OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 21, Iss. 5 — May. 1, 2004
  • pp: 973–981

Self-trapping of light in a two-dimensional photonic lattice

Ziad H. Musslimani and Jianke Yang  »View Author Affiliations


JOSA B, Vol. 21, Issue 5, pp. 973-981 (2004)
http://dx.doi.org/10.1364/JOSAB.21.000973


View Full Text Article

Enhanced HTML    Acrobat PDF (685 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 wave propagation in a two-dimensional photonic lattice with focusing Kerr nonlinearity, and report on the existence of various nonlinear localized structures in the form of fundamental, dipole, and vortex solitons. First, the linear bandgap structure induced by the two-dimensional photonic crystal is determined, and solitons are found to exist in the photonic bandgap. Next, structures of these solitons and their stability properties are analyzed in detail. When the propagation constant is not close to the edge of the bandgap, the fundamental soliton is largely confined to one lattice site; the dipole soliton consists of two π-out-of-phase, Gaussian-like humps, whereas the vortex comprises four fundamental modes superimposed in a square configuration with a phase structure that is topologically equivalent to the conventional homogeneous-bulk vortex. At high lattice potential, all these soliton states are stable against small perturbations. However, among the three states, the fundamental solitons are the most robust, whereas vortices are the least. If the propagation constant is close to the edge of the bandgap, then all three soliton states spread over many lattice sites and become linearly unstable as a result of the Vakhitov–Kolokolov instability.

© 2004 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

Citation
Ziad H. Musslimani and Jianke Yang, "Self-trapping of light in a two-dimensional photonic lattice," J. Opt. Soc. Am. B 21, 973-981 (2004)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-21-5-973


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. F. Lederer and Y. Silberberg, “Discrete solitons,” Opt. Photon. News 13, 48–53 (2002). [CrossRef]
  2. F. Lederer, S. Darmanyan, and A. Kobyakov, “Discrete solitons,” in Spatial Solitons, S. Trillo and W. Torruellas, eds. (Springer, New York, 2001), p. 269.
  3. D. N. Christodoulides and R. J. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988). [CrossRef] [PubMed]
  4. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996). [CrossRef]
  5. H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998). [CrossRef]
  6. R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726–2729 (1999). [CrossRef]
  7. R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillation,” Phys. Rev. Lett. 83, 4756–4759 (1999). [CrossRef]
  8. 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]
  9. G. Lenz, I. Talanina, and C. Martijn de Sterke, “Bloch oscillations in an array of curved optical waveguides,” Phys. Rev. Lett. 83, 963–966 (1999). [CrossRef]
  10. N. Efremidis, S. Sears, D. N. Christodoulides, J. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E 66, 046602 (2002). [CrossRef]
  11. J. Fleischer, T. Carmon, M. Segev, N. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003). [CrossRef] [PubMed]
  12. J. Fleischer, M. Segev, N. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003). [CrossRef] [PubMed]
  13. J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28, 2094–2096 (2003). [CrossRef] [PubMed]
  14. Z. Chen, H. Martin, E. D. Eugenieva, and D. N. Christodoulides, “Soliton-induced dislocations and discrete solitons in partially-coherent photonic lattices” (unpublished).
  15. P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965). [CrossRef]
  16. V. E. Zakharov, “Collapse of Langmuir waves,” Sov. Phys. JETP 35, 908 (1972).
  17. R. Grimshaw, Nonlinear Ordinary Differential Equations (CRC Press, Boca Raton, Fla., 1993).
  18. A. A. Sukhorukov and Yu. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001). [CrossRef] [PubMed]
  19. 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, 053902 (2003). [CrossRef] [PubMed]
  20. V. I. Petviashvili, Plasma Phys. 2, 469 (1976).
  21. N. G. Vakhitov and A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973). [CrossRef]
  22. L. P. Pitaevskii, “Dynamics of collapse of a confined Bose gas,” Phys. Lett. A 221, 14–18 (1996). [CrossRef]
  23. D. E. Pelinovsky, V. V. Afanasjev, and Yu. S. Kivshar, “Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation,” Phys. Rev. E 53, 1940–1953 (1996). [CrossRef]
  24. T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000). [CrossRef]
  25. J. J. Garcia-Ripoll, V. M. Perez-Garcia, E. A. Ostrovskaya, and Y. S. Kivshar, “Dipole-mode vector solitons,” Phys. Rev. Lett. 85, 82–85 (2000). [CrossRef] [PubMed]
  26. J. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E 67, 016608 (2003). [CrossRef]
  27. W. J. Firth and D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79, 2450–2453 (1997). [CrossRef]
  28. Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000). [CrossRef] [PubMed]
  29. B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multi-dimensional solitons in periodic potentials,” Europhys. Lett. 63, 642–648 (2003). [CrossRef]
  30. B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E 64, 026601 (2001). [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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited