optical fiber nonlinearity compensation,” Opt. Express, vol. 25, no. 4, pp. 4554–4563, 2017.

L. Galdinoet al., “On the limits of digital back-propagation in the presence of transceiver noise,” Opt. Express, vol. 25, no. 4, pp. 4564–4578, 2017.

G. Saavedra, D. Semrau, L. Galdino, R. I. Killey, and P. Bayvel, “Digital back-propagation for nonlinearity mitigation in distributed Raman amplified links,” Opt. Express, vol. 25, no. 5, pp. 5431–5439, 2017.

Opt. Lett (1)

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, 2017.

Photon. Technol. Lett. (1)

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

Sci. Rep. (1)

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: A study of transceiver performance,” Sci. Rep., vol. 6, 2016, Art. no. .

Other (10)

T. Naito, T. Tanaka, K. Torii, N. Shimojoh, H. Nakamoto, and M. Suyama, “A broadband distributed Raman amplifier for bandwidths beyond 100 nm,” in Proc. Opt. Fiber Commun. Conf., 2002, pp. 1–3.

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Evaluation of non-linear interference in uncompensated links using Raman amplification,” in Proc. Eur. Conf. Opt. Commun., 2012, pp. 1–3.

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proc. 2016 IEEE Photon. Conf., Waikoloa, HI, USA, 2016, pp. 795–796.

A. Carena, G. Bosco, V. Curri, P. Poggiolini, and F. Forghieri, “Impact of the transmitted signal initial dispersion transient on the accuracy of the GN model of non-linear propagation,” in Proc. Eur. Conf. Opt. Commun., 2013, pp. 1–3.

A. Nespolaet al., “Experimental validation of the EGN-model in uncompensated optical links,” in Proc. Opt. Fiber Commun. Conf., 2015, pp. 1–3.

L. Galdinoet al., “Experimental demonstration of modulation-dependent nonlinear interference in optical fibre communication,” in Proc. Eur. Conf. Opt. Commun., 2016, pp. 1–3.

G. Saavedraet al., “Experimental investigation of nonlinear signal distortions in ultra-wideband transmission systems,” in Proc. Opt. Fiber Commun. Conf., 2017, pp. 1–3.

N. A. Shevchenkoet al., “Achievable information rates estimation for 100-nm Raman-amplified optical transmission system,” in Proc. Eur. Conf. Opt. Commun., 2016, pp. 1–3.

A. Splett, C. Kurtzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, pp. 1–3.

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

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