Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit

Nature Photonics volume 11, pages 570–576 (2017)Cite this article

Subjects

Abstract

Current optical fibre transmission systems rely on modulation, coding and multiplexing techniques that were originally developed for linear communication channels. However, linear transmission techniques are not fully compatible with a transmission medium with a nonlinear response, which is the case for an optical fibre. As a consequence, the Kerr nonlinearity in fibre imposes a limit on the performance and the achievable transmission rate of the conventional optical fibre communication systems. Here we show that a transmission performance beyond the conventional Kerr nonlinearity limit can be achieved by encoding all the available degrees of freedom and nonlinearly multiplexing signals in the so-called nonlinear Fourier spectrum, which evolves linearly along the fibre link. This result strongly motivates a fundamental paradigm shift in modulation, coding and signal-processing techniques for optical fibre transmission technology.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Illustration of the nonlinear spectrum and its evolution along a fibre link.
Figure 2: NFDM systems based on multiplexing signals in the nonlinear-spectrum domain.
Figure 3: Experimental set-up and performance of 64 × 0.5 GBd pre-compensated NFDM transmission.
Figure 4: Performance of fully modulated NFDM transmissions with the continuous part modulated by 64 overlapping sinc channels with 16 QAM, 32 QAM and 64 QAM formats and the discrete part modulated by two purely imaginary 8 PSK phase-modulated eigenvalues.

Similar content being viewed by others

References

  1. Nowell, M. Cisco Visual Networking Index (VNI) Global IP Traffic Forecast Update; 2010–2015 (Cisco, 2016); www.ieee802.org/3/ad_hoc/bwa/public/sep11/nowell_01_0911.pdf.

  2. Chraplyvy, A. R. The coming capacity crunch. In European Conference on Optical Communication Plenary talk (IEEE, 2009).

  3. Essiambre, R. J., Kramer, G., Winzer, P. J., Foschini, G. J. & Goebel, B. Capacity limits of optical fiber networks. J. Lightwave Technol. 28, 662–701 (2010).

    Article  ADS  Google Scholar 

  4. Agrawal, G. P. Fiber-Optic Communication Systems (Wiley-Blackwell, 2010).

    Book  Google Scholar 

  5. Savory, S. Digital filters for coherent optical receivers. Opt. Express 16, 804–817 (2008).

    Article  ADS  Google Scholar 

  6. Splett, A., Kurtzke, C. & Petermann, K. Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities. In Tech. Digest 19th European Conference on Optical Communication Paper MoC2.4 (IEEE, 1993).

  7. Mitra, P. P. & Stark, J. B. Nonlinear limits to the information capacity of optical fibre communications. Nature 411, 1027–1030 (2001).

    Article  ADS  Google Scholar 

  8. Poggiolini, P. et al. The GN model of fiber non-linear propagation and its applications. J. Lightwave Technol. 32, 694–721 (2014).

    Article  ADS  Google Scholar 

  9. Dar, R., Feder, M., Mecozzi, A. & Shtaif, M. Accumulation of nonlinear interference noise in fiber-optic systems. Opt. Express 22, 14199–14211 (2014).

    Article  ADS  Google Scholar 

  10. Ellis, A. D., Zhao, J. & Cotter, D. Approaching the nonlinear Shannon limit. J. Lightwave Technol. 28, 423–433 (2010).

    Article  ADS  Google Scholar 

  11. Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948).

    Article  MathSciNet  Google Scholar 

  12. Ip, E. & Kahn, J. Compensation of dispersion and nonlinear impairments using digital backpropagation. J. Lightwave Technol. 26, 3416–3425 (2008).

    Article  ADS  Google Scholar 

  13. Temprana, E. et al. Overcoming Kerr-induced capacity limit in optical fiber transmission. Science 26, 1445–1448 (2015).

    Article  ADS  Google Scholar 

  14. Maher, R. et al. Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation. Sci. Rep. 5, 8214 (2015).

    Article  Google Scholar 

  15. Jansen, S. L. et al. Optical phase conjugation for ultra-long-haul phase-shift-keyed transmission. J. Lightwave Technol. 24, 54–64 (2006).

    Article  ADS  Google Scholar 

  16. Phillips, I. et al. Exceeding the nonlinear-Shannon limit using Raman laser based amplification and optical phase conjugation. In Optical Fibre Communication Conference Paper M3C.1 (OSA, 2014).

  17. Ellis, A. D. et al. 4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation. J. Lightwave Technol. 34, 1717–1723 (2016).

    Article  ADS  Google Scholar 

  18. Liu, X., Winzer, P. J., Tkach, R. W. & Chandrasekhar, S. Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit. Nat. Photon. 7, 560–568 (2013).

    Article  ADS  Google Scholar 

  19. Zakharov, V. E. & Shabat, A. B. Exact theory of 2-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62–69 (1972).

    ADS  MathSciNet  Google Scholar 

  20. Hasegawa, A. & Nyu, T. Eigenvalue communication. J. Lightwave Technol. 11, 395–399 (1993).

    Article  ADS  Google Scholar 

  21. Ablowitz, N. J., Kaup, D. J., Newell, A. C. & Segur, H. The inverse scattering transform-Fourier analysis for nonlinear problems. Stud. Appl. Math. 53, 249–315 (1974).

    Article  MathSciNet  Google Scholar 

  22. Turitsyna, E. G. & Turitsyn, S. K. Digital signal processing based on inverse scattering transform. Opt. Lett. 38, 4186–4188 (2013).

    Article  ADS  Google Scholar 

  23. Yousefi, M. I. & Kschischang, F. R. Information transmission using the nonlinear Fourier transform, Part I–III. IEEE Trans. Inf. Theory 60, 4312–4328 (2014).

    Article  MathSciNet  Google Scholar 

  24. Prilepsky, J. E., Derevyanko, S. A., Blow, K. J., Gabitov, I. & Turitsyn, S. K. Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels. Phys. Rev. Lett. 113, 013901 (2014).

    Article  ADS  Google Scholar 

  25. Le, S. T., Prilepsky, J. E. & Turitsyn, S. K. Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers. Opt. Express 22, 26720–26741 (2014).

    Article  ADS  Google Scholar 

  26. Le, S. T., Prilepsky, J. E. & Turitsyn, S. K. Nonlinear inverse synthesis technique for optical links with lumped amplification. Opt. Express 23, 8317–8328 (2015).

    Article  ADS  Google Scholar 

  27. Le, S. T. et al. Modified nonlinear inverse synthesis for optical links with distributed Raman amplification. In European Conference on Optical Communication Paper Tu1.1.3 (IEEE, 2015).

  28. Aref, V., Bülow, H., Schuh, K. & Idler, W. Experimental demonstration of nonlinear frequency division multiplexed transmission. In European Conference on Optical Communication Paper Tu1.1.2 (IEEE, 2015).

  29. Wahls, S., Le, S. T., Prilepsky, J. E ., Poor, H. V. & Turitsyn, S. K. Digital backpropagation in the nonlinear Fourier domain. In Proc. IEEE SPAWC 445–449 (IEEE, 2015).

  30. Dong, Z. et al. Nonlinear frequency division multiplexed transmissions based on NFT. IEEE Photon. Tech. Lett. 27, 1621–1623 (2015).

    Article  ADS  Google Scholar 

  31. Maruta, A. Eigenvalue modulated optical transmission system. In 20th Opto Electronics and Communications Conference Paper JThA.21 (IEEE, 2015).

  32. Aref, V., Le, S. T. & Bülow, H. Demonstration of fully nonlinear spectrum modulated system in the highly nonlinear optical transmission regime. In European Conference on Optical Communication Paper Th.3.B.2 (IEEE, 2016).

  33. Le, S. T. et al. Demonstration of nonlinear inverse synthesis transmission over transoceanic distances. J. Lightwave Technol. 34, 2459–2466 (2016).

    Article  ADS  Google Scholar 

  34. Buelow, H., Aref, V. & Idler, W. Transmission of waveforms determined by 7 eigenvalues with PSK-modulated spectral amplitudes. In European Conference on Optical Communication Paper Tu3E.2 (IEEE, 2016).

  35. Le, S. T., Buelow, H. & Aref, V. Demonstration of 64 × 0. 5Gbaud nonlinear frequency division multiplexed transmission with 32 QAM. In Optical Fibre Communication Paper W3J.1 (IEEE, 2017).

  36. Turitsyn, S. K. et al. Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives. Optica 4, 307–322 (2017).

    Article  ADS  Google Scholar 

  37. Hasegawa, A. & Kodama, Y. Solitons in Optical Communications (Oxford Univ. Press, 1995).

    MATH  Google Scholar 

  38. Kivshar, Y. S. & Agrawal, G. P. Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

    Google Scholar 

  39. Ania-Castañón, J. D. et al. Ultralong Raman fibre lasers as virtually lossless optical media. Phys. Rev. Lett. 96, 023902 (2006).

    Article  ADS  Google Scholar 

  40. Tavakkolnia, I. & Safari, M. Dispersion pre-compensation for NFT-based optical fiber communication systems. In Conference on Lasers and Electro-Optics, OSA Technical Digest Paper SM4F.4 (OSA, 2016).

  41. Aref, V. Control and detection of discrete spectral amplitudes in nonlinear Fourier spectrum. Preprint at http://arXiv.org/abs/1605.06328 (2016).

  42. Wahls, S. & Poor, H. V. Fast numerical nonlinear Fourier transforms. IEEE Trans. Inf. Theory 61, 6957–6974 (2015).

    Article  MathSciNet  Google Scholar 

  43. Hari, S. & Kschischang, F. R. Bi-directional algorithm for computing discrete spectral amplitudes in the NFT. J. Lightwave Technol. 34, 3529–3537 (2016).

    Article  ADS  Google Scholar 

  44. Derevyanko, S. A., Prilepsky, J. E. & Turitsyn, S. K. Capacity estimates for optical transmission based on the nonlinear Fourier transform. Nat. Commun. 7, 12710 (2016).

    Article  ADS  Google Scholar 

  45. Yousefi, M. I. & Yangzhang, X. Linear and nonlinear frequency-division multiplexing. Preprint at http://arXiv.org/cs.IT/1207.0297 (2016).

  46. Schmidl, T. M. & Cox, D. C. Robust frequency and timing synchronization for OFDM communications. IEEE Trans. Commun. 45, 1613–1621 (1997).

    Article  Google Scholar 

  47. Boffetta, G. & Osborne, A. R. Computation of the direct scattering transform for the nonlinear Schrödinger equation. J. Comput. Phys. 102, 252–264 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  48. Frumin, L. L., Belai, O. V., Podivilov, E. V. & Shapiro, D. A. Efficient numerical method for solving the direct Zakharov–Shabat scattering problem. J. Opt. Soc. Am. B 32, 290–295 (2015).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nokia Bell Labs, Lorenzstraße 10, Stuttgart, 70435, Germany

    Son Thai Le, Vahid Aref & Henning Buelow

Authors
  1. Son Thai Le
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vahid Aref
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Henning Buelow
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.T.L., V.A. and H.B. jointly discussed the general idea, planned the experiments and analysed the results. S.T.L. designed and detected the continuous spectrum. V.A. proposed the inverse NFT, and designed and detected the discrete spectrum. S.T.L. and H.B. performed the experiments. S.T.L. wrote the paper.

Corresponding author

Correspondence to Son Thai Le.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 306 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Le, S., Aref, V. & Buelow, H. Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit. Nature Photon 11, 570–576 (2017). https://doi.org/10.1038/nphoton.2017.118

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2017.118

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing