Skip to main content

Dynamic characteristics of nonlinear Bragg gratings in photonic crystal fibres


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.

This is a preview of subscription content, access via your institution.


  • Aceves A., De Angelis C., Wabnitz S. (1992). Generation of solitons in a nonlinear periodic medium. Opt. Lett. 17(22): 1566–1568

    ADS  Google Scholar 

  • 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

    Article  Google Scholar 

  • de Sterke C., Sipe J. (1990). Switching dynamics of finite periodic nonlinear media: a numerical study. Phys. Rev. A 42(5): 2858–2869

    Article  ADS  Google Scholar 

  • 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

    ADS  Article  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Erdogan T. (1997). Fiber grating spectra. J. Lightwave Technol. 15: 1277–1294

    Article  ADS  Google Scholar 

  • Kotynski R., Antkowiak M., Berghmans F., Thienpont H., Panajotov K. (2005). Photonic crystal fibers with material anisotropy. Opt. Quantum Electron. 37: 253–264

    Article  Google Scholar 

  • Lee H., Agrawal G.P. (2003). Nonlinear switching of optical pulses on fiber Bragg gratings. IEEE J. Quantum Electron. 39: 508–515

    Article  ADS  Google Scholar 

  • Leon J., Spire A. (2004). Gap soliton formation by nonlinear supratransmission in Bragg media. Phys. Lett. A 327(5–6): 474–480

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Pelinovsky D., Sargent E.H. (2002). Stable all-optical limiting in nonlinear periodic structures. II. Computations. J. Opt. Soc. Am. B 19: 1873–1889

    ADS  Article  Google Scholar 

  • Winful H., Cooperman G. (1982). Self-pulsing and chaos in distributed feedback bistable optical devices. Appl. Phys. Lett. 40(4): 298–300

    Article  ADS  Google Scholar 

  • Winful H., Marburger J., Garmire E. (1979). Theory of bistability in nonlinear distributed feedback structures. Appl. Phys. Lett. 35: 379–381

    Article  ADS  Google Scholar 

  • Winful H., Zamir R., Feldman S. (1991). Modulational instability in nonlinear periodic structures: implications for “gap solitons”. Appl. Phys. Lett. 58(10): 1001–1003

    Article  ADS  Google Scholar 

  • Yosia S.P., Chao L. (2005). Bistability threshold inside hysteresis loop of nonlinear fiber Bragg gratings. Opt. Express 13: 5127–5135

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Maciej Antkowiak.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Antkowiak, M., Kotyński, R., Panajotov, K. et al. Dynamic characteristics of nonlinear Bragg gratings in photonic crystal fibres. Opt Quant Electron 39, 455–467 (2007).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Photonic crystal fibres
  • Nonlinear Bragg gratings
  • Nonlinear dynamics