OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 7 — Jul. 1, 2014
  • pp: 1484–1493

Modulation instability with arbitrarily high perturbation frequencies in metamaterials with nonlinear dispersion and saturable nonlinearity

Xianqiong Zhong, Ke Cheng, and Kin Seng Chiang  »View Author Affiliations


JOSA B, Vol. 31, Issue 7, pp. 1484-1493 (2014)
http://dx.doi.org/10.1364/JOSAB.31.001484


View Full Text Article

Enhanced HTML    Acrobat PDF (2471 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present an analytical study of modulation instability (MI) in metamaterial (MM) with first-order and second-order nonlinear dispersion for three types of saturable nonlinearity. Apart from the conventional MI gain spectrum, we find two additional MI gain spectra that arise from the second-order nonlinear dispersion in the MM (provided that the group-velocity dispersion does not vanish): one showing a low cutoff frequency but no high cutoff frequency and the other showing no cutoff frequency. Under certain conditions, a threshold power may be required for MI to occur. These MI gain spectra rarely exist in conventional materials and suggest the possibility of observing MI at arbitrarily high perturbation frequencies, which could be explored for the generation of high-repetition-rate ultrashort electromagnetic pulse trains.

© 2014 Optical Society of America

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(190.3100) Nonlinear optics : Instabilities and chaos
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 2, 2014
Revised Manuscript: April 9, 2014
Manuscript Accepted: May 5, 2014
Published: June 5, 2014

Citation
Xianqiong Zhong, Ke Cheng, and Kin Seng Chiang, "Modulation instability with arbitrarily high perturbation frequencies in metamaterials with nonlinear dispersion and saturable nonlinearity," J. Opt. Soc. Am. B 31, 1484-1493 (2014)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-31-7-1484


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. N. Akhmediev and A. Ankiewicz, “Modulation instability, Fermi–Pasta–Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz–Ladik equation,” Phys. Rev. E 83, 046603 (2011). [CrossRef]
  2. N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995). [CrossRef]
  3. R. E. Kennedy, S. V. Popov, and J. R. Tayor, “Ytterbium gain band self-induced modulation instability laser,” Opt. Lett. 31, 167–168 (2006). [CrossRef]
  4. J. Fatome, S. Pitois, and G. Millot, “Measurement of nonlinear and chromatic dispersion parameters of optical fibers using modulation instability,” Opt. Fiber Technol. 12, 243–250 (2006).
  5. W. P. Hong, “Modulation instability of optical waves in the high dispersive cubic–quintic nonlinear Schrödinger equation,” Opt. Commun. 213, 173–182 (2002). [CrossRef]
  6. A. Demircan and U. Bandelow, “Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation,” Appl. Phys. B 86, 31–39 (2007). [CrossRef]
  7. D. F. Grosz, J. M. Chavez Boggio, and H. L. Fragnito, “Modulation instability effects on three-channel optically multiplexed communication systems,” Opt. Commun. 171, 53–60 (1999). [CrossRef]
  8. P. Tchofo 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]
  9. J. H. Li, K. S. Chiang, and K. W. Chow, “Modulation instabilities in two-core optical fibers,” J. Opt. Soc. Am. B 28, 1693–1701 (2011). [CrossRef]
  10. 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]
  11. X. Zhong and A. Xiang, “Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion,” Chin. Phys. B 19, 0642121 (2010). [CrossRef]
  12. F. II. Ndzana, A. Mohamadou, and T. C. Kofané, “Modulational instability in the cubic–quintic nonlinear Schrödinger equation through the variational approach,” Opt. Commun. 275, 421–428 (2007). [CrossRef]
  13. P. Béjot, B. Kibler, E. Hertz, B. Lavorel, and O. Faucher, “General approach to spatiotemporal modulational instability processes,” Phys. Rev. A 83, 013830 (2011). [CrossRef]
  14. J. S. Chen, G. K. Wong, S. G. Murdoch, R. J. Kruhlak, R. Leonhardt, J. D. Harvey, N. Y. Joly, and J. C. Knight, “Cross-phase modulation instability in photonic crystal fibers,” Opt. Lett. 31, 873–875 (2006). [CrossRef]
  15. 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]
  16. 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]
  17. W. Zhou, W. H. Su, X. Cheng, Y. Xiang, X. Dai, and S. Wen, “Copropagation of two pulses of different frequencies and modulation instabilities induced by cross-phase modulation in metamaterials,” Opt. Commun. 282, 1440–1447 (2009). [CrossRef]
  18. Y. Xiang, S. Wen, X. Dai, and D. Fan, “Modulation instability in nonlinear oppositely directed coupler with a negative-index metamaterial channel,” Phys. Rev. E 82, 056605 (2010). [CrossRef]
  19. P. H. Tatsing, A. Mohamadou, C. Bouri, C. G. L. Tiofack, and T. C. Kofane, “Modulation instability in nonlinear positive–negative index couplers with saturable nonlinearity,” J. Opt. Soc. Am. B 29, 3218–3225 (2012). [CrossRef]
  20. Y. Xiang, X. Dai, S. Wen, and D. Fan, “Modulation instability in metamaterials with saturable nonlinearity,” J. Opt. Soc. Am. B 28, 908–916 (2011). [CrossRef]
  21. A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Left-handed metamaterials with saturable nonlinearity,” Phys. Rev. E 77, 046607 (2008). [CrossRef]
  22. C. G. L. Tiofacka, A. Mohamadou, Alim, K. Pporsezian, and T. C. Kofane, “Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion,” J. Mod. Opt. 59, 972–979 (2012).
  23. X. Zhong, T. Tang, A. Xiang, and K. Cheng, “Modulation instability in negative refractive metamaterials with exponential saturable nonlinearity and self-steepening effects,” Opt. Commun. 284, 4727–4731 (2011). [CrossRef]
  24. X. Zhong, K. Cheng, and A. Xiang, “Impacts of higher-order dispersions and saturable nonlinearities on modulation instability in negative-refractive metamaterials,” Chin. Phys. B 22, 034205 (2013). [CrossRef]
  25. M. Saha and A. K. Sarma, “Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects,” Opt. Commun. 291, 321–325 (2013). [CrossRef]
  26. 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]
  27. 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]
  28. M. L. Lyra and A. S. Gouveia-Neto, “Saturation effects on modulation instability in non-Kerr-like monomode optical fibers,” Opt. Commun. 108, 117–120 (1994). [CrossRef]
  29. A. K. Sarma and M. Saha, “Modulation instability of coupled nonlinear field equations for pulse propagation in a negative index material embedded into a Kerr medium,” J. Opt. Soc. Am. B 28, 944–948 (2011). [CrossRef]
  30. X. Zhong and A. Xiang, “Cross-phase modulation induced modulation instability in single-mode optical fibers with saturable nonlinearity,” Opt. Fiber Technol. 13, 271–279 (2007).
  31. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecomminication wavelengths,” Opt. Lett. 31, 1800–1802 (2006). [CrossRef]
  32. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).

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