OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 9 — Sep. 1, 2002
  • pp: 2241–2249

Nonlinear transmission and light localization in photonic-crystal waveguides

Sergei F. Mingaleev and Yuri S. Kivshar  »View Author Affiliations

JOSA B, Vol. 19, Issue 9, pp. 2241-2249 (2002)

View Full Text Article

Acrobat PDF (1120 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We study light transmission in two-dimensional photonic-crystal waveguides with embedded nonlinear defects. First, we derive effective discrete equations with long-range interaction for describing the waveguide modes and demonstrate that they provide a highly accurate generalization of the familiar tight-binding models that are employed, e.g., for the study of coupled-resonator optical waveguides. Using these equations, we investigate the properties of straight waveguides and waveguide bends with embedded linear and nonlinear defects. We emphasize the role of evanescent modes in the transmission properties of such waveguides and demonstrate the possibility of the nonlinearity-induced bistable (all-optical switcher) and unidirectional (optical diode) transmission. Additionally, we demonstrate adaptability of our approach for investigation of multimode waveguides by the example of the bound states in their constrictions. © 2002 Optical Society of America

© 2002 Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices
(230.7370) Optical devices : Waveguides

Sergei F. Mingaleev and Yuri S. Kivshar, "Nonlinear transmission and light localization in photonic-crystal waveguides," J. Opt. Soc. Am. B 19, 2241-2249 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. J. D. Joannoupoulos, R. B. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  2. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001).
  3. T. F. Krauss and R. M. De la Rue, “Photonic crystals in the optical regime—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999), and references therein.
  4. See, e.g., K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999), and discussions therein.
  5. S. John and N. Aközbek, “Nonlinear optical solitary waves in a photonic band gap,” Phys. Rev. Lett. 71, 1168–1171 (1993).
  6. S. John and N. Aközbek, “Optical solitary waves in two- and three-dimensional nonlinear photonic band-gap structures,” Phys. Rev. E 57, 2287–2319 (1998).
  7. S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, “Long-range interaction and nonlinear localized modes in photonic crystal waveguides,” Phys. Rev. E 62, 5777–5782 (2000).
  8. S. F. Mingaleev and Yu. S. Kivshar, “Self-trapping and stable localized modes in nonlinear photonic crystals,” Phys. Rev. Lett. 86, 5474–5477 (2001).
  9. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane-wave basis,” Opt. Express 8, 173–190 (2001), http://epubs.osa.org//optics.express.
  10. A. Mekis, S. H. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B 58, 4809–4817 (1998).
  11. A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
  12. S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
  13. S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).
  14. S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23, 1855–1857 (1998).
  15. S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
  16. T. Zijlstra, E. van der Drift, M. J. A. de Dood, E. Snoeks, and A. Polman, “Fabrication of two-dimensional photonic crystal waveguides for 1.5 μm in silicon by deep anisotropic dry etching,” J. Vac. Sci. Technol. B 17, 2734–2739 (1999).
  17. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
  18. Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
  19. M. Bayindir, B. Temelkuran, and E. Ozbay, “Propagation of photons by hopping: a waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals,” Phys. Rev. B 61, R11855–R11858 (2000).
  20. E. Lidorikis, M. M. Sigalas, E. Economou, and C. M. Soukoulis, “Tight-binding parametrization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
  21. A. R. McGurn, “Green’s-function theory for row and periodic defect arrays in photonic band structures,” Phys. Rev. B 53, 7059–7064 (1996).
  22. S. F. Mingaleev and Yu. S. Kivshar, “Effective equations for photonic crystal waveguides and circuits,” Opt. Lett. 27, 231–233 (2002).
  23. F. Delyon, Y.-E. Lévy, and B. Souillard, “Nonperturbative bistability in periodic nonlinear media,” Phys. Rev. Lett. 57, 2010–2013 (1986).
  24. Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Wave propagation in nonlinear photonic band-gap materials,” Phys. Rev. B 53, 15577–15585 (1996).
  25. E. Centero and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, R7683–R7686 (2000).
  26. M. Scalora, J. R. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
  27. M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).

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