OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 4 — Apr. 1, 2006
  • pp: 842–847

Simulation of two-dimensional Kerr photonic crystals via fast Fourier factorization

J. J. Bonnefois, Géraldine Guida, Alain Priou, Michel Nevière, and Evgeny Popov  »View Author Affiliations

JOSA A, Vol. 23, Issue 4, pp. 842-847 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (410 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present an adaptation of the fast Fourier factorization method to the simulation of two-dimensional (2D) photonic crystals with a third-order nonlinearity. The algorithm and its performance are detailed and illustrated via the simulation of a Kerr 2D photonic crystal. A change in the transmission spectrum at high intensity is observed. We explain why the change does not reduce to a translation (redshift) but rather consists in a deformation and why one side of the bandgap is more suited to a switching application than the other one.

© 2006 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.1450) Nonlinear optics : Bistability
(190.3270) Nonlinear optics : Kerr effect

ToC Category:
Nonlinear Optics

Original Manuscript: July 27, 2005
Revised Manuscript: October 3, 2005
Manuscript Accepted: October 5, 2005

J. J. Bonnefois, Géraldine Guida, Alain Priou, Michel Nevière, and Evgeny Popov, "Simulation of two-dimensional Kerr photonic crystals via fast Fourier factorization," J. Opt. Soc. Am. A 23, 842-847 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. Joannopoulos, Photonic Crystals, Molding the Flow of Light (Princeton U. Press, 1995).
  2. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  3. A. Priou and T. Itoh, eds., Progress in Electromagnetic Research (Universita di Pisa, 2004), Vol. 43.
  4. K. Bush and S. John, "Liquid crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999). [CrossRef]
  5. D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003). [CrossRef]
  6. P. Halevi and F. R. Mendieta, "Tunable photonic crystals with semiconducting constituents," Phys. Rev. Lett. 85, 1875-1878 (2000). [CrossRef] [PubMed]
  7. W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987). [CrossRef] [PubMed]
  8. S. John and N. Akozbek, "Nonlinear optical solitary waves in a photonic band gap," Phys. Rev. Lett. 71, 1168-1171 (1993). [CrossRef] [PubMed]
  9. M. Scarola, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashortpulses in nonlinear photonic bandgap material," Phys. Rev. Lett. 73, 1368-1371 (1994). [CrossRef]
  10. H. Y. Ryu and M. Notomi, "Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab," Phys. Rev. B 68, 5209-5217 (2003). [CrossRef]
  11. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).
  12. R. Wang, J. Dong, and D. Y. Xing, "Dispersive optical bistability in one-dimensional doped photonic band gap structure," Phys. Rev. E 55, 6301-6304 (1997). [CrossRef]
  13. V. Lousse and J. P. Vigneron, "Bistable behaviour of a photonic crystal nonlinear cavity," Physica B 338, 171-177 (2003). [CrossRef]
  14. E. Lidorikis, Q. Li, and C. M. Soukoulis, "Wave propagation in nonlinear multilayer structures," Phys. Rev. B 54, 10249-10252 (1996). [CrossRef]
  15. N. Akozbek and S. John, "Optical solitary waves in two and three-dimensional nonlinear photonic band-gap structures," Phys. Rev. E 57, 2287-2319 (1998). [CrossRef]
  16. S. F. Mingaleev and Y. S. Kivshar, "Self-trapping and stable localized modes in nonlinear photonic crystals," Phys. Rev. Lett. 86, 5474-5477 (2001). [CrossRef] [PubMed]
  17. S. Pereira, P. Chark, and J. E. Sipe, "Gap-soliton switching in short microresonator structures," J. Opt. Soc. Am. B 19, 2191-2202 (2002). [CrossRef]
  18. P. Xie, Z. Q. Zhang, and X. Zhang, "Gap solitons and soliton trains in finite-size two-dimensional periodic and quasiperiodic photonic crystals," Phys. Rev. E 67, 026607-026612 (2003). [CrossRef]
  19. A. M. Kamtchatnoc, S. A. Darmanyan, and M. Nevière, "Polariton gap solitary waves in semiconductor microcavities," J. Lumin. 110, 373-377 (2004). [CrossRef]
  20. P. Tran, "Optical limiting and switching of short pulses by use of a nonlinear photonic bandgap structure with a defect," J. Opt. Soc. Am. B 14, 2589-2595 (1997). [CrossRef]
  21. L. Brzozowski and E. H. Sargent, "Nonlinear distributed-feedback structures as passive optical limiters," J. Opt. Soc. Am. B 17, 1360-1365 (2000). [CrossRef]
  22. B. Y. Soon, J. W. Haus, M. Scalora, and C. Sibilia, "One-dimensional photonic crystal limiter," Opt. Express 11, 2007-2018 (2003). [CrossRef] [PubMed]
  23. V. Lousse and J. P. Vigneron, "Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical material," Phys. Rev. E 63, 027602-027606 (2001). [CrossRef]
  24. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystal," Phys. Rev. E 66, 055601-055605 (2002). [CrossRef]
  25. E. Popov and M. Nevière, Light Propagation in Periodic Media (Marcel Dekker, 2003).
  26. E. Popov and M. Nevière, "Grating theory: new equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A 17, 1773-1784 (2000). [CrossRef]
  27. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996). [CrossRef]
  28. N. Bonod, E. Popov, and M. Neviere, "Fourier factorization of nonlinear Maxwell equations in periodic media: application to the optical Kerr effect," Opt. Commun. 244, 389-398 (2005). [CrossRef]
  29. P. Vincent, N. Paraire, M. Nevière, A. Koster, and R. Reinisch, "Gratings in nonlinear optics and optical bistability," J. Opt. Soc. Am. B 2, 1106-1116 (1985). [CrossRef]
  30. V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystals films," Phys. Rev. B 69, 155106-155117 (2004). [CrossRef]
  31. D. Felbacq, G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A 11, 2526-2534 (1994). [CrossRef]
  32. E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000). [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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited