Abstract

In this paper we propose the design of communication systems based on using periodic nonlinear Fourier transform (PNFT), following the introduction of the method in the Part I. We show that the famous “eigenvalue communication” idea [A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993)] can also be generalized for the PNFT application: In this case, the main spectrum attributed to the PNFT signal decomposition remains constant with the propagation down the optical fiber link. Therefore, the main PNFT spectrum can be encoded with data in the same way as soliton eigenvalues in the original proposal. The results are presented in terms of the bit-error rate (BER) values for different modulation techniques and different constellation sizes vs. the propagation distance, showing a good potential of the technique.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods

Morteza Kamalian, Jaroslaw E. Prilepsky, Son Thai Le, and Sergei K. Turitsyn
Opt. Express 24(16) 18353-18369 (2016)

Nonlinear spectral management: Linearization of the lossless fiber channel

Jaroslaw E. Prilepsky, Stanislav A. Derevyanko, and Sergei K. Turitsyn
Opt. Express 21(20) 24344-24367 (2013)

High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform

Tao Gui, Chao Lu, Alan Pak Tao Lau, and P. K. A. Wai
Opt. Express 25(17) 20286-20297 (2017)

References

  • View by:
  • |
  • |
  • |

  1. S. Wahls and H. V. Poor, “Fast numerical nonlinear Fourier transforms,” IEEE Trans. Inf. Theory 61, 6957–6974 (2015).
    [Crossref]
  2. A. Hasegawa and T. Nyu, “Eigenvalue communication,” J. Lightwave Technol. 11, 395–399 (1993).
    [Crossref]
  3. S. Hari, F. Kschischang, and M. Yousefi, “Multi–eigenvalue communication via the nonlinear Fourier transform,” in 27th Biennial Symposium on Communications (QBSC), 92–95 (2014).
  4. A. Maruta, Y. Matsuda, H. Terauchi, and A. Toyota, “Digital coherent technology-based eigenvalue modulated optical fiber transmission system,” in Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications, Ch. 19, edts. K. Porsezian and R. Ganapathy, eds., pp. 491–506 (CRC, 2015).
  5. A. Maruta, “Eigenvalue modulated optical transmission system (invited),” in The 20th OptoElectronics and Communications Conference (OECC), Shanghai, China, Paper JThA.21 (2015).
  6. Z. Dong and et al., “Nonlinear frequency division multiplexed transmissions based on NFT,” IEEE Photon. Tech. Lett. 27, 1621–1623 (2015).
    [Crossref]
  7. 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. 113, 013901 (2014).
    [Crossref] [PubMed]
  8. S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers,” Opt. Express 22, 26720–26741 (2014).
    [Crossref] [PubMed]
  9. S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express 23, 8317–8328 (2015).
    [Crossref] [PubMed]
  10. E. R. Tracy and H. H. Chen, “Nonlinear self-modulation: an exactly solvable model,” Phys. Rev. A 37, 815–839 (1988).
    [Crossref]
  11. G. P. Agrawal, Nonlinear Fiber Optics, 5th Ed. (Academic, 2013).
  12. 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 Physics-JETP 34, 62–69 (1972).
  13. S. T. Le, J. E. Prilepsky, M. Kamalian, P. Rosa, M. Tan, J. D. Ania-Castanon, P. Harper, and S. K. Turitsyn, “Optimized nonlinear inverse synthesis for optical links with distributed Raman amplification,” in 41st European Conference on Optical Communications (ECOC), Valencia, Spain, paper Tu 1.1.3 (2015).
  14. S. T. Le, J. E. Prilepsky, P. Rosa, J. D. Ania-Castanon, and S. K. Turitsyn, “Nonlinear inverse synthesis for optical links with distributed Raman amplification,” J. Lightwave Technol. 34, 1778–1785 (2016).
    [Crossref]
  15. M. Tan, P. Rosa, I. D. Phillips, and P. Harper, “Long–haul transmission performance evaluation of ultra–long Raman fiber laser based amplification influenced by second order co–pumping,” Asia Communications and Photonics Conference, Shanghai, China, ATh1E-4 (2014).
  16. S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proceedings of IEEE 16th International Workshop in Signal Processing Advances in Wireless Communications (SPAWC), Stockholm, Sweden, pp. 445–449 (2015).
  17. E. R. Tracy, “Topics in nonlinear wave theory with applications,” PhD Thesis, Univ. of Maryland, College Park, MD, USA (1984).
  18. O. R. Its and V. P. Kotlyarov, “Explicit formulas for the solutions of a nonlinear Schrödinger equation,” Doklady Akad. Nauk Ukrainian SSR, ser. A vol. 10, 965–968 (1976); English translation available at http://arxiv.org/abs/1401.4445v1 .
  19. A. Osborne, Nonlinear Ocean Waves and the Inverse Scattering Transform, 1st ed. (Academic, 2010).
  20. A. Bobenko and C. Klein, eds. Computational Approach to Riemann Surfaces, No. 2013, (Springer Science and Business Media, 2011).
    [Crossref]
  21. M. Bertola and P. Giavedoni, “A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems,” J. Math. Phys. 56, 061507 (2015).
    [Crossref]
  22. M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” IEEE 6th International Conference on Photonics (ICP), Sarawak, Malaysia (2016).
  23. H. Steudel and R. Meinel, “Periodic solutions generated by Bäcklund transformations,” Physica D 21, 155–162 (1986).
    [Crossref]
  24. P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Evaluation of the computational effort for chromatic dispersion compensation in coherent optical PM-OFDM and PM-QAM systems,” Opt. Express 17, 1385–1403 (2009).
    [Crossref] [PubMed]
  25. R. A. Shafik, M. S. Rahman, and A. H. M. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics,” IEEE International Conference on Electrical and Computer Engineering (ICECE), pp. 408–411 (2006).
  26. W. Shieh, W. Chen, and R.S. Tucker, “Polarisation mode dispersion mitigation in coherent optical orthogonal frequency division multiplexed systems,” Electron. Lett. 42, 996–997 (2006).
    [Crossref]
  27. T. Hirooka and M. Nakazawa, “Linear and nonlinear propagation of optical Nyquist pulses in fibers,” Opt. Express 20, 19836–19849 (2012).
    [Crossref] [PubMed]
  28. M. Cvijetic and P. Magill, “Delivering on the 100GbE promise (Message from the Series Editor),” IEEE Comm. Magazine 45, 2–3 (2007).
    [Crossref]
  29. M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part II: numerical methods,” IEEE Trans. Inf. Theory 60, 4329–4345 (2014).
    [Crossref]
  30. M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part III: spectrum modulation,” IEEE Trans. Inf. Theory 60, 4346–4369 (2014).
    [Crossref]

2016 (1)

2015 (4)

M. Bertola and P. Giavedoni, “A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems,” J. Math. Phys. 56, 061507 (2015).
[Crossref]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express 23, 8317–8328 (2015).
[Crossref] [PubMed]

S. Wahls and H. V. Poor, “Fast numerical nonlinear Fourier transforms,” IEEE Trans. Inf. Theory 61, 6957–6974 (2015).
[Crossref]

Z. Dong and et al., “Nonlinear frequency division multiplexed transmissions based on NFT,” IEEE Photon. Tech. Lett. 27, 1621–1623 (2015).
[Crossref]

2014 (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. 113, 013901 (2014).
[Crossref] [PubMed]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers,” Opt. Express 22, 26720–26741 (2014).
[Crossref] [PubMed]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part II: numerical methods,” IEEE Trans. Inf. Theory 60, 4329–4345 (2014).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part III: spectrum modulation,” IEEE Trans. Inf. Theory 60, 4346–4369 (2014).
[Crossref]

2012 (1)

2009 (1)

2007 (1)

M. Cvijetic and P. Magill, “Delivering on the 100GbE promise (Message from the Series Editor),” IEEE Comm. Magazine 45, 2–3 (2007).
[Crossref]

2006 (1)

W. Shieh, W. Chen, and R.S. Tucker, “Polarisation mode dispersion mitigation in coherent optical orthogonal frequency division multiplexed systems,” Electron. Lett. 42, 996–997 (2006).
[Crossref]

1993 (1)

A. Hasegawa and T. Nyu, “Eigenvalue communication,” J. Lightwave Technol. 11, 395–399 (1993).
[Crossref]

1988 (1)

E. R. Tracy and H. H. Chen, “Nonlinear self-modulation: an exactly solvable model,” Phys. Rev. A 37, 815–839 (1988).
[Crossref]

1986 (1)

H. Steudel and R. Meinel, “Periodic solutions generated by Bäcklund transformations,” Physica D 21, 155–162 (1986).
[Crossref]

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 Physics-JETP 34, 62–69 (1972).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 5th Ed. (Academic, 2013).

Ania-Castanon, J. D.

S. T. Le, J. E. Prilepsky, P. Rosa, J. D. Ania-Castanon, and S. K. Turitsyn, “Nonlinear inverse synthesis for optical links with distributed Raman amplification,” J. Lightwave Technol. 34, 1778–1785 (2016).
[Crossref]

S. T. Le, J. E. Prilepsky, M. Kamalian, P. Rosa, M. Tan, J. D. Ania-Castanon, P. Harper, and S. K. Turitsyn, “Optimized nonlinear inverse synthesis for optical links with distributed Raman amplification,” in 41st European Conference on Optical Communications (ECOC), Valencia, Spain, paper Tu 1.1.3 (2015).

Bertola, M.

M. Bertola and P. Giavedoni, “A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems,” J. Math. Phys. 56, 061507 (2015).
[Crossref]

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. 113, 013901 (2014).
[Crossref] [PubMed]

Carena, A.

Chen, H. H.

E. R. Tracy and H. H. Chen, “Nonlinear self-modulation: an exactly solvable model,” Phys. Rev. A 37, 815–839 (1988).
[Crossref]

Chen, W.

W. Shieh, W. Chen, and R.S. Tucker, “Polarisation mode dispersion mitigation in coherent optical orthogonal frequency division multiplexed systems,” Electron. Lett. 42, 996–997 (2006).
[Crossref]

Curri, V.

Cvijetic, M.

M. Cvijetic and P. Magill, “Delivering on the 100GbE promise (Message from the Series Editor),” IEEE Comm. Magazine 45, 2–3 (2007).
[Crossref]

Derevyanko, S. A.

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. 113, 013901 (2014).
[Crossref] [PubMed]

Dong, Z.

Z. Dong and et al., “Nonlinear frequency division multiplexed transmissions based on NFT,” IEEE Photon. Tech. Lett. 27, 1621–1623 (2015).
[Crossref]

Forghieri, F.

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. 113, 013901 (2014).
[Crossref] [PubMed]

Giavedoni, P.

M. Bertola and P. Giavedoni, “A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems,” J. Math. Phys. 56, 061507 (2015).
[Crossref]

Hari, S.

S. Hari, F. Kschischang, and M. Yousefi, “Multi–eigenvalue communication via the nonlinear Fourier transform,” in 27th Biennial Symposium on Communications (QBSC), 92–95 (2014).

Harper, P.

S. T. Le, J. E. Prilepsky, M. Kamalian, P. Rosa, M. Tan, J. D. Ania-Castanon, P. Harper, and S. K. Turitsyn, “Optimized nonlinear inverse synthesis for optical links with distributed Raman amplification,” in 41st European Conference on Optical Communications (ECOC), Valencia, Spain, paper Tu 1.1.3 (2015).

M. Tan, P. Rosa, I. D. Phillips, and P. Harper, “Long–haul transmission performance evaluation of ultra–long Raman fiber laser based amplification influenced by second order co–pumping,” Asia Communications and Photonics Conference, Shanghai, China, ATh1E-4 (2014).

Hasegawa, A.

A. Hasegawa and T. Nyu, “Eigenvalue communication,” J. Lightwave Technol. 11, 395–399 (1993).
[Crossref]

Hirooka, T.

Islam, A. H. M.

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

Its, O. R.

O. R. Its and V. P. Kotlyarov, “Explicit formulas for the solutions of a nonlinear Schrödinger equation,” Doklady Akad. Nauk Ukrainian SSR, ser. A vol. 10, 965–968 (1976); English translation available at http://arxiv.org/abs/1401.4445v1 .

Kamalian, M.

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” IEEE 6th International Conference on Photonics (ICP), Sarawak, Malaysia (2016).

S. T. Le, J. E. Prilepsky, M. Kamalian, P. Rosa, M. Tan, J. D. Ania-Castanon, P. Harper, and S. K. Turitsyn, “Optimized nonlinear inverse synthesis for optical links with distributed Raman amplification,” in 41st European Conference on Optical Communications (ECOC), Valencia, Spain, paper Tu 1.1.3 (2015).

Kotlyarov, V. P.

O. R. Its and V. P. Kotlyarov, “Explicit formulas for the solutions of a nonlinear Schrödinger equation,” Doklady Akad. Nauk Ukrainian SSR, ser. A vol. 10, 965–968 (1976); English translation available at http://arxiv.org/abs/1401.4445v1 .

Kschischang, F.

S. Hari, F. Kschischang, and M. Yousefi, “Multi–eigenvalue communication via the nonlinear Fourier transform,” in 27th Biennial Symposium on Communications (QBSC), 92–95 (2014).

Kschischang, F. R.

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part II: numerical methods,” IEEE Trans. Inf. Theory 60, 4329–4345 (2014).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part III: spectrum modulation,” IEEE Trans. Inf. Theory 60, 4346–4369 (2014).
[Crossref]

Le, S. T.

S. T. Le, J. E. Prilepsky, P. Rosa, J. D. Ania-Castanon, and S. K. Turitsyn, “Nonlinear inverse synthesis for optical links with distributed Raman amplification,” J. Lightwave Technol. 34, 1778–1785 (2016).
[Crossref]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express 23, 8317–8328 (2015).
[Crossref] [PubMed]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers,” Opt. Express 22, 26720–26741 (2014).
[Crossref] [PubMed]

S. T. Le, J. E. Prilepsky, M. Kamalian, P. Rosa, M. Tan, J. D. Ania-Castanon, P. Harper, and S. K. Turitsyn, “Optimized nonlinear inverse synthesis for optical links with distributed Raman amplification,” in 41st European Conference on Optical Communications (ECOC), Valencia, Spain, paper Tu 1.1.3 (2015).

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” IEEE 6th International Conference on Photonics (ICP), Sarawak, Malaysia (2016).

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proceedings of IEEE 16th International Workshop in Signal Processing Advances in Wireless Communications (SPAWC), Stockholm, Sweden, pp. 445–449 (2015).

Magill, P.

M. Cvijetic and P. Magill, “Delivering on the 100GbE promise (Message from the Series Editor),” IEEE Comm. Magazine 45, 2–3 (2007).
[Crossref]

Maruta, A.

A. Maruta, “Eigenvalue modulated optical transmission system (invited),” in The 20th OptoElectronics and Communications Conference (OECC), Shanghai, China, Paper JThA.21 (2015).

A. Maruta, Y. Matsuda, H. Terauchi, and A. Toyota, “Digital coherent technology-based eigenvalue modulated optical fiber transmission system,” in Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications, Ch. 19, edts. K. Porsezian and R. Ganapathy, eds., pp. 491–506 (CRC, 2015).

Matsuda, Y.

A. Maruta, Y. Matsuda, H. Terauchi, and A. Toyota, “Digital coherent technology-based eigenvalue modulated optical fiber transmission system,” in Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications, Ch. 19, edts. K. Porsezian and R. Ganapathy, eds., pp. 491–506 (CRC, 2015).

Meinel, R.

H. Steudel and R. Meinel, “Periodic solutions generated by Bäcklund transformations,” Physica D 21, 155–162 (1986).
[Crossref]

Nakazawa, M.

Nyu, T.

A. Hasegawa and T. Nyu, “Eigenvalue communication,” J. Lightwave Technol. 11, 395–399 (1993).
[Crossref]

Osborne, A.

A. Osborne, Nonlinear Ocean Waves and the Inverse Scattering Transform, 1st ed. (Academic, 2010).

Phillips, I. D.

M. Tan, P. Rosa, I. D. Phillips, and P. Harper, “Long–haul transmission performance evaluation of ultra–long Raman fiber laser based amplification influenced by second order co–pumping,” Asia Communications and Photonics Conference, Shanghai, China, ATh1E-4 (2014).

Poggiolini, P.

Poor, H. V.

S. Wahls and H. V. Poor, “Fast numerical nonlinear Fourier transforms,” IEEE Trans. Inf. Theory 61, 6957–6974 (2015).
[Crossref]

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proceedings of IEEE 16th International Workshop in Signal Processing Advances in Wireless Communications (SPAWC), Stockholm, Sweden, pp. 445–449 (2015).

Prilepsky, J. E.

S. T. Le, J. E. Prilepsky, P. Rosa, J. D. Ania-Castanon, and S. K. Turitsyn, “Nonlinear inverse synthesis for optical links with distributed Raman amplification,” J. Lightwave Technol. 34, 1778–1785 (2016).
[Crossref]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express 23, 8317–8328 (2015).
[Crossref] [PubMed]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers,” Opt. Express 22, 26720–26741 (2014).
[Crossref] [PubMed]

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. 113, 013901 (2014).
[Crossref] [PubMed]

S. T. Le, J. E. Prilepsky, M. Kamalian, P. Rosa, M. Tan, J. D. Ania-Castanon, P. Harper, and S. K. Turitsyn, “Optimized nonlinear inverse synthesis for optical links with distributed Raman amplification,” in 41st European Conference on Optical Communications (ECOC), Valencia, Spain, paper Tu 1.1.3 (2015).

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proceedings of IEEE 16th International Workshop in Signal Processing Advances in Wireless Communications (SPAWC), Stockholm, Sweden, pp. 445–449 (2015).

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” IEEE 6th International Conference on Photonics (ICP), Sarawak, Malaysia (2016).

Rahman, M. S.

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

Rosa, P.

S. T. Le, J. E. Prilepsky, P. Rosa, J. D. Ania-Castanon, and S. K. Turitsyn, “Nonlinear inverse synthesis for optical links with distributed Raman amplification,” J. Lightwave Technol. 34, 1778–1785 (2016).
[Crossref]

S. T. Le, J. E. Prilepsky, M. Kamalian, P. Rosa, M. Tan, J. D. Ania-Castanon, P. Harper, and S. K. Turitsyn, “Optimized nonlinear inverse synthesis for optical links with distributed Raman amplification,” in 41st European Conference on Optical Communications (ECOC), Valencia, Spain, paper Tu 1.1.3 (2015).

M. Tan, P. Rosa, I. D. Phillips, and P. Harper, “Long–haul transmission performance evaluation of ultra–long Raman fiber laser based amplification influenced by second order co–pumping,” Asia Communications and Photonics Conference, Shanghai, China, ATh1E-4 (2014).

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 Physics-JETP 34, 62–69 (1972).

Shafik, R. A.

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

Shieh, W.

W. Shieh, W. Chen, and R.S. Tucker, “Polarisation mode dispersion mitigation in coherent optical orthogonal frequency division multiplexed systems,” Electron. Lett. 42, 996–997 (2006).
[Crossref]

Steudel, H.

H. Steudel and R. Meinel, “Periodic solutions generated by Bäcklund transformations,” Physica D 21, 155–162 (1986).
[Crossref]

Tan, M.

M. Tan, P. Rosa, I. D. Phillips, and P. Harper, “Long–haul transmission performance evaluation of ultra–long Raman fiber laser based amplification influenced by second order co–pumping,” Asia Communications and Photonics Conference, Shanghai, China, ATh1E-4 (2014).

S. T. Le, J. E. Prilepsky, M. Kamalian, P. Rosa, M. Tan, J. D. Ania-Castanon, P. Harper, and S. K. Turitsyn, “Optimized nonlinear inverse synthesis for optical links with distributed Raman amplification,” in 41st European Conference on Optical Communications (ECOC), Valencia, Spain, paper Tu 1.1.3 (2015).

Terauchi, H.

A. Maruta, Y. Matsuda, H. Terauchi, and A. Toyota, “Digital coherent technology-based eigenvalue modulated optical fiber transmission system,” in Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications, Ch. 19, edts. K. Porsezian and R. Ganapathy, eds., pp. 491–506 (CRC, 2015).

Toyota, A.

A. Maruta, Y. Matsuda, H. Terauchi, and A. Toyota, “Digital coherent technology-based eigenvalue modulated optical fiber transmission system,” in Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications, Ch. 19, edts. K. Porsezian and R. Ganapathy, eds., pp. 491–506 (CRC, 2015).

Tracy, E. R.

E. R. Tracy and H. H. Chen, “Nonlinear self-modulation: an exactly solvable model,” Phys. Rev. A 37, 815–839 (1988).
[Crossref]

E. R. Tracy, “Topics in nonlinear wave theory with applications,” PhD Thesis, Univ. of Maryland, College Park, MD, USA (1984).

Tucker, R.S.

W. Shieh, W. Chen, and R.S. Tucker, “Polarisation mode dispersion mitigation in coherent optical orthogonal frequency division multiplexed systems,” Electron. Lett. 42, 996–997 (2006).
[Crossref]

Turitsyn, S. K.

S. T. Le, J. E. Prilepsky, P. Rosa, J. D. Ania-Castanon, and S. K. Turitsyn, “Nonlinear inverse synthesis for optical links with distributed Raman amplification,” J. Lightwave Technol. 34, 1778–1785 (2016).
[Crossref]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis technique for optical links with lumped amplification,” Opt. Express 23, 8317–8328 (2015).
[Crossref] [PubMed]

S. T. Le, J. E. Prilepsky, and S. K. Turitsyn, “Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers,” Opt. Express 22, 26720–26741 (2014).
[Crossref] [PubMed]

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. 113, 013901 (2014).
[Crossref] [PubMed]

S. T. Le, J. E. Prilepsky, M. Kamalian, P. Rosa, M. Tan, J. D. Ania-Castanon, P. Harper, and S. K. Turitsyn, “Optimized nonlinear inverse synthesis for optical links with distributed Raman amplification,” in 41st European Conference on Optical Communications (ECOC), Valencia, Spain, paper Tu 1.1.3 (2015).

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proceedings of IEEE 16th International Workshop in Signal Processing Advances in Wireless Communications (SPAWC), Stockholm, Sweden, pp. 445–449 (2015).

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” IEEE 6th International Conference on Photonics (ICP), Sarawak, Malaysia (2016).

Wahls, S.

S. Wahls and H. V. Poor, “Fast numerical nonlinear Fourier transforms,” IEEE Trans. Inf. Theory 61, 6957–6974 (2015).
[Crossref]

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proceedings of IEEE 16th International Workshop in Signal Processing Advances in Wireless Communications (SPAWC), Stockholm, Sweden, pp. 445–449 (2015).

Yousefi, M.

S. Hari, F. Kschischang, and M. Yousefi, “Multi–eigenvalue communication via the nonlinear Fourier transform,” in 27th Biennial Symposium on Communications (QBSC), 92–95 (2014).

Yousefi, M. I.

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part III: spectrum modulation,” IEEE Trans. Inf. Theory 60, 4346–4369 (2014).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part II: numerical methods,” IEEE Trans. Inf. Theory 60, 4329–4345 (2014).
[Crossref]

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 Physics-JETP 34, 62–69 (1972).

Electron. Lett. (1)

W. Shieh, W. Chen, and R.S. Tucker, “Polarisation mode dispersion mitigation in coherent optical orthogonal frequency division multiplexed systems,” Electron. Lett. 42, 996–997 (2006).
[Crossref]

IEEE Comm. Magazine (1)

M. Cvijetic and P. Magill, “Delivering on the 100GbE promise (Message from the Series Editor),” IEEE Comm. Magazine 45, 2–3 (2007).
[Crossref]

IEEE Photon. Tech. Lett. (1)

Z. Dong and et al., “Nonlinear frequency division multiplexed transmissions based on NFT,” IEEE Photon. Tech. Lett. 27, 1621–1623 (2015).
[Crossref]

IEEE Trans. Inf. Theory (3)

S. Wahls and H. V. Poor, “Fast numerical nonlinear Fourier transforms,” IEEE Trans. Inf. Theory 61, 6957–6974 (2015).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part II: numerical methods,” IEEE Trans. Inf. Theory 60, 4329–4345 (2014).
[Crossref]

M. I. Yousefi and F. R. Kschischang, “Information transmission using the nonlinear Fourier transform, part III: spectrum modulation,” IEEE Trans. Inf. Theory 60, 4346–4369 (2014).
[Crossref]

J. Lightwave Technol. (2)

J. Math. Phys. (1)

M. Bertola and P. Giavedoni, “A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems,” J. Math. Phys. 56, 061507 (2015).
[Crossref]

Opt. Express (4)

Phys. Rev. A (1)

E. R. Tracy and H. H. Chen, “Nonlinear self-modulation: an exactly solvable model,” Phys. Rev. A 37, 815–839 (1988).
[Crossref]

Phys. Rev. Lett. (1)

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. 113, 013901 (2014).
[Crossref] [PubMed]

Physica D (1)

H. Steudel and R. Meinel, “Periodic solutions generated by Bäcklund transformations,” Physica D 21, 155–162 (1986).
[Crossref]

Soviet Physics-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 Physics-JETP 34, 62–69 (1972).

Other (13)

S. T. Le, J. E. Prilepsky, M. Kamalian, P. Rosa, M. Tan, J. D. Ania-Castanon, P. Harper, and S. K. Turitsyn, “Optimized nonlinear inverse synthesis for optical links with distributed Raman amplification,” in 41st European Conference on Optical Communications (ECOC), Valencia, Spain, paper Tu 1.1.3 (2015).

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

M. Tan, P. Rosa, I. D. Phillips, and P. Harper, “Long–haul transmission performance evaluation of ultra–long Raman fiber laser based amplification influenced by second order co–pumping,” Asia Communications and Photonics Conference, Shanghai, China, ATh1E-4 (2014).

S. Wahls, S. T. Le, J. E. Prilepsky, H. V. Poor, and S. K. Turitsyn, “Digital backpropagation in the nonlinear Fourier domain,” in Proceedings of IEEE 16th International Workshop in Signal Processing Advances in Wireless Communications (SPAWC), Stockholm, Sweden, pp. 445–449 (2015).

E. R. Tracy, “Topics in nonlinear wave theory with applications,” PhD Thesis, Univ. of Maryland, College Park, MD, USA (1984).

O. R. Its and V. P. Kotlyarov, “Explicit formulas for the solutions of a nonlinear Schrödinger equation,” Doklady Akad. Nauk Ukrainian SSR, ser. A vol. 10, 965–968 (1976); English translation available at http://arxiv.org/abs/1401.4445v1 .

A. Osborne, Nonlinear Ocean Waves and the Inverse Scattering Transform, 1st ed. (Academic, 2010).

A. Bobenko and C. Klein, eds. Computational Approach to Riemann Surfaces, No. 2013, (Springer Science and Business Media, 2011).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 5th Ed. (Academic, 2013).

M. Kamalian, J. E. Prilepsky, S. T. Le, and S. K. Turitsyn, “Optical communication based on the periodic nonlinear Fourier transform signal processing,” IEEE 6th International Conference on Photonics (ICP), Sarawak, Malaysia (2016).

S. Hari, F. Kschischang, and M. Yousefi, “Multi–eigenvalue communication via the nonlinear Fourier transform,” in 27th Biennial Symposium on Communications (QBSC), 92–95 (2014).

A. Maruta, Y. Matsuda, H. Terauchi, and A. Toyota, “Digital coherent technology-based eigenvalue modulated optical fiber transmission system,” in Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications, Ch. 19, edts. K. Porsezian and R. Ganapathy, eds., pp. 491–506 (CRC, 2015).

A. Maruta, “Eigenvalue modulated optical transmission system (invited),” in The 20th OptoElectronics and Communications Conference (OECC), Shanghai, China, Paper JThA.21 (2015).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 General design of the NFT-based communication system concept. The data stream is mapped onto the NS (here – on the main spectrum) and then the signal is constructed from this main spectrum. At the receiver side, performing the direct transform, the original data are retrieved.
Fig. 2
Fig. 2 The two-phase signal in Eq. (9) with λ1 = 1.2 i (see the explanations in the text) and the time period T0 = 3 defining the remaining values λ2,3 (left). The corresponding main spectrum is shown in the right panel.
Fig. 3
Fig. 3 Main spectrum of an unperturbed plane wave with T0 = 4 and A = 2 (left), and a perturbed one with cosine waves with amplitudes ϵ1 and ϵ2.
Fig. 4
Fig. 4 Perturbed plane wave (subsection 3.2) with ϵ = 0.045 and period T0 = 3.55 (left), and its main spectrum (right).
Fig. 5
Fig. 5 Left: error vs. the number of samples in the B2B scenario for modulated CW and two-phase signals. Right: BER vs. distance in a single-symbol transmission with the constellation size K = 64 for modulated CW, two-phase and perturbed plane wave signals having −0.55 dBm power.
Fig. 6
Fig. 6 BER vs. distance, for 32 and 64-QAM constellations made up by using the perturbed plane wave profile (Subsection 3.2), with −0.5 dBm power, CP= 110% (left), and its received 64 QAM constellation at the propagation distance 1000 km (right).
Fig. 7
Fig. 7 BER vs. distance, for 32 and 64-QAM constellations made up by using the modulated CW wave (Subsection 3.3), with −0.5 dBm power, CP= 250% (left). Right pane shows the example received constellation for K = 16, 24, at the propagation distance 1000 km.
Fig. 8
Fig. 8 BER vs. distance, for 32 and 64-QAM constellations made up by using the two-phase signal of Eq. (9), with −0.5 dBm power, CP= 200% (left). Right pane shows the example received constellation for K = 8, 16, at the propagation distance 1000 km.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

i q z β 2 2 q t t + γ q | q | 2 = n ( t , z ) ,
n ( t , z ) , n ( t , z ) = α h f s K T δ ( t t , z z ) ,
γ e f f = 1 L s p a n 0 L s p a n γ e α z d z = γ 1 e α L s p a n α L s p a n ,
t T s t , z Z s z , q γ Z s 2 q , n γ Z s 2 n ,
i q z + q t t + 2 q | q | 2 = n ( t , z ) .
[ i t q ( t , z ) q * ( t , z ) i t ] [ ϕ 1 ϕ 2 ] = λ [ ϕ 1 ϕ 2 ] ,
ϕ ( t 0 , t 0 ; λ ) = ( 1 0 ) , ϕ ˜ ( t 0 , t 0 ; λ ) = ( 0 1 ) .
IM = { λ | Tr M ( t 0 ; λ ) = ± 2 } .
q ( t , z ) = A cosh ( ϕ z i σ ) + B cos ( ξ t α ) cosh ϕ z + B cos ( ξ t α ) e i N z ,
A = Im λ 1 , N = 4 Re λ 1 2 2 Im λ 1 2 , α = π , B = ( | λ 3 λ 1 | | λ 3 λ 1 * | ) 2 | λ 3 λ 3 * | | λ 1 λ 1 * | , ϕ = 4 Im [ ( λ 3 * + Re λ 1 ) ( λ 3 * λ 1 ) ( λ 3 * λ 1 * ] ] σ = 2 Im ln [ λ 3 * λ 1 * λ 3 * λ 1 λ 3 * λ 1 * + λ 3 * λ 1 ] , ξ = 2 Re ( λ 3 * λ 1 ) ( λ 3 * λ 1 * ] ,
λ n = ( π n T 0 ) 2 A 2 , n < A T 0 π , n = 1 , 2 , .
k 2 A 2 + λ , ω = 2 λ k , τ j j = 1 2 + i π ln ( k j 2 ϵ j ) , τ l j = i 2 π ln ( 1 + λ l λ j + 0.25 k l k j 1 + λ l λ j 0.25 k l k j ) , δ ± = π + i ln [ σ ( λ ± 1 2 k ) ( λ + 1 2 k ) ] ,
q ( t , 0 ) = A + 2 j = 1 g | ϵ j | cos ( k j t + a j ) + O ( ϵ 2 ) .

Metrics