OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 5 — May. 1, 2013
  • pp: 1382–1391

Impact of input profile, absorption coefficients, and chirp on modulational instability of femtosecond pulses in silicon waveguides under fourth-order dispersion

Lucien Mandeng Mandeng and Clément Tchawoua  »View Author Affiliations

JOSA B, Vol. 30, Issue 5, pp. 1382-1391 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1746 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We report the modulational instability (MI) analysis in silicon-on-insulator waveguides under fourth-order dispersion. The two-photon absorption (TPA) generates four symmetric optimum frequencies in the MI gain spectrum. The free-carrier absorption is found to enhance the value of the central MI gain. The chirp amplifies the intensity of the main pulse train peaks, leading to input profile independence. It shifts the occurrence of these peaks at short propagation distances. The absorption coefficients counteract the chirp, creating a pump dependence, and the high values of TPA destroy drastically the spontaneous breakup mechanism, leading to pump depletion.

© 2013 Optical Society of America

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(190.4180) Nonlinear optics : Multiphoton processes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Nonlinear Optics

Original Manuscript: November 20, 2012
Revised Manuscript: March 4, 2013
Manuscript Accepted: April 1, 2013
Published: May 1, 2013

Lucien Mandeng Mandeng and Clément Tchawoua, "Impact of input profile, absorption coefficients, and chirp on modulational instability of femtosecond pulses in silicon waveguides under fourth-order dispersion," J. Opt. Soc. Am. B 30, 1382-1391 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. A. Ostrovsky, “Electromagnetic waves in nonlinear media with dispersion,” Sov. Phys. Tech. Phys. 8, 679–683 (1964).
  2. V. I. Talanov, “Self-focusing of wave beams,” JETP Lett. 2, 138–141 (1965).
  3. T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech. 27, 417–430 (1967). [CrossRef]
  4. T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett. 21, 209–212 (1968). [CrossRef]
  5. V. I. Karpman and E. M. Krushkal, “Modulated waves in nonlinear dispersive media,” Sov. Phys. JETP 28, 277–281 (1969).
  6. A. Hasegawa, “Observation of self-trapping instability of a plasma cyclotron wave in a computer experiment,” Phys. Rev. Lett. 24, 1165–1168 (1970). [CrossRef]
  7. A. Hasegawa, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Opt. Lett. 9, 288–290 (1984). [CrossRef]
  8. K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986). [CrossRef]
  9. G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987). [CrossRef]
  10. J. E. Rothenberg, “Modulational instability of copropagating frequencies for normal dispersion,” Phys. Rev. Lett. 64, 813 (1990). [CrossRef]
  11. E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25, 1246–1248 (1989). [CrossRef]
  12. S. Sudo, H. Itoh, K. Okamoto, and K. Kubodora, “Generation of 5 THz repetition optical pulses by modulation instability in optical fibers,” Appl. Phys. Lett. 54, 993–994 (1989). [CrossRef]
  13. S. Trillo, S. Wabnitz, G. I. Stegeman, and E. M. Wright, “Parametric amplification and modulational instabilities in dispersive nonlinear directional couplers with relaxing nonlinearity,” J. Opt. Soc. Am. B 6, 889–900 (1989). [CrossRef]
  14. P. Drummond, T. Kennedy, and J. Dudley, “Cross-phase modulation instability in high birefringence fibers,” Opt. Commun. 78, 137–142 (1990). [CrossRef]
  15. C. C. Mei, The Applied Dynamics of Ocean Surface Waves (World Scientific, 1989).
  16. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Series in Nonlinear Dynamics (Springer-Verlag, 1991).
  17. J. R. Taylor, Optical Solitons: Theory and Experiments(Cambridge University, 1992).
  18. Y. Kodama, A. Maruta, and A. Hasegawa, “Long distance communications with solitons,” Quantum Opt. 6, 463–516 (1994). [CrossRef]
  19. N. D. Dalt, C. D. Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995). [CrossRef]
  20. S. B. Cavalcanti and M. Lyra, “Modulation instability of ultrashort pulses via a generalized nonlinear Schrödinger equation with deviating argument,” Phys. Lett. A 211, 276–280 (1996). [CrossRef]
  21. N. Akhmediev and A. Ankiewicz, Solitons. Nonlinear Pulses and Beams (Chapman and Hall, 1997).
  22. F. Kh. Abdullaev, S. A. Darmanyan, S. Bischoff, and M. P. Sorensen, “Modulational instability of electromagnetic waves in media with varying nonlinearity,” J. Opt. Soc. Am. B 14, 27–33 (1997). [CrossRef]
  23. M. Karlsson, “Four-wave mixing in fibers with randomly varying zero-dispersion wavelength,” J. Opt. Soc. Am. B 15, 2269 (1998). [CrossRef]
  24. R. S. Tasgal and B. A. Malomed, “Modulational instabilities in the dual-core nonlinear optical fiber,” Phys. Scr. 60, 418–422 (1999). [CrossRef]
  25. S. C. Wen, W. H. Su, H. Zhang, X. Q. Fu, L. J. Qian, and D. Y. Fan, “Influence of higher-order dispersions and raman delayed response on modulation instability in microstructured fibres,” Chin. Phys. Lett. 20, 852–854 (2003). [CrossRef]
  26. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  27. E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71, 023808 (2005). [CrossRef]
  28. A. Dermican and U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Commun. 244, 181–185 (2005). [CrossRef]
  29. M. Nurhuda and E. Van Groesen, “Effects of delayed Kerr nonlinearity and ionization on the filamentary ultrashort laser pulses in air,” Phys. Rev. E 71, 066502 (2005). [CrossRef]
  30. R. E. Kennedy, S. V. Popov, and J. R. Taylor, “Ytterbium gain band self-induced modulation instability laser,” Opt. Lett. 31, 167–169 (2006). [CrossRef]
  31. F. 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]
  32. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2008).
  33. G. P. Agrawal, Applications of Nonlinear Fiber Optics(Academic, 2008).
  34. X. Liu, J. W. Haus, and S. M. Shahriar, “Modulation instability for a relaxational Kerr medium,” Opt. Commun. 281, 2907–2912 (2008). [CrossRef]
  35. A. M. Kamchatnov and M. Salerno, “Dark soliton oscillations in Bose–Einstein condensates with multi-body interactions,” J. Phys. B 42, 185303 (2009).
  36. P. Das, M. Vyas, and P. K. Panigrahi, “Loss of superfluidity in the Bose–Einstein condensate in an optical lattice with cubic and quintic nonlinearity,” J. Phys. B. 42, 245304 (2009).
  37. V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Physica D 238, 540–548 (2009). [CrossRef]
  38. C. G. L. Tiofack, A. Mohamadou, T. C. Kofané, and A. B. Moubissi, “Generation of pulse trains in nonlinear optical fibers through the generalized complex Ginzburg–Landau equation,” Phys. Rev. E 80, 066604 (2009). [CrossRef]
  39. 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]
  40. R. J. R. Vasantha, K. Porsezian, and K. Nithyanandan, “Modulational-instability-induced supercontinuum generation with saturable nonlinear response,” Phys. Rev. A 82, 013825 (2010). [CrossRef]
  41. C. M. Ngabireng, S. Ambomo, P. T. Dinda, and A. B. Moubissi, “Loss effects in the spectra of polarization modulational instability in weakly birefringent optical fibers,” J. Opt. 13, 085201 (2011). [CrossRef]
  42. 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]
  43. M. Erkintalo, K. Hammami, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011). [CrossRef]
  44. J. H. Li, K. S. Chiang, B. A. Malomed, and K. W. Chow, “Modulation instabilities in birefringent two-core optical fibres,” J. Phys. B 45, 165404 (2012).
  45. P. H. Tatsing, A. Mohamadou, C. Bouri, C. G. L. Tiofack, and T. C. Kofané, “Modulation instability in nonlinear positive-negative index couplers with saturable nonlinearity,” J. Opt. Soc. Am. B 29, 3218–3225 (2012). [CrossRef]
  46. 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]
  47. J. C. Travers, “Blue extension of optical fibre supercontinuum generation,” J. Opt. 12, 113001 (2010). [CrossRef]
  48. E. J. R. Kelleher, J. C. Travers, S. V. Popov, and J. R. Taylor, “Role of pump coherence in the evolution of continuous wave supercontinuum generation initiated by modulation instability,” J. Opt. Soc. Am. B 29, 502–512 (2012). [CrossRef]
  49. G. P. Agrawal, “Effect of two-photon absorption on the amplification of ultrashort optical pulses,” Phys. Rev. E 48, 2316–2318 (1993). [CrossRef]
  50. S. Roy, S. K. Bhadra, and G. P. Agrawal, “Femtosecond pulse propagation in silicon waveguides: variational approach and its advantages,” Opt. Commun. 281, 5889–5893 (2008). [CrossRef]
  51. B. Jalali and S. Fathpour, “Silicon photonics,” IEEE J. Lightwave Technol. 24, 4600–4615 (2006). [CrossRef]
  52. R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006). [CrossRef]
  53. H. K. Tsang, C. S. Wong, and T. K. Liang, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 m wavelength,” Appl. Phys. Lett. 80, 416–418 (2002). [CrossRef]
  54. L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32, 2031–2033 (2007). [CrossRef]
  55. J. Wen, H. Liu, N. Huang, Q. Sun, and W. Zhao, “Influence of the initial chirp on the supercontinuum generation in silicon-on-insulator waveguide,” Appl. Phys. B 104, 867–871 (2011). [CrossRef]
  56. D. Castelló-Lurbe, E. Silvestre, P. Andrés, and V. Torres-Company, “Spectral broadening enhancement in silicon waveguides through pulse shaping,” Opt. Lett. 37, 2757–2759 (2012). [CrossRef]
  57. L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007). [CrossRef]
  58. M. Lipson, “Guiding, modulating, and emitting light on silicon challenges and opportunities,” J. Lightwave Technol. 23, 4222–4238 (2005). [CrossRef]
  59. C. M. Ngabireng, P. T. Dinda, A. Tonello, K. Nakkeeran, P. K. A. Wai, and T. C. Kofané, “Radiating and nonradiating behavior of hyperbolic-secant, raised-cosine, and Gaussian input light pulses in dispersion-managed fiber systems,” Phys. Rev. E 72, 036613 (2005). [CrossRef]
  60. K. Nakkeeran, Y. H. C. Kwan, P. K. A. Wai, A. Labruyere, P. T. Dinda, and A. B. Moubissi, “Analytical design of densely dispersion-managed optical fiber transmission systems with Gaussian and raised cosine return-to-zero Ansätze,” J. Opt. Soc. Am. B 21, 1901–1907 (2004). [CrossRef]
  61. W. J. Cody, “Rational Chebyshev approximations for the error function,”Math. Comput. 23, 631–637 (1969). [CrossRef]

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

OSA is a member of CrossRef.

CrossCheck Deposited