Abstract

We report a novel spontaneous soliton pattern formation in a figure-of-eight passively mode-locked erbium-doped double-clad fiber laser. It consists in a condensate phase in which there is almost periodic arrangement of alternate crystal and liquid soliton phases. Thanks to an adapted ansatz for the electric field, we perform a reconstruction allowing to clearly identify the soliton distribution along the cavity.

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  1. K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fibre ring laser,” Electron. Lett. 28(24), 2226–2228 (1992).
    [CrossRef]
  2. M. Hofer, M. H. Ober, F. Haberl, and M. E. Fermann, “Characterization of ultrashort pulse formation in passively mode-locked fiber lasers,” IEEE J. Quantum Electron. 28(3), 720–728 (1992).
    [CrossRef]
  3. V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28(15), 1391–1392 (1992).
    [CrossRef]
  4. I. N. Duling, “Subpicosecond all-fibre erbium laser,” Electron. Lett. 27(6), 544–545 (1991).
    [CrossRef]
  5. D. J. Richardson, R. I. Laming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
    [CrossRef]
  6. A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
    [CrossRef]
  7. F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, “Dissipative solitons compounds in a fiber laser: Analogy with the states of the matter,” Appl. Phys. B 99(1-2), 107–114 (2010).
    [CrossRef]
  8. D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively modelocked fiber laser,” Phys. Rev. A 64(3), 033814 (2001).
    [CrossRef]
  9. Ph. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Phase-locked soliton pairs in a stretched-pulse fiber laser,” Opt. Lett. 27(11), 966–968 (2002).
    [CrossRef] [PubMed]
  10. N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton Solutions of the Complex Ginzburg-Landau Equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
    [CrossRef]
  11. S. Chouli and P. Grelu, “Rains of solitons in a fiber laser,” Opt. Express 17(14), 11776–11781 (2009).
    [CrossRef] [PubMed]
  12. S. Chouli and Ph. Grelu, “Soliton rains in a fiber laser: an experimental study,” Phys. Rev. A 81(6), 063829 (2010).
    [CrossRef]
  13. F. Amrani, M. Salhi, Ph. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011).
    [CrossRef] [PubMed]
  14. F. Amrani, M. Salhi, H. Leblond, and F. Sanchez, “Characterization of soliton compounds in a passively mode-locked high power fiber laser,” Opt. Commun. 283(24), 5224–5230 (2010).
    [CrossRef]
  15. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Universal triangular spectra in parametrically driven systems,” Phys. Lett. A 375(3), 775–779 (2011).
    [CrossRef]

2011 (2)

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Universal triangular spectra in parametrically driven systems,” Phys. Lett. A 375(3), 775–779 (2011).
[CrossRef]

F. Amrani, M. Salhi, Ph. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011).
[CrossRef] [PubMed]

2010 (3)

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, “Dissipative solitons compounds in a fiber laser: Analogy with the states of the matter,” Appl. Phys. B 99(1-2), 107–114 (2010).
[CrossRef]

S. Chouli and Ph. Grelu, “Soliton rains in a fiber laser: an experimental study,” Phys. Rev. A 81(6), 063829 (2010).
[CrossRef]

F. Amrani, M. Salhi, H. Leblond, and F. Sanchez, “Characterization of soliton compounds in a passively mode-locked high power fiber laser,” Opt. Commun. 283(24), 5224–5230 (2010).
[CrossRef]

2009 (1)

2008 (1)

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[CrossRef]

2002 (1)

2001 (1)

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively modelocked fiber laser,” Phys. Rev. A 64(3), 033814 (2001).
[CrossRef]

1997 (1)

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton Solutions of the Complex Ginzburg-Landau Equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[CrossRef]

1992 (3)

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fibre ring laser,” Electron. Lett. 28(24), 2226–2228 (1992).
[CrossRef]

M. Hofer, M. H. Ober, F. Haberl, and M. E. Fermann, “Characterization of ultrashort pulse formation in passively mode-locked fiber lasers,” IEEE J. Quantum Electron. 28(3), 720–728 (1992).
[CrossRef]

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28(15), 1391–1392 (1992).
[CrossRef]

1991 (2)

I. N. Duling, “Subpicosecond all-fibre erbium laser,” Electron. Lett. 27(6), 544–545 (1991).
[CrossRef]

D. J. Richardson, R. I. Laming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[CrossRef]

Akhmediev, N.

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Universal triangular spectra in parametrically driven systems,” Phys. Lett. A 375(3), 775–779 (2011).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton Solutions of the Complex Ginzburg-Landau Equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[CrossRef]

Amrani, F.

F. Amrani, M. Salhi, Ph. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011).
[CrossRef] [PubMed]

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, “Dissipative solitons compounds in a fiber laser: Analogy with the states of the matter,” Appl. Phys. B 99(1-2), 107–114 (2010).
[CrossRef]

F. Amrani, M. Salhi, H. Leblond, and F. Sanchez, “Characterization of soliton compounds in a passively mode-locked high power fiber laser,” Opt. Commun. 283(24), 5224–5230 (2010).
[CrossRef]

Ankiewicz, A.

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Universal triangular spectra in parametrically driven systems,” Phys. Lett. A 375(3), 775–779 (2011).
[CrossRef]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton Solutions of the Complex Ginzburg-Landau Equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[CrossRef]

Belhache, F.

Chouli, S.

S. Chouli and Ph. Grelu, “Soliton rains in a fiber laser: an experimental study,” Phys. Rev. A 81(6), 063829 (2010).
[CrossRef]

S. Chouli and P. Grelu, “Rains of solitons in a fiber laser,” Opt. Express 17(14), 11776–11781 (2009).
[CrossRef] [PubMed]

Drummond, P. D.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively modelocked fiber laser,” Phys. Rev. A 64(3), 033814 (2001).
[CrossRef]

Dudley, J. M.

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Universal triangular spectra in parametrically driven systems,” Phys. Lett. A 375(3), 775–779 (2011).
[CrossRef]

Duling, I. N.

I. N. Duling, “Subpicosecond all-fibre erbium laser,” Electron. Lett. 27(6), 544–545 (1991).
[CrossRef]

Fermann, M. E.

M. Hofer, M. H. Ober, F. Haberl, and M. E. Fermann, “Characterization of ultrashort pulse formation in passively mode-locked fiber lasers,” IEEE J. Quantum Electron. 28(3), 720–728 (1992).
[CrossRef]

Grelu, P.

Grelu, Ph.

Gutty, F.

Haberl, F.

M. Hofer, M. H. Ober, F. Haberl, and M. E. Fermann, “Characterization of ultrashort pulse formation in passively mode-locked fiber lasers,” IEEE J. Quantum Electron. 28(3), 720–728 (1992).
[CrossRef]

Haboucha, A.

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, “Dissipative solitons compounds in a fiber laser: Analogy with the states of the matter,” Appl. Phys. B 99(1-2), 107–114 (2010).
[CrossRef]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[CrossRef]

Haus, H. A.

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fibre ring laser,” Electron. Lett. 28(24), 2226–2228 (1992).
[CrossRef]

Hofer, M.

M. Hofer, M. H. Ober, F. Haberl, and M. E. Fermann, “Characterization of ultrashort pulse formation in passively mode-locked fiber lasers,” IEEE J. Quantum Electron. 28(3), 720–728 (1992).
[CrossRef]

Ippen, E. P.

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fibre ring laser,” Electron. Lett. 28(24), 2226–2228 (1992).
[CrossRef]

Komarov, A.

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, “Dissipative solitons compounds in a fiber laser: Analogy with the states of the matter,” Appl. Phys. B 99(1-2), 107–114 (2010).
[CrossRef]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[CrossRef]

Laming, R. I.

D. J. Richardson, R. I. Laming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[CrossRef]

Leblond, H.

F. Amrani, M. Salhi, Ph. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011).
[CrossRef] [PubMed]

F. Amrani, M. Salhi, H. Leblond, and F. Sanchez, “Characterization of soliton compounds in a passively mode-locked high power fiber laser,” Opt. Commun. 283(24), 5224–5230 (2010).
[CrossRef]

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, “Dissipative solitons compounds in a fiber laser: Analogy with the states of the matter,” Appl. Phys. B 99(1-2), 107–114 (2010).
[CrossRef]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[CrossRef]

Man, W. S.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively modelocked fiber laser,” Phys. Rev. A 64(3), 033814 (2001).
[CrossRef]

Matsas, V. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28(15), 1391–1392 (1992).
[CrossRef]

D. J. Richardson, R. I. Laming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[CrossRef]

Newson, T. P.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28(15), 1391–1392 (1992).
[CrossRef]

Ober, M. H.

M. Hofer, M. H. Ober, F. Haberl, and M. E. Fermann, “Characterization of ultrashort pulse formation in passively mode-locked fiber lasers,” IEEE J. Quantum Electron. 28(3), 720–728 (1992).
[CrossRef]

Payne, D. N.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28(15), 1391–1392 (1992).
[CrossRef]

D. J. Richardson, R. I. Laming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[CrossRef]

Phillips, M. W.

D. J. Richardson, R. I. Laming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[CrossRef]

Richardson, D. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28(15), 1391–1392 (1992).
[CrossRef]

D. J. Richardson, R. I. Laming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[CrossRef]

Salhi, M.

F. Amrani, M. Salhi, Ph. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011).
[CrossRef] [PubMed]

F. Amrani, M. Salhi, H. Leblond, and F. Sanchez, “Characterization of soliton compounds in a passively mode-locked high power fiber laser,” Opt. Commun. 283(24), 5224–5230 (2010).
[CrossRef]

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, “Dissipative solitons compounds in a fiber laser: Analogy with the states of the matter,” Appl. Phys. B 99(1-2), 107–114 (2010).
[CrossRef]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[CrossRef]

Sanchez, F.

F. Amrani, M. Salhi, Ph. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011).
[CrossRef] [PubMed]

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, “Dissipative solitons compounds in a fiber laser: Analogy with the states of the matter,” Appl. Phys. B 99(1-2), 107–114 (2010).
[CrossRef]

F. Amrani, M. Salhi, H. Leblond, and F. Sanchez, “Characterization of soliton compounds in a passively mode-locked high power fiber laser,” Opt. Commun. 283(24), 5224–5230 (2010).
[CrossRef]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[CrossRef]

Soto-Crespo, J. M.

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Universal triangular spectra in parametrically driven systems,” Phys. Lett. A 375(3), 775–779 (2011).
[CrossRef]

Ph. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Phase-locked soliton pairs in a stretched-pulse fiber laser,” Opt. Lett. 27(11), 966–968 (2002).
[CrossRef] [PubMed]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton Solutions of the Complex Ginzburg-Landau Equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[CrossRef]

Tam, H. Y.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively modelocked fiber laser,” Phys. Rev. A 64(3), 033814 (2001).
[CrossRef]

Tamura, K.

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fibre ring laser,” Electron. Lett. 28(24), 2226–2228 (1992).
[CrossRef]

Tang, D. Y.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively modelocked fiber laser,” Phys. Rev. A 64(3), 033814 (2001).
[CrossRef]

Appl. Phys. B (1)

F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, “Dissipative solitons compounds in a fiber laser: Analogy with the states of the matter,” Appl. Phys. B 99(1-2), 107–114 (2010).
[CrossRef]

Electron. Lett. (4)

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fibre ring laser,” Electron. Lett. 28(24), 2226–2228 (1992).
[CrossRef]

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28(15), 1391–1392 (1992).
[CrossRef]

I. N. Duling, “Subpicosecond all-fibre erbium laser,” Electron. Lett. 27(6), 544–545 (1991).
[CrossRef]

D. J. Richardson, R. I. Laming, D. N. Payne, M. W. Phillips, and V. J. Matsas, “320 fs soliton generation with passively mode-locked erbium fibre laser,” Electron. Lett. 27(9), 730–732 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Hofer, M. H. Ober, F. Haberl, and M. E. Fermann, “Characterization of ultrashort pulse formation in passively mode-locked fiber lasers,” IEEE J. Quantum Electron. 28(3), 720–728 (1992).
[CrossRef]

Opt. Commun. (1)

F. Amrani, M. Salhi, H. Leblond, and F. Sanchez, “Characterization of soliton compounds in a passively mode-locked high power fiber laser,” Opt. Commun. 283(24), 5224–5230 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Universal triangular spectra in parametrically driven systems,” Phys. Lett. A 375(3), 775–779 (2011).
[CrossRef]

Phys. Rev. A (3)

S. Chouli and Ph. Grelu, “Soliton rains in a fiber laser: an experimental study,” Phys. Rev. A 81(6), 063829 (2010).
[CrossRef]

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively modelocked fiber laser,” Phys. Rev. A 64(3), 033814 (2001).
[CrossRef]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton Solutions of the Complex Ginzburg-Landau Equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Experimental setup. DCF: double-clad fiber; DSF: dispersion-shifted fiber; ISO: optical isolator; PC: polarization controller. NALM: nonlinear amplifying loop mirror, UR: unidirectional ring.

Fig. 2
Fig. 2

Temporal trace of the soliton distribution (experiment).

Fig. 3
Fig. 3

Autocorrelation trace (experiment).

Fig. 4
Fig. 4

Optical spectrum (experiment).

Fig. 5
Fig. 5

Temporal distribution of a diphasic mixture of solitons (reconstructed).

Fig. 6
Fig. 6

Autocorrelation trace of a diphasic mixture of solitons(a), Zoom (b), (reconstructed).

Fig. 7
Fig. 7

Optical spectrum of a diphasic mixture of solitons (reconstructed).

Equations (3)

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E n ( t ) = = 1 n A 0 sech ( t Δ τ 0 τ ) exp i ( C ( t Δ τ 0 ) 2 2 τ 2 + ω 0 ( t Δ τ 0 ) ) .
E n ( t ) = = 1 n A 0 sech ( t t , n τ ) exp i ( C ( t t , n ) 2 2 τ 2 + ω 0 ( t t , n ) + Φ , n ) ,
E ( t ) = n = 1 N E n ( t j = 1 n Δ T j ) ,

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