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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 20 — Oct. 2, 2006
  • pp: 9338–9343

Three-dimensional structures in nonlinear cavities containing left-handed materials

Philippe Tassin, Guy Van der Sande, Nikolay Veretenov, Pascal Kockaert, Irina Veretennicoff, and Mustapha Tlidi  »View Author Affiliations

Optics Express, Vol. 14, Issue 20, pp. 9338-9343 (2006)

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We study the coupling between negative diffraction and direct dispersion in a nonlinear ring cavity containing slabs of Kerr nonlinear right-handed and left-handed materials. Within the mean field approximation, we show that a portion of the homogeneous response curve is affected by a three-dimensional modulational instability. We show numerically that the light distribution evolves through a sequence of three-dimensional dissipative structures with different lattice symmetry. These structures are unstable with respect to the upswitching process, leading to a premature transition to the upper branch in the homogeneous hysteresis cycle.

© 2006 Optical Society of America

OCIS Codes
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

ToC Category:

Original Manuscript: May 31, 2006
Revised Manuscript: September 5, 2006
Manuscript Accepted: September 8, 2006
Published: October 2, 2006

Philippe Tassin, Guy Van der Sande, Nikolay Veretenov, Pascal Kockaert, Irina Veretennicoff, and Mustapha Tlidi, "Three-dimensional structures in nonlinear cavities containing left-handed materials," Opt. Express 14, 9338-9343 (2006)

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  1. N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer-Verlag, Berlin, 2002).
  2. K. Staliunas and J. V. Sanchez-Morcillo, Transverse Patterns in Nonlinear Optical Resonators (Springer-Verlag, Berlin, 2003).
  3. P. Mandel and M. Tlidi, "Transverse dynamics in cavity nonlinear optics (2000-2003)," J. Opt. B: Quantum Semiclass. Opt. 6, R60-R75 (2004). [CrossRef]
  4. N. Akhmediev and A. Ankiewicz, Dissipative Solitons (Springer, Berlin, 2005). [CrossRef]
  5. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003).
  6. M. Tlidi, M. Haelterman, and P. Mandel, "Three-dimensional structures in diffractive and dispersive nonlinear ring cavities," Europhys. Lett. 42, 505-509 (1998). [CrossRef]
  7. K. Staliunas, "Three-Dimensional Turing Structures and Spatial Solitons in Optical Parametric Oscillators," Phys. Rev. Lett. 81, 81-84 (1998). [CrossRef]
  8. M. Tlidi and P. Mandel, "Three-Dimensional Optical Crystals and Localized Structures in Cavity Second Harmonic Generation," Phys. Rev. Lett. 83, 4995-4998 (1999). [CrossRef]
  9. S. V. Fedorov, N. N. Rosanov, A. N. Shatsev, N. A. Veretenov, and A. G. Vladimirov, "Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber," IEEE J. Quantum Electron. 39, 197-205 (2003). [CrossRef]
  10. M. Brambilla, T. Maggipinto, G. Patera, and L. Columbo, "Cavity Light Bullets: Three-Dimensional Localized Structures in a Nonlinear Optical Resonator," Phys. Rev. Lett. 93, 203901 (2004). [CrossRef] [PubMed]
  11. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004). [CrossRef] [PubMed]
  12. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968). [CrossRef]
  13. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001). [CrossRef] [PubMed]
  14. A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2006). [CrossRef]
  15. J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 39663969 (2000). [CrossRef]
  16. A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear Properties of Left-Handed Metamaterials," Phys. Rev. Lett. 91, 037401 (2003). [CrossRef] [PubMed]
  17. N. Lazarides and G. P. Tsironis, "Coupled nonlinear Schr¨odinger field equations for electromagnetic wave propagation in nonlinear left-handed materials, " Phys. Rev. E 71, 036614 (2005). [CrossRef]
  18. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69, 165112 (2004). [CrossRef]
  19. M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, "Generalized Nonlinear Schr¨odinger Equation for Dispersive Susceptibility and Permeability," Phys. Rev. Lett. 95, 013902 (2005). [CrossRef] [PubMed]
  20. P. Tassin, G. Van der Sande, I. Veretennicoff, M. Tlidi, and P. Kockaert, "Analytical model for the optical propagation in a nonlinear left-handed material," in Metamaterials, T. Szoplik, E. ¨ Ozbay, C.M. Soukoulis, N. I. Zheludev, eds., Proc. SPIE 5955, 595500X (2005).
  21. M. Marklund, P. K. Shukla, and L. Stenflo, "Ultrashort solitons and kinetic effects in nonlinear metamaterials," Phys. Rev. E 73, 037601 (2006). [CrossRef]
  22. N. Engheta, "An Idea for Thin Subwavelength Cavity Resonators Using Metamaterials With Negative Permittivity and Permeability," IEEE Ant. Wireless Prop. Lett. 1, 10-13 (2002). [CrossRef]

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