Abstract

We numerically study the impact of self-frequency shift, self-steepening, and third-order dispersion on the erupting soliton solutions of the quintic complex Ginzburg–Landau equation. We find that the pulse explosions can be completely eliminated if these higher-order effects are properly conjugated two by two. In particular, we observe that positive third-order dispersion can compensate the self-frequency shift effect, whereas negative third-order dispersion can compensate the self-steepening effect. A stable propagation of a fixed-shape pulse is found under the simultaneous presence of the three higher-order effects.

© 2010 Optical Society of America

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  17. E. N. Tsoy and M. C. Sterke, J. Opt. Soc. Am. B 23, 2425 (2006).
    [CrossRef]
  18. G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997).
  19. F. If, P. Berg, P. L. Christiansen, and O. Skovgaard, J. Comput. Phys. 72, 501 (1987).
    [CrossRef]

2006

2005

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

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

2004

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

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

2003

N. N. Akhmediev and J. M. Soto-Crespo, Phys. Lett. A 317, 287 (2003).
[CrossRef]

2002

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

2001

N. N. Akhmediev, J. M. Soto-Crespo, and G. Town, Phys. Rev. E 63, 056602 (2001).
[CrossRef]

2000

J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 852937 (2000).
[CrossRef] [PubMed]

1999

1996

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

1993

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

1992

1991

1987

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

1975

H. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

Agrawal, G. P.

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

N. N. Akhmediev and J. M. Soto-Crespo, Phys. Lett. A 317, 287 (2003).
[CrossRef]

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

N. N. Akhmediev, J. M. Soto-Crespo, and G. Town, Phys. Rev. E 63, 056602 (2001).
[CrossRef]

J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 852937 (2000).
[CrossRef] [PubMed]

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

Ankiewicz, A.

J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 852937 (2000).
[CrossRef] [PubMed]

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

Belanger, P. A.

Berg, P.

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

Firth, W. J.

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

Gordon, J. P.

Haelterman, M.

Haus, H.

H. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

If, F.

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

Jian, P. S.

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]

Li, Z. H.

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

N. N. Akhmediev and J. M. Soto-Crespo, Phys. Lett. A 317, 287 (2003).
[CrossRef]

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

N. N. Akhmediev, J. M. Soto-Crespo, and G. Town, Phys. Rev. E 63, 056602 (2001).
[CrossRef]

J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 852937 (2000).
[CrossRef] [PubMed]

Sterke, M. C.

Tian, H. P.

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

Tian, J. P.

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

Torruellas, W. E.

Town, G.

N. N. Akhmediev, J. M. Soto-Crespo, and G. Town, Phys. Rev. E 63, 056602 (2001).
[CrossRef]

Trillo, S.

Tsoy, E. N.

Weiss, C. O.

C. O. Weiss, Phys. Rep. 219, 311 (1992).
[CrossRef]

Zhou, G.

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

Zhou, G. S.

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

Zi, J.

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

Appl. Phys. B

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

J. Appl. Phys.

H. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

J. Comput. Phys.

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

J. Opt. Soc. Am. B

Math. Comput. Simul.

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

Opt. Commun.

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.

Phys. Lett. A

N. N. Akhmediev and J. M. Soto-Crespo, Phys. Lett. A 317, 287 (2003).
[CrossRef]

Phys. Rep.

C. O. Weiss, Phys. Rep. 219, 311 (1992).
[CrossRef]

Phys. Rev. E

N. N. Akhmediev, J. M. Soto-Crespo, and G. Town, Phys. Rev. E 63, 056602 (2001).
[CrossRef]

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

Phys. Rev. Lett.

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. 852937 (2000).
[CrossRef] [PubMed]

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

Other

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

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

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Figures (3)

Fig. 1
Fig. 1

Pulse propagation in the presence of SFS for (a) τ R = 0.0 , (b) τ R = 0.1 , and (c) τ R = 0.275 ; (d) shows the pulse energy evolution for τ R = 0.0 (dashed-dotted curve), τ R = 0.01 (solid thin curve), and τ R = 0.275 (solid thick curve). The other parameter values are the following: δ = 0.1 , β = 0.125 , ε = 1.0 , μ = 0.1 , ν = 0.6 , β 3 = s = 0 .

Fig. 2
Fig. 2

Erupting pulse propagation in the presence of SFS and positive TOD, considering four cases: (a) τ R = 0.0 and β 3 = 0.2 , (b) τ R = 0.1 and β 3 = 0.2 , (c) τ R = 0.275 and β 3 = 0.2 , (d) τ R = 0.275 and β 3 = 0.075 . The other parameter values are the following: δ = 0.1 , β = 0.125 , ε = 1.0 , μ = 0.1 , ν = 0.6 .

Fig. 3
Fig. 3

Erupting pulse propagation in the presence of (a) SST ( s = 0.2 ) and negative TOD ( β 3 = 0.2 ) and (b) SFS ( τ R = 0.25 ), SST ( s = 0.125 ), and negative TOD ( β 3 = 0.125 ). The other parameter values are the following: δ = 0.1 , β = 0.125 , ε = 1.0 , μ = 0.1 , 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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