Skip to main content
SpringerLink
Log in

Periodic and Localized Structures in a Photonic Crystal Fiber Resonator

  • Conference paper
  • First Online:
Book cover Recent Trends in Applied Nonlinear Mechanics and Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 199))

  • 688 Accesses

Abstract

We consider a photonic crystal fiber resonator , driven by a coherent beam. The threshold for appearance of dark localized structures is estimated analytically and numerically by using a weakly nonlinear analysis in the vicinity of the modulational instability threshold. The nonlinear analysis allows to determine the parameter regime where the transition from supercritical to subcritical modulational instability takes place. This transition determines the threshold associated with the formation of dark cavity solitons. Numerical simulations of the governing model equation are in good agreement with the analytical results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Leblond, H., Mihalache, D.: Models of few optical cycle solitons beyond the slowly varying envelope approximation. Phys. Rep. 523(2), 61–126 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  2. Tlidi, M., Staliunas, K., Panajotov, K., Vladimirov, A.G., Clerc, M.G.: Localized structures in dissipative media: from optics to plant ecology. Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 372, 20140101 (2014)

    Article  ADS  Google Scholar 

  3. Lapine, M., Shadrivov, I.V., Kivshar, Y.S.: Colloquium: nonlinear metamaterials. Rev. Mod. Phys. 86 (2014) 1093–1123. http://dx.doi.org/10.1103/RevModPhys.86.1093. http://link.aps.org/doi/10.1103/RevModPhys.86.1093

  4. Knobloch, E.: Spatial localization in dissipative systems. Ann. Rev. Condens. Matter Phys. 6(1), 325–359 (2015). https://doi.org/10.1146/annurev-conmatphys-031214-014514

  5. Lugiato, L., Prati, F., Brambilla, M.: Nonlinear Optical Systems. Cambridge University Press (2015)

    Google Scholar 

  6. McLaughlin, D.W., Moloney, J.V., Newell, A.C.: Solitary waves as fixed points of infinite-dimensional maps in an optical bistable ring cavity. Phys. Rev. Lett. 51, 75 (1983). http://dx.doi.org/10.1103/PhysRevLett.51.75. http://link.aps.org/doi/10.1103/PhysRevLett.51.75

  7. Rosanov, N.N., Khodova, G.V.: Autosolitons in bistable interferometers. Opt. Spectrosc. 65, 449–450 (1988)

    ADS  Google Scholar 

  8. Tlidi, M., Mandel, P., Lefever, R.: Localized structures and localized patterns in optical bistability. Phys. Rev. Lett. 73, 640–643 (1994). http://dx.doi.org/10.1103/PhysRevLett.73.640. http://link.aps.org/doi/10.1103/PhysRevLett.73.640

  9. Vladimirov, A., McSloy, J., Skryabin, D., Firth, W.: Two-dimensional clusters of solitary structures in driven optical cavities. Phys. Rev. E 65, 046606 (2002). http://dx.doi.org/10.1103/PhysRevE.65.046606. http://link.aps.org/doi/10.1103/PhysRevE.65.046606

  10. Tlidi, M., Vladimirov, A.G., Mandel, P.: Interaction and stability of periodic and localized structures in optical bistable systems. IEEE J. Quantum Electron. 39(2), 216–226 (2003). http://dx.doi.org/10.1109/JQE.2002.807193

  11. Tlidi, M., Lefever, R., Vladimirov, A.: On vegetation clustering, localized bare soil spots and fairy circles. Lect. Notes Phys. 751, 381 (2008)

    MATH  MathSciNet  Google Scholar 

  12. Vladimirov, A.G., Lefever, R., Tlidi, M.: Relative stability of multipeak localized patterns of cavity solitons. Phys. Rev. A 84, 043848 (2011). http://dx.doi.org/10.1103/PhysRevA.84.043848. http://link.aps.org/doi/10.1103/PhysRevA.84.043848

  13. Haelterman, M., Trillo, S., Wabnitz, S.: Additive-modulation-instability ring laser in the normal dispersion regime of a fiber. Opt. Lett. 17(10), 745–747 (1992). http://dx.doi.org/10.1364/OL.17.000745. http://ol.osa.org/abstract.cfm?URI=ol-17-10-745

  14. Lugiato, L.A., Lefever, R.: Spatial dissipative structures in passive optical systems. Phys. Rev. Lett. 58, 2209–2211 (1987). http://dx.doi.org/10.1103/PhysRevLett.58.2209. http://link.aps.org/doi/10.1103/PhysRevLett.58.2209

  15. Scroggie, A.J., Firth, W.J., McDonald, G.S., Tlidi, M., Lefever, R., Lugiato, L.A.: Pattern formation in a passive kerr cavity, Chaos, Solitons Fractals 4(8), 1323 (1994). https://doi.org/10.1016/0960-0779(94)90084-1

  16. Leo, F., Coen, S., Kockaert, P., Gorza, S.-P., Emplit, P., Haelterman, M.: Temporal cavity solitons in one-dimensional kerr media as bits in an all-optical buffer. Nat. Photon. 4, 471 (2010). http://dx.doi.org/10.1038/nphoton.2010.120

  17. Tlidi, M., Gelens, L.: High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities. Opt. Lett. 35(3), 306–308 (2010). http://dx.doi.org/10.1364/OL.35.000306. http://ol.osa.org/abstract.cfm?URI=ol-35-3-306

  18. Cavalcanti, S.B., Cressoni, J.C., da Cruz, H.R., Gouveia-Neto, A.S.: Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation. Phys. Rev. A 43, 6162–6165 (1991). http://dx.doi.org/10.1103/PhysRevA.43.6162. http://link.aps.org/doi/10.1103/PhysRevA.43.6162

  19. Pitois, S., Millot, G.: Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber. Opt. Commun. 226(16), 415–422 (2003). https://doi.org/10.1016/j.optcom.2003.09.001. http://www.sciencedirect.com/science/article/pii/S0030401803019217

  20. Harvey, J.D., Leonhardt, R., Coen, S., Wong, G.K.L., Knight, J., Wadsworth, W.J., Russell, P.S.: Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber. Opt. Lett. 28(22), 2225–2227 (2003). http://dx.doi.org/10.1364/OL.28.002225 http://ol.osa.org/abstract.cfm?URI=ol-28-22-2225

  21. Joly, N.Y., Omenetto, F.G., Efimov, A., Taylor, A.J., Knight, J.C., Russell, P.S.J.: Competition between spectral splitting and raman frequency shift in negative-dispersion slope photonic crystal fiber, Opt. Commun. 248(13), 281–285 (2005). https://doi.org/10.1016/j.optcom.2004.11.091. http://www.sciencedirect.com/science/article/pii/S0030401804012477

  22. Yulin, A.V., Skryabin, D.V., Russell, P.S.J.: Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion. Opt. Lett. 29(20), 2411–2413 (2004). http://dx.doi.org/10.1364/OL.29.002411. http://ol.osa.org/abstract.cfm?URI=ol-29-20-2411

  23. Wadsworth, W.J., Joly, N., Knight, J.C., Birks, T.A., Biancalana, F., Russell, P.S.J.: Supercontinuum and four-wave mixing with q-switched pulses in endlessly single-mode photonic crystal fibres. Opt. Express 12(2), 299–309 (2004). http://dx.doi.org/10.1364/OPEX.12.000299. http://www.opticsexpress.org/abstract.cfm?URI=oe-12-2-299

  24. Demircan, A., Bandelow, U.: Supercontinuum generation by the modulation instability. Opt. Commun. 244(16), 181–185 (2005). https://doi.org/10.1016/j.optcom.2004.09.049. http://www.sciencedirect.com/science/article/pii/S0030401804009526

  25. Tlidi, M., Mussot, A., Louvergneaux, E., Kozyreff, G., Vladimirov, A.G., Taki, M.: Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities. Opt. Lett. 32(6), 662–664 (2007). http://dx.doi.org/10.1364/OL.32.000662. http://ol.osa.org/abstract.cfm?URI=ol-32-6-662

  26. Tlidi, M., Bahloul, L., Cherbi, L., Hariz, A., Coulibaly, S.: Drift of dark cavity solitons in a photonic-crystal fiber resonator. Phys. Rev. A 88, 035802 (2013). http://dx.doi.org/10.1103/PhysRevA.88.035802. http://link.aps.org/doi/10.1103/PhysRevA.88.035802

  27. Bahloul, L., Cherbi, L., Hariz, A., Tlidi, M.: Temporal localized structures in photonic crystal fibre resonators and their spontaneous symmetry-breaking instability. Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 372(2027) (2014). http://dx.doi.org/10.1098/rsta.2014.0020

  28. Milián, C., Skryabin, D.: Soliton families and resonant radiation in a micro-ring resonator near zero group-velocity dispersion. Opt. Express 22(3), 3732–3739 (2014). https://doi.org/10.1364/OE.22.003732. http://www.opticsexpress.org/abstract.cfm?URI=oe-22-3-3732

  29. Agrawal, G.P.: Nonlinear Fiber Optics, 5th edn, Academic Press (2012)

    Google Scholar 

  30. Manneville, P.: Dissipative Structures and Weak Turbulence. Academic Press (1990)

    Google Scholar 

  31. Tlidi, M., Lefever, R., Mandel, P.: Pattern selection in optical bistability. Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 8(4), 931 (1996). http://stacks.iop.org/1355-5111/8/i=4/a=014

Download references

Acknowledgements

M.T. received support from the Fonds National de la Recherche Scientifique (Belgium). M.T acknowledges the financial support of the Interuniversity Attraction Poles program of the Belgian Science Policy Office, under grant IAP 7–35 photonics@be.

Author information

Authors and Affiliations

  1. Laboratoire of Instrumentation, University of Sciences and Technology Houari Boumediene (USTHB), Bab Ezzouar, Algeria

    L. Bahloul, L. Cherbi & A. Hariz

  2. Physique du Rayonnement et des Interactions Laser-Matière, Faculté des Sciences, Université Moulay Ismail, B.P. 11201, Zitoune, Meknès, Morocco

    A. Makhoute

  3. Département de Physique, Faculté des Sciences, Université Libre de Bruxelles (U.L.B.), CP 231, Campus Plaine, 1050, Bruxelles, Belgium

    E. Averlant & M. Tlidi

  4. Brussels Photonics Team, Department of Applied Physics and Photonics (B-PHOT TONA), Vrije Universiteit Brussels, Pleinlaan 2, 1050, Brussels, Belgium

    E. Averlant

Authors
  1. L. Bahloul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Cherbi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Hariz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Makhoute
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. E. Averlant
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. Tlidi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Tlidi .

Editor information

Editors and Affiliations

  1. University Hassan II - Casablanca, Casablanca, Morocco

    Mohamed Belhaq

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bahloul, L., Cherbi, L., Hariz, A., Makhoute, A., Averlant, E., Tlidi, M. (2018). Periodic and Localized Structures in a Photonic Crystal Fiber Resonator. In: Belhaq, M. (eds) Recent Trends in Applied Nonlinear Mechanics and Physics. Springer Proceedings in Physics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-63937-6_10

Download citation

Publish with us

Policies and ethics

Search

Navigation