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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 15, Iss. 9 — Apr. 30, 2007
  • pp: 5687–5692

Dynamics of dark breathers in lattices with saturable nonlinearity

Ljupčo Hadžievski, Aleksandra Maluckov, and Milutin Stepić  »View Author Affiliations

Optics Express, Vol. 15, Issue 9, pp. 5687-5692 (2007)

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The problems of the existence, stability, and transversal motion of the discrete dark localized modes in the lattices with saturable nonlinearity are investigated analytically and numerically. The stability analysis shows existence of regions of the parametric space with eigenvalue spectrum branches with non-zeroth real part, which indicates possibility for the propagation of stable on-site and inter-site dark localized modes. The analysis based on the conserved system quantities reveals the existence of regions with a vanishing Peierls-Nabarro barrier which allows transverse motion of the dark breathers. Propagation of the stable on-site and inter-site dark breathers and their free transversal motion are observed numerically.

© 2007 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.5330) Nonlinear optics : Photorefractive optics

ToC Category:
Nonlinear Optics

Original Manuscript: March 20, 2007
Revised Manuscript: April 12, 2007
Manuscript Accepted: April 13, 2007
Published: April 25, 2007

Ljupco Hadzievski, Aleksandra Maluckov, and Milutin Stepic, "Dynamics of dark breathers in lattices with saturable nonlinearity," Opt. Express 15, 5687-5692 (2007)

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  1. P. G. Kevrekidis, K. Ø. Rasmussen, and A. R. Bishop, "The Discrete Nonlinear Schrödinger Eauation: a Survey of Recent Results," Int. J. mod. Phys. B 15,2833-2900 (2001). [CrossRef]
  2. A. A. Sukhorukov, Yu. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, "Spatial optical solitons in waveguide arrays," IEEE J. Quantum Electron. 39,31-50 (2003). [CrossRef]
  3. E. Trias, J. J. Mazo, and T. P. Orlando, "Dicrete breathers in nonlinear lattices: experimental detection in Josephson array," Phys. Rev. Lett. 84,741-744 (2000). [CrossRef] [PubMed]
  4. U. T. Schwarz, L. Q. English, and A. J. Sievers, "Experimental generation and observation of intrisic localized spin wave modes in an antiferromagnet," Phys. Rev. Lett. 83,223-226 (1999). [CrossRef]
  5. P. J. Y. Louis, E. A. Ostrovskaya, and Yu. S. Kivshar, "Dispersion control for matter waves and gap solitons in optical superlattices," J. Opt. B: Quantum Semiclass. Opt. 6,S309-S317 (2004).Q1 [CrossRef]
  6. Yu. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298,81-197 (1998). [CrossRef]
  7. B. Sanchez-Rey and M. Johansson, "Exact numerical solutions for dark waves on the discrete nonlinear Schr¨odinger equation," Phys. Rev. E 71,036627(2005). [CrossRef]
  8. E. Smirnov, C. E. Rüter, M, Stepić, D. Kip, and V. Shandarov, "Formation and light guiding properties of dark solions in one-dimensional waveguide arrays," Phys. Rev. E 74, 065601(R) (2006). [CrossRef]
  9. E. P. Fitrakis, P. G. Kevrekidis, H. Susanto, and D. J. Frantzeskakis, "Dark solitons in discrete lattices: Saturable versus cubic nonlinearitis," arXiv:nlin.PS/0608023 (2006).
  10. T. R. O. Melvin, A. R. Champneys, P. G. Kevrekidis, and J. Cuevas, "Radiationless traveling waves in saturable nonlinear Schr¨odinger lattices," Phys. Rev. Lett. 97,124101 (2006). [CrossRef] [PubMed]
  11. Lj. Hadzievski, A. Maluckov, M. Stepić, and D. Kip, "Power controlled soliton stability and steering in lattices with saturable nonlinearity," Phys. Rev. Lett. 93,033901 (2004). [CrossRef] [PubMed]
  12. S. Wiggins, Global Bifurcations and Chaos: Analytical Methods (Springer-Verlag New York Inc., 1988).

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