Abstract

A simple model based on the 1D nonlinear Schrödinger equation is studied, which contains both spatially and temporally dispersive terms. Parametric instabilities for plane waves are analyzed in detail, and solitary waves (both bright and dark) are found. The model presented here is able to describe the non-trivial unstable dynamics of intense, nonlinear light propagation near a material resonance in presence of negative spatial dispersion. We provide as a practical example the light propagation near the tail of an exciton-polariton resonance in a specially designed semiconductor superlattice.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001).
  2. T. B. Benjamin, K. Hasselmann, T. B. Benjamin, and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech.27, 417 (1967).
    [Crossref]
  3. 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 (1968).
    [Crossref]
  4. A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, Heidelberg, 1975).
    [Crossref]
  5. G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber,” J. Opt. Soc. Am. B,  1266 (1998).
  6. J. Klinger, H. Martin, and Z. Chen, “Experiments on induced modulational instability of an incoherent optical beam,” Opt. Lett. 26, 271 (2001).
    [Crossref]
  7. E. Fermi, J. Pasta, H. C. Ulam, M. Tsingou, G. Van Symaeys, Ph. Emplit, and M. Haelterman, “Experimental Demonstration of the Fermi-Pasta-Ulam Recurrence in a Modulationally Unstable Optical Wave,” Phys. Rev. Lett.87, 033902 (2001).
    [Crossref]
  8. N. J. Zabusky and M. D. Kruskal, “Interaction of ‘Solitons’ in a Collisionless Plasma and the Recurrence of Initial States,” Phys. Rev. Lett. 15, 240 (1965).
    [Crossref]
  9. Y. S. Kivshar and G. P. Agrawal, Optical Solitons, (Academic Press, San Diego, 2003).
  10. F. Biancalana, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E 68, 046603 (2003).
    [Crossref]
  11. F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids, (Pergamon Press, Oxford, 1976).
  12. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Non-Paraxial Solitons,” J. Mod. Opt. 45, 1111 (1998).
    [Crossref]
  13. J. M. Christian, G. S. McDonald, P. Chamorro-Posada, J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz Solitons in Cubic-Quintic Materials,” Phys. Rev. A76, 033833 (2007).
    [Crossref]
  14. T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901 (2002).
    [Crossref] [PubMed]
  15. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, (World Scientific, Singapore, 2004).
  16. S. I. Pekar, “Supplementary light waves in crystals and exciton absorption,” Sov. Phys. Uspekhi 5, 515 (1962).
    [Crossref]
  17. V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, (Springer, Berlin, 1984).
  18. S. V. Chernikov and P. V. Mamyshev, “Femtosecond soliton propagation in fibers with slowly decreasing dispersion,” J. Opt. Soc. Am. B 8, 1633 (1991).
    [Crossref]
  19. A. S. Davydov, Theory of Molecular Excitons, (Plenum Press, New York-London, 1971).
  20. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167 (2004).
    [Crossref]
  21. V. M. Agranovich and Y. N. Gartstein, “Spatial dispersion and negative refraction of light,” Phys. Usp. 49, 1029 (2006).
    [Crossref]
  22. A. Je. Semjonow, U. W. Pohl, A. Je. Semjonow, U. W. Pohl, and R. Engelhardt, “Negative exciton mass in ZnCdSe/SnSSe superlattices observed by excitonic polariton Raman scattering,” J. Phys. Condens. Matter11, 1735 (1999).
    [Crossref]
  23. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
    [Crossref]

2006 (1)

V. M. Agranovich and Y. N. Gartstein, “Spatial dispersion and negative refraction of light,” Phys. Usp. 49, 1029 (2006).
[Crossref]

2004 (1)

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167 (2004).
[Crossref]

2003 (1)

F. Biancalana, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E 68, 046603 (2003).
[Crossref]

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

2001 (1)

1998 (2)

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber,” J. Opt. Soc. Am. B,  1266 (1998).

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Non-Paraxial Solitons,” J. Mod. Opt. 45, 1111 (1998).
[Crossref]

1992 (1)

1991 (1)

1968 (1)

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 (1968).
[Crossref]

1965 (1)

N. J. Zabusky and M. D. Kruskal, “Interaction of ‘Solitons’ in a Collisionless Plasma and the Recurrence of Initial States,” Phys. Rev. Lett. 15, 240 (1965).
[Crossref]

1962 (1)

S. I. Pekar, “Supplementary light waves in crystals and exciton absorption,” Sov. Phys. Uspekhi 5, 515 (1962).
[Crossref]

Agranovich, V. M.

V. M. Agranovich and Y. N. Gartstein, “Spatial dispersion and negative refraction of light,” Phys. Usp. 49, 1029 (2006).
[Crossref]

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167 (2004).
[Crossref]

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, (Springer, Berlin, 1984).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons, (Academic Press, San Diego, 2003).

Bassani, F.

F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids, (Pergamon Press, Oxford, 1976).

Baughman, R. H.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167 (2004).
[Crossref]

Benjamin, T. B.

T. B. Benjamin, K. Hasselmann, T. B. Benjamin, and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech.27, 417 (1967).
[Crossref]

T. B. Benjamin, K. Hasselmann, T. B. Benjamin, and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech.27, 417 (1967).
[Crossref]

Biancalana, F.

F. Biancalana, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E 68, 046603 (2003).
[Crossref]

Brauer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Chamorro-Posada, P.

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Non-Paraxial Solitons,” J. Mod. Opt. 45, 1111 (1998).
[Crossref]

J. M. Christian, G. S. McDonald, P. Chamorro-Posada, J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz Solitons in Cubic-Quintic Materials,” Phys. Rev. A76, 033833 (2007).
[Crossref]

J. M. Christian, G. S. McDonald, P. Chamorro-Posada, J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz Solitons in Cubic-Quintic Materials,” Phys. Rev. A76, 033833 (2007).
[Crossref]

Chen, Z.

Chernikov, S. V.

Christian, J. M.

J. M. Christian, G. S. McDonald, P. Chamorro-Posada, J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz Solitons in Cubic-Quintic Materials,” Phys. Rev. A76, 033833 (2007).
[Crossref]

J. M. Christian, G. S. McDonald, P. Chamorro-Posada, J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz Solitons in Cubic-Quintic Materials,” Phys. Rev. A76, 033833 (2007).
[Crossref]

Davydov, A. S.

A. S. Davydov, Theory of Molecular Excitons, (Plenum Press, New York-London, 1971).

Emplit, Ph.

E. Fermi, J. Pasta, H. C. Ulam, M. Tsingou, G. Van Symaeys, Ph. Emplit, and M. Haelterman, “Experimental Demonstration of the Fermi-Pasta-Ulam Recurrence in a Modulationally Unstable Optical Wave,” Phys. Rev. Lett.87, 033902 (2001).
[Crossref]

Engelhardt, R.

A. Je. Semjonow, U. W. Pohl, A. Je. Semjonow, U. W. Pohl, and R. Engelhardt, “Negative exciton mass in ZnCdSe/SnSSe superlattices observed by excitonic polariton Raman scattering,” J. Phys. Condens. Matter11, 1735 (1999).
[Crossref]

Feir, J. E.

T. B. Benjamin, K. Hasselmann, T. B. Benjamin, and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech.27, 417 (1967).
[Crossref]

Fermi, E.

E. Fermi, J. Pasta, H. C. Ulam, M. Tsingou, G. Van Symaeys, Ph. Emplit, and M. Haelterman, “Experimental Demonstration of the Fermi-Pasta-Ulam Recurrence in a Modulationally Unstable Optical Wave,” Phys. Rev. Lett.87, 033902 (2001).
[Crossref]

Gartstein, Y. N.

V. M. Agranovich and Y. N. Gartstein, “Spatial dispersion and negative refraction of light,” Phys. Usp. 49, 1029 (2006).
[Crossref]

Ginzburg, V. L.

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, (Springer, Berlin, 1984).

Haelterman, M.

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber,” J. Opt. Soc. Am. B,  1266 (1998).

E. Fermi, J. Pasta, H. C. Ulam, M. Tsingou, G. Van Symaeys, Ph. Emplit, and M. Haelterman, “Experimental Demonstration of the Fermi-Pasta-Ulam Recurrence in a Modulationally Unstable Optical Wave,” Phys. Rev. Lett.87, 033902 (2001).
[Crossref]

Hagan, D. J.

Hasegawa, A.

A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, Heidelberg, 1975).
[Crossref]

Hasselmann, K.

T. B. Benjamin, K. Hasselmann, T. B. Benjamin, and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech.27, 417 (1967).
[Crossref]

Haug, H.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, (World Scientific, Singapore, 2004).

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons, (Academic Press, San Diego, 2003).

Klinger, J.

Koch, S. W.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, (World Scientific, Singapore, 2004).

Kruskal, M. D.

N. J. Zabusky and M. D. Kruskal, “Interaction of ‘Solitons’ in a Collisionless Plasma and the Recurrence of Initial States,” Phys. Rev. Lett. 15, 240 (1965).
[Crossref]

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Mamyshev, P. V.

Martin, H.

McDonald, G. S.

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Non-Paraxial Solitons,” J. Mod. Opt. 45, 1111 (1998).
[Crossref]

J. M. Christian, G. S. McDonald, P. Chamorro-Posada, J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz Solitons in Cubic-Quintic Materials,” Phys. Rev. A76, 033833 (2007).
[Crossref]

J. M. Christian, G. S. McDonald, P. Chamorro-Posada, J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz Solitons in Cubic-Quintic Materials,” Phys. Rev. A76, 033833 (2007).
[Crossref]

Millot, G.

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber,” J. Opt. Soc. Am. B,  1266 (1998).

New, G. H. C.

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Non-Paraxial Solitons,” J. Mod. Opt. 45, 1111 (1998).
[Crossref]

Pasta, J.

E. Fermi, J. Pasta, H. C. Ulam, M. Tsingou, G. Van Symaeys, Ph. Emplit, and M. Haelterman, “Experimental Demonstration of the Fermi-Pasta-Ulam Recurrence in a Modulationally Unstable Optical Wave,” Phys. Rev. Lett.87, 033902 (2001).
[Crossref]

Pastori Parravicini, G.

F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids, (Pergamon Press, Oxford, 1976).

Pekar, S. I.

S. I. Pekar, “Supplementary light waves in crystals and exciton absorption,” Sov. Phys. Uspekhi 5, 515 (1962).
[Crossref]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Pohl, U. W.

A. Je. Semjonow, U. W. Pohl, A. Je. Semjonow, U. W. Pohl, and R. Engelhardt, “Negative exciton mass in ZnCdSe/SnSSe superlattices observed by excitonic polariton Raman scattering,” J. Phys. Condens. Matter11, 1735 (1999).
[Crossref]

A. Je. Semjonow, U. W. Pohl, A. Je. Semjonow, U. W. Pohl, and R. Engelhardt, “Negative exciton mass in ZnCdSe/SnSSe superlattices observed by excitonic polariton Raman scattering,” J. Phys. Condens. Matter11, 1735 (1999).
[Crossref]

Russell, P. St. J.

F. Biancalana, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E 68, 046603 (2003).
[Crossref]

Said, A. A.

Semjonow, A. Je.

A. Je. Semjonow, U. W. Pohl, A. Je. Semjonow, U. W. Pohl, and R. Engelhardt, “Negative exciton mass in ZnCdSe/SnSSe superlattices observed by excitonic polariton Raman scattering,” J. Phys. Condens. Matter11, 1735 (1999).
[Crossref]

A. Je. Semjonow, U. W. Pohl, A. Je. Semjonow, U. W. Pohl, and R. Engelhardt, “Negative exciton mass in ZnCdSe/SnSSe superlattices observed by excitonic polariton Raman scattering,” J. Phys. Condens. Matter11, 1735 (1999).
[Crossref]

Seve, E.

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber,” J. Opt. Soc. Am. B,  1266 (1998).

Sheik-Bahae, M.

Shen, Y. R.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167 (2004).
[Crossref]

Skryabin, D. V.

F. Biancalana, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E 68, 046603 (2003).
[Crossref]

Taniuti, T.

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 (1968).
[Crossref]

Tsingou, M.

E. Fermi, J. Pasta, H. C. Ulam, M. Tsingou, G. Van Symaeys, Ph. Emplit, and M. Haelterman, “Experimental Demonstration of the Fermi-Pasta-Ulam Recurrence in a Modulationally Unstable Optical Wave,” Phys. Rev. Lett.87, 033902 (2001).
[Crossref]

Ulam, H. C.

E. Fermi, J. Pasta, H. C. Ulam, M. Tsingou, G. Van Symaeys, Ph. Emplit, and M. Haelterman, “Experimental Demonstration of the Fermi-Pasta-Ulam Recurrence in a Modulationally Unstable Optical Wave,” Phys. Rev. Lett.87, 033902 (2001).
[Crossref]

Van, E. W.

Van Symaeys, G.

E. Fermi, J. Pasta, H. C. Ulam, M. Tsingou, G. Van Symaeys, Ph. Emplit, and M. Haelterman, “Experimental Demonstration of the Fermi-Pasta-Ulam Recurrence in a Modulationally Unstable Optical Wave,” Phys. Rev. Lett.87, 033902 (2001).
[Crossref]

Wabnitz, S.

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber,” J. Opt. Soc. Am. B,  1266 (1998).

Wang, J.

Washimi, H.

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 (1968).
[Crossref]

Wei, T. H.

Young, J.

Zabusky, N. J.

N. J. Zabusky and M. D. Kruskal, “Interaction of ‘Solitons’ in a Collisionless Plasma and the Recurrence of Initial States,” Phys. Rev. Lett. 15, 240 (1965).
[Crossref]

Zakhidov, A. A.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167 (2004).
[Crossref]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

J. Lumin. (1)

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167 (2004).
[Crossref]

J. Mod. Opt. (1)

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Non-Paraxial Solitons,” J. Mod. Opt. 45, 1111 (1998).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Lett. (1)

Phys. Rev. E (1)

F. Biancalana, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing instabilities in photonic-crystal and tapered fibers,” Phys. Rev. E 68, 046603 (2003).
[Crossref]

Phys. Rev. Lett. (3)

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

N. J. Zabusky and M. D. Kruskal, “Interaction of ‘Solitons’ in a Collisionless Plasma and the Recurrence of Initial States,” Phys. Rev. Lett. 15, 240 (1965).
[Crossref]

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 (1968).
[Crossref]

Phys. Usp. (1)

V. M. Agranovich and Y. N. Gartstein, “Spatial dispersion and negative refraction of light,” Phys. Usp. 49, 1029 (2006).
[Crossref]

Sov. Phys. Uspekhi (1)

S. I. Pekar, “Supplementary light waves in crystals and exciton absorption,” Sov. Phys. Uspekhi 5, 515 (1962).
[Crossref]

Other (11)

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, (Springer, Berlin, 1984).

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, (World Scientific, Singapore, 2004).

F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids, (Pergamon Press, Oxford, 1976).

J. M. Christian, G. S. McDonald, P. Chamorro-Posada, J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz Solitons in Cubic-Quintic Materials,” Phys. Rev. A76, 033833 (2007).
[Crossref]

A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, Heidelberg, 1975).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001).

T. B. Benjamin, K. Hasselmann, T. B. Benjamin, and J. E. Feir, “The disintegration of wave trains on deep water. Part 1. Theory,” J. Fluid Mech.27, 417 (1967).
[Crossref]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons, (Academic Press, San Diego, 2003).

E. Fermi, J. Pasta, H. C. Ulam, M. Tsingou, G. Van Symaeys, Ph. Emplit, and M. Haelterman, “Experimental Demonstration of the Fermi-Pasta-Ulam Recurrence in a Modulationally Unstable Optical Wave,” Phys. Rev. Lett.87, 033902 (2001).
[Crossref]

A. Je. Semjonow, U. W. Pohl, A. Je. Semjonow, U. W. Pohl, and R. Engelhardt, “Negative exciton mass in ZnCdSe/SnSSe superlattices observed by excitonic polariton Raman scattering,” J. Phys. Condens. Matter11, 1735 (1999).
[Crossref]

A. S. Davydov, Theory of Molecular Excitons, (Plenum Press, New York-London, 1971).

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.


Figures (5)

Fig. 1.
Fig. 1.

Dispersion k ± of the two branches of the carrier wave in the linear excitation case (I = 0) for (a) anomalous dispersion regime (s = +1) and (b) normal dispersion regime (s = -1). D = 1 in both cases. Solid (dashed) lines indicate the real (imaginary) parts of k ±. Blue (red) lines refer to k + (k -). Gray shaded regions in (a) and (b) indicate the k-bandgap and the ω-inverted bandgap, respectively.

Fig. 2.
Fig. 2.

Dispersion k ± of the two branches of the carrier wave in the nonlinear excitation case (I = 0.3 > I t ) for (a) anomalous dispersion regime (s = +1) and (b) normal dispersion regime (s = -1). D = 1 in both cases. Solid (dashed) lines indicate the real (imaginary) parts of k ±. Blue (red) lines refer to k + (k-).

Fig. 3.
Fig. 3.

Parametric instabilities for anomalous dispersion regime, s = +1. (a,c) Nonlinear dispersion branches of the carrier wave, for D = 0.7<D t < D c [(a)], and for D = 0.85 > D t < D c [(c)]. Solid (dashed) lines are real (imaginary) parts of k ±. Blue (red) lines refer to k + (k-). (b,d) Nonlinear instability gain Im{κ j (δ)}<0 for the parameters described in (a) and (c) respectively. The carrier wave intensity is I = 0.22 in both cases. The values of D t and D c are 0.7576 and 1.1364 respectively.

Fig. 4.
Fig. 4.

Parametric instabilities for normal dispersion regime, s = -1. (a,c) Nonlinear dispersion branches of the carrier wave, for D = 0.7<D t < D c [(a)], and for D = 0.85 > D t < D c [(c)]. Solid (dashed) lines are real (imaginary) parts of k ±. Blue (red) lines refer to k + (k-). (b,d) Nonlinear instability gain Im{κ j (δ)κ<0 for the parameters described in (a) and (c) respectively. The carrier wave intensity is I = 0.22 in both cases. D t and D c are the same as in Fig. 3.

Fig. 5.
Fig. 5.

(a) Region of existence on the parameter space (ν,ω) for bright solitons (s = +1, D = 1), calculated by imposing reality conditions on Eqs. (7)(9), plus the extra condition Eq. (10). (b) Regions of existence on the parameter space (ν,ω) for dark (black + gray) solitons (s = -1, D = 1), calculated by imposing reality conditions on Eqs. (1214), plus the extra condition sνω = ±α|ν||ω|, valid for the black and the gray solitons respectively.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

i z ψ D z 2 ψ + 1 2 s t 2 ψ + ψ 2 ψ = 0 .
i α [ 1 4 D ( I 2 / 2 ) ] 1 2 z f D z 2 f + 1 2 s t 2 f i s ω t f + I ( f + f ¯ ) = 0 ,
i α σ ̂ z A ̂ z v D z 2 v + M ̂ v = 0 ,
M ̂ [ D ̂ ( i t ) + I , I I , D ̂ ( i t ) + I ] .
I { [ 2 D κ + α ( a a ¯ ) ] κ s δ 2 } + 1 4 [ 2 κ ( a ¯ α D κ ) + s δ ( δ 2 ω ) ] · [ 2 κ ( a α + D κ ) + s δ ( δ + 2 ω ) ] = 0
ψ ( z , t ) = A 0 sech ( [ v t z ] / z 0 ) e ikz i ω t ,
k α = 1 + α 1 4 D ( A 0 2 / 2 s ω 2 / 2 ) 2 D = 1 + α | v | | ω | 2 D ,
A 0 = 1 + s ω 2 ( 2 D s v 2 ) 2 D ,
z 0 = 2 D ( sv 2 2 D ) 1 + 2 ( 2 D sv 2 ) .
svw = α | v | | ω | .
ψ ( z , t ) = A 0 { cos ( θ ) tanh [ ( vt z ) / z 0 ] + i sin ( θ ) } e ikz i ω t ,
k α = 1 + α | v | | ω | 2 D ,
A 0 = 1 + 2 ( 2 D sv 2 ) 4 D ,
z 0 = 4 D ( 2 D sv 2 ) 1 + 2 ( 2 D sv 2 ) sec ( θ ) ,
sin ( θ ) = 4 D ( 2 D sv 2 ) [ 1 + 2 ( 2 D sv 2 ) ] ( α | v | | ω | svω ) ,
ε k , ω = ε b [ 1 Δ ω ω ˜ 0 Γ | k | 2 + i γ ] .
ε k , ω = c 2 | k | 2 ω 2 ,
P k , ω = ( χ k , ω X + χ ω W ) E k , ω ,
[ ε k , ω kc / ω ] E k , ω ( ± ) = 0 ,
{ ε b [ 1 Δ δ ω Γ k 2 + i γ ] 1 / 2 kc / ω } E k , ω ( + ) = 0 ,
{ ε b [ 1 Γ Δ k 2 2 δ ω 2 ] kc / ω } E k , ω ( + ) = 0 .
[ i z + i D ̂ W ( i T ) + ε b Γ Δ ω ˜ 0 2 δ ω 2 c z 2 + γ NL A 2 ] A = 0 ,
D ̂ W ( i T ) j = 1 β j j ! [ i T ] j

Metrics