OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 1 — Jan. 1, 2002
  • pp: 43–53

Stable all-optical limiting in nonlinear periodic structures. I. Analysis

Dmitry Pelinovsky, Jason Sears, Lukasz Brzozowski, and Edward H. Sargent  »View Author Affiliations

JOSA B, Vol. 19, Issue 1, pp. 43-53 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (282 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We consider propagation of coherent light through a nonlinear periodic optical structure consisting of two alternating layers with different linear and nonlinear refractive indices. A coupled-mode system is derived from the Maxwell equations and analyzed for the stationary-transmission regimes and linear time-dependent dynamics. We find the domain for existence of true all-optical limiting when the input–output transmission characteristic is monotonic and clamped below a limiting value for output intensity. True all-optical limiting can be managed by compensating the Kerr nonlinearities in the alternating layers, when the net-average nonlinearity is much smaller than the nonlinearity variance. The periodic optical structures can be used as uniform switches between lower-transmissive and higher-transmissive states if the structures are sufficiently long and out-of-phase, i.e., when the linear grating compensates the nonlinearity variations at each optical layer. We prove analytically that true all-optical limiting for zero net-average nonlinearity is asymptotically stable in time-dependent dynamics. We also show that weakly unbalanced out-of-phase gratings with small net-average nonlinearity exhibit local multistability, whereas strongly unbalanced gratings with large net-average nonlinearity display global multistability.

© 2002 Optical Society of America

OCIS Codes
(190.1450) Nonlinear optics : Bistability
(190.4360) Nonlinear optics : Nonlinear optics, devices
(230.4320) Optical devices : Nonlinear optical devices

Dmitry Pelinovsky, Jason Sears, Lukasz Brzozowski, and Edward H. Sargent, "Stable all-optical limiting in nonlinear periodic structures. I. Analysis," J. Opt. Soc. Am. B 19, 43-53 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. P. W. E. Smith and L. Qian, “Switching to optical for a faster tomorrow,” IEEE Circuits Devices Mag. 15(11), 28–33 (1999). [CrossRef]
  2. N. S. Patel, K. L. Hall, and K. A. Rauschenbach, “Interferometric all-optical switches for ultrafast signal processing,” Appl. Opt. 37, 2831–2842 (1998). [CrossRef]
  3. P. Tran, “All-optical switching with a nonlinear chiral photonic bandgap structure,” J. Opt. Soc. Am. B 16, 70–73 (1999). [CrossRef]
  4. G. L. Wood, W. W. Clark III, M. J. Miller, G. J. Salamo, and E. J. Sharp, “Evaluation of passive optical limiters and switches,” Proc. SPIE 1105, 154–166 (1989). [CrossRef]
  5. T. Xia, D. J. Hagan, A. Dogariu, A. A. Said, and E. W. Van Stryland, “Optimization of optical limiting devices based on excited-state absorption,” Appl. Opt. 36, 4110–4122 (1997). [CrossRef] [PubMed]
  6. I. C. Khoo, M. Wood, B. D. Guenther, “Nonlinear liquid crystal optical fiber array for all-optical switching/limiting,” in Proceedings of the Nineth Annual Meeting of the IEEE Lasers and Electro-Optics Society (IEEE, New York, 1996), Vol. 2, pp. 211–212.
  7. F. E. Hernandex, S. Yang, E. W. Van Stryland, and D. J. Hagan, “High-dynamic-range cascaded-focus optical limiter,” Opt. Lett. 25, 1180–1182 (2000). [CrossRef]
  8. M. W. Chbat, B. Hong, M. N. Islam, C. E. Soccoloich, and P. R. Prucnal, “Ultrafast soliton-trapping AND gate,” J. Lightwave Technol. 10, 2011–2016 (1992). [CrossRef]
  9. M. N. Islam, C. E. Soccolich, C.-J. Chen, K. S. Kim, J. R. Simpson, and U. C. Paek, “All-optical inverter with one picojoule switching energy,” Electron. Lett. 27, 130–132 (1991). [CrossRef]
  10. A. Niiyama and M. Koshiba, “Three-dimensional beam propagation analysis of nonlinear optical fibers and optical logic gates,” J. Lightwave Technol. 16, 162–168 (1998). [CrossRef]
  11. L. Brzozowski and E. H. Sargent, “Optical signal processing using nonlinear distributed feedback structures,” IEEE J. Quantum Electron. 36, 550–555 (2000). [CrossRef]
  12. H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structure,” Appl. Phys. Lett. 35, 379–381 (1979). [CrossRef]
  13. P. W. Smith, “Bistable optical devices promise subpicosecond switching,” IEEE Spectrum 8(6), 26–30 (1981). [CrossRef]
  14. C.-X. Shi, “Optical bistability in reflective fiber grating,” IEEE J. Quantum Electron. 31, 2037–2043 (1995). [CrossRef]
  15. S. Dubovitsky and W. H. Steier, “Analysis of optical bistability in a nonlinear coupled resonator,” IEEE J. Quantum Electron. 28, 585–589 (1992). [CrossRef]
  16. J. He and M. Cada, “Optical bistability in semiconductor periodic structures,” IEEE J. Quantum Electron. 27, 1182–1188 (1991). [CrossRef]
  17. H. G. Winful and G. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices,” Appl. Phys. Lett. 40, 298–300 (1982). [CrossRef]
  18. D. E. Pelinovsky, L. Brzozowski, and E. H. Sargent, “Transmission regimes of periodic nonlinear optical structures,” Phys. Rev. E 62, R4536–R4539 (2000). [CrossRef]
  19. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992). [CrossRef]
  20. A. Kobyakov, F. Lederer, O. Bang, and Yu. S. Kivshar, “Nonlinear phase shift and all-optical switching in quasi-phase-matching quadratic media,” Opt. Lett. 23, 506–508 (1998). [CrossRef]
  21. S. Trillo, C. Conti, G. Assanto, and A. V. Buryak, “From parametric gap solitons to chaos by means of second-harmonic generation in Bragg gratings,” Chaos 10, 590–599 (2000). [CrossRef]
  22. C. M. de Sterke and J. E. Sipe, “Gap solitons,” Prog. Opt. 33, 203–260 (1994). [CrossRef]
  23. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
  24. E. Kumacheva, O. Kalinina, and L. Lige, “Three-dimensional arrays in polymer nanocomposites,” Adv. Mater. 11, 231–234 (1999). [CrossRef]
  25. C. M. de Sterke, “Stability analysis of nonlinear periodic media,” Phys. Rev. A 45, 8252–8258 (1992). [CrossRef] [PubMed]
  26. 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). [CrossRef] [PubMed]
  27. M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, “The inverse scattering transform—Fourier analysis for nonlinear problems,” Stud. Appl. Math. 53, 249–315 (1974).
  28. D. E. Pelinovsky and R. H. J. Grimshaw, “Structural transformation of eigenvalues for a perturbed algebraic soliton potential,” Phys. Lett. A 229, 165–172 (1997). [CrossRef]

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