Abstract

Detailed experimental and theoretical investigations of two coupled fiber lasers, each with many longitudinal modes, reveal that the behavior of the longitudinal modes depends on both the coupling strength and the detuning between them. For low to moderate coupling strength only longitudinal modes that are common for both lasers phase lock, while those that are not common gradually disappear. For larger coupling strengths, the longitudinal modes that are not common reappear and phase lock. When the coupling strength approaches unity the coupled lasers behave as a single long cavity with correspondingly denser longitudinal modes. Finally, we show that the gradual increase in phase locking as a function of the coupling strength results from competition between phase-locked and non-phase-locked longitudinal modes.

© 2010 Optical Society of America

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  1. R. Roy and K. S. Thornburg, Jr., Phys. Rev. Lett. 72, 2009 (1997).
    [CrossRef]
  2. A. F. Glova, Quantum Electron. 33, 283 (2003).
    [CrossRef]
  3. T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005).
    [CrossRef]
  4. L. Fabiny, P. Colet, R. Roy, and D. Lensta, Phys. Rev. A 47, 4287 (1993).
    [CrossRef] [PubMed]
  5. M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, Opt. Lett. 32, 790 (2007).
    [CrossRef] [PubMed]
  6. V. Eckhouse, M. Fridman, N. Davidson, and A. A. Friesem, Phys. Rev. Lett. 100, 024102 (2008).
    [CrossRef] [PubMed]
  7. M. Nakamura, K. Aiki, N. Chinone, R. Ito, and J. Umeda, J. Appl. Phys. 49, 4644 (1978).
    [CrossRef]
  8. A. Shirakawa, T. Saitou, T. Sekiguchi, and K.-i Ueda, Opt. Lett. 10, 1167 (1999).
  9. A. Shirakawa, K. Matsuo, and K.-i. Ueda, Proc. SPIE 5662, 482 (2004).
    [CrossRef]
  10. J. E. Rothenberg, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuP3.
  11. T. Wu, W. Chang, A. Galvanauskas, and H. G. Winful, Opt. Express 17, 19509 (2009).
    [CrossRef] [PubMed]

2009

2008

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

2007

2005

T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005).
[CrossRef]

2004

A. Shirakawa, K. Matsuo, and K.-i. Ueda, Proc. SPIE 5662, 482 (2004).
[CrossRef]

2003

A. F. Glova, Quantum Electron. 33, 283 (2003).
[CrossRef]

1999

A. Shirakawa, T. Saitou, T. Sekiguchi, and K.-i Ueda, Opt. Lett. 10, 1167 (1999).

1997

R. Roy and K. S. Thornburg, Jr., Phys. Rev. Lett. 72, 2009 (1997).
[CrossRef]

1993

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

1978

M. Nakamura, K. Aiki, N. Chinone, R. Ito, and J. Umeda, J. Appl. Phys. 49, 4644 (1978).
[CrossRef]

Aiki, K.

M. Nakamura, K. Aiki, N. Chinone, R. Ito, and J. Umeda, J. Appl. Phys. 49, 4644 (1978).
[CrossRef]

Chang, W.

Chinone, N.

M. Nakamura, K. Aiki, N. Chinone, R. Ito, and J. Umeda, J. Appl. Phys. 49, 4644 (1978).
[CrossRef]

Colet, P.

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

Davidson, N.

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

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, Opt. Lett. 32, 790 (2007).
[CrossRef] [PubMed]

Eckhouse, V.

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

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, Opt. Lett. 32, 790 (2007).
[CrossRef] [PubMed]

Fabiny, L.

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

Fan, T. Y.

T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005).
[CrossRef]

Fridman, M.

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

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, Opt. Lett. 32, 790 (2007).
[CrossRef] [PubMed]

Friesem, A. A.

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

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, Opt. Lett. 32, 790 (2007).
[CrossRef] [PubMed]

Galvanauskas, A.

Glova, A. F.

A. F. Glova, Quantum Electron. 33, 283 (2003).
[CrossRef]

Ito, R.

M. Nakamura, K. Aiki, N. Chinone, R. Ito, and J. Umeda, J. Appl. Phys. 49, 4644 (1978).
[CrossRef]

Lensta, D.

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

Matsuo, K.

A. Shirakawa, K. Matsuo, and K.-i. Ueda, Proc. SPIE 5662, 482 (2004).
[CrossRef]

Nakamura, M.

M. Nakamura, K. Aiki, N. Chinone, R. Ito, and J. Umeda, J. Appl. Phys. 49, 4644 (1978).
[CrossRef]

Rothenberg, J. E.

J. E. Rothenberg, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuP3.

Roy, R.

R. Roy and K. S. Thornburg, Jr., Phys. Rev. Lett. 72, 2009 (1997).
[CrossRef]

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

Saitou, T.

A. Shirakawa, T. Saitou, T. Sekiguchi, and K.-i Ueda, Opt. Lett. 10, 1167 (1999).

Sekiguchi, T.

A. Shirakawa, T. Saitou, T. Sekiguchi, and K.-i Ueda, Opt. Lett. 10, 1167 (1999).

Shirakawa, A.

A. Shirakawa, K. Matsuo, and K.-i. Ueda, Proc. SPIE 5662, 482 (2004).
[CrossRef]

A. Shirakawa, T. Saitou, T. Sekiguchi, and K.-i Ueda, Opt. Lett. 10, 1167 (1999).

Thornburg, K. S.

R. Roy and K. S. Thornburg, Jr., Phys. Rev. Lett. 72, 2009 (1997).
[CrossRef]

Ueda, K.-i

A. Shirakawa, T. Saitou, T. Sekiguchi, and K.-i Ueda, Opt. Lett. 10, 1167 (1999).

Ueda, K.-i.

A. Shirakawa, K. Matsuo, and K.-i. Ueda, Proc. SPIE 5662, 482 (2004).
[CrossRef]

Umeda, J.

M. Nakamura, K. Aiki, N. Chinone, R. Ito, and J. Umeda, J. Appl. Phys. 49, 4644 (1978).
[CrossRef]

Winful, H. G.

Wu, T.

IEEE J. Sel. Top. Quantum Electron.

T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005).
[CrossRef]

J. Appl. Phys.

M. Nakamura, K. Aiki, N. Chinone, R. Ito, and J. Umeda, J. Appl. Phys. 49, 4644 (1978).
[CrossRef]

Opt. Express

Opt. Lett.

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, Opt. Lett. 32, 790 (2007).
[CrossRef] [PubMed]

A. Shirakawa, T. Saitou, T. Sekiguchi, and K.-i Ueda, Opt. Lett. 10, 1167 (1999).

Phys. Rev. A

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

Phys. Rev. Lett.

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

R. Roy and K. S. Thornburg, Jr., Phys. Rev. Lett. 72, 2009 (1997).
[CrossRef]

Proc. SPIE

A. Shirakawa, K. Matsuo, and K.-i. Ueda, Proc. SPIE 5662, 482 (2004).
[CrossRef]

Quantum Electron.

A. F. Glova, Quantum Electron. 33, 283 (2003).
[CrossRef]

Other

J. E. Rothenberg, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuP3.

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Figures (4)

Fig. 1
Fig. 1

Experimental configuration for investigating the phase locking and the spectrum of longitudinal modes of two coupled fiber lasers as a function of the coupling strength. FBG, fiber Bragg grating; HWP, half- wave plate; QWP, quarter-wave plate; OC, output coupler.

Fig. 2
Fig. 2

Experimental and calculated distributions of longitudinal mode beating frequencies in the output power for two coupled lasers as a function of the coupling strength κ. (a) Experimental results; (b) calculated results; (c) κ = 0 ; (d) κ = 0.28 ; (e) κ = 0.7 ; (f) κ = 1 . Solid (blue) curves denote experimental results and dotted (red) curves denote calculated results.

Fig. 3
Fig. 3

Experimental and calculated phase diagram of the longitudinal mode behavior as a function of the coupling strength between two coupled lasers and detuning between adjacent longitudinal modes. Solid curves denote experimental results. Dotted curves denote calculated results.

Fig. 4
Fig. 4

Experimental and calculated phase locking as a function of the coupling strength between two coupled fiber lasers. Dots denote the directly measured phase locking; asterisks denote the phase locking calculated from experimental results in Fig. 2a; the solid curve denotes the phase locking calculated from the results in Fig. 2b.

Equations (3)

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R 1 , 2 eff = ( 1 r ( 1 κ ) r 2 κ e ı l 2 , 1 k 1 r ( 1 κ ) e ı l 2 , 1 k ) 1 ,
R j eff e ı k l j + ( R j eff e ı k l j ) 2 + = ( 1 R j eff e ı k l j ) 1 ,
R out = ( 1 R 1 eff e ı k l 1 ) 1 + ( 1 R 2 eff e ı k l 2 ) 1 .

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