Abstract

We report the discovery of a quantization of the separation between phase-locked soliton pairs that is related to the radiation waves known as Kelly sidebands, in a passively mode-locked fiber ring laser. Our numerical simulations that predict this phenomenon have been confirmed by our experimental results.

© 2003 Optical Society of America

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    [CrossRef]
  5. H. Kitano and S. Kinoshita, Opt. Commun. 157, 128 (1998).
    [CrossRef]
  6. N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 15, 515 (1998).
    [CrossRef]
  7. E. E. Dianov, A. V. Luchnikov, A. Pilipetskii, and A. M. Prokhovov, J. Appl. Phys. B 54, 175 (1992).
    [CrossRef]
  8. A. N. Pilipestskii and C. R. Menyuk, Opt. Lett. 21, 119 (1996).
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  9. J. N. Kutz, B. C. Kollings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
    [CrossRef]
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2002 (1)

1999 (2)

1998 (3)

J. N. Kutz, B. C. Kollings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[CrossRef]

H. Kitano and S. Kinoshita, Opt. Commun. 157, 128 (1998).
[CrossRef]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 15, 515 (1998).
[CrossRef]

1997 (1)

M. Lai, J. Nicholson, and W. Rudolf, Opt. Commun. 142, 45 (1997).
[CrossRef]

1996 (1)

1995 (1)

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, Physica D 87, 201 (1995).
[CrossRef]

1994 (1)

N. N. Akhmediev, A. V. Buryak, and M. Karlsson, Opt. Commun. 110, 540 (1994).
[CrossRef]

1993 (1)

1992 (4)

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
[CrossRef]

A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 67 (1992).
[CrossRef]

E. E. Dianov, A. V. Luchnikov, A. Pilipetskii, and A. M. Prokhovov, J. Appl. Phys. B 54, 175 (1992).
[CrossRef]

Akhmediev, N. N.

M. J. Lederer, B. Luther-Davies, H. H. Tan, C. Jagadish, N. N. Akhmediev, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 16, 895 (1999).
[CrossRef]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 15, 515 (1998).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and M. Karlsson, Opt. Commun. 110, 540 (1994).
[CrossRef]

Ankiewicz, A.

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 15, 515 (1998).
[CrossRef]

Belhache, F.

Bergman, K.

J. N. Kutz, B. C. Kollings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[CrossRef]

Buryak, A. V.

N. N. Akhmediev, A. V. Buryak, and M. Karlsson, Opt. Commun. 110, 540 (1994).
[CrossRef]

Dianov, E. E.

E. E. Dianov, A. V. Luchnikov, A. Pilipetskii, and A. M. Prokhovov, J. Appl. Phys. B 54, 175 (1992).
[CrossRef]

Elgin, J. N.

Gordon, J. P.

Grelu, Ph.

Grudinin, A. B.

A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 67 (1992).
[CrossRef]

Gutty, F.

Jagadish, C.

Karlsson, M.

N. N. Akhmediev, A. V. Buryak, and M. Karlsson, Opt. Commun. 110, 540 (1994).
[CrossRef]

Kelly, S. M. J.

Kinoshita, S.

H. Kitano and S. Kinoshita, Opt. Commun. 157, 128 (1998).
[CrossRef]

Kitano, H.

H. Kitano and S. Kinoshita, Opt. Commun. 157, 128 (1998).
[CrossRef]

Knox, W. H.

J. N. Kutz, B. C. Kollings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[CrossRef]

Kollings, B. C.

J. N. Kutz, B. C. Kollings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[CrossRef]

Kutz, J. N.

J. N. Kutz, B. C. Kollings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[CrossRef]

Kuznetsov, E. A.

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, Physica D 87, 201 (1995).
[CrossRef]

Lai, M.

M. Lai, J. Nicholson, and W. Rudolf, Opt. Commun. 142, 45 (1997).
[CrossRef]

Lederer, M. J.

Luchnikov, A. V.

E. E. Dianov, A. V. Luchnikov, A. Pilipetskii, and A. M. Prokhovov, J. Appl. Phys. B 54, 175 (1992).
[CrossRef]

Luther-Davies, B.

Menyuk, C. R.

Mikhailov, A. V.

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, Physica D 87, 201 (1995).
[CrossRef]

Nicholson, J.

M. Lai, J. Nicholson, and W. Rudolf, Opt. Commun. 142, 45 (1997).
[CrossRef]

Payne, D. N.

A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 67 (1992).
[CrossRef]

Pilipestskii, A. N.

Pilipetskii, A.

E. E. Dianov, A. V. Luchnikov, A. Pilipetskii, and A. M. Prokhovov, J. Appl. Phys. B 54, 175 (1992).
[CrossRef]

Prokhovov, A. M.

E. E. Dianov, A. V. Luchnikov, A. Pilipetskii, and A. M. Prokhovov, J. Appl. Phys. B 54, 175 (1992).
[CrossRef]

Richardson, D. J.

A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 67 (1992).
[CrossRef]

Romagnoli, M.

Rudolf, W.

M. Lai, J. Nicholson, and W. Rudolf, Opt. Commun. 142, 45 (1997).
[CrossRef]

Shimokhin, I. A.

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, Physica D 87, 201 (1995).
[CrossRef]

Socci, L.

Soto-Crespo, J. M.

Tan, H. H.

Electron. Lett. (2)

A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 67 (1992).
[CrossRef]

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. N. Kutz, B. C. Kollings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[CrossRef]

J. Appl. Phys. B (1)

E. E. Dianov, A. V. Luchnikov, A. Pilipetskii, and A. M. Prokhovov, J. Appl. Phys. B 54, 175 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 15, 515 (1998).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (3)

N. N. Akhmediev, A. V. Buryak, and M. Karlsson, Opt. Commun. 110, 540 (1994).
[CrossRef]

H. Kitano and S. Kinoshita, Opt. Commun. 157, 128 (1998).
[CrossRef]

M. Lai, J. Nicholson, and W. Rudolf, Opt. Commun. 142, 45 (1997).
[CrossRef]

Opt. Lett. (3)

Physica D (1)

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, Physica D 87, 201 (1995).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Model of a passively mode-locked fiber laser used in the simulations.

Fig. 2
Fig. 2

Phase difference versus soliton separation for a discrete set of stable pairs obtained for the same cavity parameters.

Fig. 3
Fig. 3

Numerical spectra of the two-soliton solutions denoted 19 and 21 in Fig. 2. The solid curve corresponds to the spectrum of a single pulse.

Fig. 4
Fig. 4

Experimental spectra of the two-soliton solution.

Equations (2)

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iUz+D2Utt+ΓU2U=igQU+iβUtt,
iϕz+γϕ+12ϕtt+ϕ2ϕ+23ψ2ϕ+13ψ2ϕ*=0,iψz-γψ+12ψtt+ψ2ψ+23ψ2ϕ+13ϕ2ψ*=0,

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