Abstract

Two coupled fiber laser arrangements demonstrating isochronal and achronal phase locking with long-time-delayed coupling are presented. Experimental results show that stable phase locking with coupling delay lines as long as 4km can be obtained and that phase locking can be invariant to the time delay.

© 2009 Optical Society of America

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  1. R. Roy and K. S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994).
    [CrossRef] [PubMed]
  2. L. Fabiny, P. Colet, R. Roy, and D. Lenstra, Phys. Rev. A 47, 4287 (1993).
    [CrossRef] [PubMed]
  3. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  6. S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J.-M. Liu, IEEE J. Sel. Top. Quantum Electron. 10, 936 (2004).
    [CrossRef]
  7. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
    [CrossRef]
  8. G. Kozyreff, A. G. Vladimirov, and P. Mandel, Phys. Rev. Lett. 85, 3809 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  11. J. E. Baldwin and C. A. Haniff, Philos. Trans. R. Soc. London, Ser. A 360, 969 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2008 (2)

V. Eckhouse, M. Fridman, N. Davidson, and A. A. Friesem, Phys. Rev. Lett. 100, 024102 (2008).
[CrossRef] [PubMed]

O. D'Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, Chaos 18, 037116 (2008).
[CrossRef] [PubMed]

2006 (1)

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, Phys. Rev. E 73, 066214 (2006).
[CrossRef]

2005 (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

2004 (1)

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J.-M. Liu, IEEE J. Sel. Top. Quantum Electron. 10, 936 (2004).
[CrossRef]

2003 (1)

S. Tang and J. M. Liu, Phys. Rev. Lett. 90, 194101 (2003).
[CrossRef] [PubMed]

2002 (1)

J. E. Baldwin and C. A. Haniff, Philos. Trans. R. Soc. London, Ser. A 360, 969 (2002).
[CrossRef]

2001 (1)

S. Kim, B. Lee, and D. H. Kim, IEEE Photon. Technol. Lett. 13, 290 (2001).
[CrossRef]

2000 (1)

G. Kozyreff, A. G. Vladimirov, and P. Mandel, Phys. Rev. Lett. 85, 3809 (2000).
[CrossRef] [PubMed]

1997 (1)

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

1994 (1)

R. Roy and K. S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994).
[CrossRef] [PubMed]

1993 (1)

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

1992 (1)

M. Shao and M. M. Colavita, Annu. Rev. Astron. Astrophys. 30, 457 (1992).
[CrossRef]

1989 (1)

H. G. Schuster and P. Wagner, Prog. Theor. Phys. 81, 939 (1989).
[CrossRef]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Argyris, A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Baldwin, J. E.

J. E. Baldwin and C. A. Haniff, Philos. Trans. R. Soc. London, Ser. A 360, 969 (2002).
[CrossRef]

Chiang, M.

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J.-M. Liu, IEEE J. Sel. Top. Quantum Electron. 10, 936 (2004).
[CrossRef]

Colavita, M. M.

M. Shao and M. M. Colavita, Annu. Rev. Astron. Astrophys. 30, 457 (1992).
[CrossRef]

Colet, P.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Danckaert, J.

O. D'Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, Chaos 18, 037116 (2008).
[CrossRef] [PubMed]

Davidson, N.

V. Eckhouse, M. Fridman, N. Davidson, and A. A. Friesem, Phys. Rev. Lett. 100, 024102 (2008).
[CrossRef] [PubMed]

D'Huys, O.

O. D'Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, Chaos 18, 037116 (2008).
[CrossRef] [PubMed]

Eckhouse, V.

V. Eckhouse, M. Fridman, N. Davidson, and A. A. Friesem, Phys. Rev. Lett. 100, 024102 (2008).
[CrossRef] [PubMed]

Erneux, T.

O. D'Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, Chaos 18, 037116 (2008).
[CrossRef] [PubMed]

Fabiny, L.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Fischer, I.

O. D'Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, Chaos 18, 037116 (2008).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Fridman, M.

V. Eckhouse, M. Fridman, N. Davidson, and A. A. Friesem, Phys. Rev. Lett. 100, 024102 (2008).
[CrossRef] [PubMed]

Friesem, A. A.

V. Eckhouse, M. Fridman, N. Davidson, and A. A. Friesem, Phys. Rev. Lett. 100, 024102 (2008).
[CrossRef] [PubMed]

Garcia-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Gross, N.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, Phys. Rev. E 73, 066214 (2006).
[CrossRef]

Haniff, C. A.

J. E. Baldwin and C. A. Haniff, Philos. Trans. R. Soc. London, Ser. A 360, 969 (2002).
[CrossRef]

Kanter, I.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, Phys. Rev. E 73, 066214 (2006).
[CrossRef]

Khaykovich, L.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, Phys. Rev. E 73, 066214 (2006).
[CrossRef]

Kim, D. H.

S. Kim, B. Lee, and D. H. Kim, IEEE Photon. Technol. Lett. 13, 290 (2001).
[CrossRef]

Kim, S.

S. Kim, B. Lee, and D. H. Kim, IEEE Photon. Technol. Lett. 13, 290 (2001).
[CrossRef]

Kinzel, W.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, Phys. Rev. E 73, 066214 (2006).
[CrossRef]

Klein, E.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, Phys. Rev. E 73, 066214 (2006).
[CrossRef]

Kozyreff, G.

G. Kozyreff, A. G. Vladimirov, and P. Mandel, Phys. Rev. Lett. 85, 3809 (2000).
[CrossRef] [PubMed]

Kurths, J.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

Larger, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Lee, B.

S. Kim, B. Lee, and D. H. Kim, IEEE Photon. Technol. Lett. 13, 290 (2001).
[CrossRef]

Lenstra, D.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Liu, J. M.

S. Tang and J. M. Liu, Phys. Rev. Lett. 90, 194101 (2003).
[CrossRef] [PubMed]

Liu, J.-M.

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J.-M. Liu, IEEE J. Sel. Top. Quantum Electron. 10, 936 (2004).
[CrossRef]

Mandel, P.

G. Kozyreff, A. G. Vladimirov, and P. Mandel, Phys. Rev. Lett. 85, 3809 (2000).
[CrossRef] [PubMed]

Mirasso, C.

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J.-M. Liu, IEEE J. Sel. Top. Quantum Electron. 10, 936 (2004).
[CrossRef]

Mirasso, C. R.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Pikovsky, A. S.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

Rosenbluh, M.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, Phys. Rev. E 73, 066214 (2006).
[CrossRef]

Rosenblum, M. G.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

Roy, R.

R. Roy and K. S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994).
[CrossRef] [PubMed]

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Schuster, H. G.

H. G. Schuster and P. Wagner, Prog. Theor. Phys. 81, 939 (1989).
[CrossRef]

Shao, M.

M. Shao and M. M. Colavita, Annu. Rev. Astron. Astrophys. 30, 457 (1992).
[CrossRef]

Shore, K. A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Syvridis, D.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Tang, S.

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J.-M. Liu, IEEE J. Sel. Top. Quantum Electron. 10, 936 (2004).
[CrossRef]

S. Tang and J. M. Liu, Phys. Rev. Lett. 90, 194101 (2003).
[CrossRef] [PubMed]

Thornburg, K. S.

R. Roy and K. S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994).
[CrossRef] [PubMed]

Vicente, R.

O. D'Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, Chaos 18, 037116 (2008).
[CrossRef] [PubMed]

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J.-M. Liu, IEEE J. Sel. Top. Quantum Electron. 10, 936 (2004).
[CrossRef]

Vladimirov, A. G.

G. Kozyreff, A. G. Vladimirov, and P. Mandel, Phys. Rev. Lett. 85, 3809 (2000).
[CrossRef] [PubMed]

Wagner, P.

H. G. Schuster and P. Wagner, Prog. Theor. Phys. 81, 939 (1989).
[CrossRef]

Annu. Rev. Astron. Astrophys. (1)

M. Shao and M. M. Colavita, Annu. Rev. Astron. Astrophys. 30, 457 (1992).
[CrossRef]

Chaos (1)

O. D'Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, Chaos 18, 037116 (2008).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J.-M. Liu, IEEE J. Sel. Top. Quantum Electron. 10, 936 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Kim, B. Lee, and D. H. Kim, IEEE Photon. Technol. Lett. 13, 290 (2001).
[CrossRef]

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Philos. Trans. R. Soc. London, Ser. A (1)

J. E. Baldwin and C. A. Haniff, Philos. Trans. R. Soc. London, Ser. A 360, 969 (2002).
[CrossRef]

Phys. Rev. A (1)

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Phys. Rev. E (1)

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, Phys. Rev. E 73, 066214 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

S. Tang and J. M. Liu, Phys. Rev. Lett. 90, 194101 (2003).
[CrossRef] [PubMed]

R. Roy and K. S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994).
[CrossRef] [PubMed]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

G. Kozyreff, A. G. Vladimirov, and P. Mandel, Phys. Rev. Lett. 85, 3809 (2000).
[CrossRef] [PubMed]

V. Eckhouse, M. Fridman, N. Davidson, and A. A. Friesem, Phys. Rev. Lett. 100, 024102 (2008).
[CrossRef] [PubMed]

Prog. Theor. Phys. (1)

H. G. Schuster and P. Wagner, Prog. Theor. Phys. 81, 939 (1989).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental arrangements for phase locking two fiber lasers with time-delayed coupling. (A) Delayed coupling with delayed self-feedback; (B) delayed coupling only.

Fig. 2
Fig. 2

Results of normalized fringe visibility as a function of coupling delay time τ d obtained for the arrangement that includes self-feedback. Points and bars (red) denote experimental results, and the solid (blue) curve denotes the numerical results. Inset, interference pattern of two lasers coupled by a 4-km-long delay line, i.e., τ d 20 μ s .

Fig. 3
Fig. 3

Experimental results for the fringe visibility as a function of the camera delay line for the arrangement that contains delayed coupling only.

Fig. 4
Fig. 4

Calculated fringe visibility as a function of the time difference between two lasers for a time-delayed coupling of τ d = 20 μ s . Dashed (blue) curve, numerical results obtained for coupling that includes self-feedback (first arrangement); solid (red) curve, numerical results obtained for coupling only (second arrangement).

Equations (2)

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d E i d t = 1 τ c [ ( G i α ) E i ( t ) + κ E 3 i ( t τ d ) ] + σ τ c E i ( t τ d ) + j ω i E i ( t ) + j ξ η i ( t ) ,
d G i d t = 1 τ f ( P i G i ( E i 2 + 1 ) ) ,

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