Abstract

Nonlinear Fourier transform (NFT) based transmission technique relies on the integrability of the nonlinear Schrödinger equation (NLSE). However, the lossless NLSE is not directly applicable for the description of light evolution in fibre links with lumped amplification such as Erbium-doped fibre amplifier (EDFA) because of the nonuniform loss and gain evolution. In this case, the path-averaged model is usually applied as an approximation of the true NLSE model including the fibre loss. However, the inaccuracy of the lossless path-average model, even though being small, can also result in a notable performance degradation in NFT-based transmission systems. In this paper, we extend the theoretical approach, which was first proposed for solitons in EDFA systems, to the case of NFT-based systems to constructively diminish the aforementioned performance penalty. Based on the quantitative analysis of distortions due to the use of path-average model, we optimise the signal launch and detection points to minimise the models mismatch. Without loss of generality, we demonstrate how this approach works for the NFT systems that use continuous NFT spectrum modulation (vanishing signals) and NFT main spectrum modulation (periodic signals). Through numerical modelling, we quantify the corresponding improvements in system performance.

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  25. M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear Fourier transform for fiber-optic communications, Part II: eigenvalue communication,” Opt. Express, vol. 24, pp. 18370–18381, 2016.
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  36. M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear fourier transform based transmissions with high order QAM formats,” in Proc. Eur. Conf. Opt. Commun., 2016, pp. 1–3.
  37. M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Statistical analysis of a communication system based on the periodic nonlinear Fourier transform,” in Proc. Aust. Conf. Opt. Fibre Technol., Sydney, 2016, Paper no. ATh1C. 4.
  38. A. Hasegawa and Y. Kodama, “Guiding-center Soliton,” Phys. Rev. Lett., vol. 66, pp. 161–164, 1991.

2017 (1)

2016 (6)

S. Hari, M. I. Yousefi, and F. R. Kschischang, “Multieigenvalue communication,” J. Lightw. Technol., vol. 34, no. 13, pp. 3110–3117, 2016.

S. Hari and F. R. Kschischang, “Bi-directional algorithm for computing discrete spectral amplitudes in the NFT,” J. Lightw. Technol., vol. 34, no. 15, pp. 3529–3537, 2016.

S. A. Derevyanko, J. E. Prilepsky, and S. K. Turitsyn, “Capacity estimates for optical transmission based on the nonlinear Fourier transform,” Nature Commun., vol. 7, 2016, Art. no. .

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods,” Opt. Express, vol. 24, pp. 18353–18369, 2016.

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear Fourier transform for fiber-optic communications, Part II: eigenvalue communication,” Opt. Express, vol. 24, pp. 18370–18381, 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, pp. 2459–2466, 2016.

2015 (4)

L. L. Frumin, O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Efficient numerical method for solving the direct Zakharov–Shabat scattering problem,” J. Opt. Soc. Amer. B, vol. 32, pp. 290–295, 2015.

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express, vol. 23, pp. 8317–8328, 2015.

S. Wahls and H. V. Poor, “Fast numerical nonlinear Fourier transforms,” IEEE Trans. Inf. Theory, vol. 61, no. 2, pp. 6957–6974, 2015.

H. Bülow, “Experimental demonstration of optical signal detection using nonlinear fourier transform,” J. Lightw. Technol., vol. 33, no. 7, pp. 1433–1439, 2015.

2014 (3)

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers,” Opt. Express, vol. 22, pp. 26720–26741, 2014.

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Parts I–III,” IEEE Trans. Inf. Theory, vol. 60, no. 7, pp. 4312–4369, 2014.

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett., vol. 113, 2014, Art. no. .

2013 (2)

2010 (1)

R.-J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

2008 (1)

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett., vol. 101, 2008, Art. no. .

2006 (2)

T J Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-lossless optical links for broad-band transmission and data processing,” IEEE Photon. Technol. Lett., vol. 18, no. 1, pp. 268–270, 2006.

J. D. Ania-Castañónet al., “Ultralong Raman fibre lasers as virtually lossless optical media,” Phys. Rev. Lett., vol. 96, 2006, Art. no. .

1999 (1)

T.-S. Yang, W. L. Kath, and S. K. Turitsyn, “The multiple-scale averaging and dynamics of dispersion-managed optical solitons,” J. Eng. Math., vol. 36, pp. 163–184, 1999.

1998 (1)

1997 (1)

1995 (1)

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun., vol. 117, pp. 65–70, 1995.

1993 (1)

A. Hasegawa and T. Nyu, “Eigenvalue communication,” J. Lightw. Technol., vol. 11, no. 3, pp. 395–399, 1993.

1991 (2)

K. J. Blow and N. J. Doran, “Average soliton dynamics and the operation of soliton systems with lumped amplifiers,” IEEE Photon. Technol. Lett., vol. 3, no. 4, pp. 369–371, 1991.

A. Hasegawa and Y. Kodama, “Guiding-center Soliton,” Phys. Rev. Lett., vol. 66, pp. 161–164, 1991.

1990 (1)

1972 (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Soviet Phys.-JETP, vol. 34, pp. 62–69, 1972.

Ania-Castañón, J. D.

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett., vol. 101, 2008, Art. no. .

J. D. Ania-Castañónet al., “Ultralong Raman fibre lasers as virtually lossless optical media,” Phys. Rev. Lett., vol. 96, 2006, Art. no. .

T J Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-lossless optical links for broad-band transmission and data processing,” IEEE Photon. Technol. Lett., vol. 18, no. 1, pp. 268–270, 2006.

Aref, V.

V. Aref, S. T. Le, and H. Buelow, “Demonstration of fully nonlinear spectrum modulated system in the highly nonlinear optical transmission regime,” in Proc. Eur. Conf. Opt. Commun., 2016, Paper Th.3.B.2.

Belai, O. V.

L. L. Frumin, O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Efficient numerical method for solving the direct Zakharov–Shabat scattering problem,” J. Opt. Soc. Amer. B, vol. 32, pp. 290–295, 2015.

Blow, K. J.

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett., vol. 113, 2014, Art. no. .

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun., vol. 117, pp. 65–70, 1995.

K. J. Blow and N. J. Doran, “Average soliton dynamics and the operation of soliton systems with lumped amplifiers,” IEEE Photon. Technol. Lett., vol. 3, no. 4, pp. 369–371, 1991.

Buelow, H.

V. Aref, S. T. Le, and H. Buelow, “Demonstration of fully nonlinear spectrum modulated system in the highly nonlinear optical transmission regime,” in Proc. Eur. Conf. Opt. Commun., 2016, Paper Th.3.B.2.

Bülow, H.

H. Bülow, “Experimental demonstration of optical signal detection using nonlinear fourier transform,” J. Lightw. Technol., vol. 33, no. 7, pp. 1433–1439, 2015.

Chen, X.

T J Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-lossless optical links for broad-band transmission and data processing,” IEEE Photon. Technol. Lett., vol. 18, no. 1, pp. 268–270, 2006.

Derevyanko, S. A.

S. A. Derevyanko, J. E. Prilepsky, and S. K. Turitsyn, “Capacity estimates for optical transmission based on the nonlinear Fourier transform,” Nature Commun., vol. 7, 2016, Art. no. .

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett., vol. 113, 2014, Art. no. .

J. Prilepsky, S. A. Derevyanko, and S. K. Turitsyn, “Nonlinear spectral management: Linearization of the lossless fiber channel,” Opt. Express, vol. 21, pp. 24344–24367, 2013.

Doran, N. J.

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun., vol. 117, pp. 65–70, 1995.

K. J. Blow and N. J. Doran, “Average soliton dynamics and the operation of soliton systems with lumped amplifiers,” IEEE Photon. Technol. Lett., vol. 3, no. 4, pp. 369–371, 1991.

Ellingham, T J

T J Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-lossless optical links for broad-band transmission and data processing,” IEEE Photon. Technol. Lett., vol. 18, no. 1, pp. 268–270, 2006.

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, pp. 2459–2466, 2016.

Essiambre, R.-J.

R.-J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Forysiak, W.

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun., vol. 117, pp. 65–70, 1995.

Foschini, G.J.

R.-J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Frumin, L. L.

L. L. Frumin, O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Efficient numerical method for solving the direct Zakharov–Shabat scattering problem,” J. Opt. Soc. Amer. B, vol. 32, pp. 290–295, 2015.

Gabitov, I.

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett., vol. 113, 2014, Art. no. .

Goebel, B.

R.-J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Gordon, J.P.

L. F. Mollenauer and J.P. Gordon, Solitons in Optical Fibe, New York, NY, USA: Academic, 2006.

Hari, S.

S. Hari and F. R. Kschischang, “Bi-directional algorithm for computing discrete spectral amplitudes in the NFT,” J. Lightw. Technol., vol. 34, no. 15, pp. 3529–3537, 2016.

S. Hari, M. I. Yousefi, and F. R. Kschischang, “Multieigenvalue communication,” J. Lightw. Technol., vol. 34, no. 13, pp. 3110–3117, 2016.

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, pp. 2459–2466, 2016.

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett., vol. 101, 2008, Art. no. .

Hasegawa, A.

A. Hasegawa and T. Nyu, “Eigenvalue communication,” J. Lightw. Technol., vol. 11, no. 3, pp. 395–399, 1993.

A. Hasegawa and Y. Kodama, “Guiding-center Soliton,” Phys. Rev. Lett., vol. 66, pp. 161–164, 1991.

A. Hasegawa and Y. Kodama, “Guiding-center soliton in optical fibers,” Opt. Lett., vol. 15, pp. 1443–1445, 1990.

Ibbotson, R.

T J Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-lossless optical links for broad-band transmission and data processing,” IEEE Photon. Technol. Lett., vol. 18, no. 1, pp. 268–270, 2006.

Kamalian, M.

Karalekas, V.

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett., vol. 101, 2008, Art. no. .

Kath, W. L.

T.-S. Yang, W. L. Kath, and S. K. Turitsyn, “The multiple-scale averaging and dynamics of dispersion-managed optical solitons,” J. Eng. Math., vol. 36, pp. 163–184, 1999.

T.-S. Yang, W. L. Kath, and S. K. Turitsyn, “Optimal dispersion maps for wavelength-division-multiplexed soliton transmission,” Opt. Lett., vol. 23, pp. 597–599, 1998.

Knox, F. M.

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun., vol. 117, pp. 65–70, 1995.

Kodama, Y.

Kopae, M. Kamalian

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Spectral efficiency estimation in periodic nonlinear Fourier transform based communication systems,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Th2A.54.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Statistical analysis of a communication system based on the periodic nonlinear Fourier transform,” in Proc. Aust. Conf. Opt. Fibre Technol., Sydney, 2016, Paper no. ATh1C. 4.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” in Proc. IEEE 6th Int. Conf. Photon., Kuching, 2016, pp. 1–3.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear fourier transform based transmissions with high order QAM formats,” in Proc. Eur. Conf. Opt. Commun., 2016, pp. 1–3.

Kramer, G.

R.-J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Kschischang, F. R.

S. Hari and F. R. Kschischang, “Bi-directional algorithm for computing discrete spectral amplitudes in the NFT,” J. Lightw. Technol., vol. 34, no. 15, pp. 3529–3537, 2016.

S. Hari, M. I. Yousefi, and F. R. Kschischang, “Multieigenvalue communication,” J. Lightw. Technol., vol. 34, no. 13, pp. 3110–3117, 2016.

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Parts I–III,” IEEE Trans. Inf. Theory, vol. 60, no. 7, pp. 4312–4369, 2014.

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, pp. 2459–2466, 2016.

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods,” Opt. Express, vol. 24, pp. 18353–18369, 2016.

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear Fourier transform for fiber-optic communications, Part II: eigenvalue communication,” Opt. Express, vol. 24, pp. 18370–18381, 2016.

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express, vol. 23, pp. 8317–8328, 2015.

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers,” Opt. Express, vol. 22, pp. 26720–26741, 2014.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Statistical analysis of a communication system based on the periodic nonlinear Fourier transform,” in Proc. Aust. Conf. Opt. Fibre Technol., Sydney, 2016, Paper no. ATh1C. 4.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Spectral efficiency estimation in periodic nonlinear Fourier transform based communication systems,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Th2A.54.

S. T. Leet al., “Achievable information rate of nonlinear inverse synthesis based 16QAM OFDM transmission,” in Proc. 42nd Eur. Conf. Opt. Commun., 2016, Paper Th.2.PS2.SC5.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear fourier transform based transmissions with high order QAM formats,” in Proc. Eur. Conf. Opt. Commun., 2016, pp. 1–3.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” in Proc. IEEE 6th Int. Conf. Photon., Kuching, 2016, pp. 1–3.

S. T. Leet al., “First experimental demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” in Proc. Opt. Fiber Commun. Conf., OSA Tech. Dig., Anaheim, 2016, Paper Tu2A.1.

V. Aref, S. T. Le, and H. Buelow, “Demonstration of fully nonlinear spectrum modulated system in the highly nonlinear optical transmission regime,” in Proc. Eur. Conf. Opt. Commun., 2016, Paper Th.3.B.2.

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proc. IEEE Int. Workshop Signal Process. Adv. Wireless Commun., Stockholm, 2015, pp. 445–449.

Maruta, A.

Mollenauer, L. F.

L. F. Mollenauer and J.P. Gordon, Solitons in Optical Fibe, New York, NY, USA: Academic, 2006.

Nyu, T.

A. Hasegawa and T. Nyu, “Eigenvalue communication,” J. Lightw. Technol., vol. 11, no. 3, pp. 395–399, 1993.

Philips, I. 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, pp. 2459–2466, 2016.

Podivilov, E. V.

L. L. Frumin, O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Efficient numerical method for solving the direct Zakharov–Shabat scattering problem,” J. Opt. Soc. Amer. B, vol. 32, pp. 290–295, 2015.

Poor, H. V.

S. Wahls and H. V. Poor, “Fast numerical nonlinear Fourier transforms,” IEEE Trans. Inf. Theory, vol. 61, no. 2, pp. 6957–6974, 2015.

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proc. IEEE Int. Workshop Signal Process. Adv. Wireless Commun., Stockholm, 2015, pp. 445–449.

Prilepsky, J.

Prilepsky, J. E.

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods,” Opt. Express, vol. 24, pp. 18353–18369, 2016.

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear Fourier transform for fiber-optic communications, Part II: eigenvalue communication,” Opt. Express, vol. 24, pp. 18370–18381, 2016.

S. A. Derevyanko, J. E. Prilepsky, and S. K. Turitsyn, “Capacity estimates for optical transmission based on the nonlinear Fourier transform,” Nature Commun., vol. 7, 2016, Art. no. .

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, pp. 2459–2466, 2016.

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express, vol. 23, pp. 8317–8328, 2015.

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers,” Opt. Express, vol. 22, pp. 26720–26741, 2014.

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett., vol. 113, 2014, Art. no. .

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proc. IEEE Int. Workshop Signal Process. Adv. Wireless Commun., Stockholm, 2015, pp. 445–449.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” in Proc. IEEE 6th Int. Conf. Photon., Kuching, 2016, pp. 1–3.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear fourier transform based transmissions with high order QAM formats,” in Proc. Eur. Conf. Opt. Commun., 2016, pp. 1–3.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Statistical analysis of a communication system based on the periodic nonlinear Fourier transform,” in Proc. Aust. Conf. Opt. Fibre Technol., Sydney, 2016, Paper no. ATh1C. 4.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Spectral efficiency estimation in periodic nonlinear Fourier transform based communication systems,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Th2A.54.

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Soviet Phys.-JETP, vol. 34, pp. 62–69, 1972.

Shapiro, D. A.

L. L. Frumin, O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Efficient numerical method for solving the direct Zakharov–Shabat scattering problem,” J. Opt. Soc. Amer. B, vol. 32, pp. 290–295, 2015.

Turitsyn, S.

Turitsyn, S. K.

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear Fourier transform for fiber-optic communications, Part II: eigenvalue communication,” Opt. Express, vol. 24, pp. 18370–18381, 2016.

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods,” Opt. Express, vol. 24, pp. 18353–18369, 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, pp. 2459–2466, 2016.

S. A. Derevyanko, J. E. Prilepsky, and S. K. Turitsyn, “Capacity estimates for optical transmission based on the nonlinear Fourier transform,” Nature Commun., vol. 7, 2016, Art. no. .

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express, vol. 23, pp. 8317–8328, 2015.

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers,” Opt. Express, vol. 22, pp. 26720–26741, 2014.

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett., vol. 113, 2014, Art. no. .

E. G. Turitsyna and S. K. Turitsyn, “Digital signal processing based on inverse scattering transform,” Opt. Lett., vol. 38, pp. 4186–4188, 2013.

J. Prilepsky, S. A. Derevyanko, and S. K. Turitsyn, “Nonlinear spectral management: Linearization of the lossless fiber channel,” Opt. Express, vol. 21, pp. 24344–24367, 2013.

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett., vol. 101, 2008, Art. no. .

T J Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-lossless optical links for broad-band transmission and data processing,” IEEE Photon. Technol. Lett., vol. 18, no. 1, pp. 268–270, 2006.

T.-S. Yang, W. L. Kath, and S. K. Turitsyn, “The multiple-scale averaging and dynamics of dispersion-managed optical solitons,” J. Eng. Math., vol. 36, pp. 163–184, 1999.

T.-S. Yang, W. L. Kath, and S. K. Turitsyn, “Optimal dispersion maps for wavelength-division-multiplexed soliton transmission,” Opt. Lett., vol. 23, pp. 597–599, 1998.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Statistical analysis of a communication system based on the periodic nonlinear Fourier transform,” in Proc. Aust. Conf. Opt. Fibre Technol., Sydney, 2016, Paper no. ATh1C. 4.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Spectral efficiency estimation in periodic nonlinear Fourier transform based communication systems,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Th2A.54.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” in Proc. IEEE 6th Int. Conf. Photon., Kuching, 2016, pp. 1–3.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear fourier transform based transmissions with high order QAM formats,” in Proc. Eur. Conf. Opt. Commun., 2016, pp. 1–3.

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proc. IEEE Int. Workshop Signal Process. Adv. Wireless Commun., Stockholm, 2015, pp. 445–449.

Turitsyna, E. G.

Wahls, S.

S. Wahls and H. V. Poor, “Fast numerical nonlinear Fourier transforms,” IEEE Trans. Inf. Theory, vol. 61, no. 2, pp. 6957–6974, 2015.

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proc. IEEE Int. Workshop Signal Process. Adv. Wireless Commun., Stockholm, 2015, pp. 445–449.

Winzer, P.J.

R.-J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Yang, T.-S.

T.-S. Yang, W. L. Kath, and S. K. Turitsyn, “The multiple-scale averaging and dynamics of dispersion-managed optical solitons,” J. Eng. Math., vol. 36, pp. 163–184, 1999.

T.-S. Yang, W. L. Kath, and S. K. Turitsyn, “Optimal dispersion maps for wavelength-division-multiplexed soliton transmission,” Opt. Lett., vol. 23, pp. 597–599, 1998.

Yousefi, M. I.

S. Hari, M. I. Yousefi, and F. R. Kschischang, “Multieigenvalue communication,” J. Lightw. Technol., vol. 34, no. 13, pp. 3110–3117, 2016.

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Parts I–III,” IEEE Trans. Inf. Theory, vol. 60, no. 7, pp. 4312–4369, 2014.

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Soviet Phys.-JETP, vol. 34, pp. 62–69, 1972.

Zhang, L.

T J Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-lossless optical links for broad-band transmission and data processing,” IEEE Photon. Technol. Lett., vol. 18, no. 1, pp. 268–270, 2006.

IEEE Photon. Technol. Lett. (2)

T J Ellingham, J. D. Ania-Castañón, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Quasi-lossless optical links for broad-band transmission and data processing,” IEEE Photon. Technol. Lett., vol. 18, no. 1, pp. 268–270, 2006.

K. J. Blow and N. J. Doran, “Average soliton dynamics and the operation of soliton systems with lumped amplifiers,” IEEE Photon. Technol. Lett., vol. 3, no. 4, pp. 369–371, 1991.

IEEE Trans. Inf. Theory (2)

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, Parts I–III,” IEEE Trans. Inf. Theory, vol. 60, no. 7, pp. 4312–4369, 2014.

S. Wahls and H. V. Poor, “Fast numerical nonlinear Fourier transforms,” IEEE Trans. Inf. Theory, vol. 61, no. 2, pp. 6957–6974, 2015.

J. Eng. Math. (1)

T.-S. Yang, W. L. Kath, and S. K. Turitsyn, “The multiple-scale averaging and dynamics of dispersion-managed optical solitons,” J. Eng. Math., vol. 36, pp. 163–184, 1999.

J. Lightw. Technol. (6)

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, pp. 2459–2466, 2016.

A. Hasegawa and T. Nyu, “Eigenvalue communication,” J. Lightw. Technol., vol. 11, no. 3, pp. 395–399, 1993.

H. Bülow, “Experimental demonstration of optical signal detection using nonlinear fourier transform,” J. Lightw. Technol., vol. 33, no. 7, pp. 1433–1439, 2015.

S. Hari, M. I. Yousefi, and F. R. Kschischang, “Multieigenvalue communication,” J. Lightw. Technol., vol. 34, no. 13, pp. 3110–3117, 2016.

S. Hari and F. R. Kschischang, “Bi-directional algorithm for computing discrete spectral amplitudes in the NFT,” J. Lightw. Technol., vol. 34, no. 15, pp. 3529–3537, 2016.

R.-J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

J. Opt. Soc. Amer. B (1)

L. L. Frumin, O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Efficient numerical method for solving the direct Zakharov–Shabat scattering problem,” J. Opt. Soc. Amer. B, vol. 32, pp. 290–295, 2015.

Nature Commun. (1)

S. A. Derevyanko, J. E. Prilepsky, and S. K. Turitsyn, “Capacity estimates for optical transmission based on the nonlinear Fourier transform,” Nature Commun., vol. 7, 2016, Art. no. .

Opt. Commun. (1)

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun., vol. 117, pp. 65–70, 1995.

Opt. Express (5)

Opt. Lett. (4)

Optica (1)

Phys. Rev. Lett. (4)

J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, “Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels,” Phys. Rev. Lett., vol. 113, 2014, Art. no. .

J. D. Ania-Castañónet al., “Ultralong Raman fibre lasers as virtually lossless optical media,” Phys. Rev. Lett., vol. 96, 2006, Art. no. .

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett., vol. 101, 2008, Art. no. .

A. Hasegawa and Y. Kodama, “Guiding-center Soliton,” Phys. Rev. Lett., vol. 66, pp. 161–164, 1991.

Soviet Phys.-JETP (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Soviet Phys.-JETP, vol. 34, pp. 62–69, 1972.

Other (9)

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proc. IEEE Int. Workshop Signal Process. Adv. Wireless Commun., Stockholm, 2015, pp. 445–449.

V. Aref, S. T. Le, and H. Buelow, “Demonstration of fully nonlinear spectrum modulated system in the highly nonlinear optical transmission regime,” in Proc. Eur. Conf. Opt. Commun., 2016, Paper Th.3.B.2.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Periodic nonlinear fourier transform based transmissions with high order QAM formats,” in Proc. Eur. Conf. Opt. Commun., 2016, pp. 1–3.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Statistical analysis of a communication system based on the periodic nonlinear Fourier transform,” in Proc. Aust. Conf. Opt. Fibre Technol., Sydney, 2016, Paper no. ATh1C. 4.

S. T. Leet al., “Achievable information rate of nonlinear inverse synthesis based 16QAM OFDM transmission,” in Proc. 42nd Eur. Conf. Opt. Commun., 2016, Paper Th.2.PS2.SC5.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” in Proc. IEEE 6th Int. Conf. Photon., Kuching, 2016, pp. 1–3.

S. T. Leet al., “First experimental demonstration of nonlinear inverse synthesis transmission over transoceanic distances,” in Proc. Opt. Fiber Commun. Conf., OSA Tech. Dig., Anaheim, 2016, Paper Tu2A.1.

L. F. Mollenauer and J.P. Gordon, Solitons in Optical Fibe, New York, NY, USA: Academic, 2006.

M. Kamalian Kopae, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Spectral efficiency estimation in periodic nonlinear Fourier transform based communication systems,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Th2A.54.

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