Abstract

We investigate experimentally the dynamics of Akhmediev breathers in an optical fiber with a longitudinally tailored dispersion that allows to nearly freeze the breather evolution near their point of maximal compression. Our results are in good agreement with numerical simulations.

© 2014 Optical Society of America

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  1. V. E. Zakharov and L. A. Ostrovsky, Physica D 238, 540 (2009).
    [CrossRef]
  2. A. Hasegawa, Opt. Lett. 9, 288 (1984).
    [CrossRef]
  3. K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
    [CrossRef]
  4. M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators (Cambridge University, 2007).
  5. N. N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
    [CrossRef]
  6. N. N. Akhmediev, Nature 413, 267 (2001).
    [CrossRef]
  7. G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett 87, 033902 (2001).
    [CrossRef]
  8. A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, Phys. Rev. X 4, 011054 (2014).
    [CrossRef]
  9. B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
    [CrossRef]
  10. B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
    [CrossRef]
  11. Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).
    [CrossRef]
  12. C. Q. Dai, C. L. Zheng, and H. P. Zhu, Eur. Phys. J. D 66, 112 (2012).
    [CrossRef]
  13. C. Q. Dai, Y. Y. Wang, Q. Tian, and J. F. Zhang, Ann. Phys. 327, 512 (2012).
    [CrossRef]
  14. M. Onorato, D. Proment, and A. Toffoli, Phys. Rev. Lett. 107, 184502 (2011).
    [CrossRef]
  15. M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, Phys. Lett. A 375, 2029 (2011).
    [CrossRef]
  16. J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
    [CrossRef]
  17. C. Mahnke and F. Mitschke, Phys. Rev. A 85, 033808 (2012).
    [CrossRef]
  18. N. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
    [CrossRef]
  19. K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
    [CrossRef]
  20. G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2013).

2014

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, Phys. Rev. X 4, 011054 (2014).
[CrossRef]

2012

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

C. Q. Dai, C. L. Zheng, and H. P. Zhu, Eur. Phys. J. D 66, 112 (2012).
[CrossRef]

C. Q. Dai, Y. Y. Wang, Q. Tian, and J. F. Zhang, Ann. Phys. 327, 512 (2012).
[CrossRef]

C. Mahnke and F. Mitschke, Phys. Rev. A 85, 033808 (2012).
[CrossRef]

2011

N. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[CrossRef]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

M. Onorato, D. Proment, and A. Toffoli, Phys. Rev. Lett. 107, 184502 (2011).
[CrossRef]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, Phys. Lett. A 375, 2029 (2011).
[CrossRef]

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).
[CrossRef]

2010

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

2009

2001

N. N. Akhmediev, Nature 413, 267 (2001).
[CrossRef]

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett 87, 033902 (2001).
[CrossRef]

1986

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

N. N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[CrossRef]

1984

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2013).

Akhmediev, N.

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, Phys. Rev. X 4, 011054 (2014).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[CrossRef]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

N. N. Akhmediev, Nature 413, 267 (2001).
[CrossRef]

N. N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[CrossRef]

Ankiewicz, A.

N. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[CrossRef]

Dai, C. Q.

C. Q. Dai, C. L. Zheng, and H. P. Zhu, Eur. Phys. J. D 66, 112 (2012).
[CrossRef]

C. Q. Dai, Y. Y. Wang, Q. Tian, and J. F. Zhang, Ann. Phys. 327, 512 (2012).
[CrossRef]

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).
[CrossRef]

Dias, F.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

Droques, M.

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, Phys. Rev. X 4, 011054 (2014).
[CrossRef]

Dudley, J. M.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, Phys. Lett. A 375, 2029 (2011).
[CrossRef]

N. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

Emplit, P.

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett 87, 033902 (2001).
[CrossRef]

Erkintalo, M.

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, Phys. Lett. A 375, 2029 (2011).
[CrossRef]

Fatome, J.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Finot, C.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Genty, G.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, Phys. Lett. A 375, 2029 (2011).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

Haelterman, M.

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett 87, 033902 (2001).
[CrossRef]

Hammani, K.

Hasegawa, A.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

A. Hasegawa, Opt. Lett. 9, 288 (1984).
[CrossRef]

Jewell, J. L.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Kibler, B.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

Korneev, V. I.

N. N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[CrossRef]

Kudlinski, A.

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, Phys. Rev. X 4, 011054 (2014).
[CrossRef]

Mahnke, C.

C. Mahnke and F. Mitschke, Phys. Rev. A 85, 033808 (2012).
[CrossRef]

Marhic, M. E.

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators (Cambridge University, 2007).

Millot, G.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Mitschke, F.

C. Mahnke and F. Mitschke, Phys. Rev. A 85, 033808 (2012).
[CrossRef]

Mussot, A.

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, Phys. Rev. X 4, 011054 (2014).
[CrossRef]

Onorato, M.

M. Onorato, D. Proment, and A. Toffoli, Phys. Rev. Lett. 107, 184502 (2011).
[CrossRef]

Ostrovsky, L. A.

V. E. Zakharov and L. A. Ostrovsky, Physica D 238, 540 (2009).
[CrossRef]

Proment, D.

M. Onorato, D. Proment, and A. Toffoli, Phys. Rev. Lett. 107, 184502 (2011).
[CrossRef]

Soto-Crespo, J. M.

N. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[CrossRef]

Szriftgiser, P.

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, Phys. Rev. X 4, 011054 (2014).
[CrossRef]

Tai, K.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Tian, Q.

C. Q. Dai, Y. Y. Wang, Q. Tian, and J. F. Zhang, Ann. Phys. 327, 512 (2012).
[CrossRef]

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).
[CrossRef]

Toffoli, A.

M. Onorato, D. Proment, and A. Toffoli, Phys. Rev. Lett. 107, 184502 (2011).
[CrossRef]

Tomita, A.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Van Simaeys, G.

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett 87, 033902 (2001).
[CrossRef]

Wang, Y. Y.

C. Q. Dai, Y. Y. Wang, Q. Tian, and J. F. Zhang, Ann. Phys. 327, 512 (2012).
[CrossRef]

Wetzel, B.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, Phys. Lett. A 375, 2029 (2011).
[CrossRef]

Yang, Q.

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov and L. A. Ostrovsky, Physica D 238, 540 (2009).
[CrossRef]

Zhang, J. F.

C. Q. Dai, Y. Y. Wang, Q. Tian, and J. F. Zhang, Ann. Phys. 327, 512 (2012).
[CrossRef]

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).
[CrossRef]

Zheng, C. L.

C. Q. Dai, C. L. Zheng, and H. P. Zhu, Eur. Phys. J. D 66, 112 (2012).
[CrossRef]

Zhu, H. P.

C. Q. Dai, C. L. Zheng, and H. P. Zhu, Eur. Phys. J. D 66, 112 (2012).
[CrossRef]

Ann. Phys.

C. Q. Dai, Y. Y. Wang, Q. Tian, and J. F. Zhang, Ann. Phys. 327, 512 (2012).
[CrossRef]

Appl. Phys. Lett.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Eur. Phys. J. D

C. Q. Dai, C. L. Zheng, and H. P. Zhu, Eur. Phys. J. D 66, 112 (2012).
[CrossRef]

Nat. Phys.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Nature

N. N. Akhmediev, Nature 413, 267 (2001).
[CrossRef]

Opt. Commun.

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

N. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 775 (2011).
[CrossRef]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, Phys. Lett. A 375, 2029 (2011).
[CrossRef]

Phys. Rev. A

C. Mahnke and F. Mitschke, Phys. Rev. A 85, 033808 (2012).
[CrossRef]

Phys. Rev. Lett

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett 87, 033902 (2001).
[CrossRef]

Phys. Rev. Lett.

M. Onorato, D. Proment, and A. Toffoli, Phys. Rev. Lett. 107, 184502 (2011).
[CrossRef]

Phys. Rev. X

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, Phys. Rev. X 4, 011054 (2014).
[CrossRef]

Physica D

V. E. Zakharov and L. A. Ostrovsky, Physica D 238, 540 (2009).
[CrossRef]

Sci. Rep.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

Theor. Math. Phys.

N. N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[CrossRef]

Other

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators (Cambridge University, 2007).

G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2013).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Longitudinal dispersion profiles used in simulations. (b) and (d) Simulation of the spatiotemporal representation of ABs in the uniform fiber and in the dispersion varying fiber, respectively. (c) and (e) Corresponding spectral dynamics. The parameters used for simulations are γ=2W1·km1, ωmod=2π400·109rad·s1, a=0.1, and amod=0.05.

Fig. 2.
Fig. 2.

(a) Longitudinal outer diameter evolution of the two manufactured fibers and (b) experimental setup. C1-PM, polarization maintaining coupler; EDFA, erbium-doped fiber amplifier; PRBS, pseudorandom bit sequence; IM, intensity modulator; C2, coupler; ISO, isolator; PC, polarization controller; OSA, optical spectrum analyzer.

Fig. 3.
Fig. 3.

(a) and (b) Cutback measurement of the spectral dynamics of sideband formation in the uniform fiber (a) and in the dispersion varying fiber (b). (c) and (d) Longitudinal evolution of the pump power (c) and the probe power (d) in the uniform fiber (black lines and squares) and in the dispersion varying fiber (red lines and squares) (d). Solid lines depict GNLSE simulation results (see text for details).

Fig. 4.
Fig. 4.

Simulations showing the evolution of the maximum peak power of the pulse train in the temporal domain with fiber length in the uniform (black line) and in the dispersion varying fiber (red line).

Equations (3)

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

Az=iβ222At2+iγ|A|2A,
A(z,T)=P0[(14a)cosh(bz)+ibsinh(bz)2acos(ωmodT)cosh(bz)+2acos(ωmodT)2acos(ωmodT)cosh(bz)]eiz,
Az=α2Aiβ2(z)22At2+β363At3+iγ(A(z,t)0R(T)|A(z,tT)|2dT)),

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