Abstract

The impact of some higher-order effects (HOEs), namely, intrapulse Raman scattering, self-steepening, and third-order dispersion, on a chaotic pulsating soliton, solution of the quintic complex Ginzburg–Landau equation, is numerically investigated. We show that a proper combination of the three HOEs can control the pulse chaotic behavior and provide a fixed-shape solution. The region of existence of fixed-shape pulses is also presented for some range of the parameter values.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons (Springer-Verlag, 2005).
  2. M. Ferreira, Nonlinear Effects in Optical Fibers (Wiley, 2011).
  3. J. M. Soto-Crespo, N. N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. 85, 2937 (2000).
    [CrossRef]
  4. N. N. Akhmediev, J. M. Soto-Crespo, and G. Town, Phys. Rev. E 63, 056602 (2001), and references therein.
    [CrossRef]
  5. W. Chang, A. Ankiewicz, N. Akhmediev, and J. M. Soto-Crespo, Phys. Rev. E 76, 016607 (2007). (And ref therein)
    [CrossRef]
  6. Eduard N. Tsoy and N. N. Akhmediev, Phys. Lett. A 343, 417 (2005).
    [CrossRef]
  7. H. Tian, Z. Li, J. Tian, G. Zhou, and J. Zi, Appl. Phys. B 78, 199 (2004).
    [CrossRef]
  8. L. Song, L. Li, Z. Li, and G. Zhou, Opt. Commun. 249, 301 (2005).
    [CrossRef]
  9. S. C. Latas, M. F. S. Ferreira, and M. V. Facão, Appl. Phys. B 104, 131 (2011).
    [CrossRef]
  10. M. V. Facão and M. I. Carvalho, Phys. Lett A 375, 2327 (2011).
    [CrossRef]
  11. V. V. Afanasjev, N. N. Akhmediev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1931 (1996).
    [CrossRef]
  12. J. M. Soto-Crespo, V. V. Afanasjev, N. N. Akhmediev, and G. E. Town, Opt. Commun. 130, 245 (1996).
    [CrossRef]

2011 (2)

S. C. Latas, M. F. S. Ferreira, and M. V. Facão, Appl. Phys. B 104, 131 (2011).
[CrossRef]

M. V. Facão and M. I. Carvalho, Phys. Lett A 375, 2327 (2011).
[CrossRef]

2007 (1)

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

2005 (2)

Eduard N. Tsoy and N. N. Akhmediev, Phys. Lett. A 343, 417 (2005).
[CrossRef]

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

2004 (1)

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

2001 (1)

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

2000 (1)

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

1996 (2)

V. V. Afanasjev, N. N. Akhmediev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1931 (1996).
[CrossRef]

J. M. Soto-Crespo, V. V. Afanasjev, N. N. Akhmediev, and G. E. Town, Opt. Commun. 130, 245 (1996).
[CrossRef]

Afanasjev, V. V.

V. V. Afanasjev, N. N. Akhmediev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1931 (1996).
[CrossRef]

J. M. Soto-Crespo, V. V. Afanasjev, N. N. Akhmediev, and G. E. Town, Opt. Commun. 130, 245 (1996).
[CrossRef]

Akhmediev, N.

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

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

Akhmediev, N. N.

Eduard N. Tsoy and N. N. Akhmediev, Phys. Lett. A 343, 417 (2005).
[CrossRef]

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

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

J. M. Soto-Crespo, V. V. Afanasjev, N. N. Akhmediev, and G. E. Town, Opt. Commun. 130, 245 (1996).
[CrossRef]

V. V. Afanasjev, N. N. Akhmediev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1931 (1996).
[CrossRef]

Ankiewicz, A.

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

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

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

Carvalho, M. I.

M. V. Facão and M. I. Carvalho, Phys. Lett A 375, 2327 (2011).
[CrossRef]

Chang, W.

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

Facão, M. V.

S. C. Latas, M. F. S. Ferreira, and M. V. Facão, Appl. Phys. B 104, 131 (2011).
[CrossRef]

M. V. Facão and M. I. Carvalho, Phys. Lett A 375, 2327 (2011).
[CrossRef]

Ferreira, M.

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

Ferreira, M. F. S.

S. C. Latas, M. F. S. Ferreira, and M. V. Facão, Appl. Phys. B 104, 131 (2011).
[CrossRef]

Latas, S. C.

S. C. Latas, M. F. S. Ferreira, and M. V. Facão, Appl. Phys. B 104, 131 (2011).
[CrossRef]

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]

Song, L.

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

Soto-Crespo, J. M.

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

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

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

J. M. Soto-Crespo, V. V. Afanasjev, N. N. Akhmediev, and G. E. Town, Opt. Commun. 130, 245 (1996).
[CrossRef]

V. V. Afanasjev, N. N. Akhmediev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1931 (1996).
[CrossRef]

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]

Town, G.

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

Town, G. E.

J. M. Soto-Crespo, V. V. Afanasjev, N. N. Akhmediev, and G. E. Town, Opt. Commun. 130, 245 (1996).
[CrossRef]

Tsoy, Eduard N.

Eduard N. Tsoy and N. N. Akhmediev, Phys. Lett. A 343, 417 (2005).
[CrossRef]

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 (2)

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

S. C. Latas, M. F. S. Ferreira, and M. V. Facão, Appl. Phys. B 104, 131 (2011).
[CrossRef]

Opt. Commun. (2)

J. M. Soto-Crespo, V. V. Afanasjev, N. N. Akhmediev, and G. E. Town, Opt. Commun. 130, 245 (1996).
[CrossRef]

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

Phys. Lett A (1)

M. V. Facão and M. I. Carvalho, Phys. Lett A 375, 2327 (2011).
[CrossRef]

Phys. Lett. A (1)

Eduard N. Tsoy and N. N. Akhmediev, Phys. Lett. A 343, 417 (2005).
[CrossRef]

Phys. Rev. E (3)

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

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

V. V. Afanasjev, N. N. Akhmediev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1931 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

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

Other (2)

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Amplitude and (b) soliton peak power versus soliton energy of a chaotic soliton in the absence of HOEs ( τ R = β 3 = s = 0 ). The other parameter values are the following: δ = 0.1 , β = 0.04 , ε = 0.75 , μ = 0.1 , and ν = 0.08 .

Fig. 2.
Fig. 2.

(a) Amplitude evolution for the chaotic soliton in the presence of IRS, negative TOD, and SST, from two different initial conditions. (b) Initial pulses profiles, namely a narrow pulse (NP) at Z = 140 , and a wide pulse (WP) at Z = 130 . (c) Final pulse profiles. The higher-order parameter values are: τ R = 0.02 , β 3 = 0.00375 , and s = 0.015 . The remaining parameter values are the same as for Fig. 1.

Fig. 3.
Fig. 3.

(a) Amplitude contour plot and (b) peak power versus energy for a chaotic soliton in the presence of IRS, negative TOD, and SST. The higher-order parameter values are τ R = 0.015 , β 3 = 0.003 , and s = 0.01 . The remaining parameter values are the same as for Fig. 1.

Fig. 4.
Fig. 4.

Region in the plane ( β 3 τ R ) where fixed-shape solitons exist for a constant value of SST ( s = 0.015 ). Line L , of null TOD, separates a region of negative TOD on the left from a region of positive TOD on the right. Curves C1 and C2, are the upper and the lower limits, respectively, of the region. The two dots correspond to particular solutions presented in Figs. 2 and 5.

Fig. 5.
Fig. 5.

(a) Amplitude contour plot and (b) amplitude evolution (detail), for a chaotic pulsating soliton in the presence of IRS, positive TOD, and SST. The higher-order parameter values are: τ R = 0.025 , β 3 = 0.03 , and s = 0.015 . The remaining parameter values are the same as for Fig. 1.

Equations (2)

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

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 6 3 u T 3 is ( | u | 2 u ) T + τ R u | u | 2 T ,

Metrics