Abstract

We investigate numerically the impact of some higher-order effects, namely, self-frequency shift, self-steepening, and third-order dispersion, on the erupting soliton solutions of the quintic complex Ginzburg–Landau equation. We consider particularly the impact of these higher-order effects in the spectral domain from which we can describe the pulse characteristics in the time domain. These effects can filter in different ways the spectral perturbations that contribute to pulse explosions. We show that a proper combination of the three higher-order effects can provide a filtering of the spectral perturbations in such a way that a stable fixed-shape pulse propagation is achieved.

© 2011 Optical Society of America

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References

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  1. N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman & Hall, 1997).
  2. N.Akhmediev and A.Ankiewicz, eds., Dissipative Solitons (Springer-Verlag, 2005).
    [CrossRef]
  3. M. Ferreira, Nonlinear Effects in Optical Fibers (Wiley, 2011).
    [CrossRef]
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  5. L. F. Mollenauer, J. P. Gordon, and S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
    [CrossRef] [PubMed]
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  7. P. S. Jian, W. E. Torruellas, M. Haelterman, S. Trillo, U. Peschel, and F. Lederer, Opt. Lett. 24, 400 (1999).
    [CrossRef]
  8. W. Chang, A. Ankiewicz, N. Akhmediev, and J. Soto-Crespo, Phys. Rev. E 76, 016607 (2007).
    [CrossRef]
  9. S. Mancas and S. Choudhury, Chaos Solitons Fractals 40, 91 (2009).
    [CrossRef]
  10. J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 85, 2937 (2000).
    [CrossRef] [PubMed]
  11. N. N. Akhmediev and J. M. Soto-Crespo, Phys. Rev. E 70, 036613 (2004).
    [CrossRef]
  12. J. M. Soto-Crespo and N. N. Akhmediev, Math. Comput. Simul. 69, 526 (2005).
    [CrossRef]
  13. S. T. Cundiff, J. M. Soto-Crespo, and N. N. Akhmediev, Phys. Rev. Lett. 88, 073903 (2002).
    [CrossRef] [PubMed]
  14. H. Tian, Z. Li, J. Tian, G. Zhou, and J. Zi, Appl. Phys. B 78, 199 (2004).
    [CrossRef]
  15. L. Song, L. Li, Z. Li, and G. Zhou, Opt. Commun. 249, 301(2005).
    [CrossRef]
  16. S. Latas and M. Ferreira, Opt. Lett. 35, 1771 (2010).
    [CrossRef] [PubMed]
  17. G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997).
  18. F. If, P. Berg, P. L. Christiansen, and O. Skovgaard, J. Comput. Phys. 72, 501 (1987).
    [CrossRef]
  19. M. Facão, I. Carvalho, S. Latas, and M. Ferreira, Phys. Lett. A 374, 4844 (2010).
    [CrossRef]

2011 (1)

M. Ferreira, Nonlinear Effects in Optical Fibers (Wiley, 2011).
[CrossRef]

2010 (2)

S. Latas and M. Ferreira, Opt. Lett. 35, 1771 (2010).
[CrossRef] [PubMed]

M. Facão, I. Carvalho, S. Latas, and M. Ferreira, Phys. Lett. A 374, 4844 (2010).
[CrossRef]

2009 (1)

S. Mancas and S. Choudhury, Chaos Solitons Fractals 40, 91 (2009).
[CrossRef]

2007 (1)

W. Chang, A. Ankiewicz, N. Akhmediev, and J. Soto-Crespo, Phys. Rev. E 76, 016607 (2007).
[CrossRef]

2005 (3)

J. M. Soto-Crespo and N. N. Akhmediev, Math. Comput. Simul. 69, 526 (2005).
[CrossRef]

L. Song, L. Li, Z. Li, and G. Zhou, Opt. Commun. 249, 301(2005).
[CrossRef]

N.Akhmediev and A.Ankiewicz, eds., Dissipative Solitons (Springer-Verlag, 2005).
[CrossRef]

2004 (2)

H. Tian, Z. Li, J. Tian, G. Zhou, and J. Zi, Appl. Phys. B 78, 199 (2004).
[CrossRef]

N. N. Akhmediev and J. M. Soto-Crespo, Phys. Rev. E 70, 036613 (2004).
[CrossRef]

2002 (1)

S. T. Cundiff, J. M. Soto-Crespo, and N. N. Akhmediev, Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

2000 (1)

J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 85, 2937 (2000).
[CrossRef] [PubMed]

1999 (1)

1997 (2)

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

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997).

1996 (1)

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623(1996).
[CrossRef] [PubMed]

1993 (1)

J. D. Moores, Opt. Commun. 96, 65 (1993).
[CrossRef]

1992 (1)

1987 (1)

F. If, P. Berg, P. L. Christiansen, and O. Skovgaard, J. Comput. Phys. 72, 501 (1987).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997).

Akhmediev, N.

W. Chang, A. Ankiewicz, N. Akhmediev, and J. Soto-Crespo, Phys. Rev. E 76, 016607 (2007).
[CrossRef]

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

Akhmediev, N. N.

J. M. Soto-Crespo and N. N. Akhmediev, Math. Comput. Simul. 69, 526 (2005).
[CrossRef]

N. N. Akhmediev and J. M. Soto-Crespo, Phys. Rev. E 70, 036613 (2004).
[CrossRef]

S. T. Cundiff, J. M. Soto-Crespo, and N. N. Akhmediev, Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 85, 2937 (2000).
[CrossRef] [PubMed]

Ankiewicz, A.

W. Chang, A. Ankiewicz, N. Akhmediev, and J. Soto-Crespo, Phys. Rev. E 76, 016607 (2007).
[CrossRef]

J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 85, 2937 (2000).
[CrossRef] [PubMed]

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

Berg, P.

F. If, P. Berg, P. L. Christiansen, and O. Skovgaard, J. Comput. Phys. 72, 501 (1987).
[CrossRef]

Carvalho, I.

M. Facão, I. Carvalho, S. Latas, and M. Ferreira, Phys. Lett. A 374, 4844 (2010).
[CrossRef]

Chang, W.

W. Chang, A. Ankiewicz, N. Akhmediev, and J. Soto-Crespo, Phys. Rev. E 76, 016607 (2007).
[CrossRef]

Choudhury, S.

S. Mancas and S. Choudhury, Chaos Solitons Fractals 40, 91 (2009).
[CrossRef]

Christiansen, P. L.

F. If, P. Berg, P. L. Christiansen, and O. Skovgaard, J. Comput. Phys. 72, 501 (1987).
[CrossRef]

Cundiff, S. T.

S. T. Cundiff, J. M. Soto-Crespo, and N. N. Akhmediev, Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

Evangelides, S. G.

Facão, M.

M. Facão, I. Carvalho, S. Latas, and M. Ferreira, Phys. Lett. A 374, 4844 (2010).
[CrossRef]

Ferreira, M.

M. Ferreira, Nonlinear Effects in Optical Fibers (Wiley, 2011).
[CrossRef]

S. Latas and M. Ferreira, Opt. Lett. 35, 1771 (2010).
[CrossRef] [PubMed]

M. Facão, I. Carvalho, S. Latas, and M. Ferreira, Phys. Lett. A 374, 4844 (2010).
[CrossRef]

Firth, W. J.

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623(1996).
[CrossRef] [PubMed]

Gordon, J. P.

Haelterman, M.

If, F.

F. If, P. Berg, P. L. Christiansen, and O. Skovgaard, J. Comput. Phys. 72, 501 (1987).
[CrossRef]

Jian, P. S.

Latas, S.

S. Latas and M. Ferreira, Opt. Lett. 35, 1771 (2010).
[CrossRef] [PubMed]

M. Facão, I. Carvalho, S. Latas, and M. Ferreira, Phys. Lett. A 374, 4844 (2010).
[CrossRef]

Lederer, F.

Li, L.

L. Song, L. Li, Z. Li, and G. Zhou, Opt. Commun. 249, 301(2005).
[CrossRef]

Li, Z.

L. Song, L. Li, Z. Li, and G. Zhou, Opt. Commun. 249, 301(2005).
[CrossRef]

H. Tian, Z. Li, J. Tian, G. Zhou, and J. Zi, Appl. Phys. B 78, 199 (2004).
[CrossRef]

Mancas, S.

S. Mancas and S. Choudhury, Chaos Solitons Fractals 40, 91 (2009).
[CrossRef]

Mollenauer, L. F.

Moores, J. D.

J. D. Moores, Opt. Commun. 96, 65 (1993).
[CrossRef]

Peschel, U.

Scroggie, A. J.

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623(1996).
[CrossRef] [PubMed]

Skovgaard, O.

F. If, P. Berg, P. L. Christiansen, and O. Skovgaard, J. Comput. Phys. 72, 501 (1987).
[CrossRef]

Song, L.

L. Song, L. Li, Z. Li, and G. Zhou, Opt. Commun. 249, 301(2005).
[CrossRef]

Soto-Crespo, J.

W. Chang, A. Ankiewicz, N. Akhmediev, and J. Soto-Crespo, Phys. Rev. E 76, 016607 (2007).
[CrossRef]

Soto-Crespo, J. M.

J. M. Soto-Crespo and N. N. Akhmediev, Math. Comput. Simul. 69, 526 (2005).
[CrossRef]

N. N. Akhmediev and J. M. Soto-Crespo, Phys. Rev. E 70, 036613 (2004).
[CrossRef]

S. T. Cundiff, J. M. Soto-Crespo, and N. N. Akhmediev, Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 85, 2937 (2000).
[CrossRef] [PubMed]

Tian, H.

H. Tian, Z. Li, J. Tian, G. Zhou, and J. Zi, Appl. Phys. B 78, 199 (2004).
[CrossRef]

Tian, J.

H. Tian, Z. Li, J. Tian, G. Zhou, and J. Zi, Appl. Phys. B 78, 199 (2004).
[CrossRef]

Torruellas, W. E.

Trillo, S.

Zhou, G.

L. Song, L. Li, Z. Li, and G. Zhou, Opt. Commun. 249, 301(2005).
[CrossRef]

H. Tian, Z. Li, J. Tian, G. Zhou, and J. Zi, Appl. Phys. B 78, 199 (2004).
[CrossRef]

Zi, J.

H. Tian, Z. Li, J. Tian, G. Zhou, and J. Zi, Appl. Phys. B 78, 199 (2004).
[CrossRef]

Appl. Phys. B (1)

H. Tian, Z. Li, J. Tian, G. Zhou, and J. Zi, Appl. Phys. B 78, 199 (2004).
[CrossRef]

Chaos Solitons Fractals (1)

S. Mancas and S. Choudhury, Chaos Solitons Fractals 40, 91 (2009).
[CrossRef]

J. Comput. Phys. (1)

F. If, P. Berg, P. L. Christiansen, and O. Skovgaard, J. Comput. Phys. 72, 501 (1987).
[CrossRef]

Math. Comput. Simul. (1)

J. M. Soto-Crespo and N. N. Akhmediev, Math. Comput. Simul. 69, 526 (2005).
[CrossRef]

Opt. Commun. (2)

L. Song, L. Li, Z. Li, and G. Zhou, Opt. Commun. 249, 301(2005).
[CrossRef]

J. D. Moores, Opt. Commun. 96, 65 (1993).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

M. Facão, I. Carvalho, S. Latas, and M. Ferreira, Phys. Lett. A 374, 4844 (2010).
[CrossRef]

Phys. Rev. E (2)

W. Chang, A. Ankiewicz, N. Akhmediev, and J. Soto-Crespo, Phys. Rev. E 76, 016607 (2007).
[CrossRef]

N. N. Akhmediev and J. M. Soto-Crespo, Phys. Rev. E 70, 036613 (2004).
[CrossRef]

Phys. Rev. Lett. (3)

J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 85, 2937 (2000).
[CrossRef] [PubMed]

W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623(1996).
[CrossRef] [PubMed]

S. T. Cundiff, J. M. Soto-Crespo, and N. N. Akhmediev, Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

Other (4)

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997).

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

N.Akhmediev and A.Ankiewicz, eds., Dissipative Solitons (Springer-Verlag, 2005).
[CrossRef]

M. Ferreira, Nonlinear Effects in Optical Fibers (Wiley, 2011).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Evolution of (a) amplitude and (b) spectrum of an erupting soliton in the absence of higher-order effects ( τ R = β 3 = s = 0 ). The other parameter values are δ = 0.1 , β = 0.125 , ε = 1.0 , μ = 0.1 , and ν = 0.6 .

Fig. 2
Fig. 2

Erupting pulse propagation in the presence of self- frequency shift for (a)  τ R = 0.275 and (c)  τ R = 0.525 . (b) and (d) Spectra corresponding to (a) and (c), respectively. The remaining parameter values are the same as for Fig. 1.

Fig. 3
Fig. 3

Erupting pulse propagation in the presence of positive third-order dispersion and self-frequency shift for (a)  β 3 = 0.2 and τ R = 0.0 and (c)  β 3 = 0.2 . and τ R = 0.275 . (b) and (d) Spectra corresponding to (a) and (c), respectively. The other parameter values are δ = 0.1 , β = 0.125 , ε = 1.0 , μ = 0.1 , ν = 0.6 , and s = 0 .

Fig. 4
Fig. 4

Erupting pulse propagation in the presence of (a) SST only ( s = 0.125 ) and (c) SST ( s = 0.125 ), negative third-order dispersion ( β 3 = 0.125 ) and self-frequency shift ( τ R = 0.25 ). (b) and (d) Spectra corresponding to (a) and (c), respectively. The other parameter values are δ = 0.1 , β = 0.125 , ε = 1.0 , μ = 0.1 , and ν = 0.6 .

Equations (2)

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i u Z + 1 2 2 u T 2 + | u | 2 u = i δ u + i β 2 u T 2 + i ε | u | 2 u + i μ | u | 4 u ν | u | 4 u + H . O . E . ,
H . O . E . = i β 3 3 u T 3 i s ( | u | 2 u ) T + τ R u | u | 2 T ,

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