Abstract

We find the analytical expression for the threshold intensity necessary to launch ultraslow light pulses in a metamaterial with simultaneous cubic electric and magnetic nonlinearity. The roles played by the permittivity, the permeability, the electric cubic nonlinearity, the magnetic cubic nonlinearity and the pulse duration are clearly identified and discussed.

© 2008 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  2. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).
  3. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  4. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic microwave cloak at microwave frequencies,” Science 314, 977-980 (2006).
    [CrossRef] [PubMed]
  5. G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and dark gap solitons in a negative index Fabry-Perot etalon,” Phys. Rev. Lett. 93, 213902 (2004).
    [CrossRef] [PubMed]
  6. M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
    [CrossRef] [PubMed]
  7. S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007); and references therein.
    [CrossRef]
  8. P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
    [CrossRef]
  9. P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
    [CrossRef] [PubMed]
  10. R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photonics News 17, 19-23 (2006).
    [CrossRef]
  11. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  12. T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282-3285 (1997).
    [CrossRef]
  13. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  14. G. D'Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998-2000 (2005).
    [CrossRef] [PubMed]
  15. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, 1995).
  16. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
    [CrossRef] [PubMed]

2007 (2)

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007); and references therein.
[CrossRef]

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

2006 (4)

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photonics News 17, 19-23 (2006).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic microwave cloak at microwave frequencies,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

2005 (2)

G. D'Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998-2000 (2005).
[CrossRef] [PubMed]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
[CrossRef] [PubMed]

2004 (1)

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and dark gap solitons in a negative index Fabry-Perot etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1997 (1)

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Agrawal, G. P.

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

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

Akozbek, N.

G. D'Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998-2000 (2005).
[CrossRef] [PubMed]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
[CrossRef] [PubMed]

Bloemer, M. J.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
[CrossRef] [PubMed]

G. D'Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998-2000 (2005).
[CrossRef] [PubMed]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and dark gap solitons in a negative index Fabry-Perot etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photonics News 17, 19-23 (2006).
[CrossRef]

Brabec, T.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic microwave cloak at microwave frequencies,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

D'Aguanno, G.

G. D'Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998-2000 (2005).
[CrossRef] [PubMed]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
[CrossRef] [PubMed]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and dark gap solitons in a negative index Fabry-Perot etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

Dai, X.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007); and references therein.
[CrossRef]

Danckaert, J.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

Dolling, G.

Enkrich, C.

Fan, D.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007); and references therein.
[CrossRef]

Gaeta, A. L.

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photonics News 17, 19-23 (2006).
[CrossRef]

Gauthier, D. J.

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photonics News 17, 19-23 (2006).
[CrossRef]

Gelens, L.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

Hasegawa, A.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, 1995).

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic microwave cloak at microwave frequencies,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Kivshar, Y. S.

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

Kockaert, P.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Kodama, Y.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, 1995).

Krausz, F.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

Linden, S.

Mattiucci, N.

G. D'Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998-2000 (2005).
[CrossRef] [PubMed]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
[CrossRef] [PubMed]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and dark gap solitons in a negative index Fabry-Perot etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic microwave cloak at microwave frequencies,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic microwave cloak at microwave frequencies,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Polyakov, E. Y.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
[CrossRef] [PubMed]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Scalora, M.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
[CrossRef] [PubMed]

G. D'Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998-2000 (2005).
[CrossRef] [PubMed]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and dark gap solitons in a negative index Fabry-Perot etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic microwave cloak at microwave frequencies,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic microwave cloak at microwave frequencies,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Soukoulis, C. M.

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic microwave cloak at microwave frequencies,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Su, W.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007); and references therein.
[CrossRef]

Syrchin, M. S.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
[CrossRef] [PubMed]

Tang, Z.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007); and references therein.
[CrossRef]

Tassin, P.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Tlidi, M.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Van der Sande, G.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Veretennicoff, I.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Wegener, M.

Wen, S.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007); and references therein.
[CrossRef]

Xiang, Y.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007); and references therein.
[CrossRef]

Zheltikov, A. M.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
[CrossRef] [PubMed]

G. D'Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998-2000 (2005).
[CrossRef] [PubMed]

Chaos (1)

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Opt. Lett. (2)

Opt. Photonics News (1)

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photonics News 17, 19-23 (2006).
[CrossRef]

Phys. Rev. A (2)

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007); and references therein.
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Bright and dark gap solitons in a negative index Fabry-Perot etalon,” Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Polyakov, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005); and references therein.
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

Science (1)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic microwave cloak at microwave frequencies,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (3)

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, 1995).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

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

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Figures (4)

Fig. 1
Fig. 1

(a) n (dashed curve) and V g in units of c (solid curve) versus ω ω ep for a metamaterial described by a Drude model with ω mp ω ep = 0.8 as outlined in the main text. (b) GVD parameter β 2 versus ω ω ep .

Fig. 2
Fig. 2

( S thr χ ̃ fiber ( 3 ) ) ( S thr fiber χ ̃ ε ( 3 ) ) (left y axis) and V g in units of c (right y axis) versus δ ω ω ep where δ ω = ω 0 ω ep is the detuning from the high frequency band edge.

Fig. 3
Fig. 3

β 3 β 2 (units of 1 ω ep ) versus δ ω ω ep .

Fig. 4
Fig. 4

V g ( 1 ) V g V g versus δ ω ω ep .

Equations (20)

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

β 2 ( d d ω ( 1 V g ) ) .
D t 1 2 e i ω 0 t [ i ω 0 ε E ̃ + ( ( ε ω ) ω ) ω = ω 0 E ̃ t + i 2 ( 2 ( ε ω ) ω 2 ) ω = ω 0 2 E ̃ t 2 i ω 0 ε χ ̃ ε ( 3 ) E ̃ 2 E ̃ ] + c.c. ,
B t 1 2 e i ω 0 t [ i ω 0 μ H ̃ + ( ( μ ω ) ω ) ω = ω 0 H ̃ t + i 2 ( 2 ( μ ω ) ω 2 ) ω = ω 0 2 H ̃ t 2 i ω 0 μ χ ̃ μ ( 3 ) H ̃ 2 H ̃ ] + c.c. ,
E ̂ z + i k E ̂ = i ω 0 ( μ + χ ̃ μ ( 3 ) H ̂ 2 ) H ̂ β 1 , μ H ̂ t i 2 β 2 , μ 2 H ̂ t 2 ,
H ̂ z + i k H ̂ = i ω 0 ( ε + χ ̃ ε ( 3 ) E ̂ 2 ) E ̂ β 1 , ε E ̂ t i 2 β 2 , ε 2 E ̂ t 2 ,
β m , ε ( d m ( ω ε ) d ω m ) ω = ω 0 ,
β m , μ ( d m ( ω μ ) d ω m ) ω = ω 0 ( m = 1 , 2 , ) .
1 2 n ω 0 2 E ̂ z 2 + i E ̂ z + i ( ε β 1 , μ + μ β 1 , ε ) 2 n E ̂ t ( β 1 , ε β 1 , μ 2 n ω 0 + β 2 , ε μ 4 n + β 2 , ε n 4 μ ) 2 E ̂ t 2 + ω 0 2 ( μ n χ ̃ ε ( 3 ) E ̂ 2 E ̂ + χ ̃ μ ( 3 ) H ̂ 2 H ̂ ) = 0 .
β m ( d m ( n ω ) d ω m ) ω = ω 0 ( m = 1 , 2 ) ,
i E ̂ ξ β 2 2 2 E ̂ τ 2 + ω 0 2 ( μ n χ ̃ ε ( 3 ) E ̂ 2 E ̂ + χ ̃ μ ( 3 ) H ̂ 2 H ̂ ) = 0 .
β 1 = ( ε β 1 , μ + μ β 1 , ε ) 2 n ,
β 2 = 1 n ω 0 ( 1 V g 2 β 1 , ε β 1 , μ β 2 , ε ω 0 μ 2 β 2 , μ ω 0 ε 2 ) ,
i H ̂ ξ β 2 2 2 H ̂ τ 2 + ω 0 2 ( ε n χ ̃ μ ( 3 ) H ̂ 2 H ̂ + χ ̃ ε ( 3 ) E ̂ 2 E ̂ ) = 0 .
i u 1 z ̃ sgn ( β 2 ) 2 2 u 1 t ̃ 2 + ( Z χ ̃ ε ( 3 ) u 1 2 u 1 + χ ̃ μ ( 3 ) u 2 2 u 2 ) = 0 ,
i u 2 z ̃ sgn ( β 2 ) 2 2 u 2 t ̃ 2 + ( 1 Z χ ̃ μ ( 3 ) u 2 2 u 2 + χ ̃ ε ( 3 ) u 1 2 u 1 ) = 0 ,
i u z ̃ sgn ( β 2 ) 2 2 u t ̃ 2 + Γ u 2 u = 0 ,
S thr = Z L D ω 0 Γ = β 2 ε μ T 0 2 ω 0 μ 2 χ ̃ ε ( 3 ) + ε 2 χ ̃ μ ( 3 ) .
i u z ̃ sgn ( β 2 ) 2 2 u t ̃ 2 + Γ u 2 u = i δ 3 3 u t ̃ 3 ,
u ( z ̃ , t ̃ ) = ( sech ( t ̃ δ 3 z ̃ ) Γ ) exp ( i z ̃ 2 ) .
V g ( 1 ) = V g 1 + V g β 3 6 T 0 2 ,

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