OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 26 — Dec. 26, 2005
  • pp: 10571–10588

Bandgap lattices: low index solitons and linear properties

Nikolaos K. Efremidis and Kyriakos Hizanidis  »View Author Affiliations


Optics Express, Vol. 13, Issue 26, pp. 10571-10588 (2005)
http://dx.doi.org/10.1364/OPEX.13.010571


View Full Text Article

Enhanced HTML    Acrobat PDF (733 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A new type of waveguide lattice that relies on the effect of bandgap guidance, rather than total internal reflection, in the regions between the waveguide defects is proposed. Two different setting, for low index and high index defects are suggested. We analyze the linear bandgap and diffraction properties of such lattices. In the nonlinear regime the Kerr effect can counteract diffraction leading to the formation of gap lattice solitons. Interestingly enough, in the case of low index defects, stable soliton solutions are localized in the low index areas. This finding challenges the widely accepted idea that stable solitons can be sustained in high refractive index regions. In addition, in the case of high index defects, the coupling coefficient can become negative. Physical settings where the linear and nonlinear properties for bandgap lattices can be experimentally realized are presented.

© 2005 Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Research Papers

Citation
Nikolaos K. Efremidis and Kyriakos Hizanidis, "Bandgap lattices: low index solitons and linear properties," Opt. Express 13, 10571-10588 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-26-10571


Sort:  Journal  |  Reset  

References

  1. E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  2. S. John, "Strong Localization of Photons in Certain Disordered Dielectric Superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  3. J. Joannopoulos, R. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, NJ, 1995).
  4. J. Knight, J. Broeng, T. A. Birks, and P. Russell, "Photonic band gap guidance in optical fibers," Science 282, 1476-1478 (1998). [CrossRef] [PubMed]
  5. P. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003). [CrossRef] [PubMed]
  6. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988). [CrossRef] [PubMed]
  7. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete Spatial Optical Solitons in Waveguide Arrays," Phys. Rev. Lett. 81, 3383-3386 (1998). [CrossRef]
  8. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003). [CrossRef] [PubMed]
  9. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High Transmission through Sharp Bends in Photonic Crystal Waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996). [CrossRef] [PubMed]
  10. S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, "Microwave Propagation in Two-Dimensional Dielectric Lattices," Phys. Rev. Lett. 67, 2017-2020 (1991). [CrossRef] [PubMed]
  11. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Donor and Acceptor Modes in Photonic Band Strucure," Phys. Rev. Lett. 67, 3380-3383 (1991). [CrossRef] [PubMed]
  12. N. Stefanou and A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12,127-12,133 (1998). [CrossRef]
  13. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999). [CrossRef]
  14. M. Bayindir, B. Temelkuran, and E. Ozbay, "Tight-Binding Description of the Coupled Defect Modes in Three-Dimensional Photonic Crystals," Phys. Rev. Lett. 84, 2140-2143 (2000). [CrossRef] [PubMed]
  15. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Dynamics of Discrete Solitons in Optical Waveguide Arrays," Phys. Rev. Lett. (1999). [CrossRef]
  16. R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. ederer, Y. Min, and W. Sohler, "Observation of Discrete Quadratic Solitons," Phys. Rev. Lett. 93, 113,902-1-4 (2004). [CrossRef]
  17. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, "Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays," Phys. Rev. Lett. 83, 4752-4755 (1999). [CrossRef]
  18. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999). [CrossRef]
  19. J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays," Phys. Rev. Lett. 91, 143,907-1-4 (2003). [CrossRef]
  20. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-Gap Structure of Waveguide Arrays and Excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053,902-1-4 (2003). [CrossRef]
  21. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically-induced real-time waveguide arrays," Phys. Rev. Lett. 90, 023,902-1-4 (2003). [CrossRef]
  22. J. Feng, "Alternative scheme for studying gap solitons in an infinite periodic Kerr medium," Opt. Lett. 18, 1302-1304 (1993). [CrossRef] [PubMed]
  23. D. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap Solitons inWaveguide Arrays," Phys. Rev. Lett. 92, 093,904-1-4 (2004). [CrossRef]
  24. D. Neshev, A. A. Sukhorukov, B. Hanna,W. Krolikowski, and Y. S. Kivshar, "Controlled Generation and Steering of Spatial Gap Solitons," Phys. Rev. Lett. 93, 083,905-1-4 (2004). [CrossRef]
  25. P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, "Bose-Einstein condensates in optical lattices: Band-gap structure and solitons," Phys. Rev. A 67, 013,602-1-9 (2003). [CrossRef]
  26. N. K. Efremidis and D. N. Christodoulides, "Lattice solitons in Bose-Einstein condensates," Phys. Rev. A 67, 063,608-1-9 (2003). [CrossRef]
  27. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton trains in photonic lattices," Opt. Express 12, 2831-2837 (2004). [CrossRef] [PubMed]
  28. J. Wang, F. Ye, L. Dong, T. Cai, and Y.-P. Li, "Lattice solitons supported by competing cubic-quintic nonlinearity," Phys. Lett. A 339, 74-82 (2005). [CrossRef]
  29. P. Kevrekidis, B. Malomed, and Z. Musslimani, "Discrete gap solitons in a diffraction-managed waveguide array," Eur. Phys. J. D 23, 421-436 (2003). [CrossRef]
  30. D. N. Christodoulides and R. I. Joseph, "Slow Bragg Solitons in Nonlinear Periodic Structures," Phys. Rev. Lett. 62, 1746-1749 (1989). [CrossRef] [PubMed]
  31. A. B. Aceves and S. Wabnitz, "Self-induced transparency solitons in nonlinear refractive periodic media," Phys. Lett. A 141, 37-42 (1989). [CrossRef]
  32. 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). [CrossRef] [PubMed]
  33. C. M. de Sterke and J. E. Sipe, "Gap solitons," in Progress in Optics, E. Wolf, ed., vol. XXXIII, p. 203 (North-Holland, Amsterdam, 1994).
  34. F. Fedele, J. Yang, and Z. Chen, "Defect modes in one-dimensional photonic lattices," Opt. Lett. 30, 1506-1508 (2005). [CrossRef] [PubMed]
  35. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, "Diffraction management of focused light beams in optical lattices with a quadratic frequency modulation," Opt. Express 13, 4244-4249 (2005). [CrossRef] [PubMed]
  36. N. K. Efremidis, D. N. Christodoulides, S. Sears, J. W. Fleischer, and M. Segev, "Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices," Phys. Rev. E 66, 046,602-1-5 (2002). [CrossRef]
  37. J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices," Nature 422, 147-150 (2003). [CrossRef] [PubMed]
  38. N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, "Two-dimensional optical lattice solitons," Phys. Rev. Lett. 91, 213,906-1-4 (2003). [CrossRef]
  39. J. Yang and Z. H. Musslimani, "Fundamental and vortex solitons in a two-dimensional optical lattice," Opt. Lett. 21, 2094-2096 (2003). [CrossRef]
  40. B. A. Malomed and P. G. Kevrekidis, "Discrete vortex solitons," Phys. Rev. E 64, 026,601-1-6 (2001).
  41. B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642-648 (2003). [CrossRef]
  42. J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of Vortex-Ring "Discrete" Solitons in 2D Photonic Lattices," Phys. Rev. Lett. 92, 123,904-1-4 (2004). [CrossRef]
  43. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices," Phys. Rev. Lett. 92, 123,903-1-4 (2004). [CrossRef]
  44. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 93, 093,904-1-4 (2004). [CrossRef]
  45. Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, "Stable soliton complexes in two-dimensional photonic lattices," Opt. Lett. 29, 1918-1920 (2004). [CrossRef] [PubMed]
  46. J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freeman, M. Segev, H. Buljan, and N. K. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Express 13, 1780-1796 (2005). [CrossRef] [PubMed]
  47. P. Yeh and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976). [CrossRef]
  48. A. Y. Cho, A. Yariv, and P. Yeh, "Observation of confined propagation in Bragg waveguides," Appl. Phys. Lett. 30, 471 (1977). [CrossRef]
  49. A. Yariv, "Coupled-wave formalism for optical waveguiding by transverse Bragg reflection," Opt. Lett. 27, 936-938 (2002). [CrossRef]
  50. S. Linden, J. P. Mondia, H. M. V. Driel, T. C. Kleckner, C. R. Stanley, D. Modotto, A. Locatelli, C. D. Angelis, R. Morandotti, and J. S. Aitchison, "Nonlinear transmission properties of a deep-etched microstructured waveguide," Appl. Phys. Lett. 84, 5437-5439 (2004). [CrossRef]
  51. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete Solitons and Soliton-Induced Dislocations in Partially Coherent Photonic Lattices," Phys. Rev. Lett. 92, 123,902-1-4 (2004). [CrossRef]
  52. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, "Holey Optical Fibers: An Efficient Modal Model," J. Lightwave Technol. 17, 1093-1102 (1999). [CrossRef]
  53. R. d. L. Kronig and W. G. Penney, "Quantum Mechanics of Electrons in Crystal Lattices," P. Roy. Soc. Lond. A Mat. 814, 499-513 (1931). [CrossRef]
  54. S. Theodorakis and E. Leontidis, "Bound states in a nonlinear Kronig-Penney model," J. Phys. A 30, 4835-4849 (1997). [CrossRef]
  55. W. Li and A. Smerzi, "Nonlinear Krönig-Penney model," Phys. Rev. E 70, 016,605-1-4 (2004). [CrossRef]
  56. I. M. Merhasin, B. V. Gisin, R. Driben, and B. A. Malomed, "Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity," Phys. Rev. E 71, 016,613-1-12 (2005). [CrossRef]
  57. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986).
  58. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction Management," Phys. Rev. Lett. 85, 1863-1866 (2000). [CrossRef] [PubMed]
  59. S. F. Mingaleev and R. A. Kivshar, Yuri S.and Sammut, "Long-range interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 62, 5777-5782 (2000). [CrossRef]
  60. J. Sipe and H. G.Winful, "Nonlinear Schrödinger solitons in a periodic structure," Opt. Lett. 13, 132-133 (1988). [CrossRef] [PubMed]

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