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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 26500–26506

Discrete dissipative localized modes in nonlinear magnetic metamaterials

Nikolay N. Rosanov, Nina V. Vysotina, Anatoly N. Shatsev, Ilya V. Shadrivov, David A. Powell, and Yuri S. Kivshar  »View Author Affiliations


Optics Express, Vol. 19, Issue 27, pp. 26500-26506 (2011)
http://dx.doi.org/10.1364/OE.19.026500


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Abstract

We analyze the existence, stability, and propagation of dissipative discrete localized modes in one- and two-dimensional nonlinear lattices composed of weakly coupled split-ring resonators (SRRs) excited by an external electromagnetic field. We employ the near-field interaction approach for describing quasi-static electric and magnetic interaction between the resonators, and demonstrate the crucial importance of the electric coupling, which can completely reverse the sign of the overall interaction between the resonators. We derive the effective nonlinear model and analyze the properties of nonlinear localized modes excited in one-and two-dimensional lattices. In particular, we study nonlinear magnetic domain walls (the so-called switching waves) separating two different states of nonlinear magnetization, and reveal the bistable dependence of the domain wall velocity on the external field. Then, we study two-dimensional localized modes in nonlinear lattices of SRRs and demonstrate that larger domains may experience modulational instability and splitting.

© 2011 OSA

OCIS Codes
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

ToC Category:
Metamaterials

History
Original Manuscript: November 9, 2011
Revised Manuscript: November 30, 2011
Manuscript Accepted: November 30, 2011
Published: December 13, 2011

Citation
Nikolay N. Rosanov, Nina V. Vysotina, Anatoly N. Shatsev, Ilya V. Shadrivov, David A. Powell, and Yuri S. Kivshar, "Discrete dissipative localized modes in nonlinear magnetic metamaterials," Opt. Express 19, 26500-26506 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26500


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References

  1. N. Engheta and R. W. Ziolkowski, eds. Electromagnetic Metamaterials: Physics and Engineering Explorations (Wiley-IEEE Press, 2006), 440 pp.
  2. D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Yu. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B82, 155128 (2010). [CrossRef]
  3. M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, “Effective magnetic properties of a composite material with circular conductive elements,” Eur. Phys. J. B28, 263–269 (2002). [CrossRef]
  4. A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Yu. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011). [CrossRef]
  5. C. Denz, S. Flach, and Yu. S. Kivshar, eds. Nonlinearities in Periodic Structures and Metamaterials (Springer-Verlag, Heidelberg, 2009). [CrossRef]
  6. I. V. Shadrivov, A. A. Zharov, N. A. Zharova, and Yu. S. Kivshar, “Nonlinear magnetoinductive waves and domain walls in composite metamaterials,” Photonics Nanostruct. Fundam. Appl.4, 69–74 (2006). [CrossRef]
  7. J. S. Hong and J. Lancaster, “Couplings of microstrip square open-loop resonators for cross-coupled planar microwave filters,” IEEE Trans. Microw. Theory Tech.44, 2099–2109 (1996). [CrossRef]
  8. E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magneto-inductive waveguide,” Electron. Lett.38, 371–373 (2002). [CrossRef]
  9. M. Beruete, F. Falcone, M. J. Freire, R. Marqus, and J. D. Baena, “Electroinductive Waves in Chain of Complementary Metamaterials Elements,” Appl. Phys. Lett.88, 083503 (2006). [CrossRef]
  10. N. Lazarides, M. Eleftheriou, and G. P. Tsironis, “Discrete breathers in nonlinear magnetic metamaterials,” Phys. Rev. Lett.97, 157406 (2006). [CrossRef] [PubMed]
  11. M. Eleftheriou, N. Lazarides, and G. P. Tsironis, “Magnetoinductive breathers in metamaterials,” Phys. Rev. E77, 036608 (2008). [CrossRef]
  12. N. Lazarides, G. P. Tsironis, and Yu. S. Kivshar, “Surface breathers in discrete magnetic metamaterials,” Phys. Rev. E77, 065601(R) (2008). [CrossRef]
  13. M. Molina, N. Lazarides, and G. P. Tsironis, “Bulk and surface magnetoinductive breathers in binary metamaterials,” Phys. Rev. E80, 046605 (2009). [CrossRef]
  14. W. Cui, Y. Zhu, H. Li, and S. Liu, “Soliton excitations in a one-dimensional nonlinear diatomic chain of split-ring resonators,” Phys. Rev. E81, 016604 (2010). [CrossRef]
  15. D. A. Powell, K. Hannam, I. V. Shadrivov, and Yu. S. Kivshar, “Near-field interaction of twisted split-ring resonators,” Phys. Rev. B83, 235420 (2011). [CrossRef]
  16. F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi B244, 1170–1175 (2007). [CrossRef]
  17. M. D. Turner, Md M. Hossain, and M. Gu, “The effects of metallic nanostructures,” New J. Phys.12, 083062 (2010). [CrossRef]
  18. N. N. Rosanov, N. V. Vysotina, A. N. Shatsev, I. V. Shadrivov, and Yu.S. Kivshar, “Hysteresis of switching waves and dissipative solitons in nonlinear magnetic metamaterials,” JETP Lett.93, 743–746 (2011). [CrossRef]
  19. N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, Berlin, 2002).
  20. Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett.99, 153901 (2007). [CrossRef] [PubMed]

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