Abstract

The strong permittivity fluctuation theory was employed to determine the effective linear relative permittivity and the effective nonlinear susceptibility of a two-phase, isotropic, nonlinear, particulate composite medium. Propagation in the homogenized composite medium obeys the complex Ginzburg–Landau equation, and therefore the medium can support the propagation of chirped solitons that are either Pereira–Stenflo (PS) bright solitons or Nozaki–Bekki (NB) dark solitons, when linear loss is counterbalanced by nonlinear gain. Soliton propagation depends on the volume fraction of the component phases as well as on the correlation length of the spatial fluctuation of the dielectric properties in the composite medium.

© 2012 Optical Society of America

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  1. A. Lakhtakia ed., Selected Papers on Linear Optical Composite Materials (SPIE, 1996).
  2. R. J. Martín-Palma and A. Lakhtakia, Nanotechnology—A Crash Course (SPIE, 2010).
  3. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  4. A. Lakhtakia and T. G. Mackay, “Meet the metamaterials,” Opt. Photon. News 18(1), 32–39 (2007).
    [CrossRef]
  5. Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40, 2494–2507 (2011).
    [CrossRef]
  6. P. S. Neelakanta, Handbook of Electromagnetic Materials (CRC Press, 1995).
  7. T. G. Mackay, “Effective constitutive parameters of linear nanocomposites in the long-wavelength regime,” J. Nanophoton. 5, 051001 (2011).
    [CrossRef]
  8. X. C. Zheng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B 38, 10970–10973 (1988).
    [CrossRef]
  9. J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614–1629 (1992).
    [CrossRef]
  10. K. W. Yu, P. M. Hui, and D. Stroud, “Effective dielectric response of nonlinear composites,” Phys. Rev. B 47, 14150–14156 (1993).
    [CrossRef]
  11. R. W. Boyd, R. J. Gehr, G. L. Fischer, and J. E. Sipe, “Nonlinear optical properties of nanocomposite materials,” Pure Appl. Opt. 5, 505–512 (1996).
    [CrossRef]
  12. A. Lakhtakia and W. S. Weiglhofer, “Maxwell Garnett formalism for weakly nonlinear, bianisotropic, dilute, particulate composite media,” Int. J. Electron. 87, 1401–1408 (2000).
    [CrossRef]
  13. T. G. Mackay, “Geometrically derived anisotropy in cubically nonlinear dielectric composites,” J. Phys. D 36, 583–591 (2003).
    [CrossRef]
  14. A. C. Newell, Solitons in Mathematics and Physics (SIAM1985).
  15. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003).
  16. N. C. Kothari and C. Flytzanis, “Light propagation in a two-component nonlinear composite medium,” Opt. Lett. 12, 492–495 (1987).
    [CrossRef]
  17. K. Porsezian, “Soliton propagation in semiconductor-doped glass fibres with higher-order dispersion,” Pure Appl. Opt. 5, 345–348 (1996).
    [CrossRef]
  18. N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).
    [CrossRef]
  19. P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. A 137, 801–818 (1965).
  20. P. D. Maker and R. W. Terhune, “Erratum: study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. A 148, 990 (1966).
  21. A. Lakhtakia, “Application of strong permittivity fluctuation theory for isotropic, cubically nonlinear, composite mediums,” Opt. Commun. 192, 145–151 (2001).
    [CrossRef]
  22. I. S. Aranson and L. Kramers, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
    [CrossRef]
  23. N. R. Pereira and L. Stenflo, “Nonlinear Schrödinger equation including growth and damping,” Phys. Fluids 20, 1733–1734 (1977).
    [CrossRef]
  24. K. Nozaki and N. Bekki, “Exact solutions of the generalized Ginzburg–Landau equation,” J. Phys. Soc. Jpn. 53, 1581–1582 (1984).
    [CrossRef]
  25. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).
  26. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, 1995).
  27. R. W. Boyd, Nonlinear Optics (Academic Press, 1992).
  28. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  29. A. Lakhtakia, “Extended Maxwell Garnett formulae for weakly nonlinear dielectric-in-dielectric composites,” Optik 103, 85–87 (1996).
  30. N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601(2009).
    [CrossRef]
  31. N. L. Tsitsas, A. Lakhtakia, and D. J. Frantzeskakis, “Vector solitons in nonlinear isotropic chiral metamaterials,” J. Phys. A 44, 435203 (2011).
    [CrossRef]
  32. M. J. Ablowitz, B. Prinari, and A. D. Trubatch, Discrete and Continuous Nonlinear Schrödinger Systems (Cambridge University Press, 2004).
  33. N. N. Akhmediev and A. Ankiewicz, Solitons. Nonlinear Pulses and Beams (Chapman & Hall, 1997).
  34. B. A. Malomed and H. G. Winful, “Stable solitons in two-component active systems,” Phys. Rev. E 53, 5365–5368 (1996).
    [CrossRef]
  35. B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg–Landau equations,” Chaos 17, 037117 (2007).
    [CrossRef]
  36. N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilizing the Pereira–Stenflo solitons in nonlinear optical fibers,” Phys. Scr. T84, 18–21 (2000).
    [CrossRef]
  37. N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilization of dark solitons in the cubic Ginzburg–Landau equation,” Phys. Rev. E 62, 7410–7414(2000).
    [CrossRef]
  38. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (IoP Publishing, 1999).
  39. P. W. Baumeister, Optical Coating Technology (SPIE, 2004).

2011 (3)

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40, 2494–2507 (2011).
[CrossRef]

T. G. Mackay, “Effective constitutive parameters of linear nanocomposites in the long-wavelength regime,” J. Nanophoton. 5, 051001 (2011).
[CrossRef]

N. L. Tsitsas, A. Lakhtakia, and D. J. Frantzeskakis, “Vector solitons in nonlinear isotropic chiral metamaterials,” J. Phys. A 44, 435203 (2011).
[CrossRef]

2009 (1)

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601(2009).
[CrossRef]

2007 (2)

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg–Landau equations,” Chaos 17, 037117 (2007).
[CrossRef]

A. Lakhtakia and T. G. Mackay, “Meet the metamaterials,” Opt. Photon. News 18(1), 32–39 (2007).
[CrossRef]

2005 (1)

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).
[CrossRef]

2003 (1)

T. G. Mackay, “Geometrically derived anisotropy in cubically nonlinear dielectric composites,” J. Phys. D 36, 583–591 (2003).
[CrossRef]

2002 (1)

I. S. Aranson and L. Kramers, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[CrossRef]

2001 (1)

A. Lakhtakia, “Application of strong permittivity fluctuation theory for isotropic, cubically nonlinear, composite mediums,” Opt. Commun. 192, 145–151 (2001).
[CrossRef]

2000 (3)

A. Lakhtakia and W. S. Weiglhofer, “Maxwell Garnett formalism for weakly nonlinear, bianisotropic, dilute, particulate composite media,” Int. J. Electron. 87, 1401–1408 (2000).
[CrossRef]

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilizing the Pereira–Stenflo solitons in nonlinear optical fibers,” Phys. Scr. T84, 18–21 (2000).
[CrossRef]

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilization of dark solitons in the cubic Ginzburg–Landau equation,” Phys. Rev. E 62, 7410–7414(2000).
[CrossRef]

1996 (4)

B. A. Malomed and H. G. Winful, “Stable solitons in two-component active systems,” Phys. Rev. E 53, 5365–5368 (1996).
[CrossRef]

A. Lakhtakia, “Extended Maxwell Garnett formulae for weakly nonlinear dielectric-in-dielectric composites,” Optik 103, 85–87 (1996).

K. Porsezian, “Soliton propagation in semiconductor-doped glass fibres with higher-order dispersion,” Pure Appl. Opt. 5, 345–348 (1996).
[CrossRef]

R. W. Boyd, R. J. Gehr, G. L. Fischer, and J. E. Sipe, “Nonlinear optical properties of nanocomposite materials,” Pure Appl. Opt. 5, 505–512 (1996).
[CrossRef]

1993 (1)

K. W. Yu, P. M. Hui, and D. Stroud, “Effective dielectric response of nonlinear composites,” Phys. Rev. B 47, 14150–14156 (1993).
[CrossRef]

1992 (1)

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614–1629 (1992).
[CrossRef]

1988 (1)

X. C. Zheng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B 38, 10970–10973 (1988).
[CrossRef]

1987 (1)

1984 (1)

K. Nozaki and N. Bekki, “Exact solutions of the generalized Ginzburg–Landau equation,” J. Phys. Soc. Jpn. 53, 1581–1582 (1984).
[CrossRef]

1977 (1)

N. R. Pereira and L. Stenflo, “Nonlinear Schrödinger equation including growth and damping,” Phys. Fluids 20, 1733–1734 (1977).
[CrossRef]

1966 (1)

P. D. Maker and R. W. Terhune, “Erratum: study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. A 148, 990 (1966).

1965 (1)

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. A 137, 801–818 (1965).

Ablowitz, M. J.

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, Discrete and Continuous Nonlinear Schrödinger Systems (Cambridge University Press, 2004).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003).

Akhmediev, N. N.

N. N. Akhmediev and A. Ankiewicz, Solitons. Nonlinear Pulses and Beams (Chapman & Hall, 1997).

Ankiewicz, A.

N. N. Akhmediev and A. Ankiewicz, Solitons. Nonlinear Pulses and Beams (Chapman & Hall, 1997).

Aranson, I. S.

I. S. Aranson and L. Kramers, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[CrossRef]

Baumeister, P. W.

P. W. Baumeister, Optical Coating Technology (SPIE, 2004).

Bekki, N.

K. Nozaki and N. Bekki, “Exact solutions of the generalized Ginzburg–Landau equation,” J. Phys. Soc. Jpn. 53, 1581–1582 (1984).
[CrossRef]

Bergman, D. J.

X. C. Zheng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B 38, 10970–10973 (1988).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Boyd, R. W.

R. W. Boyd, R. J. Gehr, G. L. Fischer, and J. E. Sipe, “Nonlinear optical properties of nanocomposite materials,” Pure Appl. Opt. 5, 505–512 (1996).
[CrossRef]

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614–1629 (1992).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic Press, 1992).

Efremidis, N.

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilizing the Pereira–Stenflo solitons in nonlinear optical fibers,” Phys. Scr. T84, 18–21 (2000).
[CrossRef]

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilization of dark solitons in the cubic Ginzburg–Landau equation,” Phys. Rev. E 62, 7410–7414(2000).
[CrossRef]

Fischer, G. L.

R. W. Boyd, R. J. Gehr, G. L. Fischer, and J. E. Sipe, “Nonlinear optical properties of nanocomposite materials,” Pure Appl. Opt. 5, 505–512 (1996).
[CrossRef]

Flytzanis, C.

Frantzeskakis, D. J.

N. L. Tsitsas, A. Lakhtakia, and D. J. Frantzeskakis, “Vector solitons in nonlinear isotropic chiral metamaterials,” J. Phys. A 44, 435203 (2011).
[CrossRef]

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601(2009).
[CrossRef]

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilizing the Pereira–Stenflo solitons in nonlinear optical fibers,” Phys. Scr. T84, 18–21 (2000).
[CrossRef]

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilization of dark solitons in the cubic Ginzburg–Landau equation,” Phys. Rev. E 62, 7410–7414(2000).
[CrossRef]

Gehr, R. J.

R. W. Boyd, R. J. Gehr, G. L. Fischer, and J. E. Sipe, “Nonlinear optical properties of nanocomposite materials,” Pure Appl. Opt. 5, 505–512 (1996).
[CrossRef]

Hasegawa, A.

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

Hizanidis, K.

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilization of dark solitons in the cubic Ginzburg–Landau equation,” Phys. Rev. E 62, 7410–7414(2000).
[CrossRef]

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilizing the Pereira–Stenflo solitons in nonlinear optical fibers,” Phys. Scr. T84, 18–21 (2000).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Hui, P. M.

K. W. Yu, P. M. Hui, and D. Stroud, “Effective dielectric response of nonlinear composites,” Phys. Rev. B 47, 14150–14156 (1993).
[CrossRef]

X. C. Zheng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B 38, 10970–10973 (1988).
[CrossRef]

Kevrekidis, P. G.

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601(2009).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003).

Kodama, Y.

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

Kothari, N. C.

Kourakis, I.

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601(2009).
[CrossRef]

Kramers, L.

I. S. Aranson and L. Kramers, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[CrossRef]

Lakhtakia, A.

N. L. Tsitsas, A. Lakhtakia, and D. J. Frantzeskakis, “Vector solitons in nonlinear isotropic chiral metamaterials,” J. Phys. A 44, 435203 (2011).
[CrossRef]

A. Lakhtakia and T. G. Mackay, “Meet the metamaterials,” Opt. Photon. News 18(1), 32–39 (2007).
[CrossRef]

A. Lakhtakia, “Application of strong permittivity fluctuation theory for isotropic, cubically nonlinear, composite mediums,” Opt. Commun. 192, 145–151 (2001).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, “Maxwell Garnett formalism for weakly nonlinear, bianisotropic, dilute, particulate composite media,” Int. J. Electron. 87, 1401–1408 (2000).
[CrossRef]

A. Lakhtakia, “Extended Maxwell Garnett formulae for weakly nonlinear dielectric-in-dielectric composites,” Optik 103, 85–87 (1996).

R. J. Martín-Palma and A. Lakhtakia, Nanotechnology—A Crash Course (SPIE, 2010).

Lazarides, N.

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).
[CrossRef]

Liu, Y.

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40, 2494–2507 (2011).
[CrossRef]

Mackay, T. G.

T. G. Mackay, “Effective constitutive parameters of linear nanocomposites in the long-wavelength regime,” J. Nanophoton. 5, 051001 (2011).
[CrossRef]

A. Lakhtakia and T. G. Mackay, “Meet the metamaterials,” Opt. Photon. News 18(1), 32–39 (2007).
[CrossRef]

T. G. Mackay, “Geometrically derived anisotropy in cubically nonlinear dielectric composites,” J. Phys. D 36, 583–591 (2003).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (IoP Publishing, 1999).

Maker, P. D.

P. D. Maker and R. W. Terhune, “Erratum: study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. A 148, 990 (1966).

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. A 137, 801–818 (1965).

Malomed, B. A.

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg–Landau equations,” Chaos 17, 037117 (2007).
[CrossRef]

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilizing the Pereira–Stenflo solitons in nonlinear optical fibers,” Phys. Scr. T84, 18–21 (2000).
[CrossRef]

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilization of dark solitons in the cubic Ginzburg–Landau equation,” Phys. Rev. E 62, 7410–7414(2000).
[CrossRef]

B. A. Malomed and H. G. Winful, “Stable solitons in two-component active systems,” Phys. Rev. E 53, 5365–5368 (1996).
[CrossRef]

Martín-Palma, R. J.

R. J. Martín-Palma and A. Lakhtakia, Nanotechnology—A Crash Course (SPIE, 2010).

Neelakanta, P. S.

P. S. Neelakanta, Handbook of Electromagnetic Materials (CRC Press, 1995).

Newell, A. C.

A. C. Newell, Solitons in Mathematics and Physics (SIAM1985).

Nistazakis, H. E.

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilization of dark solitons in the cubic Ginzburg–Landau equation,” Phys. Rev. E 62, 7410–7414(2000).
[CrossRef]

N. Efremidis, K. Hizanidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Stabilizing the Pereira–Stenflo solitons in nonlinear optical fibers,” Phys. Scr. T84, 18–21 (2000).
[CrossRef]

Nozaki, K.

K. Nozaki and N. Bekki, “Exact solutions of the generalized Ginzburg–Landau equation,” J. Phys. Soc. Jpn. 53, 1581–1582 (1984).
[CrossRef]

Pereira, N. R.

N. R. Pereira and L. Stenflo, “Nonlinear Schrödinger equation including growth and damping,” Phys. Fluids 20, 1733–1734 (1977).
[CrossRef]

Porsezian, K.

K. Porsezian, “Soliton propagation in semiconductor-doped glass fibres with higher-order dispersion,” Pure Appl. Opt. 5, 345–348 (1996).
[CrossRef]

Prinari, B.

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, Discrete and Continuous Nonlinear Schrödinger Systems (Cambridge University Press, 2004).

Rompotis, N.

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601(2009).
[CrossRef]

Sipe, J. E.

R. W. Boyd, R. J. Gehr, G. L. Fischer, and J. E. Sipe, “Nonlinear optical properties of nanocomposite materials,” Pure Appl. Opt. 5, 505–512 (1996).
[CrossRef]

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614–1629 (1992).
[CrossRef]

Stenflo, L.

N. R. Pereira and L. Stenflo, “Nonlinear Schrödinger equation including growth and damping,” Phys. Fluids 20, 1733–1734 (1977).
[CrossRef]

Stroud, D.

K. W. Yu, P. M. Hui, and D. Stroud, “Effective dielectric response of nonlinear composites,” Phys. Rev. B 47, 14150–14156 (1993).
[CrossRef]

X. C. Zheng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B 38, 10970–10973 (1988).
[CrossRef]

Terhune, R. W.

P. D. Maker and R. W. Terhune, “Erratum: study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. A 148, 990 (1966).

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. A 137, 801–818 (1965).

Trubatch, A. D.

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, Discrete and Continuous Nonlinear Schrödinger Systems (Cambridge University Press, 2004).

Tsironis, G. P.

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).
[CrossRef]

Tsitsas, N. L.

N. L. Tsitsas, A. Lakhtakia, and D. J. Frantzeskakis, “Vector solitons in nonlinear isotropic chiral metamaterials,” J. Phys. A 44, 435203 (2011).
[CrossRef]

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601(2009).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Weiglhofer, W. S.

A. Lakhtakia and W. S. Weiglhofer, “Maxwell Garnett formalism for weakly nonlinear, bianisotropic, dilute, particulate composite media,” Int. J. Electron. 87, 1401–1408 (2000).
[CrossRef]

Winful, H. G.

B. A. Malomed and H. G. Winful, “Stable solitons in two-component active systems,” Phys. Rev. E 53, 5365–5368 (1996).
[CrossRef]

Yu, K. W.

K. W. Yu, P. M. Hui, and D. Stroud, “Effective dielectric response of nonlinear composites,” Phys. Rev. B 47, 14150–14156 (1993).
[CrossRef]

Zhang, X.

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40, 2494–2507 (2011).
[CrossRef]

Zheng, X. C.

X. C. Zheng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B 38, 10970–10973 (1988).
[CrossRef]

Chaos (1)

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg–Landau equations,” Chaos 17, 037117 (2007).
[CrossRef]

Chem. Soc. Rev. (1)

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40, 2494–2507 (2011).
[CrossRef]

Int. J. Electron. (1)

A. Lakhtakia and W. S. Weiglhofer, “Maxwell Garnett formalism for weakly nonlinear, bianisotropic, dilute, particulate composite media,” Int. J. Electron. 87, 1401–1408 (2000).
[CrossRef]

J. Nanophoton. (1)

T. G. Mackay, “Effective constitutive parameters of linear nanocomposites in the long-wavelength regime,” J. Nanophoton. 5, 051001 (2011).
[CrossRef]

J. Phys. A (1)

N. L. Tsitsas, A. Lakhtakia, and D. J. Frantzeskakis, “Vector solitons in nonlinear isotropic chiral metamaterials,” J. Phys. A 44, 435203 (2011).
[CrossRef]

J. Phys. D (1)

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Figures (4)

Fig. 1.
Fig. 1.

Normalized dispersion cω0kc (left) and nonlinearity nnR(ωc) (right) coefficients versus normalized frequency ωc/ω0(0.2,2), for f1=0.35, ϵ2=2, ϵ1(0) given by Eq. (19) with b=ω0 and δ=2×103ω0, and Λ=0.1.

Fig. 2.
Fig. 2.

Dimensionless loss coefficients γ (dashed blue line) and γn (solid red line), appearing on the right side of the CGL Eq. (15), for f1=0.35, ϵ2=2, ϵ1 given by Eq. (19) with b=ω0 and δ=2×103ω0, and Λ=0.1.

Fig. 3.
Fig. 3.

Distinct frequency bands of the nonlinear HCM, supporting different types of propagating solitons, according to the values of the coefficients s, σ, γ, and γn, involved in the CGL Eq. (15). For 0<ωc<ω0Δω, the HCM is lossless (i.e., γ=γn=0) and dark solitons, obeying the NLS equation, propagate because sσ>0. For ω0+Δω<ωc<ω1Δω, the HCM exhibits linear loss (i.e., γ>0) and nonlinear gain (i.e., γn<0); hence, soliton propagation is governed by the CGL equation. For ωc>ω1+Δω, the HCM is lossless and bright solitons, obeying the NLS equation, propagate because sσ<0. In the two narrow frequency bands of width 2Δω, centered at the two resonant frequencies ω0 and ω1, pulse propagation is prohibited.

Fig. 4.
Fig. 4.

Bandwidth Bω1ω02Δω of the CGL band versus the volume fraction f1 when Λ=0.1 (left) and the normalized correlation length Λ when f1=0.35 (right), for ϵ2=2, and ϵ1 given by Eq. (19) with b=ω0 and δ=2×103ω0.

Equations (31)

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ϵ1(ω)=ϵ1(0)(ω)+χ1|E1|2,
ϵba(ω)=ϵba(0)(ω)+χba(ω)|EHCM|2,
ϵba(0)=ϵBr(0){1+3Λ2ϵBr(0)Ψ12[1+iπ2ΛϵBr(0)]},
χ˜ba=χ˜Br+3Λ2ϵBr(0){iπ4ΛϵBr(0)χ˜BrΨ12+[2χ˜BrΨ12+6ϵBr(0)(f1Ψ1(gϵBr(0)χ˜Brϵ1(0))(ϵ1(0)ϵBr(0))(ϵ1(0)+2ϵBr(0))f2χ˜BrΨ2ϵ2(ϵ2+2ϵBr(0))(ϵ2ϵBr(0)))]×[1+iπ2ΛϵBr(0)]}.
ϵBr(0)=f1ϵ1(0)(ϵ2+2ϵBr(0))+f2ϵ2(ϵ1(0)+2ϵBr(0))f1(ϵ2+2ϵBr(0))+f2(ϵ1(0)+2ϵBr(0)),
χ˜Br=gϵBr(0)ϵ1(0)=f1ϵBr(0)(ϵ2+2ϵBr(0))2f1ϵ1(0)(ϵ2+2ϵBr(0))2+f2ϵ2(ϵ1(0)+2ϵBr(0))2.
Ψ1=(ϵ1(0)ϵBr(0)ϵ1(0)+2ϵBr(0))2Ψ2=(ϵ2ϵBr(0)ϵ2+2ϵBr(0))2Ψ12=f1Ψ1+f2Ψ2},
Λ=ωL/c,
nba(ω)=ϵba(0)(ω)+χba(ω)2ϵba(0)(ω)|EHCM|2=n(ω)+nn(ω)|EHCM|2,
k(ω)=ωcn(ω)=kR(ω)+ikI(ω).
k(ω)kc+kc(ωωc)+12kc(ωωc)2+Δk,
Δk=iωccnI(ωc)+ωccnn(ωc)|u|2
iXukc2T2u+Δku=0.
iXukc2T2u+ωccnnR(ωc)|u|2u=iωcc[nI(ωc)u+nnI(ωc)|u|2u].
iXus2T2u+σ|u|2u=i(γ+γn|u|2)u,
XP=is2(uT2u*u*T2u)2(γ+γnP)P.
γγn<0,
Peq=γ/γn.
ϵ1(0)(ω)=1b2ω2ω02+2iδω.
u(X,T)=A[sech(ΩT)]1+iαexp(iKX),
αα±=3σ±9+8γn22γn,
Ω2=γsα,
K=γ1α22α,
A2=32γγn.
uBS(X,T)=Asech(AT)exp(iA2X/2).
u(X,T)=Aexp[i(ΩTKX)]1exp(2νT)[1+exp(2νT)]1+iα,
Ω=αν,
ν2=23γsα,
K=γα3+γγn,
A2=γγn.
uDS(X,T)=Atanh(AT)exp(iA2X).

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