Abstract

We present a theoretical investigation of dispersive wave (DW) generation in nonlinear metamaterials (MMs). The role of the anomalous self-steepening (SS) effect, which can be either positive or negative, and the negative SS parameter can have a very large value compared to an ordinary positive-index material, in DW generation is particularly identified. It is demonstrated that the SS effect exerts a great impact on the peak power while has little effect on the frequency shift of DW. For positive third-order dispersion (TOD), the negative SS broadens the pulse spectrum and weakens the DW’s peak power significantly, opposite to the case of positive SS. For negative TOD, however, the negative SS narrows the pulse spectrum and enhances the DW’s peak power, also opposite to the case of positive SS. The results suggest that the DW generation in nonlinear MMs can be manipulated by SS effect to a large extent.

© 2012 OSA

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    [CrossRef] [PubMed]
  4. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phy.78, 1135–1175 (2006).
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  6. S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A79, 023824 (2009).
    [CrossRef]
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  8. S. Roy, S. K. Bhadra, and G. P. Agrawal, “Perturbation of higher-order solitons by fourth-order dispersion in optical fibers,” Opt. Commun.282, 3798–3803 (2009).
    [CrossRef]
  9. S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun.283, 3081–3088 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
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  13. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1, 41–48 (2007).
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  14. C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).
  15. N. I. Zheludev, “The road ahead for metamaterials,” Science328, 582–583 (2010).
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  16. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85, 3966–3969 (2000).
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  20. N. Engheta, “An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability,” IEEE Antennas Wireless Propagat. Lett.1, 10–13 (2002).
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  21. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006).
    [CrossRef] [PubMed]
  22. W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1, 224–227 (2007).
    [CrossRef]
  23. A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett.91, 037401 (2003).
    [CrossRef] [PubMed]
  24. M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E67, 065601 (2003).
    [CrossRef]
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    [CrossRef]
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  27. M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
    [CrossRef] [PubMed]
  28. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A.A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B69, 165112 (2004).
    [CrossRef]
  29. S. C. Wen, Y. J. Xiang, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A75, 033815 (2007).
    [CrossRef]
  30. S. C. Wen, Y. J. Xiang, W. H. Su, H. Y. Hu, X. Q. Fu, and D. Y. Fan, “Role of the anomalous self-steepening effect in modulation instability in negative-index material,” Opt. Express14, 1568–1575 (2006).
    [CrossRef] [PubMed]
  31. X. Y. Dai, Y. J. Xiang, S. C. Wen, and D. Y. Fan, “Modulation instability of copropagating light beams in nonlinear metamaterials,” J. Opt. Soc. Am. B26, 564–571 (2009).
    [CrossRef]
  32. Y. J. Xiang, S. C. Wen, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B24, 3058–3063 (2007).
    [CrossRef]
  33. Y. J. Xiang, X. Y. Dai, S. C. Wen, J. Guo, and D. Y. Fan, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A84, 033815 (2011).
    [CrossRef]

2011 (3)

G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Fiber-optic Cherenkov radiation in the few-cycle regime,” Opt. Express19, 6635–6647 (2011).
[CrossRef] [PubMed]

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

Y. J. Xiang, X. Y. Dai, S. C. Wen, J. Guo, and D. Y. Fan, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A84, 033815 (2011).
[CrossRef]

2010 (3)

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photonics Nanostruct.8, 228–243 (2010).
[CrossRef]

N. I. Zheludev, “The road ahead for metamaterials,” Science328, 582–583 (2010).
[CrossRef] [PubMed]

S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun.283, 3081–3088 (2010).
[CrossRef]

2009 (5)

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A79, 023824 (2009).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Effects of higher-order dispersion on resonant dispersive waves emitted by solitons,” Opt. Lett.34, 2072–2074 (2009).
[CrossRef] [PubMed]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Perturbation of higher-order solitons by fourth-order dispersion in optical fibers,” Opt. Commun.282, 3798–3803 (2009).
[CrossRef]

D. J. Lei, H. Dong, S. C. Wen, and H. Yang, “Manipulating dispersive wave generation by frequency chirp in photonic crystal fibers,” J. Lightwave. Technol.27, 4501–4507 (2009).
[CrossRef]

X. Y. Dai, Y. J. Xiang, S. C. Wen, and D. Y. Fan, “Modulation instability of copropagating light beams in nonlinear metamaterials,” J. Opt. Soc. Am. B26, 564–571 (2009).
[CrossRef]

2007 (4)

Y. J. Xiang, S. C. Wen, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B24, 3058–3063 (2007).
[CrossRef]

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1, 224–227 (2007).
[CrossRef]

S. C. Wen, Y. J. Xiang, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A75, 033815 (2007).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1, 41–48 (2007).
[CrossRef]

2006 (3)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phy.78, 1135–1175 (2006).
[CrossRef]

S. C. Wen, Y. J. Xiang, W. H. Su, H. Y. Hu, X. Q. Fu, and D. Y. Fan, “Role of the anomalous self-steepening effect in modulation instability in negative-index material,” Opt. Express14, 1568–1575 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

2005 (6)

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E72, 016626 (2005).
[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
[CrossRef] [PubMed]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffaction-limited optical imaging with a silver superlens,” Science308, 534–537 (2005).
[CrossRef] [PubMed]

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B72, 193101 (2005).
[CrossRef]

P. A. Belov and C. R. Simovski, “Subwavelength metallic waveguides loaded by uniaxial resonant scatterers,” Phys. Rev. E72, 036618 (2005).
[CrossRef]

2004 (2)

I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express12, 124–135 (2004).
[CrossRef] [PubMed]

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A.A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B69, 165112 (2004).
[CrossRef]

2003 (2)

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett.91, 037401 (2003).
[CrossRef] [PubMed]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E67, 065601 (2003).
[CrossRef]

2002 (2)

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

N. Engheta, “An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability,” IEEE Antennas Wireless Propagat. Lett.1, 10–13 (2002).
[CrossRef]

2000 (1)

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

1995 (1)

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995).
[CrossRef] [PubMed]

Agranovich, V. M.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A.A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B69, 165112 (2004).
[CrossRef]

Agrawal, G. P.

S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun.283, 3081–3088 (2010).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Perturbation of higher-order solitons by fourth-order dispersion in optical fibers,” Opt. Commun.282, 3798–3803 (2009).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A79, 023824 (2009).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Effects of higher-order dispersion on resonant dispersive waves emitted by solitons,” Opt. Lett.34, 2072–2074 (2009).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (San Diego, Academic, 2001).

Akhmediev, N.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995).
[CrossRef] [PubMed]

Akozbek, N.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
[CrossRef] [PubMed]

Baughman, R. H.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A.A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B69, 165112 (2004).
[CrossRef]

Belov, P. A.

P. A. Belov and C. R. Simovski, “Subwavelength metallic waveguides loaded by uniaxial resonant scatterers,” Phys. Rev. E72, 036618 (2005).
[CrossRef]

Bhadra, S. K.

S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun.283, 3081–3088 (2010).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Perturbation of higher-order solitons by fourth-order dispersion in optical fibers,” Opt. Commun.282, 3798–3803 (2009).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A79, 023824 (2009).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Effects of higher-order dispersion on resonant dispersive waves emitted by solitons,” Opt. Lett.34, 2072–2074 (2009).
[CrossRef] [PubMed]

Bloemer, M. J.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
[CrossRef] [PubMed]

Boardman, A. D.

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photonics Nanostruct.8, 228–243 (2010).
[CrossRef]

Cai, W. S.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1, 224–227 (2007).
[CrossRef]

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B72, 193101 (2005).
[CrossRef]

Chang, G. Q.

Chen, L. J.

Chettiar, U. K.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1, 224–227 (2007).
[CrossRef]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phy.78, 1135–1175 (2006).
[CrossRef]

Cristiani, I.

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 cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

D’Aguanno, G.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
[CrossRef] [PubMed]

Dai, X. Y.

Y. J. Xiang, X. Y. Dai, S. C. Wen, J. Guo, and D. Y. Fan, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A84, 033815 (2011).
[CrossRef]

X. Y. Dai, Y. J. Xiang, S. C. Wen, and D. Y. Fan, “Modulation instability of copropagating light beams in nonlinear metamaterials,” J. Opt. Soc. Am. B26, 564–571 (2009).
[CrossRef]

Y. J. Xiang, S. C. Wen, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B24, 3058–3063 (2007).
[CrossRef]

S. C. Wen, Y. J. Xiang, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A75, 033815 (2007).
[CrossRef]

Degiorgio, V.

Dong, H.

D. J. Lei, H. Dong, S. C. Wen, and H. Yang, “Manipulating dispersive wave generation by frequency chirp in photonic crystal fibers,” J. Lightwave. Technol.27, 4501–4507 (2009).
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phy.78, 1135–1175 (2006).
[CrossRef]

Efimov, A.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005).
[CrossRef] [PubMed]

Engheta, N.

N. Engheta, “An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability,” IEEE Antennas Wireless Propagat. Lett.1, 10–13 (2002).
[CrossRef]

Fan, D. Y.

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffaction-limited optical imaging with a silver superlens,” Science308, 534–537 (2005).
[CrossRef] [PubMed]

Fu, X. Q.

Genov, D. A.

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B72, 193101 (2005).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phy.78, 1135–1175 (2006).
[CrossRef]

Ghosh, D.

S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun.283, 3081–3088 (2010).
[CrossRef]

Gorkunov, M.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E67, 065601 (2003).
[CrossRef]

Griebner, U.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

Guo, J.

Y. J. Xiang, X. Y. Dai, S. C. Wen, J. Guo, and D. Y. Fan, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A84, 033815 (2011).
[CrossRef]

Herrmann, J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

Hess, O.

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photonics Nanostruct.8, 228–243 (2010).
[CrossRef]

Hu, H. Y.

Husakou, A.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

Joly, N.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005).
[CrossRef] [PubMed]

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 cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995).
[CrossRef] [PubMed]

Kärtner, F. X.

Kildishev, A. V.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1, 224–227 (2007).
[CrossRef]

Kivshar, Y. S.

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett.91, 037401 (2003).
[CrossRef] [PubMed]

Knight, J. C.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

Korn, G.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

Kourakis, I.

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E72, 016626 (2005).
[CrossRef]

Lapine, M.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E67, 065601 (2003).
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffaction-limited optical imaging with a silver superlens,” Science308, 534–537 (2005).
[CrossRef] [PubMed]

Lei, D. J.

D. J. Lei, H. Dong, S. C. Wen, and H. Yang, “Manipulating dispersive wave generation by frequency chirp in photonic crystal fibers,” J. Lightwave. Technol.27, 4501–4507 (2009).
[CrossRef]

Mattiucci, N.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
[CrossRef] [PubMed]

Mitchell-Thomas, R. C.

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photonics Nanostruct.8, 228–243 (2010).
[CrossRef]

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 cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

Nickel, D.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

Omenetto, F. G.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005).
[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 cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

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

Poliakov, E. Y.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
[CrossRef] [PubMed]

Rapoport, Y. G.

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photonics Nanostruct.8, 228–243 (2010).
[CrossRef]

Ringhofer, K. H.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E67, 065601 (2003).
[CrossRef]

Roy, S.

S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun.283, 3081–3088 (2010).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Perturbation of higher-order solitons by fourth-order dispersion in optical fibers,” Opt. Commun.282, 3798–3803 (2009).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A79, 023824 (2009).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Effects of higher-order dispersion on resonant dispersive waves emitted by solitons,” Opt. Lett.34, 2072–2074 (2009).
[CrossRef] [PubMed]

Russell, P.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005).
[CrossRef] [PubMed]

Russell, P. St. J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

Scalora, M.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
[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 cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

Shadrivov, I. V.

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett.91, 037401 (2003).
[CrossRef] [PubMed]

Shalaev, V. M.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1, 224–227 (2007).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1, 41–48 (2007).
[CrossRef]

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B72, 193101 (2005).
[CrossRef]

Shen, Y. R.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A.A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B69, 165112 (2004).
[CrossRef]

Shukla, P. K.

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E72, 016626 (2005).
[CrossRef]

Simovski, C. R.

P. A. Belov and C. R. Simovski, “Subwavelength metallic waveguides loaded by uniaxial resonant scatterers,” Phys. Rev. E72, 036618 (2005).
[CrossRef]

Skryabin, D. V.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005).
[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 cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

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 cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

Su, W. H.

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffaction-limited optical imaging with a silver superlens,” Science308, 534–537 (2005).
[CrossRef] [PubMed]

Syrchin, M. S.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
[CrossRef] [PubMed]

Tang, Z. X.

S. C. Wen, Y. J. Xiang, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A75, 033815 (2007).
[CrossRef]

Y. J. Xiang, S. C. Wen, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B24, 3058–3063 (2007).
[CrossRef]

Tartara, L.

Taylor, A. J.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005).
[CrossRef] [PubMed]

Tediosi, R.

Velasco, L.

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photonics Nanostruct.8, 228–243 (2010).
[CrossRef]

Wadsworth, W. J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

Wegener, M.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

Wen, S. C.

Y. J. Xiang, X. Y. Dai, S. C. Wen, J. Guo, and D. Y. Fan, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A84, 033815 (2011).
[CrossRef]

X. Y. Dai, Y. J. Xiang, S. C. Wen, and D. Y. Fan, “Modulation instability of copropagating light beams in nonlinear metamaterials,” J. Opt. Soc. Am. B26, 564–571 (2009).
[CrossRef]

D. J. Lei, H. Dong, S. C. Wen, and H. Yang, “Manipulating dispersive wave generation by frequency chirp in photonic crystal fibers,” J. Lightwave. Technol.27, 4501–4507 (2009).
[CrossRef]

S. C. Wen, Y. J. Xiang, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A75, 033815 (2007).
[CrossRef]

Y. J. Xiang, S. C. Wen, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B24, 3058–3063 (2007).
[CrossRef]

S. C. Wen, Y. J. Xiang, W. H. Su, H. Y. Hu, X. Q. Fu, and D. Y. Fan, “Role of the anomalous self-steepening effect in modulation instability in negative-index material,” Opt. Express14, 1568–1575 (2006).
[CrossRef] [PubMed]

Xiang, Y. J.

Yang, H.

D. J. Lei, H. Dong, S. C. Wen, and H. Yang, “Manipulating dispersive wave generation by frequency chirp in photonic crystal fibers,” J. Lightwave. Technol.27, 4501–4507 (2009).
[CrossRef]

Yulin, A. V.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005).
[CrossRef] [PubMed]

Zakhidov, A.A.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A.A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B69, 165112 (2004).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffaction-limited optical imaging with a silver superlens,” Science308, 534–537 (2005).
[CrossRef] [PubMed]

Zharov, A. A.

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett.91, 037401 (2003).
[CrossRef] [PubMed]

Zhavoronkov, N.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

Zheltikov, A. M.

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
[CrossRef] [PubMed]

Zheludev, N. I.

N. I. Zheludev, “The road ahead for metamaterials,” Science328, 582–583 (2010).
[CrossRef] [PubMed]

IEEE Antennas Wireless Propagat. Lett. (1)

N. Engheta, “An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability,” IEEE Antennas Wireless Propagat. Lett.1, 10–13 (2002).
[CrossRef]

J. Lightwave. Technol. (1)

D. J. Lei, H. Dong, S. C. Wen, and H. Yang, “Manipulating dispersive wave generation by frequency chirp in photonic crystal fibers,” J. Lightwave. Technol.27, 4501–4507 (2009).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nat. Photonics (3)

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1, 224–227 (2007).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1, 41–48 (2007).
[CrossRef]

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

Opt. Commun. (2)

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Perturbation of higher-order solitons by fourth-order dispersion in optical fibers,” Opt. Commun.282, 3798–3803 (2009).
[CrossRef]

S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun.283, 3081–3088 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Photonics Nanostruct. (1)

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photonics Nanostruct.8, 228–243 (2010).
[CrossRef]

Phys. Rev. A (4)

Y. J. Xiang, X. Y. Dai, S. C. Wen, J. Guo, and D. Y. Fan, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A84, 033815 (2011).
[CrossRef]

S. C. Wen, Y. J. Xiang, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A75, 033815 (2007).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A79, 023824 (2009).
[CrossRef]

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995).
[CrossRef] [PubMed]

Phys. Rev. B (2)

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B72, 193101 (2005).
[CrossRef]

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A.A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B69, 165112 (2004).
[CrossRef]

Phys. Rev. E (3)

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E72, 016626 (2005).
[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E67, 065601 (2003).
[CrossRef]

P. A. Belov and C. R. Simovski, “Subwavelength metallic waveguides loaded by uniaxial resonant scatterers,” Phys. Rev. E72, 036618 (2005).
[CrossRef]

Phys. Rev. Lett. (5)

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

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002).
[CrossRef] [PubMed]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, 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).
[CrossRef] [PubMed]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett.91, 037401 (2003).
[CrossRef] [PubMed]

Rev. Mod. Phy. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phy.78, 1135–1175 (2006).
[CrossRef]

Science (3)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffaction-limited optical imaging with a silver superlens,” Science308, 534–537 (2005).
[CrossRef] [PubMed]

N. I. Zheludev, “The road ahead for metamaterials,” Science328, 582–583 (2010).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (San Diego, Academic, 2001).

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Figures (6)

Fig. 1
Fig. 1

Contour and output spectra of a second-order soliton (N = 2) at the different SS coefficients, (a)s1 = 0, (b)s1 = 0.05, (c)s1 = 0.1 and (d)s1 = 0.2, where δ3 = 0.04.

Fig. 2
Fig. 2

(a) Frequency shift and (b) relative peak power of the DW peak plotted as a function of SS coefficient s1, where δ3 = 0.04. The square symbols show the results obtained when the Raman effect is neglected, and the circle symbols show the results obtained when the Raman effect is considered.

Fig. 3
Fig. 3

Contour and output spectra of a second-order soliton (N = 2) at the different SS coefficients, (a)s1 = −0.02, (b)s1 = −0.04, (c)s1 = −0.06 and (d)s1 = −0.08, where δ3 = 0.04.

Fig. 4
Fig. 4

Frequency shift (Square symbol line) and relative peak power (Circle symbol line) of the DW peak plotted as a function of negative SS coefficient s1, where δ3 = 0.04.

Fig. 5
Fig. 5

(a) Frequency shift and (b) relative peak power of the DW peak plotted as a function of TOD coefficient δ3, where s1 = −0.06 (triangle symbol line), 0 (square symbol line) and 0.2 (circus symbol line).

Fig. 6
Fig. 6

Contour and output spectra of a second-order soliton (N = 2) at the different SS coefficients, (a)s1 = −0.1, (b)s1 = 0, (c)s1 = 0.06, where δ3 = −0.04. (d) Frequency shift and relative peak power of the DW peak plotted as a function of SS coefficient s1.

Equations (1)

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U ξ = i sgn ( β 2 ) 2 2 U τ 2 + δ 3 3 U τ 3 + i ϑ N 2 [ | U | 2 U + i s 1 ( | U | 2 U ) τ τ R U | U | 2 τ ]

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