OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 28, Iss. 4 — Apr. 1, 2011
  • pp: 908–916

Modulation instability in metamaterials with saturable nonlinearity

Yuanjiang Xiang, Xiaoyu Dai, Shuangchun Wen, and Dianyuan Fan  »View Author Affiliations


JOSA B, Vol. 28, Issue 4, pp. 908-916 (2011)
http://dx.doi.org/10.1364/JOSAB.28.000908


View Full Text Article

Enhanced HTML    Acrobat PDF (1550 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We analyze modulation instability (MI) in metamaterials with saturable and focusing nonlinearity according to the propagation model, including the self-steepening (SS) parameter and the second-order nonlinear dispersion (SOND). A detailed discussion on the common role of saturable nonlinearity, SS, and SOND terms on the MI is presented. It is found that MI is irrespective of the sign of the SS parameter and dependent on the sign of SOND. Generally, SS and saturable nonlinearity suppress the MI generation, and SOND promotes the MI in the anomalous group-velocity dispersion (GVD) region. Moreover, linear stability analysis predicts that MI may occur in both the abnormal GVD and normal GVD regime, even at the zero-GVD point, which is to say that some interesting MI phenomena appear involving the additional excited SOND term induced by the dispersive magnetic permeability. In particular, the saturable nonlinearity changes the generation condition of MI seriously. Finally, the numerical simulation is performed to confirm the theoretical predictions.

© 2011 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: September 22, 2010
Revised Manuscript: January 23, 2011
Manuscript Accepted: February 7, 2011
Published: March 24, 2011

Citation
Yuanjiang Xiang, Xiaoyu Dai, Shuangchun Wen, and Dianyuan Fan, "Modulation instability in metamaterials with saturable nonlinearity," J. Opt. Soc. Am. B 28, 908-916 (2011)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-28-4-908


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  2. V. A. Vysloukh and N. A. Sukhotskova, “Influence of third-order dispersion on the generation of a train of picosecond pulses in fiber waveguides due to self-modulation instability,” Sov. J. Quantum Electron. 17, 1509–1511 (1987). [CrossRef]
  3. K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138(1986). [CrossRef] [PubMed]
  4. F. K. 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]
  5. A. Hook and M. Karlsson, “Ultrashort solitons at the minimum-dispersion wavelength: effects of fourth-order dispersion,” Opt. Lett. 18, 1388–1390 (1993). [CrossRef] [PubMed]
  6. J. M. Soto-Crespo and E. M. Wright, “Generation of pulse trains in the normal dispersion regime of a dielectric medium,” Appl. Phys. Lett. 59, 2489–2491 (1991). [CrossRef]
  7. G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Modulation instability induced by cross-phase modulation in optical fibers,” Phys. Rev. A 39, 3406–3413 (1989). [CrossRef] [PubMed]
  8. J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42, 682–685 (1990). [CrossRef] [PubMed]
  9. J. Miguel Hickmann, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Lett. 18, 182–184 (1993). [CrossRef] [PubMed]
  10. X. Q. Zhong and A. P. Xiang, “Cross-phase modulation induced modulation instability in single-mode optical fibers with saturable nonlinearity,” Opt. Fiber Technol. 13, 271–279 (2007). [CrossRef]
  11. P. T. Dinda and K. Porsezian, “Impact of fourth-order dispersion in the modulational instability spectra of wave propagation in glass fibers with saturable nonlinearity,” J. Opt. Soc. Am. B 27, 1143–1152 (2010). [CrossRef]
  12. G. L. da Silva, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Modulational instability in lossless fibers with saturable delayed nonlinear response,” J. Opt. Soc. Am. B 26, 183–188 (2009). [CrossRef]
  13. J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57 (6), 37–43 (2004). [CrossRef]
  14. 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]
  15. A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91, 037401 (2003). [CrossRef] [PubMed]
  16. 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]
  17. 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]
  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. 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]
  20. I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626 (2005). [CrossRef]
  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. 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]
  23. 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]
  24. Y. Xiang, S. Wen, X. Dai, Z. Tang, W. Su, and D. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063 (2007). [CrossRef]
  25. X. Dai, Y. Xiang, S. Wen, and D. Fan, “Modulation instability of copropagating light beams in nonlinear metamaterials,” J. Opt. Soc. Am. B 26, 564–571 (2009). [CrossRef]
  26. A. Maluckov, L. Hadžievski, N. Lazarides, G. P. Tsironis, “Left-handed metamaterials with saturable nonlinearity,” Phys. Rev. E 77, 046607 (2008). [CrossRef]
  27. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited