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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 9180–9191

Dynamics of one-dimensional Kerr cavity solitons

François Leo, Lendert Gelens, Philippe Emplit, Marc Haelterman, and Stéphane Coen  »View Author Affiliations

Optics Express, Vol. 21, Issue 7, pp. 9180-9191 (2013)

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We present an experimental observation of an oscillating Kerr cavity soliton, i.e., a time-periodic oscillating one-dimensional temporally localized structure excited in a driven nonlinear fiber cavity with a Kerr-type nonlinearity. More generally, these oscillations result from a Hopf bifurcation of a (spatially or temporally) localized state in the generic class of driven dissipative systems close to the 1 : 1 resonance tongue. Furthermore, we theoretically analyze dynamical instabilities of the one-dimensional cavity soliton, revealing oscillations and different chaotic states in previously unexplored regions of parameter space. As cavity solitons are closely related to Kerr frequency combs, we expect these dynamical regimes to be highly relevant for the field of microresonator-based frequency combs.

© 2013 OSA

OCIS Codes
(190.3100) Nonlinear optics : Instabilities and chaos
(190.4370) Nonlinear optics : Nonlinear optics, fibers

ToC Category:
Nonlinear Optics

Original Manuscript: February 13, 2013
Revised Manuscript: March 20, 2013
Manuscript Accepted: March 21, 2013
Published: April 5, 2013

François Leo, Lendert Gelens, Philippe Emplit, Marc Haelterman, and Stéphane Coen, "Dynamics of one-dimensional Kerr cavity solitons," Opt. Express 21, 9180-9191 (2013)

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  1. L. A. Lugiato, “Introduction to the feature section on cavity solitons: an overview,” IEEE J. Quantum Elec.39, 193–196 (2003). [CrossRef]
  2. G. S. McDonald and W. J. Firth, “Spatial solitary-wave optical memory,” J. Opt. Soc. Am. B7, 1328–1335 (1990). [CrossRef]
  3. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature419, 699–702 (2002). [CrossRef] [PubMed]
  4. F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photon.4, 471–476 (2010). [CrossRef]
  5. V. Odent, M. Taki, and E. Louvergneaux, “Experimental evidence of dissipative spatial solitons in an optical passive Kerr cavity,” New J. Phys.13, 113026/1–13 (2011). [CrossRef]
  6. S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett.38, 37–39 (2013). [CrossRef] [PubMed]
  7. M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys.65, 851–1112 (1993). [CrossRef]
  8. J. Wu, R. Keolian, and I. Rudnick, “Observation of a nonpropagating hydrodynamic soliton,” Phys. Rev. Lett.52, 1421–1424 (1984). [CrossRef]
  9. H. C. Kim, R. L. Stenzel, and A. Y. Wong, “Development of ‘cavitons’ and trapping of RF field,” Phys. Rev. Lett.33, 886–889 (1974). [CrossRef]
  10. R. Richter and I. V. Barashenkov, “Two-dimensional solitons on the surface of magnetic fluids,” Phys. Rev. Lett.94, 184503/1–4 (2005). [CrossRef]
  11. P. B. Umbanhowar, F. Melo, and H. L. Swinney, “Localized excitations in a vertically vibrated granular layer,” Nature382, 793–796 (1996). [CrossRef]
  12. A. Ustinov, “Solitons in Josephson junctions,” Physica D123, 315–329 (1998). [CrossRef]
  13. B. Ermentrout, X. Chen, and Z. Chen, “Transition fronts and localized structures in bistable reaction-diffusion equations,” Physica D108, 147–167 (1997). [CrossRef]
  14. V. K. Vanag, A. M. Zhabotinsky, and I. R. Epstein, “Oscillatory clusters in the periodically illuminated, spatially extended Belousov-Zhabotinsky reaction,” Phys. Rev. Lett.86, 552–555 (2001). [CrossRef] [PubMed]
  15. O. Lejeune, M. Tlidi, and P. Couteron, “Localized vegetation patches: A self-organized response to resource scarcity,” Phys. Rev. E66, 010901 (2002). [CrossRef]
  16. B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, “Interaction of localized structures in an optical pattern-forming system,” Phys. Rev. Lett.85, 748–751 (2000). [CrossRef] [PubMed]
  17. S. Barbay, X. Hachair, T. Elsass, I. Sagnes, and R. Kuszelewicz, “Homoclinic snaking in a semiconductor-based optical system,” Phys. Rev. Lett.101, 253902 (2008). [CrossRef] [PubMed]
  18. O. Lioubashevski, Y. Hamiel, A. Agnon, Z. Reches, and J. Fineberg, “Oscillons and propagating solitary waves in a vertically vibrated colloidal suspension,” Phys. Rev. Lett.83, 3190–3193 (1999). [CrossRef]
  19. C. Elphick, G. Iooss, and E. Tirapegui, “Normal form reduction for time-periodically driven differential equations,” Phys. Lett. A120, 459–463 (1987). [CrossRef]
  20. L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett.58, 2209–2211 (1987). [CrossRef] [PubMed]
  21. K. Nozaki and N. Bekki, “Chaotic solitons in a plasma driven by an RF field,” J. Phys. Soc. Jpn.54, 2363–2366 (1985); ibid. Physica D 21, 381 (1986) [CrossRef]
  22. D. Turaev, A. G. Vladimirov, and S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons,” Phys. Rev. Lett.108, 263906/1–5 (2012). [CrossRef]
  23. A. B. Matsko, A. A. Savchenkov, and L. Maleki, “On excitation of breather solitons in an optical microresonator,” Opt. Lett.37, 4856–4858 (2012). [CrossRef] [PubMed]
  24. D. Gomila, A. Scroggie, and W. Firth, “Bifurcation structure of dissipative solitons,” Physica D227, 70–77 (2007). [CrossRef]
  25. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007). [CrossRef]
  26. M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express19, 14233–14239 (2011). [CrossRef] [PubMed]
  27. A. Tierno, F. Gustave, and S. Barland, “Class A mode-locked semiconductor ring laser,” Opt. Lett.37, 2004–2006 (2012). [CrossRef] [PubMed]
  28. W. J. Firth, G. K. Harkness, A. Lord, J. M. McSloy, D. Gomila, and P. Colet, “Dynamical properties of two-dimensional Kerr cavity solitons,” J. Opt. Soc. Am. B19, 747–752 (2002). [CrossRef]
  29. M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun.91, 401–407 (1992). [CrossRef]
  30. A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, and L. A. Lugiato, “Pattern formation in a passive Kerr cavity,” Chaos, Solitons & Fractals4, 1323–1354 (1994). [CrossRef]
  31. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2006).
  32. K. Wiesenfeld, “Noisy precursors of nonlinear instabilities,” J. Stat. Phys.38, 1071–1097 (1985). [CrossRef]
  33. I. S. Aranson and L. Kramer, “The world of the complex Ginzburg-Landau equation,” Rev. Mod. Phys.74, 99–143 (2002). [CrossRef]
  34. O. Descalzi, C. Cartes, J. Cisternas, and H. R. Brand, “Exploding dissipative solitons: The analog of the Ruelle-Takens route for spatially localized solutions,” Phys. Rev. E83, 056214/1–6 (2011). [CrossRef]
  35. J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett.85, 2937–2940 (2000). [CrossRef] [PubMed]
  36. T. Kapitula and B. Sandstede, “Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations,” Physica D124, 58–103 (1998). [CrossRef]
  37. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photon.6, 84–92 (2012). [CrossRef]
  38. L. Gelens and E. Knobloch, “Traveling waves and defects in the complex Swift-Hohenberg equation,” Phys. Rev. E84, 056203/1–22 (2011). [CrossRef]
  39. A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, and N. N. Rosanov, “Numerical investigation of laser localized structures,” J. Opt. B: Quantum Semiclass. Opt.1, 101–106 (1999). [CrossRef]
  40. N. V. Alexeeva, I. V. Barashenkov, and D. E. Pelinovsky, “Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability,” Nonlinearity12, 103–140 (1999). [CrossRef]
  41. J. Burke, A. Yochelis, and E. Knobloch, “Classification of spatially localized oscillations in periodically forced dissipative systems,” SIAM J. Appl. Dyn. Syst.7, 651–711 (2008). [CrossRef]
  42. Y.-P. Ma, J. Burke, and E. Knobloch, “Defect-mediated snaking: A new growth mechanism for localized structures,” Physica D239, 1867–1883 (2010). [CrossRef]
  43. D. Gomila, A. Jacobo, M. A. Matías, and P. Colet, “Phase-space structure of two-dimensional excitable localized structures,” Phys. Rev. E75, 026217/1–10 (2007). [CrossRef]
  44. C. Grebogi, E. Ott, and J. A. Yorke, “Crises, sudden changes in chaotic attractors, and transient chaos,” Physica D7, 181–200 (1983). [CrossRef]
  45. E. M. Izhikevich, “Neural excitability, spiking and bursting,” Int. J. Bifurcation Chaos10, 1171–1266 (2000). [CrossRef]
  46. L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization,” Phys. Rev. A82, 063841/1–9 (2010). [CrossRef]
  47. W. Coomans, L. Gelens, S. Beri, J. Danckaert, and G. Van der Sande, “Solitary and coupled semiconductor ring lasers as optical spiking neurons,” Phys. Rev. E84, 036209/1–8 (2011). [CrossRef]
  48. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science332, 555–559 (2011). [CrossRef] [PubMed]

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