Optical and Quantum Electronics

, Volume 39, Issue 4–6, pp 455–467 | Cite as

Dynamic characteristics of nonlinear Bragg gratings in photonic crystal fibres

  • Maciej AntkowiakEmail author
  • Rafał Kotyński
  • Krassimir Panajotov
  • Francis Berghmans
  • Hugo Thienpont


We study numerically the temporal and spatial dynamics of light in Bragg gratings in highly nonlinear photonic crystal fibre for a CW input signal. Our numerical model is based on the plane wave mode solver and a set of nonlinear coupled-mode equations which we solve using a variation of implicit fourth order Runge-Kutta method. We observe not only bistability of the intensity versus transmitted and reflected light but also complex dynamics. We demonstrate that for values of input intensity above the bistable region the steady state may undergo a supercritical Hopf bifurcation. For some ranges of the input intensity we also observe a coexistence of two periodic attractors. The dynamics found, in particular the features in the bifurcation diagram, strongly depend on the parameters of the fibre. Consequently, we suggest that by proper design of the photonic crystal in the cladding we can adjust such nonlinear features of the Bragg gratings as the width of the bistable region, the intensity at which the bifurcation occurs and also the characteristics of the dynamics at high values of input intensity.


Photonic crystal fibres Nonlinear Bragg gratings Nonlinear dynamics 


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  1. Aceves A., De Angelis C., Wabnitz S. (1992). Generation of solitons in a nonlinear periodic medium. Opt. Lett. 17(22): 1566–1568 ADSGoogle Scholar
  2. Antkowiak M., Kotynski R., Panajotov K., Berghmans F., Thienpont H. (2006). Numerical analysis of highly birefringent photonic crystal fibers with Bragg reflectors. Opt. Quantum Electron. 38: 535–545 CrossRefGoogle Scholar
  3. de Sterke C., Sipe J. (1990). Switching dynamics of finite periodic nonlinear media: a numerical study. Phys. Rev. A 42(5): 2858–2869 CrossRefADSGoogle Scholar
  4. de Sterke C.M., Jackson K.R., Robert B.D. (1991). Nonlinear coupled-mode equations on a finite interval: a numerical procedure. J. Opt. Soc. Am. B 8: 403–412 ADSCrossRefGoogle Scholar
  5. Ebendorff-Heidepriem H., Petropoulos P., Asimakis S., Finazzi V., Moore R., Frampton K., Koizumi F., Richardson D., Monro T. (2004). Bismuth glass holey fibers with high nonlinearity. Opt. Express 12: 5082–5087 CrossRefADSGoogle Scholar
  6. Efimov A., Taylor A., Omenetto F., Yulin A., Joly N., Biancalana F., Skryabin D., Knight J., Russell P. (2004). Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: experiment and modelling. Opt. Express 12: 6498–6507 CrossRefADSGoogle Scholar
  7. Erdogan T. (1997). Fiber grating spectra. J. Lightwave Technol. 15: 1277–1294 CrossRefADSGoogle Scholar
  8. Kotynski R., Antkowiak M., Berghmans F., Thienpont H., Panajotov K. (2005). Photonic crystal fibers with material anisotropy. Opt. Quantum Electron. 37: 253–264 CrossRefGoogle Scholar
  9. Lee H., Agrawal G.P. (2003). Nonlinear switching of optical pulses on fiber Bragg gratings. IEEE J. Quantum Electron. 39: 508–515 CrossRefADSGoogle Scholar
  10. Leon J., Spire A. (2004). Gap soliton formation by nonlinear supratransmission in Bragg media. Phys. Lett. A 327(5–6): 474–480 CrossRefADSGoogle Scholar
  11. Leong J.Y.Y., Petropoulos P., Price J.H.V., Ebendorff-Heidepriem H., Asimakis S., Moore R.C., Frampton K.E., Finazzi V., Feng X., Monro T.M., Richardson D.J. (2006). High-nonlinearity dispersion-shifted lead–silicate holey fibers for efficient 1-um pumped supercontinuum generation. J. Lightwave Technol. 24: 183–190 CrossRefADSGoogle Scholar
  12. Pelinovsky D., Sargent E.H. (2002). Stable all-optical limiting in nonlinear periodic structures. II. Computations. J. Opt. Soc. Am. B 19: 1873–1889 ADSCrossRefGoogle Scholar
  13. Winful H., Cooperman G. (1982). Self-pulsing and chaos in distributed feedback bistable optical devices. Appl. Phys. Lett. 40(4): 298–300 CrossRefADSGoogle Scholar
  14. Winful H., Marburger J., Garmire E. (1979). Theory of bistability in nonlinear distributed feedback structures. Appl. Phys. Lett. 35: 379–381 CrossRefADSGoogle Scholar
  15. Winful H., Zamir R., Feldman S. (1991). Modulational instability in nonlinear periodic structures: implications for “gap solitons”. Appl. Phys. Lett. 58(10): 1001–1003 CrossRefADSGoogle Scholar
  16. Yosia S.P., Chao L. (2005). Bistability threshold inside hysteresis loop of nonlinear fiber Bragg gratings. Opt. Express 13: 5127–5135 CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Maciej Antkowiak
    • 1
    • 2
    Email author
  • Rafał Kotyński
    • 1
    • 3
  • Krassimir Panajotov
    • 1
    • 4
  • Francis Berghmans
    • 1
    • 2
  • Hugo Thienpont
    • 1
  1. 1.Vrije Universiteit BrusselBrusselsBelgium
  2. 2.SCK.CENMolBelgium
  3. 3.Warsaw UniversityWarsawPoland
  4. 4.Institute of Solid State PhysicsSofiaBulgaria

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