Abstract

We experimentally and numerically observe the synchronization between two semiconductor lasers induced by common optical injection with constant-amplitude and random-phase modulation in configurations with and without optical feedback. Large cross correlation (~0.9) between the intensity oscillations of the two response lasers can be achieved although the correlation between the drive laser and either one of the two response lasers is very small (~0.2). High quality synchronization is achieved in the presence of optical feedback in response lasers with matched feedback phase offset. We investigate the dependence of synchronization on parameter values over wide parameter ranges.

© 2012 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  24. K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
    [CrossRef] [PubMed]
  25. S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
    [CrossRef]
  26. K. Yoshimura, A. Uchida, P. Davis, J. Muramatsu, T. Harayama, and S. Sunada, “Synchronization of semiconductor lasers by common optical injection with constant-amplitude and random-phase modulation,” Rev. Laser Eng. 39, 520–524 (2011) (in Japanese).
  27. R. Vicente, T. Pérez, and C. R. Mirasso, “Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
    [CrossRef]
  28. M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett. 21(7), 426–428 (2009).
    [CrossRef]
  29. M. Peil, T. Heil, I. Fischer, and W. Elsäßer, “Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario,” Phys. Rev. Lett. 88(17), 174101 (2002).
    [CrossRef] [PubMed]
  30. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
    [CrossRef]
  31. T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
    [CrossRef]

2012 (1)

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[CrossRef] [PubMed]

2011 (1)

K. Yoshimura, A. Uchida, P. Davis, J. Muramatsu, T. Harayama, and S. Sunada, “Synchronization of semiconductor lasers by common optical injection with constant-amplitude and random-phase modulation,” Rev. Laser Eng. 39, 520–524 (2011) (in Japanese).

2010 (1)

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[CrossRef]

2009 (5)

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett. 21(7), 426–428 (2009).
[CrossRef]

S. Wieczorek, “Stochastic bifurcation in noise-driven lasers and Hopf oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(3), 036209 (2009).
[CrossRef] [PubMed]

S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. 282(12), 2367–2379 (2009).
[CrossRef]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[CrossRef] [PubMed]

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[CrossRef]

2008 (4)

K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time-delay systems,” Physica D 237(23), 3146–3152 (2008).
[CrossRef]

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Some results on secret key agreement using correlated sources,” NTT Tech. Rev. 6(2), 1–7 (2008).

K. Yoshimura, P. Davis, and A. Uchida, “Invariance of frequency difference in nonresonant entrainment of detuned oscillators induced by common white noise,” Prog. Theor. Phys. 120(4), 621–633 (2008).
[CrossRef]

O. Buskila, A. Eyal, and M. Shtaif, “Secure communication in fiber optic systems via transmission of broad-band optical noise,” Opt. Express 16(5), 3383–3396 (2008).
[CrossRef] [PubMed]

2007 (3)

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[CrossRef] [PubMed]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026208 (2007).
[CrossRef] [PubMed]

H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
[CrossRef] [PubMed]

2005 (2)

D. S. Goldobin and A. Pikovsky, “Synchronization of self-sustained oscillators by common white noise,” Physica A 351(1), 126–132 (2005).
[CrossRef]

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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

2004 (1)

J. N. Teramae and D. Tanaka, “Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,” Phys. Rev. Lett. 93(20), 204103 (2004).
[CrossRef] [PubMed]

2002 (4)

C. Zhou and J. Kurths, “Noise-induced phase synchronization and synchronization transitions in chaotic oscillators,” Phys. Rev. Lett. 88(23), 230602 (2002).
[CrossRef] [PubMed]

R. Vicente, T. Pérez, and C. R. Mirasso, “Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
[CrossRef]

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, “Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario,” Phys. Rev. Lett. 88(17), 174101 (2002).
[CrossRef] [PubMed]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[CrossRef]

2001 (1)

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[CrossRef] [PubMed]

1998 (1)

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[CrossRef] [PubMed]

1993 (1)

U. M. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39(3), 733–742 (1993).
[CrossRef]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[CrossRef]

Aida, H.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[CrossRef] [PubMed]

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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

Arai, K.

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Some results on secret key agreement using correlated sources,” NTT Tech. Rev. 6(2), 1–7 (2008).

H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
[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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

Ariizumi, H.

Buskila, O.

Chow, W. W.

S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. 282(12), 2367–2379 (2009).
[CrossRef]

Colet, P.

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett. 21(7), 426–428 (2009).
[CrossRef]

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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[CrossRef]

Davis, P.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[CrossRef] [PubMed]

K. Yoshimura, A. Uchida, P. Davis, J. Muramatsu, T. Harayama, and S. Sunada, “Synchronization of semiconductor lasers by common optical injection with constant-amplitude and random-phase modulation,” Rev. Laser Eng. 39, 520–524 (2011) (in Japanese).

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[CrossRef]

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[CrossRef]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[CrossRef] [PubMed]

K. Yoshimura, P. Davis, and A. Uchida, “Invariance of frequency difference in nonresonant entrainment of detuned oscillators induced by common white noise,” Prog. Theor. Phys. 120(4), 621–633 (2008).
[CrossRef]

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Some results on secret key agreement using correlated sources,” NTT Tech. Rev. 6(2), 1–7 (2008).

K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time-delay systems,” Physica D 237(23), 3146–3152 (2008).
[CrossRef]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026208 (2007).
[CrossRef] [PubMed]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[CrossRef] [PubMed]

Elsäßer, W.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, “Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario,” Phys. Rev. Lett. 88(17), 174101 (2002).
[CrossRef] [PubMed]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[CrossRef]

Eyal, A.

Fischer, I.

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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[CrossRef]

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, “Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario,” Phys. Rev. Lett. 88(17), 174101 (2002).
[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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

Goldobin, D. S.

D. S. Goldobin and A. Pikovsky, “Synchronization of self-sustained oscillators by common white noise,” Physica A 351(1), 126–132 (2005).
[CrossRef]

Goto, S.

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[CrossRef]

Goto, S. I.

Harayama, T.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[CrossRef] [PubMed]

K. Yoshimura, A. Uchida, P. Davis, J. Muramatsu, T. Harayama, and S. Sunada, “Synchronization of semiconductor lasers by common optical injection with constant-amplitude and random-phase modulation,” Rev. Laser Eng. 39, 520–524 (2011) (in Japanese).

Heil, T.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, “Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario,” Phys. Rev. Lett. 88(17), 174101 (2002).
[CrossRef] [PubMed]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[CrossRef]

Hernandez-Garcia, E.

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[CrossRef] [PubMed]

Kawamura, Y.

H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
[CrossRef] [PubMed]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[CrossRef]

Kurths, J.

C. Zhou and J. Kurths, “Noise-induced phase synchronization and synchronization transitions in chaotic oscillators,” Phys. Rev. Lett. 88(23), 230602 (2002).
[CrossRef] [PubMed]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

Li, M.

Maurer, U. M.

U. M. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39(3), 733–742 (1993).
[CrossRef]

Mirasso, C. R.

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett. 21(7), 426–428 (2009).
[CrossRef]

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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[CrossRef]

R. Vicente, T. Pérez, and C. R. Mirasso, “Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
[CrossRef]

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[CrossRef] [PubMed]

Morikatsu, S.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[CrossRef] [PubMed]

Mulet, J.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[CrossRef]

Muramatsu, J.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[CrossRef] [PubMed]

K. Yoshimura, A. Uchida, P. Davis, J. Muramatsu, T. Harayama, and S. Sunada, “Synchronization of semiconductor lasers by common optical injection with constant-amplitude and random-phase modulation,” Rev. Laser Eng. 39, 520–524 (2011) (in Japanese).

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[CrossRef]

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Some results on secret key agreement using correlated sources,” NTT Tech. Rev. 6(2), 1–7 (2008).

K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time-delay systems,” Physica D 237(23), 3146–3152 (2008).
[CrossRef]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[CrossRef] [PubMed]

Nakao, H.

H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
[CrossRef] [PubMed]

Okumura, H.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[CrossRef] [PubMed]

Oowada, I.

Peil, M.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, “Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario,” Phys. Rev. Lett. 88(17), 174101 (2002).
[CrossRef] [PubMed]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[CrossRef]

Pérez, T.

R. Vicente, T. Pérez, and C. R. Mirasso, “Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
[CrossRef]

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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

Pikovsky, A.

D. S. Goldobin and A. Pikovsky, “Synchronization of self-sustained oscillators by common white noise,” Physica A 351(1), 126–132 (2005).
[CrossRef]

Piro, O.

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[CrossRef] [PubMed]

Roy, R.

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[CrossRef] [PubMed]

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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

Shtaif, M.

Soriano, M. C.

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett. 21(7), 426–428 (2009).
[CrossRef]

Sunada, S.

K. Yoshimura, A. Uchida, P. Davis, J. Muramatsu, T. Harayama, and S. Sunada, “Synchronization of semiconductor lasers by common optical injection with constant-amplitude and random-phase modulation,” Rev. Laser Eng. 39, 520–524 (2011) (in Japanese).

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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

Tanaka, D.

J. N. Teramae and D. Tanaka, “Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,” Phys. Rev. Lett. 93(20), 204103 (2004).
[CrossRef] [PubMed]

Teramae, J. N.

J. N. Teramae and D. Tanaka, “Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,” Phys. Rev. Lett. 93(20), 204103 (2004).
[CrossRef] [PubMed]

Toral, R.

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[CrossRef] [PubMed]

Uchida, A.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[CrossRef] [PubMed]

K. Yoshimura, A. Uchida, P. Davis, J. Muramatsu, T. Harayama, and S. Sunada, “Synchronization of semiconductor lasers by common optical injection with constant-amplitude and random-phase modulation,” Rev. Laser Eng. 39, 520–524 (2011) (in Japanese).

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[CrossRef] [PubMed]

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[CrossRef]

K. Yoshimura, P. Davis, and A. Uchida, “Invariance of frequency difference in nonresonant entrainment of detuned oscillators induced by common white noise,” Prog. Theor. Phys. 120(4), 621–633 (2008).
[CrossRef]

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[CrossRef] [PubMed]

Valiusaityte, I.

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026208 (2007).
[CrossRef] [PubMed]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[CrossRef] [PubMed]

Vicente, R.

R. Vicente, T. Pérez, and C. R. Mirasso, “Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
[CrossRef]

Wieczorek, S.

S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. 282(12), 2367–2379 (2009).
[CrossRef]

S. Wieczorek, “Stochastic bifurcation in noise-driven lasers and Hopf oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(3), 036209 (2009).
[CrossRef] [PubMed]

Yamamoto, T.

Yip, H.

Yoshimori, S.

Yoshimura, K.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[CrossRef] [PubMed]

K. Yoshimura, A. Uchida, P. Davis, J. Muramatsu, T. Harayama, and S. Sunada, “Synchronization of semiconductor lasers by common optical injection with constant-amplitude and random-phase modulation,” Rev. Laser Eng. 39, 520–524 (2011) (in Japanese).

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[CrossRef]

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[CrossRef]

I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express 17(12), 10025–10034 (2009).
[CrossRef] [PubMed]

K. Yoshimura, P. Davis, and A. Uchida, “Invariance of frequency difference in nonresonant entrainment of detuned oscillators induced by common white noise,” Prog. Theor. Phys. 120(4), 621–633 (2008).
[CrossRef]

K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time-delay systems,” Physica D 237(23), 3146–3152 (2008).
[CrossRef]

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Some results on secret key agreement using correlated sources,” NTT Tech. Rev. 6(2), 1–7 (2008).

T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express 15(7), 3974–3980 (2007).
[CrossRef] [PubMed]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026208 (2007).
[CrossRef] [PubMed]

Zhou, C.

C. Zhou and J. Kurths, “Noise-induced phase synchronization and synchronization transitions in chaotic oscillators,” Phys. Rev. Lett. 88(23), 230602 (2002).
[CrossRef] [PubMed]

Chaos (1)

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, and O. Piro, “Analytical and numerical studies of noise-induced synchronization of chaotic systems,” Chaos 11(3), 665–673 (2001).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (3)

R. Vicente, T. Pérez, and C. R. Mirasso, “Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1197–1204 (2002).
[CrossRef]

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[CrossRef]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, “ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38(9), 1162–1170 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett. 21(7), 426–428 (2009).
[CrossRef]

IEEE Trans. Inf. Theory (1)

U. M. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inf. Theory 39(3), 733–742 (1993).
[CrossRef]

Lect. Notes Comput. Sci. (1)

J. Muramatsu, K. Yoshimura, and P. Davis, “Information theoretic security based on bounded observability,” Lect. Notes Comput. Sci. 5973, 128–139 (2010).
[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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef] [PubMed]

NTT Tech. Rev. (1)

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, “Some results on secret key agreement using correlated sources,” NTT Tech. Rev. 6(2), 1–7 (2008).

Opt. Commun. (1)

S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. 282(12), 2367–2379 (2009).
[CrossRef]

Opt. Express (3)

Opt. Quantum Electron. (1)

S. Goto, P. Davis, K. Yoshimura, and A. Uchida, “Synchronization of chaotic semiconductor lasers by optical injection with random phase modulation,” Opt. Quantum Electron. 41(3), 137–149 (2009).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

S. Wieczorek, “Stochastic bifurcation in noise-driven lasers and Hopf oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(3), 036209 (2009).
[CrossRef] [PubMed]

K. Yoshimura, I. Valiusaityte, and P. Davis, “Synchronization induced by common colored noise in limit cycle and chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026208 (2007).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

H. Nakao, K. Arai, and Y. Kawamura, “Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,” Phys. Rev. Lett. 98(18), 184101 (2007).
[CrossRef] [PubMed]

C. Zhou and J. Kurths, “Noise-induced phase synchronization and synchronization transitions in chaotic oscillators,” Phys. Rev. Lett. 88(23), 230602 (2002).
[CrossRef] [PubMed]

J. N. Teramae and D. Tanaka, “Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,” Phys. Rev. Lett. 93(20), 204103 (2004).
[CrossRef] [PubMed]

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, “Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario,” Phys. Rev. Lett. 88(17), 174101 (2002).
[CrossRef] [PubMed]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[CrossRef] [PubMed]

Physica A (1)

D. S. Goldobin and A. Pikovsky, “Synchronization of self-sustained oscillators by common white noise,” Physica A 351(1), 126–132 (2005).
[CrossRef]

Physica D (1)

K. Yoshimura, J. Muramatsu, and P. Davis, “Conditions for common-noise-induced synchronization in time-delay systems,” Physica D 237(23), 3146–3152 (2008).
[CrossRef]

Prog. Theor. Phys. (1)

K. Yoshimura, P. Davis, and A. Uchida, “Invariance of frequency difference in nonresonant entrainment of detuned oscillators induced by common white noise,” Prog. Theor. Phys. 120(4), 621–633 (2008).
[CrossRef]

Rev. Laser Eng. (1)

K. Yoshimura, A. Uchida, P. Davis, J. Muramatsu, T. Harayama, and S. Sunada, “Synchronization of semiconductor lasers by common optical injection with constant-amplitude and random-phase modulation,” Rev. Laser Eng. 39, 520–524 (2011) (in Japanese).

Science (1)

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[CrossRef] [PubMed]

Other (5)

A. Uchida, F. Rogister, J. Garcia-Ojalvo, and R. Roy, “Synchronization and communication with chaotic laser systems,” Progress in Optics, E. Wolf, ed. (Elsevier, 2005), Vol. 48, Chap. 5, pp. 203–341.

Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, 1984).

A. S. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization (Cambridge University Press, 2001).

J. Ohtsubo, Semiconductor Lasers - Stability, Instability and Chaos (Springer-Verlag, 2008).

A. Uchida, Optical Communication with Chaotic Lasers - Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).

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Figures (17)

Fig. 1
Fig. 1

Experimental setup for the synchronization of semiconductor lasers subject to a common constant-amplitude random-phase (CARP) light. Amp, electronic amplifier; ISO, optical isolator; PD, photodetector; SL, semiconductor laser.

Fig. 2
Fig. 2

Experimental result of optical spectra (a) without and (b) with optical injection from the Drive to Response lasers. Solid black curve: Drive laser, dashed red curve: Response 1 laser, dotted blue curve: Response 2 laser. The injection strengths from the Drive to Response 1 lasers and from the Drive to Response 2 lasers are 20.1 and 18.4 μW, respectively (the maximum values obtained in the experiment). The initial optical wavelength detunings between the Drive and Response 1 lasers and between the Drive and Response 2 lasers are ΔλR1D = −0.018 nm and ΔλR2D = −0.019 nm, respectively.

Fig. 3
Fig. 3

Experimental result of (a) temporal waveforms and (b) corresponding correlation plots for the outputs of the Drive and Response 1 lasers. The injection strengths and the initial optical wavelength detunings for the three lasers are the same as shown in Fig. 2. (b) The cross correlation value is C = 0.158.

Fig. 4
Fig. 4

Experimental result of (a) temporal waveforms and (b) corresponding correlation plots for the outputs of the Response 1 and Response 2 lasers. The injection strengths and the initial optical wavelength detunings for the three lasers are the same as shown in Fig. 2. (b) The cross correlation value is C = 0.929.

Fig. 5
Fig. 5

Experimental result of RF spectra for (a) Drive, (b) Response 1, and (c) Response 2 lasers. The injection strengths and the initial optical wavelength detunings for the three lasers are the same as shown in Fig. 2.

Fig. 6
Fig. 6

Experimental results of the cross correlation between the Response 1 and Response 2 lasers (solid orange curve), between the Drive and Response 1 (solid black curve), and the optical wavelength detuning between the Drive and Response 1 lasers under optical injection (dashed blue curve) as a function of (a) the injection strength and (b) the initial optical wavelength detuning between the Drive and Response 1 lasers (ΔλRD). (a) The injection strength is normalized by the maximum injection strength obtained in the experiment. The initial optical wavelength detuning is fixed at −0.025 nm. (b) The injection strength is fixed at 1. The green dotted vertical lines indicate the injection locking range, where the average optical wavelengths of the Drive and Response lasers are matched due to optical injection.

Fig. 7
Fig. 7

Experimental result of (a) the RF spectra and (b) the corresponding optical spectra for the Response 1 and 2 lasers under optical injection from the Drive laser. The initial optical wavelength detuning is set to 0.000 nm. The difference between the first and second peaks of the optical spectra is 0.044 nm (5.5 GHz), corresponding to the peak frequency of the RF spectra. The maximum injection strength is used in the experiment.

Fig. 8
Fig. 8

Experimental result of the difference between the first and second peak frequencies of the optical spectra of the Response laser 1 (open circles), and the peak frequency of the RF spectra (solid curve with solid dots), as a function of the initial optical wavelength detuning between the Drive and Response 1 lasers without optical injection. The difference between the two peak frequencies of the optical spectra cannot be measured in the range −0.080 nm < ΔλRD < −0.030 nm due to the limited resolution of the optical spectrum analyzer. The green dotted vertical lines indicate the injection locking range, where the average optical wavelengths of the Drive and Response lasers are matched due to optical injection.

Fig. 9
Fig. 9

Experimental result of temporal waveforms and their correlation plots for Response 1and 2 in the closed-loop configuration at (a), (b) the parameter mismatching condition (Δθr1,r2 = π) and (c), (d) the parameter matching condition (Δθr1,r2 = 0), where Δθr1,r2 = θr1 – θr2 and θ is the optical feedback phase. The cross correlation values are (b) 0.002 and (d) 0.949. The injection strengths from the Drive to Response 1 lasers and from the Drive to Response 2 lasers are 20.3 and 18.8 μW, respectively (the maximum values obtained in the experiment). The feedback strengths for the Response 1 and 2 lasers are 1.96 and 1.87 μW, respectively (0.10 and 0.10, normalized by the injection strengths). The initial optical wavelength detunings between the Drive and Response 1 lasers and between the Drive and Response 2 lasers are ΔλR1D = −0.021 nm and ΔλR2D = −0.025 nm, respectively.

Fig. 10
Fig. 10

Experimental result of temporal waveforms and their correlation plots for Drive and Response 1 in the closed-loop configuration at (a), (b) the parameter mismatching condition (Δθr1,r2 = π) and (c), (d) the parameter matching condition (Δθr1,r2 = 0), where Δθr1,r2 = θr1 – θr2 and θ is the optical feedback phase. The cross correlation values are (b) 0.124 and (d) 0.123. The injection strengths, the feedback strengths, and the initial optical wavelength detunings are the same as shown in Fig. 9.

Fig. 11
Fig. 11

Experimental result of the cross correlation between the Response 1 and Response 2 lasers (solid orange curve), between the Drive and Response 1 (solid black curve), and the optical wavelength detuning between the Drive and Response 1 lasers under optical injection (dashed blue curve) as a function of (a) the injection strength and (b) the initial optical wavelength detuning between the Drive and Response 1 lasers (ΔλRD) in the closed-loop configuration. (a) The injection strength is normalized by the maximum injection strength obtained in the experiment. The initial optical wavelength detuning is fixed at −0.025 nm. (b) The injection strength is fixed at 1. The green dotted vertical lines indicate the injection locking range, where the average optical wavelengths of the Drive and Response lasers are matched due to optical injection.

Fig. 12
Fig. 12

Experimental result of the cross correlation value between (a) Response 1 and 2, and between (b) Drive and Response 1, as a function of the difference in the optical feedback phase in the external cavity between Response 1 and 2 lasers at the maximum injection strength of the two Response lasers. (a) The cross correlation changes periodically as the optical feedback phase difference is changed. The period of the correlation curve is 2π. (b) The cross correlation values stay around 0.2 and do not show periodical change. The feedback strengths normalized by the optical injection strength are 0.09 and 0.11 for Response 1 and 2, respectively. The initial optical wavelength detunings between the Drive and Response 1 lasers and between the Drive and Response 2 lasers are ΔλR1D = −0.030 nm and ΔλR2D = −0.031 nm, respectively.

Fig. 13
Fig. 13

Experimental result of the maximum (solid orange curve) and minimum (solid black curve) cross correlation values (Cmax and Cmin) between (a) Response 1 and 2, and between (b) Drive and Response 1, and the optical wavelength detuning (dashed blue curve), as a function of the feedback strength of the two Response lasers, normalized by the optical injection strength. The injection strength is fixed at 1 (i.e. the maximum injection strength obtained in the experiment). Cmax is obtained at zero phase difference, whereas Cmin is observed at π phase difference. (a) The difference between Cmax and Cmin (ΔC = Cmax - Cmin) has the maximum value at the intermediate feedback strength κr = 0.10. (b) ΔC is almost zero even though the values of maximum and minimum cross correlation gradually decrease as the feedback strength is increased.

Fig. 14
Fig. 14

Numerical result of the contour plot of the cross correlation C between Response 1 and 2 as a function of the optical wavelength detuning between Drive and Response (Δλ) and the injection strength from Drive to Response (κinj). Paremeters are κr = 0.05 and τm = 1 ns.

Fig. 15
Fig. 15

Numerical result for synchronization region with C>0.8 in (Δλ,κinj) plane for τm = 10 ns (solid line), τm = 1 ns (dashed line), and τm = 0.1 ns (dotted line), where κr = 0.05.

Fig. 16
Fig. 16

Numerical result for synchronization region with C>0.8 in (Δλ,κinj) plane for κr = 0 (solid line), 0.05 (dashed line), 0.1 (dotted line), and 0.2 (dash-dotted line), where τm = 1 ns.

Fig. 17
Fig. 17

Numerical result of the contour plot of the cross correlation difference ΔC ( = Cmax - Cmin) between Response 1 and 2 as a function of (κrinj), where Δλ = −0.025 nm and τm = 1 ns. Synchronization between Response 1 and 2 is achieved in the region above the dashed curve.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

C= ( I 1 ( t ) I ¯ 1 )( I 2 ( t ) I ¯ 2 ) σ 1 σ 2
E ˙ j (t)= 1 2 ( 1+iα ) G N ( N j (t) N th ) E j (t)+ κ r τ in E j (tτ)exp[i θ j ]+ κ inj τ in E 0 exp[i(Δ ω j t+ϕ)], N ˙ j (t)=J 1 τ s N j (t) G N ( N j (t) N 0 ) | E j (t) | 2 ,
ϕ . (t)= 1 τ m ϕ(t)+ 2 τ m σξ(t),

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