OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 3045–3053

Multistability and spontaneous breaking in pulse-shape symmetry in fiber ring cavities

M. J. Schmidberger, D. Novoa, F. Biancalana, P. St.J. Russell, and N. Y. Joly  »View Author Affiliations

Optics Express, Vol. 22, Issue 3, pp. 3045-3053 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (7692 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We describe the spatio-temporal evolution of ultrashort pulses propagating in a fiber ring cavity using an extension of the Lugiato-Lefever model. The model predicts the appearance of multistability and spontaneous symmetry breaking in temporal pulse shape. We also use a hydrodynamical approach to explain the stability of the observed regimes of asymmetry.

© 2014 Optical Society of America

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Nonlinear Optics

Original Manuscript: November 25, 2013
Revised Manuscript: January 16, 2014
Manuscript Accepted: January 22, 2014
Published: February 3, 2014

M. J. Schmidberger, D. Novoa, F. Biancalana, P. St.J. Russell, and N. Y. Joly, "Multistability and spontaneous breaking in pulse-shape symmetry in fiber ring cavities," Opt. Express 22, 3045-3053 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30(2), 257–261 (1979). [CrossRef]
  2. H. U. Voss, A. Schwache, J. Kurths, F. Mitschke, “Equations of motion from chaotic data: A driven optical fiber ring resonator,” Phys. Lett. A 256(1), 47–54 (1999). [CrossRef]
  3. R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81(6), 419–426 (1991). [CrossRef]
  4. G. Steinmeyer, F. Mitschke, “Longitudinal structure formation in a nonlinear resonator,” Appl. Phys. B 62(4), 367–374 (1996). [CrossRef]
  5. J. García-Mateos, F. C. Bienzobas, M. Haelterman, “Optical bistability and temporal symmetry-breaking instability in nonlinear fiber resonators,” Fiber Integr. Opt. 14(4), 337–346 (1995). [CrossRef]
  6. R. W. Bowman, G. M. Gibson, M. J. Padgett, F. Saglimbeni, R. Di Leonardo, “Optical trapping at gigapascal pressures,” Phys. Rev. Lett. 110(9), 095902 (2013). [CrossRef] [PubMed]
  7. P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [CrossRef]
  8. N. Brauckmann, M. Kues, P. Gross, C. Fallnich, “Noise reduction of supercontinua via optical feedback,” Opt. Express 19(16), 14763–14778 (2011). [CrossRef] [PubMed]
  9. M. Schmidberger, W. Chang, P. St. J. Russell, N. Y. Joly, “Influence of timing jitter on nonlinear dynamics of a photonic crystal fiber ring cavity,” Opt. Lett. 37(17), 3576–3578 (2012). [CrossRef] [PubMed]
  10. L. A. Lugiato, R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58(21), 2209–2211 (1987). [CrossRef] [PubMed]
  11. A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, L. A. Lugiato, “Pattern formation in a passive Kerr cavity,” Chaos Solitons Fractals 4(8–9), 1323–1354 (1994). [CrossRef]
  12. F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4(7), 471–476 (2010). [CrossRef]
  13. S. Coen, M. Tlidi, P. Emplit, M. Haelterman, “Convection versus dispersion in optical bistability,” Phys. Rev. Lett. 83(12), 2328–2331 (1999). [CrossRef]
  14. M. Kues, N. Brauckmann, P. Groß, C. Fallnich, “Basic prerequisites for limit-cycle oscillations within a synchronously pumped passive optical nonlinear fiber-ring resonator,” Phys. Rev. A 84(3), 033833 (2011). [CrossRef]
  15. M. J. Schmidberger, F. Biancalana, P. St. J. Russell, N. Y. Joly, “Semi-analytical model for the evolution of femtosecond pulses during supercontinuum generation in synchronously pumped ring cavities,” in The European Conference on Lasers and Electro-Optics (OSA, 2013).
  16. M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, M. Taki, “Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities,” Opt. Lett. 32(6), 662–664 (2007). [CrossRef] [PubMed]
  17. F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, M. Taki, “Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities,” Phys. Rev. Lett. 110(10), 104103 (2013). [CrossRef] [PubMed]
  18. G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, A. G. Vladimirov, “Localized beating between dynamically generated frequencies,” Phys. Rev. Lett. 102(4), 043905 (2009). [CrossRef] [PubMed]
  19. M. Tlidi, L. Bahloul, L. Cherbi, A. Hariz, S. Coulibaly, “Drift of dark cavity solitons in a photonic-crystal fiber resonator,” Phys. Rev. A 88(3), 035802 (2013). [CrossRef]
  20. J. K. Jang, M. Erkintalo, S. G. Murdoch, S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013). [CrossRef]
  21. Y. K. Chembo, C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87(5), 053852 (2013). [CrossRef]
  22. L. D. Landau and E. M. Lifshitz, Statistical Physics (Elsevier, 1996).
  23. P. W. Higgs, “Broken symmetries and the masses of gauge bosons,” Phys. Rev. Lett. 13(16), 508–509 (1964). [CrossRef]
  24. A. E. Miroshnichenko, B. A. Malomed, Y. S. Kivshar, “Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84(1), 012123 (2011). [CrossRef]
  25. Y. Li, J. Liu, W. Pang, B. A. Malomed, “Symmetry breaking in dipolar matter-wave solitons in dual-core couplers,” Phys. Rev. A 87(1), 013604 (2013). [CrossRef]
  26. J. R. Salgueiro, Y. S. Kivshar, “Nonlinear dual-core photonic crystal fiber couplers,” Opt. Lett. 30(14), 1858–1860 (2005). [CrossRef] [PubMed]
  27. C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990). [CrossRef] [PubMed]
  28. H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6(6), 1173–1185 (2000). [CrossRef]
  29. P. Elleaume, “Microtemporal and spectral structure of storage ring free-electron lasers,” IEEE J. Quantum Electron. 21(7), 1012–1022 (1985). [CrossRef]
  30. C. Bruni, T. Legrand, C. Szwaj, S. Bielawski, M. E. Couprie, “Equivalence between free-electron-laser oscillators and actively-mode-locked lasers: Detailed studies of temporal, spatiotemporal, and spectrotemporal dynamics,” Phys. Rev. A 84(6), 063804 (2011). [CrossRef]
  31. S. Coen, H. G. Randle, T. Sylvestre, M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38(1), 37–39 (2013). [CrossRef] [PubMed]
  32. M. Tlidi, L. Gelens, “High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities,” Opt. Lett. 35(3), 306–308 (2010). [CrossRef] [PubMed]
  33. T. A. Birks, J. C. Knight, P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997). [CrossRef] [PubMed]
  34. M. Azhar, N. Y. Joly, J. C. Travers, P. S. J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112(4), 457–460 (2013). [CrossRef]
  35. E. Doedel, H. B. Keller, J. P. Kernevez, “Numerical analysis and control of bifurcation problems (II): Bifurcation in infinite dimensions,” Int. J. Bifurcat. Chaos 01(04), 745–772 (1991). [CrossRef]
  36. A. Alexandrescu, J. R. Salgueiro, “Efficient numerical method for linear stability analysis of solitary waves,” Comput. Phys. Commun. 182(12), 2479–2485 (2011). [CrossRef]
  37. J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991). [CrossRef] [PubMed]
  38. F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21(7), 9180–9191 (2013). [CrossRef] [PubMed]
  39. Y. Xu and S. Coen, “Observation of a temporal symmetry breaking instability in a synchronously-pumped passive fibre ring cavity,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011 (Optical Society of America, 2011), p. I874. [CrossRef]
  40. C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse (Springer, 1999).
  41. N. Akhmediev and A. Ankiewicz, “Dissipative Solitons in the Complex Ginzburg-Landau and Swift-Hohenberg Equations,” in Dissipative Solitons, N. Akhmediev and A. Ankiewicz, eds., Vol. 661 in Lecture Notes in Physics (Springer, 2005), pp. 1–17.
  42. I. S. Aranson, L. Kramer, “The world of the complex Ginzburg-Landau equation,” Rev. Mod. Phys. 74(1), 99–143 (2002). [CrossRef]
  43. E. Madelung, Die mathematischen Hilfsmittel des Physikers (Springer, 1964).
  44. D. Novoa, H. Michinel, D. Tommasini, “Pressure, surface tension, and dripping of self-trapped laser beams,” Phys. Rev. Lett. 103(2), 023903 (2009). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited