OSA's Digital Library

Optics Letters

Optics Letters


  • Vol. 30, Iss. 16 — Aug. 15, 2005
  • pp: 2137–2139

Self-imaging and modulational instability in an array of periodically curved waveguides

Stefano Longhi  »View Author Affiliations

Optics Letters, Vol. 30, Issue 16, pp. 2137-2139 (2005)

View Full Text Article

Acrobat PDF (248 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Linear and nonlinear light propagation in an array of waveguides with a periodically bent axis is theoretically investigated. In the linear propagation regime, it is shown that a self-imaging effect at periodic planes may occur, a phenomenon analogous to that of dynamic localization observed when an electron in a periodic potential is subjected to an ac field. In the nonlinear propagation regime, it is shown that periodic waveguide bending under the self-imaging condition inhibits the phenomenon of discrete modulational instability.

© 2005 Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

Stefano Longhi, "Self-imaging and modulational instability in an array of periodically curved waveguides," Opt. Lett. 30, 2137-2139 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003). [CrossRef]
  2. A. Sukhorukov, Y. S. Kivshar, S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003). [CrossRef]
  3. G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999). [CrossRef]
  4. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000). [CrossRef]
  5. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002). [CrossRef]
  6. M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001). [CrossRef]
  7. M. J. Ablowitz and Z. H. Musslimani, Physica D 184, 276 (2003). [CrossRef]
  8. R. Ulrich, Opt. Commun. 13, 259 (1975). [CrossRef]
  9. D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986). [CrossRef]
  10. R. W. Micallef, Y. S. Kivshar, J. D. Love, D. Burak, and R. Binder, Opt. Quantum Electron. 30, 751 (1998). [CrossRef]
  11. A. A. Sukhorukov and Y. S. Kivshar, Opt. Lett. 28, 2345 (2003).
  12. For a constant curvature(ẍ0=constant), Eq. describes optical Bloch oscillations [see, e.g., U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998)].
  13. The condition for self-imaging beyond the NNA was studied in M. M. Dignam and C. M. de Sterke, Phys. Rev. Lett. 88, 046806 (2002). According to that analysis, beyond the NNA, self-imaging is met only approximately in a sinusoidally bent array. [CrossRef]
  14. Y. S. Kivshar and M. Peyrard, Phys. Rev. A 46, 3198 (1992). [CrossRef]
  15. For straight waveguides (gamma=0), the Floquet expon-ents read explicitly as µ+/-(q)=-2iDeltasinpsinq+/-4iDelta∣sin(q/2)∣[cos2psin2(q/2)-chiI0cosp/(2Delta)]1/2. For chi>0 (self-focusing), an instability arises at any intensity level when cosp>0, i.e., for ∣p∣<pi/2.

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