Article | Published:

Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit

Nature Photonics volume 11, pages 570576 (2017) | Download Citation

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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    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. 2.

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

  3. 3.

    , , , & Capacity limits of optical fiber networks. J. Lightwave Technol. 28, 662–701 (2010).

  4. 4.

    Fiber-Optic Communication Systems (Wiley-Blackwell, 2010).

  5. 5.

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

  6. 6.

    , & 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. 7.

    & Nonlinear limits to the information capacity of optical fibre communications. Nature 411, 1027–1030 (2001).

  8. 8.

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

  9. 9.

    , , & Accumulation of nonlinear interference noise in fiber-optic systems. Opt. Express 22, 14199–14211 (2014).

  10. 10.

    , & Approaching the nonlinear Shannon limit. J. Lightwave Technol. 28, 423–433 (2010).

  11. 11.

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

  12. 12.

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

  13. 13.

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

  14. 14.

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

  15. 15.

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

  16. 16.

    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. 17.

    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).

  18. 18.

    , , & Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit. Nat. Photon. 7, 560–568 (2013).

  19. 19.

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

  20. 20.

    & Eigenvalue communication. J. Lightwave Technol. 11, 395–399 (1993).

  21. 21.

    , , & The inverse scattering transform-Fourier analysis for nonlinear problems. Stud. Appl. Math. 53, 249–315 (1974).

  22. 22.

    & Digital signal processing based on inverse scattering transform. Opt. Lett. 38, 4186–4188 (2013).

  23. 23.

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

  24. 24.

    , , , & Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels. Phys. Rev. Lett. 113, 013901 (2014).

  25. 25.

    , & Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers. Opt. Express 22, 26720–26741 (2014).

  26. 26.

    , & Nonlinear inverse synthesis technique for optical links with lumped amplification. Opt. Express 23, 8317–8328 (2015).

  27. 27.

    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. 28.

    , , & Experimental demonstration of nonlinear frequency division multiplexed transmission. In European Conference on Optical Communication Paper Tu1.1.2 (IEEE, 2015).

  29. 29.

    , , ., & Digital backpropagation in the nonlinear Fourier domain. In Proc. IEEE SPAWC 445–449 (IEEE, 2015).

  30. 30.

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

  31. 31.

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

  32. 32.

    , & 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. 33.

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

  34. 34.

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

  35. 35.

    , & Demonstration of 64 × 0. 5Gbaud nonlinear frequency division multiplexed transmission with 32 QAM. In Optical Fibre Communication Paper W3J.1 (IEEE, 2017).

  36. 36.

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

  37. 37.

    & Solitons in Optical Communications (Oxford Univ. Press, 1995).

  38. 38.

    & Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

  39. 39.

    et al. Ultralong Raman fibre lasers as virtually lossless optical media. Phys. Rev. Lett. 96, 023902 (2006).

  40. 40.

    & 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. 41.

    Control and detection of discrete spectral amplitudes in nonlinear Fourier spectrum. Preprint at (2016).

  42. 42.

    & Fast numerical nonlinear Fourier transforms. IEEE Trans. Inf. Theory 61, 6957–6974 (2015).

  43. 43.

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

  44. 44.

    , & Capacity estimates for optical transmission based on the nonlinear Fourier transform. Nat. Commun. 7, 12710 (2016).

  45. 45.

    & Linear and nonlinear frequency-division multiplexing. Preprint at (2016).

  46. 46.

    & Robust frequency and timing synchronization for OFDM communications. IEEE Trans. Commun. 45, 1613–1621 (1997).

  47. 47.

    & Computation of the direct scattering transform for the nonlinear Schrödinger equation. J. Comput. Phys. 102, 252–264 (1992).

  48. 48.

    , , & Efficient numerical method for solving the direct Zakharov–Shabat scattering problem. J. Opt. Soc. Am. B 32, 290–295 (2015).

Download references

Author information

Affiliations

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

    • Son Thai Le
    • , Vahid Aref
    •  & Henning Buelow

Authors

  1. Search for Son Thai Le in:

  2. Search for Vahid Aref in:

  3. Search for Henning Buelow in:

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.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Son Thai Le.

Supplementary information

PDF files

  1. 1.

    Supplementary information

    Supplementary information

About this article

Publication history

Received

Accepted

Published

DOI

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

Further reading