Abstract
We report what we believe is the weakest interaction between solitons ever observed. Our experiment involves temporal optical cavity solitons recirculating in a coherently driven passive optical-fibre ring resonator. We observe pairs of solitons interacting over a range as large as 8,000 times their width. In the most extreme case, their temporal separation changes as slowly as a fraction of an attosecond per roundtrip of the 100-m-long resonator, or equivalently 1/10,000 of the wavelength of the soliton carrier wave per characteristic dispersive length. The interactions are so weak that, at the speed of light, an effective propagation distance of the order of an astronomical unit can be required to reveal the full dynamical evolution. The interaction is mediated by transverse acoustic waves generated in the optical fibre by the propagating solitons through electrostriction.
Similar content being viewed by others
References
Russell, J. S. in Report of the Fourteenth Meeting of the British Association for the Advancement of Science, York, September 1844, 311–390, Plates XLVII–LVII (John Murray, 1845).
Zabusky, N. J. & Kruskal, M. D. Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15, 240–243 (1965).
Hasegawa, A. & Tappert, F. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion. Appl. Phys. Lett. 23, 142–144 (1973).
Akhmediev, N. N. & Ankiewicz, A. Solitons — Nonlinear Pulses and Beams 1st edn (Chapman & Hall, 1997).
Stegeman, G. I. & Segev, M. Optical spatial solitons and their interactions: universality and diversity. Science 286, 1518–1523 (1999).
Craig, W., Guyenne, P., Hammack, J., Henderson, D. & Sulem, C. Solitary water wave interactions. Phys. Fluids 18, 057106 (2006).
Gardner, C. S., Greene, J. M., Kruskal, M. D. & Miura, R. M. Method for solving the Korteweg–deVries equation. Phys. Rev. Lett. 19, 1095–1097 (1967).
Lonngren, K. E. Soliton experiments in plasmas. Plasma Phys. 25, 943–982 (1983).
Saha, M. & Kofane, T. C. Long-range interactions between adjacent and distant bases in a DNA and their impact on the ribonucleic acid polymerase–DNA dynamics. Chaos 22, 013116 (2012).
Polturak, E., deVegvar, P. G. N., Zeise, E. K. & Lee, D. M. Solitonlike propagation of zero sound in superfluid 3He. Phys. Rev. Lett. 46, 1588–1591 (1981).
Burger, S. et al. Dark solitons in Bose–Einstein condensates. Phys. Rev. Lett. 83, 5198–5201 (1999).
Denschlag, J. et al. Generating solitons by phase engineering of a Bose–Einstein condensate. Science 287, 97–101 (2000).
Bjorkholm, J. E. & Ashkin, A. A. cw self-focusing and self-trapping of light in sodium vapor. Phys. Rev. Lett. 32, 129–132 (1974).
Mollenauer, L. F., Stolen, R. H. & Gordon, J. P. Experimental observation of picosecond pulse narrowing and solitons in optical fibers. Phys. Rev. Lett. 45, 1095–1098 (1980).
Barthelemy, A., Maneuf, S. & Froehly, C. Propagation soliton et auto-confinement de faisceaux laser par non linearité optique de Kerr. Opt. Commun. 55, 201–206 (1985).
Segev, M. Optical spatial solitons. Opt. Quant. Electron. 30, 503–533 (1998).
Barland, S. et al. Cavity solitons as pixels in semiconductor microcavities. Nature 419, 699–702 (2002).
Grelu, P. & Akhmediev, N. N. Dissipative solitons for mode-locked lasers. Nature Photon. 6, 84–92 (2012).
Gordon, J. P. Interaction forces among solitons in optical fibers. Opt. Lett. 8, 596–598 (1983).
Reynaud, F. & Barthelemy, A. Optically controlled interaction between two fundamental soliton beams. Europhys. Lett. 12, 401–405 (1990).
Tikhonenko, V., Christou, J. & Luther-Davies, B. Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium. Phys. Rev. Lett. 76, 2698–2701 (1996).
Shih, M., Segev, M. & Salamo, G. Three-dimensional spiraling of interacting spatial solitons. Phys. Rev. Lett. 78, 2551–2554 (1997).
Królikowski, W., Luther-Davies, B., Denz, C. & Tschudi, T. Annihilation of photorefractive solitons. Opt. Lett. 23, 97–99 (1998).
Snyder, A. W., Mitchell, D. J., Poladian, L. & Ladouceur, F. Self-induced optical fibers: spatial solitary waves. Opt. Lett. 16, 21–23 (1991).
Schäpers, B., Feldmann, M., Ackemann, T. & Lange, W. Interaction of localized structures in an optical pattern-forming system. Phys. Rev. Lett. 85, 748–751 (2000).
Ramazza, P. L. et al. Tailoring the profile and interactions of optical localized structures. Phys. Rev. E 65, 066204 (2002).
Ultanir, E. A., Stegeman, G., Lange, C. H. & Lederer, F. Coherent interactions of dissipative spatial solitons. Opt. Lett. 29, 283–285 (2004).
Bödeker, H. U., Liehr, A. W., Frank, T. D., Friedrich, R. & Purwins, H-G. Measuring the interaction law of dissipative solitons. New J. Phys. 6, 62 (2004).
Smith, K. & Mollenauer, L. F. Experimental observation of soliton interaction over long fiber paths: discovery of a long-range interaction. Opt. Lett. 14, 1284–1286 (1989).
Rotschild, C., Alfassi, B., Cohen, O. & Segev, M. Long-range interactions between optical solitons. Nature Phys. 2, 769–774 (2006).
Chouli, S. & Grelu, P. Soliton rains in a fiber laser: an experimental study. Phys. Rev. A 81, 063829 (2010).
Skryabin, D. V. & Gorbach, A. V. Colloquium: looking at a soliton through the prism of optical supercontinuum. Rev. Mod. Phys. 82, 1287–1299 (2010).
Allen, A. J., Jackson, D. P., Barenghi, C. F. & Proukakis, N. P. Long-range sound-mediated dark-soliton interactions in trapped atomic condensates. Phys. Rev. A 83, 013613 (2011).
Turaev, D., Vladimirov, A. G. & Zelik, S. Long-range interaction and synchronization of oscillating dissipative solitons. Phys. Rev. Lett. 108, 263906 (2012).
Leo, F. et al. Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer. Nature Photon. 4, 471–476 (2010).
Tlidi, M., Mandel, P. & Lefever, R. Localized structures and localized patterns in optical bistability. Phys. Rev. Lett. 73, 640–643 (1994).
Firth, W. J. & Weiss, C. O. Cavity and feedback solitons. Opt. Photon News 13, 54–58 (February 2002).
Lugiato, L. A. Introduction to the feature section on cavity solitons: an overview. IEEE J. Quantum Electron. 39, 193–196 (2003).
Akhmediev, N. N. & Ankiewicz, A. (eds) Dissipative Solitons: From Optics to Biology and Medicine, Vol. 751 (Lecture Notes in Physics, Springer, 2008).
Dianov, E. M., Luchnikov, A. V., Pilipetskii, A. N. & Prokhorov, A. M. Long-range interaction of picosecond solitons through excitation of acoustic waves in optical fibers. Appl. Phys. B 54, 175–180 (1992).
Townsend, P. D., Poustie, A. J., Hardman, P. J. & Blow, K. J. Measurement of the refractive-index modulation generated by electrostriction-induced acoustic waves in optical fibers. Opt. Lett. 21, 333–335 (1996).
Jaouën, Y. & du Mouza, L. Transverse Brillouin effect produced by electrostriction in optical fibers and its impact on soliton transmission systems. Opt. Fib. Tech. 7, 141–169 (2001).
Firth, W. Temporal cavity solitons: buffering optical data. Nature Photon. 4, 415–417 (2010).
Agrawal, G. P. Nonlinear Fiber Optics 4th edn (Academic Press, 2006).
Trebino, R. et al. Measuring ultrashort laser pulses in the time–frequency domain using frequency-resolved optical gating. Rev. Sci. Instrum. 68, 3277–3295 (1997).
Mitschke, F. M. & Mollenauer, L. F. Experimental observation of interaction forces between solitons in optical fibers. Opt. Lett. 12, 355–357 (1987).
Fellegara, A., Melloni, A. & Martinelli, M. Measurement of the frequency response induced by electrostriction in optical fibers. Opt. Lett. 22, 1615–1617 (1997).
Buckland, E. L. Mode-profile dependence of the electrostrictive response in fibers. Opt. Lett. 24, 872–874 (1999).
Biryukov, A. S., Sukharev, M. E. & Dianov, E. M. Excitation of sound waves upon propagation of laser pulses in optical fibres. Quantum Electron. 32, 765–775 (2002).
Coen, S., Randle, H. G., Sylvestre, T. & Erkintalo, M. Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato–Lefever model. Opt. Lett. 38, 37–39 (2013).
Pilipetskii, A. N., Golovchenko, E. A. & Menyuk, C. R. Acoustic effect in passively mode-locked fiber ring lasers. Opt. Lett. 20, 907–909 (1995).
Kippenberg, T. J., Rokhsari, H., Carmon, T., Scherer, A. & Vahala, K. J. Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity. Phys. Rev. Lett. 95, 033901 (2005).
Lugiato, L. A. & Lefever, R. Spatial dissipative structures in passive optical systems. Phys. Rev. Lett. 58, 2209–2211 (1987).
Buckland, E. L. & Boyd, R. W. Electrostrictive contribution to the intensity-dependent refractive index of optical fibers. Opt. Lett. 21, 1117–1119 (1996).
Acknowledgements
This work was supported by the Marsden Fund Council (government funding), administered by the Royal Society of New Zealand. The driving laser was funded from the Faculty Research Development Fund of the Faculty of Science of the University of Auckland. J.K.J. also acknowledges the support of a University of Auckland Doctoral Scholarship.
Author information
Authors and Affiliations
Contributions
J.K.J. performed the experiments. M.E. identified the physical origin of the interactions, incorporated the acoustic response into the mean field model, wrote a first draft of the paper, and performed the split-step Fourier simulations. Overall, J.K.J. and M.E. contributed equally to this work. S.G.M. supervised the experimental work. S.C. programmed the Newton solver and performed the related computations, wrote the final version of the paper, and supervised the overall project.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary information
Supplementary information (PDF 814 kb)
Rights and permissions
About this article
Cite this article
Jang, J., Erkintalo, M., Murdoch, S. et al. Ultraweak long-range interactions of solitons observed over astronomical distances. Nature Photon 7, 657–663 (2013). https://doi.org/10.1038/nphoton.2013.157
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphoton.2013.157
- Springer Nature Limited
This article is cited by
-
Ultrashort dissipative Raman solitons in Kerr resonators driven with phase-coherent optical pulses
Nature Photonics (2024)
-
Parametrically driven pure-Kerr temporal solitons in a chip-integrated microcavity
Nature Photonics (2024)
-
On the Temporal Tweezing of Cavity Solitons
Journal of Nonlinear Mathematical Physics (2024)
-
Novel optical soliton molecules formed in a fiber laser with near-zero net cavity dispersion
Light: Science & Applications (2023)
-
Reconfigurable dynamics of optical soliton molecular complexes in an ultrafast thulium fiber laser
Communications Physics (2022)