Abstract

In a passively mode-locked fiber ring laser, we report the experimental observation of relative phase locking of pulses in a wide variety of cases. Relative phase locking is observed in bunches of N pulses separated by more than 20 pulse widths as well as in close pulse pairs. In the latter case, the phase relationship between the two pulses is measured to be ±π/2, which is related to theoretical predictions formerly obtained from a Ginzburg–Landau distributed model. We have developed a simplified numerical model adapted to our laser, which keeps its essential features while significantly reducing the number of free parameters. The agreement with the experiment is excellent.

© 2003 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  8. B. Chassagne, G. Jonusauskas, J. Oberlé, and C. Rullière, “Multipulse operation regime in a self-mode-locked Cr4+: forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
    [Crossref]
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    [Crossref] [PubMed]
  15. N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Stable soliton pairs in optical transmission lines and fiber lasers,” J. Opt. Soc. Am. B 15, 515–523 (1998).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  24. N. H. Seong, D. Y. Kim, and S. K. Oh, “Self-adjustments of positions of quantised modelocked pulses in figure-eight fibre laser,” Electron. Lett. 37, 157–158 (2001).
    [Crossref]
  25. A. N. Pilipetskii, E. A. Golovchenko, and C. R. Menyuk, “Acousic effect in passively mode-locked fiber ring lasers,” Opt. Lett. 20, 907–909 (1995).
    [Crossref] [PubMed]
  26. J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
    [Crossref]
  27. D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively mode-locked fiber laser,” Phys. Rev. A 64, 33814 (2001).
    [Crossref]
  28. K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64, 149–151 (1994).
    [Crossref]
  29. K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
    [Crossref]
  30. V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1991).
    [Crossref]
  31. N. N. Akhmediev and S. Wabnitz, “Phase detecting of solitons by mixing with a continuous-wave background in an optical fiber,” J. Opt. Soc. Am. B 9, 236–242 (1992).
    [Crossref]
  32. S. Wabnitz, “Suppression of interactions in a phase-locked soliton optical memory,” Opt. Lett. 18, 601–603 (1993).
    [Crossref] [PubMed]
  33. S. Wabnitz, “Control of soliton train transmission, storage, and clock recovery by cw light injection,” J. Opt. Soc. Am. B 13, 2739–2749 (1996).
    [Crossref]
  34. J. D. Moores, “On the Ginzburg–Landau laser mode-locking model with fifth-order saturable absorption terms,” Opt. Commun. 96, 65–70 (1993).
    [Crossref]
  35. N. Akhmediev, F. Zen, and P. Chu, “Pulse–pulse interaction in dispersion-managed fiber systems with nonlinear amplifiers,” Opt. Commun. 201, 217–221 (2002).
    [Crossref]
  36. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers, Fundamentals and Technology (Academic, San Diego, Calif., 1999).
  37. J. M. Soto-Crespo, N. N. Akhmediev, B. C. Collings, S. T. Cundiff, K. Bergman, and W. H. Knox, “Polarization-locked temporal vector solitons in a fiber laser: theory,” J. Opt. Soc. Am. B 17, 366–372 (2000).
    [Crossref]

2002 (2)

N. Akhmediev, F. Zen, and P. Chu, “Pulse–pulse interaction in dispersion-managed fiber systems with nonlinear amplifiers,” Opt. Commun. 201, 217–221 (2002).
[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, 966–968 (2002).
[Crossref]

2001 (3)

F. Gutty, Ph. Grelu, N. Huot, G. Vienne, and G. Millot, “Stabilisation of modelocking in fibre laser through pulse bunching,” Electron. Lett. 37, 745–746 (2001).
[Crossref]

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively mode-locked fiber laser,” Phys. Rev. A 64, 33814 (2001).
[Crossref]

N. H. Seong, D. Y. Kim, and S. K. Oh, “Self-adjustments of positions of quantised modelocked pulses in figure-eight fibre laser,” Electron. Lett. 37, 157–158 (2001).
[Crossref]

2000 (4)

1999 (1)

1998 (3)

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
[Crossref]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Stable soliton pairs in optical transmission lines and fiber lasers,” J. Opt. Soc. Am. B 15, 515–523 (1998).
[Crossref]

B. Chassagne, G. Jonusauskas, J. Oberlé, and C. Rullière, “Multipulse operation regime in a self-mode-locked Cr4+: forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
[Crossref]

1997 (3)

1996 (2)

1995 (2)

A. N. Pilipetskii, E. A. Golovchenko, and C. R. Menyuk, “Acousic effect in passively mode-locked fiber ring lasers,” Opt. Lett. 20, 907–909 (1995).
[Crossref] [PubMed]

K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
[Crossref]

1994 (2)

K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64, 149–151 (1994).
[Crossref]

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[Crossref]

1993 (5)

1992 (4)

J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schroedinger equation,” J. Opt. Soc. Am. B 9, 91–97 (1992).
[Crossref]

N. N. Akhmediev and S. Wabnitz, “Phase detecting of solitons by mixing with a continuous-wave background in an optical fiber,” J. Opt. Soc. Am. B 9, 236–242 (1992).
[Crossref]

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[Crossref]

A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28, 67–68 (1992).
[Crossref]

1991 (4)

D. J. Richardson, R. I. Laming, D. N. Payne, V. J. Matsas, and M. W. Phillips, “Pulse repetition rates in passive, self-starting, femtosecond soliton fibre laser,” Electron. Lett. 27, 1451–1453 (1991).
[Crossref]

M. Nakazawa, E. Yoshida, and Y. Kimura, “Low threshold, 290 fs erbium-doped fiber laser with a nonlinear amplifying loop mirror pumped by InGaAsP laser diodes,” Appl. Phys. Lett. 59, 2073–2075 (1991).
[Crossref]

B. A. Malomed, “Bound solitons in the nonlinear Schrödinger–Ginzburg–Landau equation,” Phys. Rev. A 44, 6954–6957 (1991).
[Crossref] [PubMed]

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1991).
[Crossref]

Abedin, K. S.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Akhmediev, N.

N. Akhmediev, F. Zen, and P. Chu, “Pulse–pulse interaction in dispersion-managed fiber systems with nonlinear amplifiers,” Opt. Commun. 201, 217–221 (2002).
[Crossref]

Akhmediev, N. N.

Ankiewicz, A.

Becker, P. C.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers, Fundamentals and Technology (Academic, San Diego, Calif., 1999).

Belhache, F.

Bergman, K.

Bonadeo, N. H.

Brabec, T.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[Crossref]

Carruthers, T. F.

Chassagne, B.

B. Chassagne, G. Jonusauskas, J. Oberlé, and C. Rullière, “Multipulse operation regime in a self-mode-locked Cr4+: forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
[Crossref]

Chu, P.

N. Akhmediev, F. Zen, and P. Chu, “Pulse–pulse interaction in dispersion-managed fiber systems with nonlinear amplifiers,” Opt. Commun. 201, 217–221 (2002).
[Crossref]

Collings, B. C.

J. M. Soto-Crespo, N. N. Akhmediev, B. C. Collings, S. T. Cundiff, K. Bergman, and W. H. Knox, “Polarization-locked temporal vector solitons in a fiber laser: theory,” J. Opt. Soc. Am. B 17, 366–372 (2000).
[Crossref]

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
[Crossref]

Cundiff, S. T.

Curley, P. F.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[Crossref]

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 mode-locked fiber laser,” Phys. Rev. A 64, 33814 (2001).
[Crossref]

Duling, I. N.

Golovchenko, E. A.

Gordon, J. P.

Gray, S.

Grelu, Ph.

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

F. Gutty, Ph. Grelu, N. Huot, G. Vienne, and G. Millot, “Stabilisation of modelocking in fibre laser through pulse bunching,” Electron. Lett. 37, 745–746 (2001).
[Crossref]

Grudinin, A. B.

A. B. Grudinin and S. Gray, “Passive harmonic mode locking in soliton fiber lasers,” J. Opt. Soc. Am. B 14, 144–154 (1997).
[Crossref]

A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Passive harmonic mode-locking of a fibre soliton ring laser,” Electron. Lett. 29, 1860–1861 (1993).
[Crossref]

A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28, 67–68 (1992).
[Crossref]

Gutty, F.

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

F. Gutty, Ph. Grelu, N. Huot, G. Vienne, and G. Millot, “Stabilisation of modelocking in fibre laser through pulse bunching,” Electron. Lett. 37, 745–746 (2001).
[Crossref]

Guy, M. J.

Haus, H. A.

C. X. Yu, H. A. Haus, E. P. Ippen, W. S. Wong, and A. Sysoliatin, “Gigahertz-repetition-rate mode-locked fiber laser for continuum generation,” Opt. Lett. 25, 1418–1420 (2000).
[Crossref]

K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
[Crossref]

K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64, 149–151 (1994).
[Crossref]

Herrmann, J.

Horowitz, M.

Huot, N.

F. Gutty, Ph. Grelu, N. Huot, G. Vienne, and G. Millot, “Stabilisation of modelocking in fibre laser through pulse bunching,” Electron. Lett. 37, 745–746 (2001).
[Crossref]

Hyodo, M.

Ippen, E. P.

C. X. Yu, H. A. Haus, E. P. Ippen, W. S. Wong, and A. Sysoliatin, “Gigahertz-repetition-rate mode-locked fiber laser for continuum generation,” Opt. Lett. 25, 1418–1420 (2000).
[Crossref]

K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
[Crossref]

K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64, 149–151 (1994).
[Crossref]

Jonusauskas, G.

B. Chassagne, G. Jonusauskas, J. Oberlé, and C. Rullière, “Multipulse operation regime in a self-mode-locked Cr4+: forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
[Crossref]

Kalosha, V. P.

Kelly, S. M. J.

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[Crossref]

Kim, D. Y.

N. H. Seong, D. Y. Kim, and S. K. Oh, “Self-adjustments of positions of quantised modelocked pulses in figure-eight fibre laser,” Electron. Lett. 37, 157–158 (2001).
[Crossref]

Kimura, Y.

M. Nakazawa, E. Yoshida, and Y. Kimura, “Low threshold, 290 fs erbium-doped fiber laser with a nonlinear amplifying loop mirror pumped by InGaAsP laser diodes,” Appl. Phys. Lett. 59, 2073–2075 (1991).
[Crossref]

Knox, W. H.

Krausz, F.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[Crossref]

Kutz, J. N.

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
[Crossref]

Lai, M.

M. Lai, J. Nicholson, and W. Rudolph, “Multiple pulse operation of a femtosecond Ti:sapphire laser,” Opt. Commun. 142, 45–49 (1997).
[Crossref]

Laming, R. I.

D. J. Richardson, R. I. Laming, D. N. Payne, V. J. Matsas, and M. W. Phillips, “Pulse repetition rates in passive, self-starting, femtosecond soliton fibre laser,” Electron. Lett. 27, 1451–1453 (1991).
[Crossref]

Malomed, B. A.

B. A. Malomed, “Bound solitons in the nonlinear Schrödinger–Ginzburg–Landau equation,” Phys. Rev. A 44, 6954–6957 (1991).
[Crossref] [PubMed]

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 mode-locked fiber laser,” Phys. Rev. A 64, 33814 (2001).
[Crossref]

Matsas, V. J.

D. J. Richardson, R. I. Laming, D. N. Payne, V. J. Matsas, and M. W. Phillips, “Pulse repetition rates in passive, self-starting, femtosecond soliton fibre laser,” Electron. Lett. 27, 1451–1453 (1991).
[Crossref]

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1991).
[Crossref]

Menyuk, C. R.

Millot, G.

F. Gutty, Ph. Grelu, N. Huot, G. Vienne, and G. Millot, “Stabilisation of modelocking in fibre laser through pulse bunching,” Electron. Lett. 37, 745–746 (2001).
[Crossref]

Moores, J. D.

J. D. Moores, “On the Ginzburg–Landau laser mode-locking model with fifth-order saturable absorption terms,” Opt. Commun. 96, 65–70 (1993).
[Crossref]

Müller, M.

Nakazawa, M.

K. Tamura and M. Nakazawa, “Dispersion-tuned harmonically mode-locked fiber ring laser for self-synchronization to an external clock,” Opt. Lett. 21, 1984–1986 (1996).
[Crossref] [PubMed]

M. Nakazawa, E. Yoshida, and Y. Kimura, “Low threshold, 290 fs erbium-doped fiber laser with a nonlinear amplifying loop mirror pumped by InGaAsP laser diodes,” Appl. Phys. Lett. 59, 2073–2075 (1991).
[Crossref]

Nelson, L. E.

K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64, 149–151 (1994).
[Crossref]

Newson, T. P.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1991).
[Crossref]

Nicholson, J.

M. Lai, J. Nicholson, and W. Rudolph, “Multiple pulse operation of a femtosecond Ti:sapphire laser,” Opt. Commun. 142, 45–49 (1997).
[Crossref]

Noske, D. U.

Oberlé, J.

B. Chassagne, G. Jonusauskas, J. Oberlé, and C. Rullière, “Multipulse operation regime in a self-mode-locked Cr4+: forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
[Crossref]

Oh, S. K.

N. H. Seong, D. Y. Kim, and S. K. Oh, “Self-adjustments of positions of quantised modelocked pulses in figure-eight fibre laser,” Electron. Lett. 37, 157–158 (2001).
[Crossref]

Olsson, N. A.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers, Fundamentals and Technology (Academic, San Diego, Calif., 1999).

Onodera, N.

Payne, D. N.

A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Passive harmonic mode-locking of a fibre soliton ring laser,” Electron. Lett. 29, 1860–1861 (1993).
[Crossref]

A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28, 67–68 (1992).
[Crossref]

D. J. Richardson, R. I. Laming, D. N. Payne, V. J. Matsas, and M. W. Phillips, “Pulse repetition rates in passive, self-starting, femtosecond soliton fibre laser,” Electron. Lett. 27, 1451–1453 (1991).
[Crossref]

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1991).
[Crossref]

Phillips, M. W.

D. J. Richardson, R. I. Laming, D. N. Payne, V. J. Matsas, and M. W. Phillips, “Pulse repetition rates in passive, self-starting, femtosecond soliton fibre laser,” Electron. Lett. 27, 1451–1453 (1991).
[Crossref]

Pilipetskii, A. N.

Richardson, D. J.

A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Passive harmonic mode-locking of a fibre soliton ring laser,” Electron. Lett. 29, 1860–1861 (1993).
[Crossref]

A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28, 67–68 (1992).
[Crossref]

D. J. Richardson, R. I. Laming, D. N. Payne, V. J. Matsas, and M. W. Phillips, “Pulse repetition rates in passive, self-starting, femtosecond soliton fibre laser,” Electron. Lett. 27, 1451–1453 (1991).
[Crossref]

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1991).
[Crossref]

Roth, J. M.

Rudolph, W.

M. Lai, J. Nicholson, and W. Rudolph, “Multiple pulse operation of a femtosecond Ti:sapphire laser,” Opt. Commun. 142, 45–49 (1997).
[Crossref]

Rullière, C.

B. Chassagne, G. Jonusauskas, J. Oberlé, and C. Rullière, “Multipulse operation regime in a self-mode-locked Cr4+: forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
[Crossref]

Seong, N. H.

N. H. Seong, D. Y. Kim, and S. K. Oh, “Self-adjustments of positions of quantised modelocked pulses in figure-eight fibre laser,” Electron. Lett. 37, 157–158 (2001).
[Crossref]

Simpson, J. R.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers, Fundamentals and Technology (Academic, San Diego, Calif., 1999).

Soto-Crespo, J. M.

Spielmann, Ch.

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Sysoliatin, A.

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K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64, 149–151 (1994).
[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 mode-locked fiber laser,” Phys. Rev. A 64, 33814 (2001).
[Crossref]

Taylor, J. R.

Tsang, T.

Vienne, G.

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Wabnitz, S.

Wong, W. S.

Yoshida, E.

M. Nakazawa, E. Yoshida, and Y. Kimura, “Low threshold, 290 fs erbium-doped fiber laser with a nonlinear amplifying loop mirror pumped by InGaAsP laser diodes,” Appl. Phys. Lett. 59, 2073–2075 (1991).
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N. Akhmediev, F. Zen, and P. Chu, “Pulse–pulse interaction in dispersion-managed fiber systems with nonlinear amplifiers,” Opt. Commun. 201, 217–221 (2002).
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Appl. Phys. Lett. (3)

M. Nakazawa, E. Yoshida, and Y. Kimura, “Low threshold, 290 fs erbium-doped fiber laser with a nonlinear amplifying loop mirror pumped by InGaAsP laser diodes,” Appl. Phys. Lett. 59, 2073–2075 (1991).
[Crossref]

K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64, 149–151 (1994).
[Crossref]

K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
[Crossref]

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D. J. Richardson, R. I. Laming, D. N. Payne, V. J. Matsas, and M. W. Phillips, “Pulse repetition rates in passive, self-starting, femtosecond soliton fibre laser,” Electron. Lett. 27, 1451–1453 (1991).
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F. Gutty, Ph. Grelu, N. Huot, G. Vienne, and G. Millot, “Stabilisation of modelocking in fibre laser through pulse bunching,” Electron. Lett. 37, 745–746 (2001).
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A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Passive harmonic mode-locking of a fibre soliton ring laser,” Electron. Lett. 29, 1860–1861 (1993).
[Crossref]

IEEE J. Quantum Electron. (2)

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[Crossref]

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
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M. Lai, J. Nicholson, and W. Rudolph, “Multiple pulse operation of a femtosecond Ti:sapphire laser,” Opt. Commun. 142, 45–49 (1997).
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B. Chassagne, G. Jonusauskas, J. Oberlé, and C. Rullière, “Multipulse operation regime in a self-mode-locked Cr4+: forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
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N. Akhmediev, F. Zen, and P. Chu, “Pulse–pulse interaction in dispersion-managed fiber systems with nonlinear amplifiers,” Opt. Commun. 201, 217–221 (2002).
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M. J. Guy, D. U. Noske, and J. R. Taylor, “Generation of femtosecond soliton pulses by passive mode locking of an ytterbium–erbium figure-of-eight fiber laser,” Opt. Lett. 18, 1447–1449 (1993).
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T. Tsang, “Observation of high-order solitons from a mode-locked Ti:sapphire laser,” Opt. Lett. 18, 293–295 (1993).
[Crossref] [PubMed]

K. Tamura and M. Nakazawa, “Dispersion-tuned harmonically mode-locked fiber ring laser for self-synchronization to an external clock,” Opt. Lett. 21, 1984–1986 (1996).
[Crossref] [PubMed]

T. F. Carruthers, I. N. Duling, M. Horowitz, and C. R. Menyuk, “Dispersion management in a harmonically mode-locked fiber soliton laser,” Opt. Lett. 25, 153–155 (2000).
[Crossref]

K. S. Abedin, N. Onodera, and M. Hyodo, “Generation of a 64-GHz, 3.3-ps transform-limited pulse train from a fiber laser employing higher-order frequency-modulated mode locking,” Opt. Lett. 24, 1564–1566 (1999).
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Phys. Rev. A (2)

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D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively mode-locked fiber laser,” Phys. Rev. A 64, 33814 (2001).
[Crossref]

Other (2)

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers, Fundamentals and Technology (Academic, San Diego, Calif., 1999).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

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Figures (9)

Fig. 1
Fig. 1

Fiber ring laser experimental setup. The EDF is pumped by laser diodes (LDs) through a polarization-insensitive coupler-isolator (WDM-IS): λ/2, half-wave plate; λ/4, quarter-wave plate.

Fig. 2
Fig. 2

Typical recorded spectrum and autocorrelation function for single-pulse operation. The spectral FWHM is 13 nm and the autocorrelation FWHM is 640 fs.

Fig. 3
Fig. 3

(a) High-resolution spectrum of a phase-locked pulse pair. The pump power is 90 mW. The channeled-spectrum structure indicates phase locking. (b) Corresponding interferometric autocorrelation, showing two pulses separated by 20.8 ps. The insets show enlarged views of the central peak and of one lateral peak, revealing interference patterns. These patterns confirm the phase-locked state of two pulses of identical amplitude.

Fig. 4
Fig. 4

(a) High-resolution spectrum of a four-pulse bunch. (b) Fourier transform of the preceding spectrum, revealing unequal separations between pulses. (c) The preceding separations (20.8 and 23.5 ps) are confirmed by this interferometric autocorrelation. Moreover, all the peaks present fringes of interference, showing phase locking between all the pulses.

Fig. 5
Fig. 5

(a) Interferometric autocorrelation of a pulse pair with a 6.8-ps separation. Pulse-duration measurement yields 610 fs FWHM. The insets show enlarged views of the lateral peaks that feature fringes whose magnitude again shows a phase-locked state of equal-amplitude pulses. (b) Corresponding experimental spectrum (solid curve), fitted by the spectrum (open circles) of two 610-fs sech-profiled pulses, separated by 6.8 ps, and with a -π/2 phase difference. (c) Relative quadratic error between the experimental and the fitted curves versus the fitting phase. The minimum error is for a phase of -91°.

Fig. 6
Fig. 6

Characteristics of a closer pulse pair. The pump power is 29 mW. (a) Interferometric autocorrelation that yields a 2.7-ps separation between phase-locked pulses of 540-fs duration. (b) Experimental spectrum (solid curve) fitted by the spectrum (open circles) of two 540-fs sech-profiled pulses separated by 2.7 ps and with a π/2 phase difference. (c) The plot of the relative fitting error versus the phase has a minimum for a phase of +87°.

Fig. 7
Fig. 7

Scheme of the theoretical model, which is thoroughly detailed in the main text.

Fig. 8
Fig. 8

Trajectory of the numerical simulation in the (ρ, α) plane of two interacting pulses: ρ represents the pulse-to-pulse separation, whereas α is their relative phase. The values for the parameters used in this simulation are listed in the figure.

Fig. 9
Fig. 9

(a) Intensity profile (solid curve) and phase profile (dotted curve) of one stationary solution. The time unit is 145 fs. (b) Corresponding optical spectrum. The parameters have the same value as in Fig. 7.

Equations (17)

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iUz+γU+D2 Utt+Γ|U2|U+23 Γ|V2|U+13 ΓV2U*
=ig(QU)U+iβUtt,
iVz-γV+D2 Vtt+Γ|V2|V+23 Γ|U2|V+13 ΓU2V*
=ig(QV)V+iβVtt,
D=β2EDFβ2SMF,
Γ=AeffSMFAeffEDF,
g[QU(V)]=g0(z)1+QU(V)/EL,
QU=-+|U|2dt,QV=-+|V|2dt.
g0(z)=g0i+(g0f-g0i)zLEDF,
iUz+γU+12 Utt+|U|2U+23 |V|2U+13 V2U*=0,
iVz-γV+12 Vtt+|V|2V+23 |U|2V+13 U2V*=0,
U=U cos θ1+V sin θ1,
z=ZZ0,Z0=T02|β2SMF|,t=T-ZνgT0,
UEx=VEy=RT02|β2SMF|,R=2πn2λAeffSMF.
AeffSMF=80μm2,AeffEDF=27μm2,
n2=2.5×10-20 m2/W,
β2SMF=-21ps2/km,D=-2.

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