OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 15 — Jul. 23, 2007
  • pp: 9547–9552

Nonlinear diffusion and beam self-trapping in diffraction-managed waveguide arrays

Ivan L. Garanovich, Andrey A. Sukhorukov, and Yuri S. Kivshar  »View Author Affiliations


Optics Express, Vol. 15, Issue 15, pp. 9547-9552 (2007)
http://dx.doi.org/10.1364/OE.15.009547


View Full Text Article

Enhanced HTML    Acrobat PDF (546 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 nonlinear propagation of light in diffraction-managed photonic lattices created by periodically-curved arrays of optical waveguides. We identify different regimes of the nonlinear propagation of light in such structures depending on the input power. We start from the regime of self-collimation at low powers and demonstrate that, as the beam power increases, nonlinearity destroys the beam self-imaging and leads to nonlinear diffusion. At higher powers, we observe a sharp transition to the self-trapping and the formation of discrete diffraction-managed solitons.

© 2007 Optical Society of America

OCIS Codes
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(190.5940) Nonlinear optics : Self-action effects

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 1, 2007
Revised Manuscript: July 12, 2007
Manuscript Accepted: July 15, 2007
Published: July 17, 2007

Citation
Ivan L. Garanovich, Andrey A. Sukhorukov, and Yuri S. Kivshar, "Nonlinear diffusion and beam self-trapping in diffraction-managed waveguide arrays," Opt. Express 15, 9547-9552 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9547


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, 817-823 (2003). [CrossRef] [PubMed]
  2. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000). [CrossRef] [PubMed]
  3. T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901-4 (2002). [CrossRef] [PubMed]
  4. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature Mater. 5, 93-96 (2006). [CrossRef] [PubMed]
  5. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, and P. Laporta, "Observation of Dynamic Localization in Periodically Curved Waveguide Arrays," Phys. Rev. Lett. 96, 243901-4 (2006). [CrossRef] [PubMed]
  6. S. Longhi, "Self-imaging and modulational instability in an array of periodically curved waveguides," Opt. Lett. 30, 2137-2139 (2005). [CrossRef] [PubMed]
  7. R. Iyer, J. S. Aitchison, J. Wan, M. M. Dignam, C. M. de Sterke, "Exact dynamic localization in curved AlGaAs optical waveguide arrays," Opt. Express 15, 3212-3223 (2007). [CrossRef] [PubMed]
  8. I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, "Broadband diffraction management and selfcollimation of white light in photonic lattices," Phys. Rev. E 74, 066609 (2006). [CrossRef]
  9. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled wave-guides," Opt. Lett. 13, 794-796 (1988). [CrossRef] [PubMed]
  10. 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]
  11. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
  12. M. J. Ablowitz and Z. H. Musslimani, "Discrete diffraction managed spatial solitons," Phys. Rev. Lett. 87, 254102-4 (2001). [CrossRef] [PubMed]
  13. K. Staliunas, R. Herrero, and G. J. Valcarcel, de, "Arresting soliton collapse in two-dimensional nonlinear Schrodinger systems via spatiotemporal modulation of the external potential," Phys. Rev. A 75, 011604 (2007). [CrossRef]
  14. S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-47 (1973). [CrossRef]
  15. Y. V. Kartashov, L. Torner, and D. N. Christodoulides, "Soliton dragging by dynamic optical lattices," Opt. Lett. 30, 1378-1380 (2005). [CrossRef] [PubMed]
  16. I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, "Soliton control in modulated optically-induced photonic lattices," Opt. Express 13, 5704-5710 (2005). [CrossRef] [PubMed]
  17. C. R. Rosberg, I. L. Garanovich, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, "Demonstration of all-optical beam steering in modulated photonic lattices," Opt. Lett. 31, 1498-1500 (2006). [CrossRef] [PubMed]
  18. Y. Kominis and K. Hizanidis, "Continuous-wave-controlled steering of spatial solitons," J. Opt. Soc. Am. B 21, 562-567 (2004). [CrossRef]
  19. I. Tsopelas, Y. Kominis, and K. Hizanidis, "Soliton dynamics and interactions in dynamically photoinduced lattices," Phys. Rev. E 74, 036613 (2006). [CrossRef]
  20. A. C. Scott and L. Macneil, "Binding energy versus nonlinearity for a "small" stationary soliton," Phys. Lett. A 98, 87-88 (1983). [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.

Figures

Fig. 1. Fig. 2. Fig. 3.
 
Fig. 4.
 

Multimedia

Multimedia FilesRecommended Software
» Media 1: GIF (1537 KB)     
» Media 2: GIF (1537 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited