OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 28, Iss. 1 — Jan. 1, 2011
  • pp: 123–127

Exact combined solitary wave solutions in nonlinear metamaterials

Rongcao Yang and Yu Zhang  »View Author Affiliations

JOSA B, Vol. 28, Issue 1, pp. 123-127 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (611 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We consider the generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in nonlinear metamaterials and find exact combined solitary wave solutions describing the simultaneous propagation of bright and dark solitary waves in a combined form. Based on the Drude model, we discuss the existence conditions and the properties of the combined solitary waves. Furthermore, we analytically and numerically investigate the stability of the combined solitary waves under small perturbations. The results show that bright and dark solitary waves may combine together under certain conditions and propagate stably with a proper form in metamaterials.

© 2011 Optical Society of America

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(160.3918) Materials : Metamaterials

ToC Category:
Nonlinear Optics

Original Manuscript: June 14, 2010
Revised Manuscript: September 19, 2010
Manuscript Accepted: November 11, 2010
Published: December 20, 2010

Rongcao Yang and Yu Zhang, "Exact combined solitary wave solutions in nonlinear metamaterials," J. Opt. Soc. Am. B 28, 123-127 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968). [CrossRef]
  2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000). [CrossRef] [PubMed]
  3. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401 (2003). [CrossRef] [PubMed]
  4. C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refraction index at optical wavelengths,” Science 315, 47–49 (2007). [CrossRef] [PubMed]
  5. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007). [CrossRef]
  6. J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008). [CrossRef] [PubMed]
  7. A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91, 037401 (2003). [CrossRef] [PubMed]
  8. 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]
  9. 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]
  10. M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, Phys. Rev. Lett. 95, 013902 (2005). [CrossRef] [PubMed]
  11. S. C. Wen, Y. J. Xiang, X. Y. Dai, Z. X. TangW. H. Su, and D. Y. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007). [CrossRef]
  12. P. P. Banerjee and G. Nehmetallah, “Linear and nonlinear propagation in negative index materials,” J. Opt. Soc. Am. B 23, 2348–2355 (2006). [CrossRef]
  13. I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626 (2005). [CrossRef]
  14. Y. J. Xiang, S. C. Wen, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063(2007). [CrossRef]
  15. G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and dark gap solitons in a negative index Fabry–Perot etalon,” Phys. Rev. Lett. 93, 213902 (2004). [CrossRef] [PubMed]
  16. A. D. Boardman, L. Velasco, and N. King, “Ultra-narrow bright spatial solitons interacting with left-handed surfaces,” J. Opt. Soc. Am. B 22, 1443–1452 (2005). [CrossRef]
  17. M. Marklund, P. K. Shukla, and L. Stenflo, “Ultrashort solitons and kinetic effects in nonlinear metamaterials,” Phys. Rev. E 73, 037601 (2006). [CrossRef]
  18. N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction,” Opt. Express 13, 1291–1298 (2005). [CrossRef] [PubMed]
  19. N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601 (2009). [CrossRef]
  20. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  21. Z. H. Li, L. Li, H. P. Tian, and G. S. Zhou, “New types of solitary wave solutions for the higher order nonlinear Schrödinger equation,” Phys. Rev. Lett. 84, 4096–4099 (2000). [CrossRef] [PubMed]
  22. R. C. Yang, L. Li, R. Y. Hao, Z. H. Li, and G. S. Zhou, “Combined solitary wave solutions for the inhomogeneous higher-order nonlinear Schrödinger equation,” Phys. Rev. E 71, 036616 (2005). [CrossRef]
  23. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001). [CrossRef]
  24. 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]
  25. 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]

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