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

PDF Article

References

  • View by:
  • |
  • |
  • |

  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).

2013 (2)

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]

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]

2012 (2)

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).

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]

2011 (6)

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]

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]

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]

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]

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]

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]

2010 (3)

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]

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]

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]

2009 (1)

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]

2008 (1)

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Left-handed metamaterials with saturable nonlinearity,” Phys. Rev. E 77, 046607 (2008).
[CrossRef]

2007 (5)

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]

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]

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]

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).

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).

2006 (6)

2002 (1)

W. P. Hong, “Modulation instability of optical waves in the high dispersive cubic–quintic nonlinear Schrödinger equation,” Opt. Commun. 213, 173–182 (2002).
[CrossRef]

2000 (1)

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]

1999 (1)

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]

1995 (1)

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]

1994 (1)

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]

1989 (1)

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]

Agrawal, G. P.

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]

Akhmediev, N.

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]

Alfano, R. R.

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]

Alim,

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).

Ankiewicz, A.

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]

Baldeck, P. L.

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]

Bandelow, U.

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]

Béjot, P.

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]

Bouri, C.

Chavez Boggio, J. M.

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]

Chen, J. S.

Cheng, K.

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]

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]

Cheng, X.

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]

Chiang, K. S.

Chow, K. W.

Da Dalt, N.

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]

Dai, X.

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]

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]

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]

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]

De Angelis, C.

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]

Demircan, A.

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]

Dolling, G.

Enkrich, C.

Fan, D.

Fatome, J.

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).

Faucher, O.

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]

Fragnito, H. L.

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]

Fu, X.

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]

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]

Gouveia-Neto, A. S.

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]

Grosz, D. F.

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]

Hadžievski, Lj.

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Left-handed metamaterials with saturable nonlinearity,” Phys. Rev. E 77, 046607 (2008).
[CrossRef]

Harvey, J. D.

Hertz, E.

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]

Hong, W. P.

W. P. Hong, “Modulation instability of optical waves in the high dispersive cubic–quintic nonlinear Schrödinger equation,” Opt. Commun. 213, 173–182 (2002).
[CrossRef]

Hu, Y.

Joly, N. Y.

Kennedy, R. E.

Kibler, B.

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]

Knight, J. C.

Kofane, T. C.

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).

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]

Kofané, T. C.

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]

Kruhlak, R. J.

Lavorel, B.

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]

Lazarides, N.

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Left-handed metamaterials with saturable nonlinearity,” Phys. Rev. E 77, 046607 (2008).
[CrossRef]

Leonhardt, R.

Li, J. H.

Linden, S.

Lyra, M. L.

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]

Maluckov, A.

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Left-handed metamaterials with saturable nonlinearity,” Phys. Rev. E 77, 046607 (2008).
[CrossRef]

Millot, G.

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).

Mohamadou, A.

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]

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).

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]

Murdoch, S. G.

Nalesso, G. F.

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]

Ndzana, F. II.

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]

Nemat-Nasser, S. C.

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]

Padilla, W. J.

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]

Pitois, S.

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).

Popov, S. V.

Porsezian, K.

Pporsezian, K.

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).

Saha, M.

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]

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]

Santagiustina, M.

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]

Sarma, A. K.

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]

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]

Schultz, S.

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]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).

Smith, D. R.

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]

Soukoulis, C. M.

Su, W.

Su, W. H.

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]

Tang, T.

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]

Tang, Z.

Tatsing, P. H.

Tayor, J. R.

Tchofo Dinda, P.

Tiofack, C. G. L.

Tiofacka, C. G. L.

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).

Tsironis, G. P.

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Left-handed metamaterials with saturable nonlinearity,” Phys. Rev. E 77, 046607 (2008).
[CrossRef]

Vier, D. C.

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]

Wang, Y.

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]

Wegener, M.

Wen, S.

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]

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]

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]

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]

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]

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]

Wong, G. K.

Xiang, A.

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]

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]

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]

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).

Xiang, Y.

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]

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]

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]

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]

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]

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]

Zhong, X.

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]

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]

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]

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).

Zhou, W.

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]

Appl. Phys. B (1)

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]

Chin. Phys. B (2)

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]

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]

J. Mod. Opt. (1)

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).

J. Opt. Soc. Am. B (6)

Nat. Photonics (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).

Opt. Commun. (8)

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]

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]

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]

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]

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]

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]

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]

W. P. Hong, “Modulation instability of optical waves in the high dispersive cubic–quintic nonlinear Schrödinger equation,” Opt. Commun. 213, 173–182 (2002).
[CrossRef]

Opt. Express (1)

Opt. Fiber Technol. (2)

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).

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).

Opt. Lett. (3)

Phys. Rev. A (2)

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]

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]

Phys. Rev. E (4)

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]

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]

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]

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Left-handed metamaterials with saturable nonlinearity,” Phys. Rev. E 77, 046607 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

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]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics