Abstract

We present the phase-locking and coherence properties between two weakly coupled lasers. We show how the degree of coherence between the two lasers can be enhanced by nearly 1 order of magnitude after taking into account the effects of coupling on both their phases as well as their amplitudes. Specifically, correlations between synchronized spikes in the amplitude dynamics and the phase dynamics of the lasers allow for an interference pattern with a fringe visibility of 90%, even when the coupling strength is far below the critical value and they are not phase locked.

© 2011 Optical Society of America

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  1. E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, Opt. Lett. 33, 354 (2008).
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    [CrossRef]

2010

2009

2008

2005

C. J. Corcoran and F. Durville, Appl. Phys. Lett. 86, 201118(2005).
[CrossRef]

J. A. Acebrón, L. L. Bonilla, C. J. Pérez-Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005).
[CrossRef]

1997

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R. D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

1993

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

1989

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
[CrossRef]

Acebrón, J. A.

J. A. Acebrón, L. L. Bonilla, C. J. Pérez-Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005).
[CrossRef]

Bonilla, L. L.

J. A. Acebrón, L. L. Bonilla, C. J. Pérez-Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005).
[CrossRef]

Carr, T. W.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R. D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Cheung, E. C.

Colet, P.

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

Corcoran, C. J.

C. J. Corcoran and F. Durville, Appl. Phys. Lett. 86, 201118(2005).
[CrossRef]

D’Amato, F. X.

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
[CrossRef]

Davidson, N.

Durville, F.

C. J. Corcoran and F. Durville, Appl. Phys. Lett. 86, 201118(2005).
[CrossRef]

Eckhouse, V.

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

Erneux, T.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R. D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Fabiny, L.

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

Fridman, M.

Friesem, A. A.

Goodno, G. D.

Ho, J. G.

Lenstra, D.

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

Li, R. D.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R. D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Möller, M.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R. D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Nixon, M.

Pérez-Vicente, C. J.

J. A. Acebrón, L. L. Bonilla, C. J. Pérez-Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005).
[CrossRef]

Rice, R. R.

Ritort, F.

J. A. Acebrón, L. L. Bonilla, C. J. Pérez-Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005).
[CrossRef]

Ronen, E.

Rothenberg, J.

Roy, R.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R. D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

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

Roychoudhuri, C.

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
[CrossRef]

Siebert, E. T.

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
[CrossRef]

Spigler, R.

J. A. Acebrón, L. L. Bonilla, C. J. Pérez-Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005).
[CrossRef]

Thielen, P.

Thornburg, K. S.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R. D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Weber, M.

Wickham, M.

Appl. Phys. Lett.

C. J. Corcoran and F. Durville, Appl. Phys. Lett. 86, 201118(2005).
[CrossRef]

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. E

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R. D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Phys. Rev. Lett.

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

Rev. Mod. Phys.

J. A. Acebrón, L. L. Bonilla, C. J. Pérez-Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Fringe visibility V fv and phase locking parameter V pl as a function of the coupling strength κ normalized by the critical coupling κ c . Inset, intensity pattern of two interfering Gaussian beams with fringe visibility corresponding to that of point B.

Fig. 2
Fig. 2

Laser amplitudes and phase difference ϕ as a function of time, for different values of κ / κ c corresponding to points A, B, C, D, E, and F of Fig. 1. The solid blue curve denotes amplitudes, and the dashed green curve denotes ϕ.

Fig. 3
Fig. 3

Frequency difference between the two lasers normalized by the frequency detuning Δ ω / Ω as a function of the coupling strength κ / κ c . Insets, normalized intensity of the first laser I 1 as a function of the normalized intensity of the second laser I 2 , calculated for κ / κ c = 0.2 and κ / κ c = 0.93 , respectively.

Equations (8)

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d E 1 , 2 d t = 1 τ c ( G 1 , 2 α 1 , 2 ) E 1 , 2 + κ τ c E 2 , 1 + i Ω 1 , 2 E 1 , 2 , d G 1 , 2 d t = 1 τ f ( P 1 , 2 G 1 , 2 ( I 1 , 2 + 1 ) ) ,
d A 1 , 2 d t = 1 τ c ( G 1 , 2 α 1 , 2 ) A 1 , 2 + κ τ c A 2 , 1 cos ( ϕ ) .
d ϕ d t = Ω κ τ c β sin ( ϕ ) with     β A 1 A 2 + A 2 A 1 ,
V f v = I max I min I max + I min ,
V fv = 2 A 1 A 2 cos ( ϕ ) 2 + A 1 A 2 sin ( ϕ ) 2 A 1 2 + A 2 2 .
V pl = cos ( ϕ ) 2 + sin ( ϕ ) 2 .
Δ ω = lim T ϕ ( T ) ϕ ( 0 ) T .
Δ ω = Ω 1 ( κ κ c ) 2 .

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