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.
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Richardson, D. J., Fini, J. M. & Nelson, L. E. Space-division multiplexing in optical fibres. Nat. Photon. 7, 354–362 (2013).
Ho, K.-P. & Kahn, J. M. in Optical Fiber Telecommunications Vol. VIB (eds Kaminow, N. P., Li, T. & Willner, A. E.) 491–568 (2013).
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).
Fan, S. & Kahn, J. M. Principal modes in multimode waveguides. Opt. Lett. 30, 135–137 (2005).
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).
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).
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).
Plöschner, M., Tyc, T. & Čižmár, T. Seeing through chaos in multimode fibres. Nat. Photon. 9, 529–535 (2015).
Mahalati, R. N., Gu, R. Y. & Kahn, J. M. Resolution limits for imaging through multi-mode fiber. Opt. Express 21, 1656–1668 (2013).
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).
Poletti, F. & Horak, P. Description of ultrashort pulse propagation in multimode optical fibers. J. Opt. Soc. Am. B 25, 1645–1654 (2008).
Wright, L. G., Christodoulides, D. N. & Wise, F. W. Controllable spatiotemporal nonlinear effects in multimode fibres. Nat. Photon. 9, 306–310 (2015).
Wright, L. G., Renninger, W. H., Christodoulides, D. N. & Wise, F. W. Spatiotemporal dynamics of multimode optical solitons. Opt. Express 23, 3492–3506 (2015).
Nazemosadat, E. & Mafi, A. Nonlinear switching in multicore versus multimode waveguide junctions for mode-locked laser applications. Opt. Express 21, 30739–30745 (2013).
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).
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).
Krupa, K. et al. Spatial beam self-cleaning in multimode fiber. Preprint at http://arxiv.org/abs/1603.02972 (2016).
Lopez-Galmiche, G. et al. Visible supercontinuum generation in a graded index multimode fiber pumped at 1064 nm. Opt. Lett. 41, 2553–2556 (2016).
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).
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).
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).
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).
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).
Guasoni, M. Generalized modulational instability in multimode fibers: wideband multimode parametric amplification. Phys. Rev. A 92, 033849 (2015).
Longhi, S. Modulational instability and space time dynamics in nonlinear parabolic-index optical fibers. Opt. Lett. 28, 2363–2365 (2003).
Mecozzi, A., Antonelli, C. & Shtaif, M. Nonlinear propagation in multi-mode fibers in the strong coupling regime. Opt. Express 20, 11673–11678 (2012).
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).
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).
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).
Kubat, I. & Bang, O. Multimode supercontinuum generation in chalcogenide glass fibres. Opt. Express 24, 2513–2526 (2016).
Andreasen, J. & Kolesik, M. Nonlinear propagation of light in structured media: generalized unidirectional pulse propagation equations. Phys. Rev. E 86, 036706 (2012).
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).
Chiang, K. S. Stimulated Raman scattering in a multimode optical fiber: evolution of modes in Stokes waves. Opt. Lett. 17, 352–354 (1992).
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).
Longhi, S. & Janner, D. Self-focusing and nonlinear periodic beams in parabolic index optical fibres. J. Opt. B 6, S303–S308 (2004).
Strogatz, S. H. Exploring complex networks. Nature 410, 268–276 (2001).
Bianconi, G. & Barabási, A. L. Bose–Einstein condensation in complex networks. Phys. Rev. Lett. 86, 5632–5635 (2001).
Phelan, S. E. What is complexity science, really? Emergence 3, 120–136 (2001).
Frigg, R. Self-organised criticality—what it is and what it isn't. Stud. Hist. Philos. Sci. A 34, 613–632 (2003).
Wiersma, D. S. Disordered photonics. Nat. Photon. 7, 188–196 (2013).
Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007).
Segev, M., Silberberg, Y. & Christodoulides, D. N. Anderson localization of light. Nat. Photon. 7, 197–204 (2013).
Mafi, A. Transverse Anderson localization of light: a tutorial. Adv. Opt. Photon. 7, 459–515 (2015).
Bromberg, Y., Lahini, Y., Small, E. & Silberberg, Y. Hanbury Brown and Twiss interferometry with interacting photons. Nat. Photon. 4, 721–726 (2010).
Cao, H. Lasing in random media. Waves Random Media 13, R1–R39 (2003).
Bak, P., Tang, C. & Wiesenfeld, K. Self-organized criticality. Phys. Rev. A 38, 364–374 (1988).
Turcotte, D. L. Self-organized criticality. Rep. Prog. Phys. 62, 1377–1429 (1999).
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).
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).
Solli, D. R. & Jalali, B. Analog optical computing. Nat. Photon. 9, 704–706 (2015).
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.
D.A.N. and M.-J.L. are employed by Corning Incorporated, which manufactures optical fibres for applications including telecommunications.
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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
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