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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 7 — Apr. 2, 2007
  • pp: 4149–4158

How does an inclined holding beam affect discrete modulational instability and solitons in nonlinear cavities?

Oleg A. Egorov, Falk Lederer, and Yuri S. Kivshar  »View Author Affiliations

Optics Express, Vol. 15, Issue 7, pp. 4149-4158 (2007)

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We study light propagation in arrays of weakly coupled nonlinear cavities driven by an inclined holding beam. We show analytically that both discreteness and inclination of the driving field can dramatically change the conditions for modulational instability in discrete nonlinear systems. We find numerically the families of resting and moving dissipative solitons for an arbitrary inclination angle of the driving field, both in the discrete and a quasi-continuous limits. We analyze a crossover between resting and moving cavity solitons, and also observe novel features in the soliton collision.

© 2007 Optical Society of America

OCIS Codes
(190.1450) Nonlinear optics : Bistability
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(190.5940) Nonlinear optics : Self-action effects

ToC Category:
Nonlinear Optics

Original Manuscript: January 30, 2007
Manuscript Accepted: March 19, 2007
Published: April 2, 2007

Oleg A. Egorov, Falk Lederer, and Yuri S. Kivshar, "How does an inclined holding beam affect discrete modulational instability and solitons in nonlinear cavities?," Opt. Express 15, 4149-4158 (2007)

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  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Waveguides to Photonic Crystals (Academic Press, San Diego, 2003), 540 pp.
  2. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817 (2003). [CrossRef] [PubMed]
  3. N. Akhmediev and A. Ankiewicz, Dissipative Solitons (Springer, Berlin, 2005), pp. 450. [CrossRef]
  4. M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, "Spatial soliton pixels in semiconductor devices," Phys. Rev. Lett. 79, 2042 (1997). [CrossRef]
  5. D. Michaelis, U. Peschel, and F. Lederer, "Multistable localized structures and superlattices in semiconductor optical resonators," Phys. Rev. A 56, R3366 (1997). [CrossRef]
  6. U. Peschel, D. Michaelis, and C. O. Weiss, "Spatial solitons in optical cavities," IEEE J. Quantum Electron. 39, 51 (2003). [CrossRef]
  7. E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003). [CrossRef] [PubMed]
  8. E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, "Stable spatial solitons in semiconductor optical amplifiers," Opt. Lett. 28, 251 (2003). [CrossRef] [PubMed]
  9. J. F. Ravoux, S. Dizes, and P. Gal, "Stability analysis of plane wave solutions of the discrete Ginzburg-Landau equation," Phys. Rev. E 61, 390 (2000). [CrossRef]
  10. K. Maruno, A. Ankiewicz, and N. Akhmediev, "Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equations," Opt. Commun. 221, 199 (2003). [CrossRef]
  11. N. K. Efremidis and D. N. Christodoulides, "Discrete Ginzburg-Landau solitons," Phys. Rev. E 67, 26606 (2003). [CrossRef]
  12. J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, "Motion and stability properties of solitons in discrete dissipative structures," Phys. Lett. A 314, 126 (2003). [CrossRef]
  13. K. Maruno, A. Ankiewicz, and N. Akhmediev, "Dissipative solitons of the discrete complex cubic-quintic Ginzburg-Landau equation," Phys. Lett. A 347, 231 (2005). [CrossRef]
  14. A. Mohamadou and T. C. Kofane, "Modulational instability and pattern formation in discrete dissipative systems," Phys. Rev. E 73, 46607 (2006). [CrossRef]
  15. U. Peschel, O. A. Egorov, and F. Lederer, "Discrete cavity solitons," Opt. Lett. 29, 1909 (2004). [CrossRef] [PubMed]
  16. O. A. Egorov, U. Peschel, and F. Lederer, "Discrete quadratic cavity solitons," Phys. Rev. E 71, 56612 (2005). [CrossRef]
  17. O. A. Egorov, U. Peschel, and F. Lederer, "Mobility of discrete cavity solitons," Phys. Rev. E 72, 66603 (2005). [CrossRef]
  18. L. A. Lugiato and R. Lefever, "Spatial dissipative structures in passive optical systems," Phys. Rev. Lett. 58, 2209 (1987). [CrossRef] [PubMed]
  19. Yu. S. Kivshar and M. Peyrard, "Modulational instabilities in discrete lattices," Phys. Rev. A 46, 3198 (1992). [CrossRef] [PubMed]
  20. Yu. S. Kivshar and M. Salerno, "Modulational instabilities in the discrete deformable nonlinear Schr¨odinger equation," Phys. Rev. E 49, 3543 (1994). [CrossRef]
  21. S. Darmanyan, I. Relke, and F. Lederer, "Instability of continuous waves and rotating solitons in waveguide arrays," Phys. Rev. E 55, 7662 (1997). [CrossRef]
  22. M. Stepic, C. E. Rueter, D. Kip, A. Maluckov, and L. Hadzievski, "Modulational instability in one-dimensional saturable waveguide arrays: Comparison with Kerr nonlinearity," Opt. Commun. 267, 229 (2006). [CrossRef]
  23. J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902 (2004). [CrossRef] [PubMed]
  24. R. Iwanow, G. I. Stegeman, R. Schiek, Y. Min, and W. Sohler, "Discrete modulational instability in periodically poled lithium niobate waveguide arrays," Opt. Express 13, 7794 (2005). [CrossRef] [PubMed]
  25. M. Stepic, C. Wirth, C. E. Rueter, and D. Kip, "Observation of modulational instability in discrete media with self-defocusing nonlinearity," Opt. Lett. 31, 247 (2006). [CrossRef] [PubMed]
  26. H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, G. Pennelli, and J. S. Aitchison, "Optical discrete solitons in waveguide arrays. I. Solitons formation," J. Opt. Soc. Am. B 19, 2938 (2002). [CrossRef]
  27. U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, "Optical discrete solitons in waveguide arrays. II. Dynamic properties," J. Opt. Soc. Am. B 19, 2637 (2002). [CrossRef]
  28. Yu. S. Kivshar, "Self-localization in arrays of defocusing waveguides," Opt. Lett. 18, 1147 (1993). [CrossRef] [PubMed]
  29. S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, "Effects of spatial inhomogeneities on the dynamics of cavity solitons in quadratically nonlinear media," Phys. Rev. E 64, 036610 (2001). [CrossRef]
  30. M. Tlidi and A. G. Vladimirov, "Interaction and stability of periodic and localized structures in optical bistable systems," IEEE J. Quantum. Electron. 39, 216 (2003). [CrossRef]
  31. K. Staliunas, "Midband Dissipative Spatial Solitons," Phys. Rev. Lett. 91, 53901 (2003). [CrossRef]

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