Abstract

We analyze the nonlinear stage of modulation instability in passively mode-locked fiber lasers leading to chaotic or noise-like emission. We present the phase-transition diagram among different regimes of chaotic emission in terms of the key cavity parameters: amplitude or phase turbulence, and spatio-temporal intermittency.

© 2014 Optical Society of America

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  1. M. Horowitz, Y. Barad, and Y. Silberberg, Opt. Lett. 22, 799 (1997).
    [CrossRef]
  2. M. Horowitz and Y. Silberberg, Phot. Techn. Lett. 10, 1389 (1998).
    [CrossRef]
  3. Y. Takushima, K. Yasunaka, Y. Ozeki, and K. Kikuchi, Electron Lett. 41, 399 (2005).
    [CrossRef]
  4. S. Smirnov, S. Kobtsev, S. Kukarin, and A. Ivanenko, Opt. Express 20, 27447 (2012).
    [CrossRef]
  5. A. F. Runge, C. Aguergaray, N. G. R. Broderick, and M. Erkintalo, Opt. Lett. 38, 4327 (2013).
    [CrossRef]
  6. S. Chouli and Ph. Grelu, Phys. Rev. A 81, 063829 (2010).
    [CrossRef]
  7. F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, Appl. Phys. B 99, 107 (2010).
    [CrossRef]
  8. B. I. Shraiman, A. Pumir, W. van Saarloos, P. C. Hoenberg, H. Chaté, and M. Holen, Phys. D 57, 241 (1992).
    [CrossRef]
  9. Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
    [CrossRef]
  10. A. I. Chernykh and S. K. Turitsyn, Opt. Lett. 20, 398 (1995).
    [CrossRef]
  11. Ph. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
    [CrossRef]
  12. M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
    [CrossRef]
  13. H. Chaté, Nonlinearity 7, 185 (1994).
    [CrossRef]
  14. Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
    [CrossRef]
  15. H. Leblond, A. Niang, F. Amrani, M. Salhi, and F. Sanchez, Phys. Rev. A 88, 033809 (2013).
    [CrossRef]
  16. C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
    [CrossRef]

2013 (2)

A. F. Runge, C. Aguergaray, N. G. R. Broderick, and M. Erkintalo, Opt. Lett. 38, 4327 (2013).
[CrossRef]

H. Leblond, A. Niang, F. Amrani, M. Salhi, and F. Sanchez, Phys. Rev. A 88, 033809 (2013).
[CrossRef]

2012 (3)

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

Ph. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
[CrossRef]

S. Smirnov, S. Kobtsev, S. Kukarin, and A. Ivanenko, Opt. Express 20, 27447 (2012).
[CrossRef]

2010 (2)

S. Chouli and Ph. Grelu, Phys. Rev. A 81, 063829 (2010).
[CrossRef]

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, Appl. Phys. B 99, 107 (2010).
[CrossRef]

2005 (1)

Y. Takushima, K. Yasunaka, Y. Ozeki, and K. Kikuchi, Electron Lett. 41, 399 (2005).
[CrossRef]

1998 (1)

M. Horowitz and Y. Silberberg, Phot. Techn. Lett. 10, 1389 (1998).
[CrossRef]

1997 (1)

1995 (1)

1994 (1)

H. Chaté, Nonlinearity 7, 185 (1994).
[CrossRef]

1992 (3)

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

B. I. Shraiman, A. Pumir, W. van Saarloos, P. C. Hoenberg, H. Chaté, and M. Holen, Phys. D 57, 241 (1992).
[CrossRef]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

1976 (1)

Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
[CrossRef]

Aguergaray, C.

Akhmediev, N.

Ph. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
[CrossRef]

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

Amrani, F.

H. Leblond, A. Niang, F. Amrani, M. Salhi, and F. Sanchez, Phys. Rev. A 88, 033809 (2013).
[CrossRef]

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, Appl. Phys. B 99, 107 (2010).
[CrossRef]

Barad, Y.

Broderick, N. G. R.

Chaté, H.

H. Chaté, Nonlinearity 7, 185 (1994).
[CrossRef]

B. I. Shraiman, A. Pumir, W. van Saarloos, P. C. Hoenberg, H. Chaté, and M. Holen, Phys. D 57, 241 (1992).
[CrossRef]

Chernykh, A. I.

Chouli, S.

S. Chouli and Ph. Grelu, Phys. Rev. A 81, 063829 (2010).
[CrossRef]

Erkintalo, M.

Grelu, Ph.

Ph. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
[CrossRef]

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

S. Chouli and Ph. Grelu, Phys. Rev. A 81, 063829 (2010).
[CrossRef]

Haboucha, A.

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, Appl. Phys. B 99, 107 (2010).
[CrossRef]

Haelterman, M.

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Hoenberg, P. C.

B. I. Shraiman, A. Pumir, W. van Saarloos, P. C. Hoenberg, H. Chaté, and M. Holen, Phys. D 57, 241 (1992).
[CrossRef]

Holen, M.

B. I. Shraiman, A. Pumir, W. van Saarloos, P. C. Hoenberg, H. Chaté, and M. Holen, Phys. D 57, 241 (1992).
[CrossRef]

Horowitz, M.

M. Horowitz and Y. Silberberg, Phot. Techn. Lett. 10, 1389 (1998).
[CrossRef]

M. Horowitz, Y. Barad, and Y. Silberberg, Opt. Lett. 22, 799 (1997).
[CrossRef]

Ivanenko, A.

Kikuchi, K.

Y. Takushima, K. Yasunaka, Y. Ozeki, and K. Kikuchi, Electron Lett. 41, 399 (2005).
[CrossRef]

Kobtsev, S.

Kodama, Y.

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Komarov, A.

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, Appl. Phys. B 99, 107 (2010).
[CrossRef]

Kukarin, S.

Kuramoto, Y.

Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
[CrossRef]

Leblond, H.

H. Leblond, A. Niang, F. Amrani, M. Salhi, and F. Sanchez, Phys. Rev. A 88, 033809 (2013).
[CrossRef]

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, Appl. Phys. B 99, 107 (2010).
[CrossRef]

Lecaplain, C.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

Niang, A.

H. Leblond, A. Niang, F. Amrani, M. Salhi, and F. Sanchez, Phys. Rev. A 88, 033809 (2013).
[CrossRef]

Ozeki, Y.

Y. Takushima, K. Yasunaka, Y. Ozeki, and K. Kikuchi, Electron Lett. 41, 399 (2005).
[CrossRef]

Pumir, A.

B. I. Shraiman, A. Pumir, W. van Saarloos, P. C. Hoenberg, H. Chaté, and M. Holen, Phys. D 57, 241 (1992).
[CrossRef]

Romagnoli, M.

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Runge, A. F.

Salhi, M.

H. Leblond, A. Niang, F. Amrani, M. Salhi, and F. Sanchez, Phys. Rev. A 88, 033809 (2013).
[CrossRef]

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, Appl. Phys. B 99, 107 (2010).
[CrossRef]

Sanchez, F.

H. Leblond, A. Niang, F. Amrani, M. Salhi, and F. Sanchez, Phys. Rev. A 88, 033809 (2013).
[CrossRef]

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, Appl. Phys. B 99, 107 (2010).
[CrossRef]

Shraiman, B. I.

B. I. Shraiman, A. Pumir, W. van Saarloos, P. C. Hoenberg, H. Chaté, and M. Holen, Phys. D 57, 241 (1992).
[CrossRef]

Silberberg, Y.

M. Horowitz and Y. Silberberg, Phot. Techn. Lett. 10, 1389 (1998).
[CrossRef]

M. Horowitz, Y. Barad, and Y. Silberberg, Opt. Lett. 22, 799 (1997).
[CrossRef]

Smirnov, S.

Soto-Crespo, J. M.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

Takushima, Y.

Y. Takushima, K. Yasunaka, Y. Ozeki, and K. Kikuchi, Electron Lett. 41, 399 (2005).
[CrossRef]

Trillo, S.

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Tsuzuki, T.

Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
[CrossRef]

Turitsyn, S. K.

van Saarloos, W.

B. I. Shraiman, A. Pumir, W. van Saarloos, P. C. Hoenberg, H. Chaté, and M. Holen, Phys. D 57, 241 (1992).
[CrossRef]

Wabnitz, S.

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Yasunaka, K.

Y. Takushima, K. Yasunaka, Y. Ozeki, and K. Kikuchi, Electron Lett. 41, 399 (2005).
[CrossRef]

Appl. Phys. B (1)

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, Appl. Phys. B 99, 107 (2010).
[CrossRef]

Electron Lett. (1)

Y. Takushima, K. Yasunaka, Y. Ozeki, and K. Kikuchi, Electron Lett. 41, 399 (2005).
[CrossRef]

Electron. Lett. (1)

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Nat. Photonics (1)

Ph. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
[CrossRef]

Nonlinearity (1)

H. Chaté, Nonlinearity 7, 185 (1994).
[CrossRef]

Opt. Commun. (1)

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phot. Techn. Lett. (1)

M. Horowitz and Y. Silberberg, Phot. Techn. Lett. 10, 1389 (1998).
[CrossRef]

Phys. D (1)

B. I. Shraiman, A. Pumir, W. van Saarloos, P. C. Hoenberg, H. Chaté, and M. Holen, Phys. D 57, 241 (1992).
[CrossRef]

Phys. Rev. A (2)

S. Chouli and Ph. Grelu, Phys. Rev. A 81, 063829 (2010).
[CrossRef]

H. Leblond, A. Niang, F. Amrani, M. Salhi, and F. Sanchez, Phys. Rev. A 88, 033809 (2013).
[CrossRef]

Phys. Rev. Lett. (1)

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

Prog. Theor. Phys. (1)

Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Phase diagram of turbulent behavior of CGLE solutions.

Fig. 2.
Fig. 2.

Contour plots showing the evolution of the (a), (c) intensity |U(t,τ)|2 and (b), (d) phase arg(U) versus fast time τ and slow time t: (a), (b) β=2, γ=0.9 (PT regime, point 1 in Fig. 1); (c), (d) β=2, γ=2 (AT regime, point 2 in Fig. 1).

Fig. 3.
Fig. 3.

Intensity |U(t=200,τ)|2 and power spectrum for (a), (b) β=2, γ=0.9 (PT regime); (c), (d) β=2, γ=2 (AT regime).

Fig. 4.
Fig. 4.

Frequency chirp ν(t=200,τ) from the KSE (4) for the PT solution of point 1 in Fig. 1.

Fig. 5.
Fig. 5.

As in Fig. 2 in the STI regime with: (a), (b) β=0.5, γ=1.5 (point 3 in Fig. 1); (c), (d) β=0, γ=4 (point 4 in Fig. 1).

Fig. 6.
Fig. 6.

As in Fig. 3, in the STI regime with (a), (b) β=0.5, γ=1.5; (c), (d) β=0, γ=4.

Fig. 7.
Fig. 7.

As in Fig. 2(a) in STI regime with (a), (b) β=0.5, γ=8 (point 5 in Fig. 1) (c), (d) β=1, γ=16 (point 6 in Fig. 1).

Fig. 8.
Fig. 8.

Numerical intensity autocorrelation traces. Labels indicate corresponding points in Fig. 1.

Equations (5)

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

trtE=(g0LT2)2E+L(β0+iβ22)τ2EL(σ02iγ0)|E|2E,
tU=U+(1+iβ)τ2U(1iγ)|U|2U,
tν=ητ2νλντν,
tν=|η|τ2νμτ4νλντν,
ν˜(x)=(60ρ3+3019ρ)tanh(ρx)+60ρ3tanh3(ρx),

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