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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 29, Iss. 12 — Dec. 1, 2012
  • pp: 3218–3225

Modulation instability in nonlinear positive–negative index couplers with saturable nonlinearity

Patrick Herbert Tatsing, Alidou Mohamadou, Celsus Bouri, Camus Gaston Latchio Tiofack, and Timoleon Crepin Kofane  »View Author Affiliations

JOSA B, Vol. 29, Issue 12, pp. 3218-3225 (2012)

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We have investigated the modulation instability (MI) in a nonlinear optical coupler using a generalized model describing the pulse propagation of a waveguiding structure composed of two adjacent waveguides. The model consists of a nonlinear tunnel-coupled structure consisting of right- and left-handed media. The optical coupler considered here includes a local saturable nonlinear refractive index. In particular, we discuss the impact of the saturable nonlinearity for the MI of plane waves and formation of spatial solitons. The results show that MI can exist not only in the normal group velocity dispersion (GVD) regime but also in the normal GVD regime in the nonlinear positive-negative index coupler in the presence of saturable nonlinearity. The saturable nonlinearity can increase/decrease the number of sidebands or shift the existing sidebands. The maximum value of the MI gain, as well as its bandwidth, has been also affected by the saturable nonlinearity. Moreover, the saturable nonlinearity may influence considerably the number of wave trains induced by MI.

© 2012 Optical Society of America

OCIS Codes
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(160.4330) Materials : Nonlinear optical materials
(160.3918) Materials : Metamaterials

ToC Category:
Nonlinear Optics

Original Manuscript: August 8, 2012
Revised Manuscript: September 18, 2012
Manuscript Accepted: September 18, 2012
Published: November 6, 2012

Patrick Herbert Tatsing, Alidou Mohamadou, Celsus Bouri, Camus Gaston Latchio Tiofack, and Timoleon Crepin Kofane, "Modulation instability in nonlinear positive–negative index couplers with saturable nonlinearity," J. Opt. Soc. Am. B 29, 3218-3225 (2012)

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  1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). [CrossRef]
  2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004). [CrossRef]
  3. J. B. Pendry, “Negative refraction,” Contemp. Phys. 45, 191–202 (2004). [CrossRef]
  4. S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005). [CrossRef]
  5. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Young, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996). [CrossRef]
  6. D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000). [CrossRef]
  7. R. A. Shelby, D. R. Smith, S. N. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489–491 (2001). [CrossRef]
  8. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005). [CrossRef]
  9. G. Dolling, C. Enkrich, M. Wegener, and C. M. Soukoulis, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800–1802 (2006). [CrossRef]
  10. V. M. Agranovich, and Y. N. Gartstein, “Spatial dispersion and negative refraction of light,” Phys. Uspekhi 49, 1029–1044 (2006). [CrossRef]
  11. P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004). [CrossRef]
  12. A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004). [CrossRef]
  13. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).
  14. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973). [CrossRef]
  15. S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1137 (1987). [CrossRef]
  16. D. R. Heatley, E. M. Wright, and G. I. Stegeman, “Soliton coupler,” Appl. Phys. Lett. 53, 172–174 (1988). [CrossRef]
  17. A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, 1990).
  18. S. M. Jensen, “The nonlinear coherent coupler,” IEEE. J. Quantum Electron. 18, 1580–1583 (1982). [CrossRef]
  19. R. Hoffe and J. Chrostowki, “Optical pulse compression and breaking in nonlinear fibre couplers,” Opt. Commun. 57, 34–38 (1986). [CrossRef]
  20. P. Li Kam Wa, J. E. Sitch, N. J. Mason, J. S. Roberts, and P. N. Robson, “All optical multiple-quantum-well waveguide switch,” Appl. Phys. Lett. 21, 26–28 (1985).
  21. D. D. Gusovskii, E. M. Dianov, A. A. Maier, V. B. Neustruev, E. I. Shklovskii, and I. A. Shcherbakov, “Nonlinear light transfer in tunnel-coupled optical waveguides,” Sov. J. Quantum Electron. 15, 1523–1526 (1985). [CrossRef]
  22. K. Halterman, J. M. Elson, and P. L. Overfelt, “Characteristics of bound modes in coupled dielectric waveguides containing negative index media,” Opt. Express 11, 521–529 (2003). [CrossRef]
  23. Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. Au Kong, “Backward coupling waveguide coupler using left-handed material,” Appl. Phys. Lett. 88, 211903 (2006). [CrossRef]
  24. A. Alu and N. Engheta, “An overview of salient properties of planar guided-wave structures with double-negative (DNG) and single-negative (SNG) layers,” in Negative-Refraction Metamaterials: Fundamental Principles and Applications, G. V. Eleftheriades and K. G. Balmain, eds. (John Wiley and Sons Inc., 2005), pp. 339–380.
  25. A. I. Maimistov, I. R. Gabitov, and N. M. Litchinitser, “Solitary waves in a nonlinear oppositely directed coupler,” Opt. Spectrosc. 104, 253–257 (2008). [CrossRef]
  26. R. Schiek, A. S. Solntsev, and D. N. Neshev, “Temporal dynamics of all-optical switching in quadratic nonlinear directional couplers,” Appl. Phys. Lett. 100, 111117 (2012). [CrossRef]
  27. N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007). [CrossRef]
  28. 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]
  29. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  30. S. Wen, Y. Wang, Su, Y. Xiang, and X. Fu, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617 (2006). [CrossRef]
  31. A. Mohamadou, C. G. LatchioTiofack, and T. C. Kofane, “Wave train generation of solitons in systems with higher-order nonlinearities,” Phys. Rev. E 82, 016601 (2010). [CrossRef]
  32. C. G. L. Tiofack, A. Mohamadou, Alim, K. Porsezian, and T. C. Kofane, “Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion,” J. Mod. Opt. 59, 972–979 (2012). [CrossRef]
  33. Z. Kudyshev, G. Venugopal, and N. M. Litchinitser, “Generalized analytical solutions for nonlinear positive-negative index couplers,” Phys. Res. Int. 2012, 945807 (2012). [CrossRef]
  34. G. I. Stegeman, C. T. Seaton, C. N. Ironside, and T. Cullen, “Effects of saturation and loss on nonlinear directional couplers,” Appl. Phys. Lett. 50, 1035–1037 (1987). [CrossRef]
  35. V. E. Wood, E. D. Evan, and R. P. Kenan, “Soluble saturable refractive-index model,” Opt. Commun. 69, 156–160(1988). [CrossRef]
  36. U. Langbein, F. Lederer, T. Peschel, and H. -E. Ponath, “Nonlinear guided waves in saturable nonlinear media,” Opt. Lett. 10, 571–573 (1985). [CrossRef]
  37. 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]
  38. 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]
  39. R. V. J. Raja, K. Porsezian, and K. Nithyanandan, “Modulational-instability-induced supercontinuum generation with saturable nonlinear response,” Phys. Rev. A 82, 013825 (2010). [CrossRef]
  40. A. Maluckov, L. Hadzievski, N. Lazarides, and G. P. Tsironis, “Left-handed metamaterials with saturable nonlinearity,” Phys. Rev. E 77, 046607 (2008). [CrossRef]
  41. 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]
  42. J. Herrmann, “Propagation of ultrashort light pulses in fibers with saturable nonlinearity in the normal-dispersion region,” J. Opt. Soc. Am. B 8, 1507–1511 (1991). [CrossRef]
  43. S. Gatz and J. Herrmann, “Soliton propagation in materials with saturable nonlinearity,” J. Opt. Soc. Am. B 8, 2296–2302 (1991). [CrossRef]
  44. S. Konar and A. Sengupta, “Propagation of an elliptic Gaussian laser beam in a medium with saturable nonlinearity,” J. Opt. Soc. Am. B 11, 1644–1646 (1994). [CrossRef]
  45. M. S. Sodha, S. Medhekar, S. Konar, A. Saxena, and Rajkamal, “Absorption/amplification induced self-tapering and uptapering of a laser beam in a saturable nonlinear medium: large nonlinearity,” Opt. Lett. 19, 1110–1112 (1994). [CrossRef]

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