Abstract

The synchronization of chaotic lasers and the optical phase synchronization of light originating in multiple coupled lasers have both been extensively studied. However, the interplay between these two phenomena, especially at the network level, is unexplored. Here, we experimentally compare these phenomena by controlling the heterogeneity of the coupling delay times of two lasers. While chaotic lasers exhibit deterioration in synchronization as the time delay heterogeneity increases, phase synchronization is found to be independent of heterogeneity. The experimental results are found to be in agreement with numerical simulations for semiconductor lasers.

© 2013 Optical Society of America

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  1. S. H. Strogatz, Nature 410, 268 (2001).
    [CrossRef]
  2. L. Fabiny, P. Colet, R. Roy, and D. Lenstra, Phys. Rev. A 47, 4287 (1993).
    [CrossRef]
  3. D. J. DeShazer, R. Breban, E. Ott, and R. Roy, Phys. Rev. Lett. 87, 044101 (2001).
    [CrossRef]
  4. M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, Phys. Rev. Lett. 108, 214101 (2012).
    [CrossRef]
  5. R. Vicente, S. Tang, J. Mulet, C. R. Mirasso, and J.-M. Liu, Phys. Rev. E 73, 047201 (2006).
    [CrossRef]
  6. K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, Phys. Rev. E 83, 056211 (2011).
    [CrossRef]
  7. I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, J. Stat. Phys. 145, 713 (2011).
    [CrossRef]
  8. O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, Chaos 18, 037116 (2008).
    [CrossRef]
  9. C. R. Williams, T. E. Murphy, R. Roy, F. Sorrentino, T. Dahms, and E. Schöll, Phys. Rev. Lett. 110, 064104 (2013).
    [CrossRef]
  10. Y. Aviad, I. Reidler, M. Zigzag, M. Rosenbluh, and I. Kanter, Opt. Express 20, 4352 (2012).
    [CrossRef]
  11. M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, Rev. Mod. Phys. 85, 421 (2013).
    [CrossRef]
  12. B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 107, 034102 (2011).
    [CrossRef]
  13. V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
    [CrossRef]
  14. Y. Takiguchi, H. Fujino, and J. Ohtsubo, Opt. Lett. 24, 1570 (1999).
    [CrossRef]
  15. J. A. Arnaud, Appl. Opt. 8, 1909 (1969).
    [CrossRef]
  16. J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005).
    [CrossRef]
  17. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
    [CrossRef]
  18. Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, Phys. Rev. E 78, 025204 (2008).
    [CrossRef]

2013

C. R. Williams, T. E. Murphy, R. Roy, F. Sorrentino, T. Dahms, and E. Schöll, Phys. Rev. Lett. 110, 064104 (2013).
[CrossRef]

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, Rev. Mod. Phys. 85, 421 (2013).
[CrossRef]

2012

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Y. Aviad, I. Reidler, M. Zigzag, M. Rosenbluh, and I. Kanter, Opt. Express 20, 4352 (2012).
[CrossRef]

2011

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 107, 034102 (2011).
[CrossRef]

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, Phys. Rev. E 83, 056211 (2011).
[CrossRef]

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, J. Stat. Phys. 145, 713 (2011).
[CrossRef]

2008

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

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, Phys. Rev. E 78, 025204 (2008).
[CrossRef]

2006

R. Vicente, S. Tang, J. Mulet, C. R. Mirasso, and J.-M. Liu, Phys. Rev. E 73, 047201 (2006).
[CrossRef]

2005

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

2001

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, Phys. Rev. Lett. 87, 044101 (2001).
[CrossRef]

S. H. Strogatz, Nature 410, 268 (2001).
[CrossRef]

1999

1998

V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
[CrossRef]

1993

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

1980

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
[CrossRef]

1969

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]

Ahlers, V.

V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
[CrossRef]

Arnaud, J. A.

Aviad, Y.

Y. Aviad, I. Reidler, M. Zigzag, M. Rosenbluh, and I. Kanter, Opt. Express 20, 4352 (2012).
[CrossRef]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, Phys. Rev. E 78, 025204 (2008).
[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]

Breban, R.

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, Phys. Rev. Lett. 87, 044101 (2001).
[CrossRef]

Cohen, A. B.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 107, 034102 (2011).
[CrossRef]

Cohen, D.

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, J. Stat. Phys. 145, 713 (2011).
[CrossRef]

Colet, P.

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

D’Huys, O.

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, Phys. Rev. E 83, 056211 (2011).
[CrossRef]

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

Dahms, T.

C. R. Williams, T. E. Murphy, R. Roy, F. Sorrentino, T. Dahms, and E. Schöll, Phys. Rev. Lett. 110, 064104 (2013).
[CrossRef]

Danckaert, J.

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, Phys. Rev. E 83, 056211 (2011).
[CrossRef]

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

Davidson, N.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

DeShazer, D. J.

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, Phys. Rev. Lett. 87, 044101 (2001).
[CrossRef]

Erneux, T.

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

Fabiny, L.

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

Fischer, I.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, Rev. Mod. Phys. 85, 421 (2013).
[CrossRef]

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, Phys. Rev. E 83, 056211 (2011).
[CrossRef]

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

Flunkert, V.

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, Phys. Rev. E 83, 056211 (2011).
[CrossRef]

Fridman, M.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Friesem, A. A.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Fujino, H.

García-Ojalvo, J.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, Rev. Mod. Phys. 85, 421 (2013).
[CrossRef]

Hicke, K.

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, Phys. Rev. E 83, 056211 (2011).
[CrossRef]

Kanter, I.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Y. Aviad, I. Reidler, M. Zigzag, M. Rosenbluh, and I. Kanter, Opt. Express 20, 4352 (2012).
[CrossRef]

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, J. Stat. Phys. 145, 713 (2011).
[CrossRef]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, Phys. Rev. E 78, 025204 (2008).
[CrossRef]

Kinzel, W.

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, J. Stat. Phys. 145, 713 (2011).
[CrossRef]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, Phys. Rev. E 78, 025204 (2008).
[CrossRef]

Kobayashi, K.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
[CrossRef]

Kopelowitz, E.

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, J. Stat. Phys. 145, 713 (2011).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
[CrossRef]

Lauterborn, W.

V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
[CrossRef]

Lenstra, D.

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

Liu, J.-M.

R. Vicente, S. Tang, J. Mulet, C. R. Mirasso, and J.-M. Liu, Phys. Rev. E 73, 047201 (2006).
[CrossRef]

Mirasso, C. R.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, Rev. Mod. Phys. 85, 421 (2013).
[CrossRef]

R. Vicente, S. Tang, J. Mulet, C. R. Mirasso, and J.-M. Liu, Phys. Rev. E 73, 047201 (2006).
[CrossRef]

Motter, A. E.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 107, 034102 (2011).
[CrossRef]

Mulet, J.

R. Vicente, S. Tang, J. Mulet, C. R. Mirasso, and J.-M. Liu, Phys. Rev. E 73, 047201 (2006).
[CrossRef]

Murphy, T. E.

C. R. Williams, T. E. Murphy, R. Roy, F. Sorrentino, T. Dahms, and E. Schöll, Phys. Rev. Lett. 110, 064104 (2013).
[CrossRef]

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 107, 034102 (2011).
[CrossRef]

Nixon, M.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Ohtsubo, J.

Ott, E.

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, Phys. Rev. Lett. 87, 044101 (2001).
[CrossRef]

Parlitz, U.

V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
[CrossRef]

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]

Ravoori, B.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 107, 034102 (2011).
[CrossRef]

Reidler, I.

Y. Aviad, I. Reidler, M. Zigzag, M. Rosenbluh, and I. Kanter, Opt. Express 20, 4352 (2012).
[CrossRef]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, Phys. Rev. E 78, 025204 (2008).
[CrossRef]

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.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Rosenbluh, M.

Y. Aviad, I. Reidler, M. Zigzag, M. Rosenbluh, and I. Kanter, Opt. Express 20, 4352 (2012).
[CrossRef]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, Phys. Rev. E 78, 025204 (2008).
[CrossRef]

Roy, R.

C. R. Williams, T. E. Murphy, R. Roy, F. Sorrentino, T. Dahms, and E. Schöll, Phys. Rev. Lett. 110, 064104 (2013).
[CrossRef]

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 107, 034102 (2011).
[CrossRef]

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, Phys. Rev. Lett. 87, 044101 (2001).
[CrossRef]

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

Schöll, E.

C. R. Williams, T. E. Murphy, R. Roy, F. Sorrentino, T. Dahms, and E. Schöll, Phys. Rev. Lett. 110, 064104 (2013).
[CrossRef]

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, Phys. Rev. E 83, 056211 (2011).
[CrossRef]

Soriano, M. C.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, Rev. Mod. Phys. 85, 421 (2013).
[CrossRef]

Sorrentino, F.

C. R. Williams, T. E. Murphy, R. Roy, F. Sorrentino, T. Dahms, and E. Schöll, Phys. Rev. Lett. 110, 064104 (2013).
[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]

Strogatz, S. H.

S. H. Strogatz, Nature 410, 268 (2001).
[CrossRef]

Sun, J.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 107, 034102 (2011).
[CrossRef]

Takiguchi, Y.

Tang, S.

R. Vicente, S. Tang, J. Mulet, C. R. Mirasso, and J.-M. Liu, Phys. Rev. E 73, 047201 (2006).
[CrossRef]

Vardi, R.

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, J. Stat. Phys. 145, 713 (2011).
[CrossRef]

Vicente, R.

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

R. Vicente, S. Tang, J. Mulet, C. R. Mirasso, and J.-M. Liu, Phys. Rev. E 73, 047201 (2006).
[CrossRef]

Williams, C. R.

C. R. Williams, T. E. Murphy, R. Roy, F. Sorrentino, T. Dahms, and E. Schöll, Phys. Rev. Lett. 110, 064104 (2013).
[CrossRef]

Zigzag, M.

Y. Aviad, I. Reidler, M. Zigzag, M. Rosenbluh, and I. Kanter, Opt. Express 20, 4352 (2012).
[CrossRef]

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, J. Stat. Phys. 145, 713 (2011).
[CrossRef]

Appl. Opt.

Chaos

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

IEEE J. Quantum Electron.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
[CrossRef]

J. Stat. Phys.

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, J. Stat. Phys. 145, 713 (2011).
[CrossRef]

Nature

S. H. Strogatz, Nature 410, 268 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. E

R. Vicente, S. Tang, J. Mulet, C. R. Mirasso, and J.-M. Liu, Phys. Rev. E 73, 047201 (2006).
[CrossRef]

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, Phys. Rev. E 83, 056211 (2011).
[CrossRef]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, Phys. Rev. E 78, 025204 (2008).
[CrossRef]

V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
[CrossRef]

Phys. Rev. Lett.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 107, 034102 (2011).
[CrossRef]

C. R. Williams, T. E. Murphy, R. Roy, F. Sorrentino, T. Dahms, and E. Schöll, Phys. Rev. Lett. 110, 064104 (2013).
[CrossRef]

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, Phys. Rev. Lett. 87, 044101 (2001).
[CrossRef]

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Rev. Mod. Phys.

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, Rev. Mod. Phys. 85, 421 (2013).
[CrossRef]

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 (4)

Fig. 1.
Fig. 1.

Examples for the minimal number of additional imaginary lasers required to achieve a homogeneous delay times. Imaginary lasers on the mutual delay couplings, τc, (green circles) and on the self-coupling delay, τd, (purple circles). (a) τd/τc=1, 0 imaginary lasers. (b) τd/τc=2/1, 1 imaginary laser and (c) τd/τc=3/2, 4 imaginary lasers.

Fig. 2.
Fig. 2.

(a) Chaotic synchronization experimental setup: mutually coupled chaotic lasers A and B with tunable coupling intensities and delay times. Laser B receives self-feedback from mirror M. Mutual coupling intensities are controlled by rotating a polarizing beam splitter, PBS1, while the Faraday rotator (FR) is set to rotate any incoming linear polarization by 45°. A half-wave plate (λ/2) adjusts the incoming linear polarization entering laser A to be along the solitary laser polarization direction and PBS2,3 are set so that the feedback light entering laser B is parallel to the solitary laser polarization. (b) Phase synchronization experimental setup: two mutually coupled independent solid state lasers. A degenerate cavity (middle), a coupling arrangement (right) and a detection arrangement used to detect phase synchronization between the two lasers (left). (c) Schematic representation of the two coupled lasers for (a) and (b): τc, τd—mutual coupling and self-feedback delay times, respectively, σ1, σ2 are mutual coupling intensities of lasers B to A and A to B, respectively, and κ is the self-feedback intensity for laser B.

Fig. 3.
Fig. 3.

(a) and (b) Average intensity correlation for chaotic lasers over 0.8 μs recording for τd/τc=1 and τd/τc=2/1, respectively, with laser injection current at 1.07 times threshold current. (c) 10 ns recording of the laser intensity corresponding to light gray area in (a), indicating chaotic intensity synchronization. (d) 10 ns recording of the laser intensity corresponding to light gray area in (b), indicating the lack of chaotic intensity synchronization. (e) Far-field intensity distribution for τd/τc=1 indicating zero–lag phase synchronization. (f) Far-field intensity distribution for τd/τc=2/1 indicating the lack of phase synchronization.

Fig. 4.
Fig. 4.

(a) Average correlation and fringe visibility as a function of the heterogeneity as defined in the text, for topologies with GCD=1. The results are shown for experimental chaotic intensity synchronization, (green circles) and numerical simulation (purple triangles), phase synchronization (red squares), and numerical simulation (blue diamonds). The top horizontal scale identifies the self/mutual coupling delay times τd/τc. (b) Similar to panel (a) but for GCD=2. (c) Numerical simulation for the averaged correlation of chaotic lasers for τd/τc=3/2 for different injection currents, P=1.07, 1.05, 1.01, 1.001, 1.0001.

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