OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 17, Iss. 11 — Nov. 1, 2000
  • pp: 1894–1900

Stability of nonlinear Bragg gratings with a finite material response time

Kazuhiko Ogusu  »View Author Affiliations

JOSA B, Vol. 17, Issue 11, pp. 1894-1900 (2000)

View Full Text Article

Acrobat PDF (392 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A linear stability analysis to investigate the instabilities in nonlinear distributed-feedback gratings with a finite material response time is presented. The amplification (or attenuation) rate and the frequency of sinusoidal perturbations generated in the grating are calculated for different values of the material response time, detuning, and coupling strength. To give the full picture of the stability boundaries, stability maps are plotted in the two cases of a weak grating and a strong grating. The stable region can be enlarged by increasing a response time of the nonlinearity. The required response time increases with the grating strength. A comparison with numerical simulations of the coupled-mode equations is done to confirm the validity of the stability analysis.

© 2000 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(190.1450) Nonlinear optics : Bistability
(190.3100) Nonlinear optics : Instabilities and chaos
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

Kazuhiko Ogusu, "Stability of nonlinear Bragg gratings with a finite material response time," J. Opt. Soc. Am. B 17, 1894-1900 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
  2. M. Cada, J. He, B. Acklin, M. Proctor, D. Martin, F. Morier-Genoud, M.-A. Dupertuis, and J. M. Glinski, “All-optical reflectivity tuning and logic gating in a GaAs/AlAs periodic layered structure,” Appl. Phys. Lett. 60, 404–406 (1992).
  3. N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All-optical switching in a nonlinear periodic-waveguide structure,” Appl. Phys. Lett. 60, 1427–1429 (1992).
  4. C. J. Herbert, W. S. Capinski, and M. S. Malcuit, “Optical power limiting with nonlinear periodic structures,” Opt. Lett. 17, 1037–1039 (1992).
  5. C. J. Herbert and M. S. Malcuit, “Optical bistability in nonlinear periodic structures,” Opt. Lett. 18, 1783–1785 (1993).
  6. H. G. Winful and G. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices,” Appl. Phys. Lett. 40, 298–300 (1982).
  7. H. G. Winful, R. Zamir, and S. Feldman, “Modulational instability in nonlinear periodic structures: implications for ‘gap solitons’,” Appl. Phys. Lett. 58, 1001–1003 (1991).
  8. W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
  9. C. M. de Sterke, “Stability analysis of nonlinear periodic media,” Phys. Rev. A 45, 8252–8258 (1992).
  10. C. M. de Sterke and J. E. Sipe, “Switching dynamics of finite periodic nonlinear media: a numerical study,” Phys. Rev. A 42, 2858–2869 (1990).
  11. C. M. de Sterke, “Simulations of gap-soliton generation,” Phys. Rev. A 45, 2012–2018 (1992).
  12. B. J. Eggleton, C. M. de Sterke, R. E. Slusher, and J. E. Sipe, “Distributed feedback pulse generator based on nonlinear fiber grating,” Electron. Lett. 32, 2341–2342 (1996).
  13. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
  14. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
  15. B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
  16. W. J. Firth, “Stability of nonlinear Fabry–Perot resonators,” Opt. Commun. 39, 343–346 (1981).
  17. K. Ogusu, H. Li, and T. Kamizono, “Analysis of transient optical bistability and stability in a nonlinear fiber Fabry– Perot resonator based on an iterative method,” Opt. Rev. 5, 185–190 (1998).
  18. A. L. Steele, S. Lynch, and J. E. Hoad, “Analysis of optical instabilities and bistability in a nonlinear optical fiber loop mirror with feedback,” Opt. Commun. 137, 136–142 (1997).
  19. H. Li and K. Ogusu, “Analysis of optical instability in a double-coupler nonlinear fiber ring resonator,” Opt. Commun. 157, 27–32 (1998).
  20. K. Ogusu and T. Kamizono, “Effect of material response time on optical bistability in nonlinear distributed feedback gratings,” Opt. Rev. 7, 83–88 (2000).

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited