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:

Self-organized instability in graded-index multimode fibres

Nature Photonics volume 10, pages 771–776 (2016)Cite this article

Subjects

Abstract

Multimode fibres (MMFs) are attracting interest in the study of spatiotemporal dynamics as well as in the context of ultrafast fibre sources, imaging and telecommunications. This interest stems from three differences compared with single-mode fibre structures: their spatiotemporal complexity (information capacity), the role of disorder, and their complex intermodal interactions. To date, MMFs have been studied in limiting cases in which one or more of these properties can be neglected. Here, we study a regime in which all these elements are integral. We observe a spatial beam-cleaning phenomenon that precedes spatiotemporal modulation instability. We provide evidence that the origin of these processes is a universal unstable attractor in graded-index MMFs. The self-organization and instability of the attractor are both caused by intermodal interactions characterized by cooperating disorder, nonlinearity and dissipation. Disorder-enhanced nonlinear processes in MMFs have important implications for future telecommunications, and the multifaceted nature of the considered dynamics showcases MMFs as potential laboratories for a variety of topics in complexity science.

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: Experimental measurements of self-organized instability in normal-dispersion GRIN fibre.
Figure 2: Characteristics of mode coupling in GRIN MMF.
Figure 3: Spatiotemporal modulation instability.
Figure 4: Maximal instability of the attractor.

Similar content being viewed by others

References

  1. Richardson, D. J., Fini, J. M. & Nelson, L. E. Space-division multiplexing in optical fibres. Nat. Photon. 7, 354–362 (2013).

    Article  ADS  Google Scholar 

  2. Ho, K.-P. & Kahn, J. M. in Optical Fiber Telecommunications Vol. VIB (eds Kaminow, N. P., Li, T. & Willner, A. E.) 491–568 (2013).

    Book  Google Scholar 

  3. Essiambre, R. J., Tkach, R. W. & Ryf, R. in Optical Fiber Telecommunications Vol. VIB (eds Kaminow, N. P., Li, T. & Willner, A. E.) 1–37 (2013).

    Book  Google Scholar 

  4. Fan, S. & Kahn, J. M. Principal modes in multimode waveguides. Opt. Lett. 30, 135–137 (2005).

    Article  ADS  Google Scholar 

  5. Shemirani, M. B., Wei, M., Panicker, R. A. & Kahn, J. M. Principal modes in graded-index multimode fiber in presence of spatial-and polarization-mode coupling. J. Light. Technol. 27, 1248–1261 (2009).

    Article  ADS  Google Scholar 

  6. Carpenter, J., Eggleton, B. J. & Schröder, J. Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre. Nat. Photon. 9, 751–757 (2015).

    Article  ADS  Google Scholar 

  7. Milione, G., Nolan, D. A. & Alfano, R. Determining principal modes in a multimode optical fiber using the mode dependent signal delay method. J. Opt. Soc. Am. B 32, 143–149 (2015).

    Article  ADS  Google Scholar 

  8. Plöschner, M., Tyc, T. & Čižmár, T. Seeing through chaos in multimode fibres. Nat. Photon. 9, 529–535 (2015).

    Article  ADS  Google Scholar 

  9. Mahalati, R. N., Gu, R. Y. & Kahn, J. M. Resolution limits for imaging through multi-mode fiber. Opt. Express 21, 1656–1668 (2013).

    Article  ADS  Google Scholar 

  10. Mosk, A. P., Lagendijk, A., Lerosey, G. & Fink, M. Controlling waves in space and time for imaging and focusing in complex media. Nat. Photon. 6, 283–292 (2012).

    Article  ADS  Google Scholar 

  11. Poletti, F. & Horak, P. Description of ultrashort pulse propagation in multimode optical fibers. J. Opt. Soc. Am. B 25, 1645–1654 (2008).

    Article  ADS  Google Scholar 

  12. Wright, L. G., Christodoulides, D. N. & Wise, F. W. Controllable spatiotemporal nonlinear effects in multimode fibres. Nat. Photon. 9, 306–310 (2015).

    Article  ADS  Google Scholar 

  13. Wright, L. G., Renninger, W. H., Christodoulides, D. N. & Wise, F. W. Spatiotemporal dynamics of multimode optical solitons. Opt. Express 23, 3492–3506 (2015).

    Article  ADS  Google Scholar 

  14. Nazemosadat, E. & Mafi, A. Nonlinear switching in multicore versus multimode waveguide junctions for mode-locked laser applications. Opt. Express 21, 30739–30745 (2013).

    Article  ADS  Google Scholar 

  15. Nazemosadat, E., Pourbeyram, H. & Mafi, A. Phase matching for spontaneous frequency conversion via four-wave mixing in graded-index multimode optical fibers. J. Opt. Soc. Am. B 33, 144–150 (2016).

    Article  ADS  Google Scholar 

  16. Krupa, K. et al. Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves. Phys. Rev. Lett. 116, 183901 (2016).

    Article  ADS  Google Scholar 

  17. Krupa, K. et al. Spatial beam self-cleaning in multimode fiber. Preprint at http://arxiv.org/abs/1603.02972 (2016).

  18. Lopez-Galmiche, G. et al. Visible supercontinuum generation in a graded index multimode fiber pumped at 1064 nm. Opt. Lett. 41, 2553–2556 (2016).

    Article  ADS  Google Scholar 

  19. Aschieri, P., Garnier, J., Michel, C., Doya, V. & Picozzi, A. Condensation and thermalization of classical optical waves in a waveguide. Phys. Rev. A 83, 033838 (2011).

    Article  ADS  Google Scholar 

  20. Hill, K. O., Johnson, D. C. & Kawasaki, B. S. Efficient conversion of light over a wide spectral range by four-photon mixing in a multimode graded-index fiber. Appl. Opt. 20, 1075–1079 (1981).

    Article  ADS  Google Scholar 

  21. Pourbeyram, H., Agrawal, G. P. & Mafi, A. Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750 nm using a graded-index multimode optical fiber. Appl. Phys. Lett. 102, 201107 (2013).

    Article  ADS  Google Scholar 

  22. Ramsay, J. et al. Generation of infrared supercontinuum radiation: spatial mode dispersion and higher-order mode propagation in ZBLAN step-index fibers. Opt. Express 21, 10764–10771 (2013).

    Article  ADS  Google Scholar 

  23. Tani, F., Travers, J. C. & Russell, P. S. J. Multimode ultrafast nonlinear optics in optical waveguides: numerical modeling and experiments in Kagomé photonic-crystal fiber. J. Opt. Soc. Am. B 31, 311–320 (2014).

    Article  ADS  Google Scholar 

  24. Guasoni, M. Generalized modulational instability in multimode fibers: wideband multimode parametric amplification. Phys. Rev. A 92, 033849 (2015).

    Article  ADS  Google Scholar 

  25. Longhi, S. Modulational instability and space time dynamics in nonlinear parabolic-index optical fibers. Opt. Lett. 28, 2363–2365 (2003).

    Article  ADS  Google Scholar 

  26. Mecozzi, A., Antonelli, C. & Shtaif, M. Nonlinear propagation in multi-mode fibers in the strong coupling regime. Opt. Express 20, 11673–11678 (2012).

    Article  ADS  Google Scholar 

  27. Mumtaz, S., Essiambre, R.-J. & Agrawal, G. P. Nonlinear propagation in multimode and multicore fibers: generalization of the Manakov equations. J. Light. Technol. 31, 398–406 (2013).

    Article  ADS  Google Scholar 

  28. Rademacher, G., Warm, S. & Petermann, K. Influence of discrete mode coupling on nonlinear interaction in mode-multiplexed systems. IEEE Photon. Technol. Lett. 22, 1203–1206 (2013).

    Article  ADS  Google Scholar 

  29. Xiao, Y. et al. Theory of intermodal four-wave mixing with random linear mode coupling in few-mode fibers. Opt. Express 22, 32039–32059 (2014).

    Article  ADS  Google Scholar 

  30. Kubat, I. & Bang, O. Multimode supercontinuum generation in chalcogenide glass fibres. Opt. Express 24, 2513–2526 (2016).

    Article  ADS  Google Scholar 

  31. Andreasen, J. & Kolesik, M. Nonlinear propagation of light in structured media: generalized unidirectional pulse propagation equations. Phys. Rev. E 86, 036706 (2012).

    Article  ADS  Google Scholar 

  32. Terry, N. B., Alley, T. G. & Russell, T. H. An explanation of SRS beam cleanup in graded-index fibers and the absence of SRS beam cleanup in step-index fibers. Opt. Express 15, 17509 (2007).

    Article  ADS  Google Scholar 

  33. Chiang, K. S. Stimulated Raman scattering in a multimode optical fiber: evolution of modes in Stokes waves. Opt. Lett. 17, 352–354 (1992).

    Article  ADS  Google Scholar 

  34. Mussot, A., Sylvestre, T., Provino, L. & Maillotte, H. Generation of a broadband single-mode supercontinuum in a conventional dispersion-shifted fiber by use of a subnanosecond microchip laser. Opt. Lett. 28, 1820–1822 (2003).

    Article  ADS  Google Scholar 

  35. Longhi, S. & Janner, D. Self-focusing and nonlinear periodic beams in parabolic index optical fibres. J. Opt. B 6, S303–S308 (2004).

    Article  ADS  Google Scholar 

  36. Strogatz, S. H. Exploring complex networks. Nature 410, 268–276 (2001).

    Article  ADS  Google Scholar 

  37. Bianconi, G. & Barabási, A. L. Bose–Einstein condensation in complex networks. Phys. Rev. Lett. 86, 5632–5635 (2001).

    Article  ADS  Google Scholar 

  38. Phelan, S. E. What is complexity science, really? Emergence 3, 120–136 (2001).

    Article  Google Scholar 

  39. Frigg, R. Self-organised criticality—what it is and what it isn't. Stud. Hist. Philos. Sci. A 34, 613–632 (2003).

    Article  Google Scholar 

  40. Wiersma, D. S. Disordered photonics. Nat. Photon. 7, 188–196 (2013).

    Article  ADS  Google Scholar 

  41. Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007).

    Article  ADS  Google Scholar 

  42. Segev, M., Silberberg, Y. & Christodoulides, D. N. Anderson localization of light. Nat. Photon. 7, 197–204 (2013).

    Article  ADS  Google Scholar 

  43. Mafi, A. Transverse Anderson localization of light: a tutorial. Adv. Opt. Photon. 7, 459–515 (2015).

    Article  Google Scholar 

  44. Bromberg, Y., Lahini, Y., Small, E. & Silberberg, Y. Hanbury Brown and Twiss interferometry with interacting photons. Nat. Photon. 4, 721–726 (2010).

    Article  ADS  Google Scholar 

  45. Cao, H. Lasing in random media. Waves Random Media 13, R1–R39 (2003).

    Article  ADS  Google Scholar 

  46. Bak, P., Tang, C. & Wiesenfeld, K. Self-organized criticality. Phys. Rev. A 38, 364–374 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  47. Turcotte, D. L. Self-organized criticality. Rep. Prog. Phys. 62, 1377–1429 (1999).

    Article  ADS  Google Scholar 

  48. Liou, L. W., Cao, X. D., McKinstrie, C. J. & Agrawal, G. P. Spatiotemporal instabilities in dispersive nonlinear media. Phys. Rev. A 46, 4202–4208 (1992).

    Article  ADS  Google Scholar 

  49. Sivan, Y., Rozenberg, S. & Halstuch, A. Coupled-mode theory for electromagnetic pulse propagation in dispersive media undergoing a spatiotemporal perturbation: exact derivation, numerical validation, and peculiar wave mixing. Phys. Rev. B 93, 144303 (2016).

    Article  ADS  Google Scholar 

  50. Solli, D. R. & Jalali, B. Analog optical computing. Nat. Photon. 9, 704–706 (2015).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Portions of this work were funded by Office of Naval Research grant N00014-13-1-0649 and by National Science Foundation grant ECCS-1609129. We thank OFS for providing some of the fibre used in the experiments. We thank Z. Zhu, K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, G. Millot and S. Wabnitz for discussions.

Author information

Authors and Affiliations

  1. School of Applied and Engineering Physics, Cornell University, Ithaca, 14853, New York, USA

    Logan G. Wright, Zhanwei Liu & Frank W. Wise

  2. Corning Incorporated, Sullivan Park, Corning, 14830, New York, USA

    Daniel A. Nolan & Ming-Jun Li

  3. CREOL, College of Optics and Photonics, University of Central Florida, Orlando, 32816, Florida, USA

    Demetrios N. Christodoulides

Authors
  1. Logan G. Wright
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhanwei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel A. Nolan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ming-Jun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Demetrios N. Christodoulides
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Frank W. Wise
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

L.G.W. performed simulations and experiments, with assistance provided by Z.L. D.A.N. and M.-J. L. made and provided small-core GRIN fibres. F.W.W. and D.N.C. supervised the project. L.G.W. and F.W.W. wrote the first drafts of the manuscript and all the authors contributed to the final version.

Corresponding author

Correspondence to Logan G. Wright.

Ethics declarations

Competing interests

D.A.N. and M.-J.L. are employed by Corning Incorporated, which manufactures optical fibres for applications including telecommunications.

Supplementary information

Supplementary information

Supplementary information (PDF 2367 kb)

Supplementary information

Supplementary Movie 1 (MOV 365 kb)

Supplementary information

Supplementary Movie 2 (MOV 6556 kb)

Supplementary information

Supplementary Movie 3 (MOV 328 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wright, L., Liu, Z., Nolan, D. et al. Self-organized instability in graded-index multimode fibres. Nature Photon 10, 771–776 (2016). https://doi.org/10.1038/nphoton.2016.227

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2016.227

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