OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 12 — Dec. 1, 2007
  • pp: 3058–3063

Modulation instability induced by nonlinear dispersion in nonlinear metamaterials

Yuanjiang Xiang, Shuangchun Wen, Xiaoyu Dai, Zhixiang Tang, Wenhua Su, and Dianyuan Fan  »View Author Affiliations


JOSA B, Vol. 24, Issue 12, pp. 3058-3063 (2007)
http://dx.doi.org/10.1364/JOSAB.24.003058


View Full Text Article

Enhanced HTML    Acrobat PDF (438 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We show that modulation instability may occur even in the normal group-velocity dispersion regime, or in the case of no group-velocity dispersion in metamaterials with a nonlinear electric polarization. The physical origin of the modulation instability is the additional second-order nonlinear dispersion effect resulted from the combination of the linear dispersive magnetic permeability with the nonlinear electric polarization. Based on the Drude model, a numerical simulation is performed to confirm the theoretical predictions, and a detailed discussion on the role of the second-order nonlinear dispersion effect in modulation instability in both negative-index and positive-index regions of metamaterial is presented.

© 2008 Optical Society of America

OCIS Codes
(190.3100) Nonlinear optics : Instabilities and chaos
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 29, 2007
Revised Manuscript: September 10, 2007
Manuscript Accepted: October 27, 2007
Published: November 30, 2007

Citation
Yuanjiang Xiang, Shuangchun Wen, Xiaoyu Dai, Zhixiang Tang, Wenhua Su, and Dianyuan Fan, "Modulation instability induced by nonlinear dispersion in nonlinear metamaterials," J. Opt. Soc. Am. B 24, 3058-3063 (2007)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-12-3058


Sort:  Year  |  Journal  |  Reset  

References

  1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  2. K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986). [CrossRef] [PubMed]
  3. S. Wen and D. Fan, "Spatiotemporal instabilities in nonlinear Kerr media in the presence of arbitrary higher-order dispersions," J. Opt. Soc. Am. B 19, 1653-1659 (2002). [CrossRef]
  4. A. Höök and M. Karlsson, "Ultrashort solitons at the minimum-dispersion wavelength: effects of fourth-order dispersion," Opt. Lett. 18, 1388-1390 (1993). [CrossRef] [PubMed]
  5. F. Kh. Abdullaev, S. A. Darmanyan, S. Bischoff, P. L. Christiansen, and M. P. Sørensen, "Modulational instability in optical fibers near the zero dispersion point," Opt. Commun. 108, 60-64 (1994). [CrossRef]
  6. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. Knight, W. J. Wadsworth, and P. St. J. Russell, "Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber," Opt. Lett. 28, 2225-2227 (2003). [CrossRef] [PubMed]
  7. T. Tanemura, Y. Ozeki, and K. Kikuchi, "Modulational instability and parametric amplification induced by loss dispersion in optical fibers," Phys. Rev. Lett. 93, 163902 (2004). [CrossRef] [PubMed]
  8. G. P. Agrawal, "Modulation instability induced by cross-phase modulation," Phys. Rev. Lett. 59, 880-883 (1987). [CrossRef] [PubMed]
  9. S. Coen and M. Haelterman, "Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber," Phys. Rev. Lett. 79, 4139-4142 (1997). [CrossRef]
  10. J. B. Pendry and D. R. Smith, "Reversing light with negative refraction," Phys. Today 57, 37-43 (2004). [CrossRef]
  11. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005). [CrossRef]
  12. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780nm wavelength," Opt. Lett. 32, 53-55 (2007). [CrossRef]
  13. A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91, 037401 (2003). [CrossRef] [PubMed]
  14. M. Lapine, M. Gorkunov, and K. H. Ringhofer, "Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements," Phys. Rev. E 67, 065601 (2003). [CrossRef]
  15. V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007). [CrossRef]
  16. 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]
  17. A. K. Popov and V. M. Shalaev, "Negative-index metamaterials: second-harmonic generation, Manley-Rowe relations and parametric amplification," Appl. Phys. B 84, 131-137 (2006). [CrossRef]
  18. M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, "Second-harmonic generation from magnetic metamaterials," Science 313, 502-504 (2006). [CrossRef] [PubMed]
  19. M. W. Klein, M. Wegener, N. Feth, and S. Linden, "Experiments on second- and third-harmonic generation from magnetic metamaterials," Opt. Express 15, 5238-5247 (2007). [CrossRef] [PubMed]
  20. M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, "Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials," Phys. Rev. Lett. 95, 013902 (2005). [CrossRef] [PubMed]
  21. S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, "Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials," Phys. Rev. A 75, 033815 (2007). [CrossRef]
  22. N. Lazarides and G. P. Tsironis, "Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials," Phys. Rev. E 71, 036614 (2005). [CrossRef]
  23. I. Kourakis and P. K. Shukla, "Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials," Phys. Rev. E 72, 016626 (2005). [CrossRef]
  24. S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, "Modulation instability in nonlinear negative-index material," Phys. Rev. E 73, 036617 (2006). [CrossRef]
  25. S. Wen, Y. Xiang, W. Su, Y. Hu, X. Fu, and D. Fan, "Role of the anomalous self-steepening effect in modulation instability in negative-index material," Opt. Express 14, 1568-1575 (2006). [CrossRef] [PubMed]
  26. M. J. Potosek, "Modulation instability in an extended nonlinear Schrödinger equation," Opt. Lett. 12, 921-923 (1987). [CrossRef]
  27. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
  28. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005). [CrossRef]
  29. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2006). [CrossRef] [PubMed]
  30. A. K. Popov and V. M. Shalaev, "Compensating losses in negative-index metamaterials by optical parametric amplification," Opt. Lett. 31, 2169-2171 (2006). [CrossRef] [PubMed]

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited