OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 19 — Sep. 13, 2010
  • pp: 20170–20182

Linear discrete diffraction and transverse localization of light in two-dimensional backbone lattices

Yiling Qi and Guoquan Zhang  »View Author Affiliations


Optics Express, Vol. 18, Issue 19, pp. 20170-20182 (2010)
http://dx.doi.org/10.1364/OE.18.020170


View Full Text Article

Enhanced HTML    Acrobat PDF (1573 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We study the linear discrete diffraction characteristics of light in two-dimensional backbone lattices. It is found that, as the refractive index modulation depth of the backbone lattice increases, high-order band gaps become open and broad in sequence, and the allowed band curves of the Floquet-Bloch modes become flat gradually. As a result, the diffraction pattern at the exit face converges gradually for both the on-site and off-site excitation cases. Particularly, when the refractive index modulation depth of the backbone lattice is high enough, for example, on the order of 0.01 for a square lattice, the light wave propagating in the backbone lattice will be localized in transverse dimension for both the on-site and off-site excitation cases. This is because only the first several allowed bands with nearly flat band curves are excited in the lattice, and the transverse expansion velocities of the Floquet-Bloch modes in these flat allowed bands approach to zero. Such a linear transverse localization of light may have potential applications in navigating light propagation dynamics and optical signal processing.

© 2010 OSA

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(350.5500) Other areas of optics : Propagation

ToC Category:
Diffraction and Gratings

History
Original Manuscript: July 22, 2010
Revised Manuscript: August 27, 2010
Manuscript Accepted: August 28, 2010
Published: September 7, 2010

Citation
Yiling Qi and Guoquan Zhang, "Linear discrete diffraction and transverse localization of light in two-dimensional backbone lattices," Opt. Express 18, 20170-20182 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-20170


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003). [CrossRef] [PubMed]
  2. J. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express 13(6), 1780–1796 (2005). [CrossRef] [PubMed]
  3. A. L. Jones, “Coupling of Optical Fibers and Scattering in Fibers,” J. Opt. Soc. Am. 55(3), 261–269 (1965). [CrossRef]
  4. S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22(1), 46–47 (1973). [CrossRef]
  5. D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13(9), 794–796 (1988). [CrossRef] [PubMed]
  6. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008). [CrossRef]
  7. Y. S. Kivshar and G. P. Agrawal, Optical solitons: from fibers to phototonic crystals (Academic Press, 2003).
  8. 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(16), 3383–3386 (1998). [CrossRef]
  9. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002). [CrossRef] [PubMed]
  10. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000). [CrossRef] [PubMed]
  11. 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(2), 023902 (2003). [CrossRef] [PubMed]
  12. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28(9), 710–712 (2003). [CrossRef] [PubMed]
  13. F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005). [CrossRef] [PubMed]
  14. 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(5), 053902 (2003). [CrossRef] [PubMed]
  15. M. J. Ablowitz and Z. H. Musslimani, “Discrete diffraction managed spatial solitons,” Phys. Rev. Lett. 87(25), 254102 (2001). [CrossRef] [PubMed]
  16. 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(21), 213906 (2003). [CrossRef] [PubMed]
  17. 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(6928), 147–150 (2003). [CrossRef] [PubMed]
  18. Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92(14), 143902 (2004). [CrossRef] [PubMed]
  19. X. S. Wang, A. Bezryadina, Z. G. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98(12), 123903 (2007). [CrossRef] [PubMed]
  20. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. G. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004). [CrossRef] [PubMed]
  21. X. Qi, G. Zhang, N. Xu, Y. Qi, B. Han, Y. Fu, C. Duan, and J. Xu, “Linear and nonlinear discrete light propagation in weakly modulated large-area two-dimensional photonic lattice slab in LiNbO3:Fe crystal,” Opt. Express 17(25), 23078–23084 (2009). [CrossRef]
  22. O. Borovkova, V. Lobanov, A. Sukhorukova, and A. Sukhorukov, “Discrete diffraction and waveguiding of optical beams in a cascade-induced lattice,” Bull. Russ. Acad. Sci. Phys. 72(5), 718–720 (2008). [CrossRef]
  23. O. Manela, M. Segev, and D. N. Christodoulides, “Nondiffracting beams in periodic media,” Opt. Lett. 30(19), 2611–2613 (2005). [CrossRef] [PubMed]
  24. R. J. Elliott and A. F. Gibson, An Introduction to Solid State Physics and its Applications (The Macmillan Press, 1974).
  25. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4 Pt 2), 046602 (2002). [CrossRef] [PubMed]
  26. C. Lou, X. S. Wang, J. J. Xu, Z. G. Chen, and J. Yang, “Nonlinear spectrum reshaping and gap-soliton-train trapping in optically induced photonic structures,” Phys. Rev. Lett. 98(21), 213903 (2007). [CrossRef] [PubMed]
  27. N. K. Efremidis, J. W. Feischer, G. Bartal, O. Cohen, H. Buljan, D. N. Christodoulides, and M. Segev, “Introduction to Solitons in Photonic Lattices,” in Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Y. S. Kivshar, eds., (Springer, 2008), p. 295.
  28. S. P. Guo and S. Albin, “Simple plane wave implementation for photonic crystal calculations,” Opt. Express 11(2), 167–175 (2003). [CrossRef] [PubMed]
  29. K. Kawano and T. Kitoh, Introduction to optical waveguide analysis:Solving Maxwell's Equations and the Schrodinger Equation (John Wiley & Sons, Inc., 2001).
  30. B. Lv, Laser Optics: Beam Characterization, Propagation and Transformation, Resonator Technology and Physics (Higher Education Press, 2003).
  31. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729–1731 (1996). [CrossRef] [PubMed]
  32. P. R. Villeneuve and M. Piché, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B Condens. Matter 46(8), 4969–4972 (1992). [CrossRef] [PubMed]
  33. C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Observation of nonlinear self-trapping in triangular photonic lattices,” Opt. Lett. 32(4), 397–399 (2007). [CrossRef] [PubMed]
  34. T. J. Alexander, A. S. Desyatnikov, and Y. S. Kivshar, “Multivortex solitons in triangular photonic lattices,” Opt. Lett. 32(10), 1293–1295 (2007). [CrossRef] [PubMed]
  35. O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett. 98(10), 103901 (2007). [CrossRef] [PubMed]
  36. J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996). [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