Abstract

The synchronization of unidirectionally coupled multi-transverse-mode vertical-cavity surface-emitting lasers (VCSELs) is numerically studied. It is demonstrated that synchronization can be achieved between each transverse mode of a master laser and its counterpart, a slave laser. This result opens the opportunity for multichannel chaotic communications by use of multi-transverse-mode VCSELs. It is further shown that two distinct synchronization regimes exist, complete synchronization and injection locking, which can be distinguished by the lag time between the master and the slave laser intensities.

© 2004 Optical Society of America

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2004 (1)

2003 (15)

N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, “Observation of the synchronization of chaos in mutually injected vertical-cavity surface-emitting semiconductor lasers,” Opt. Lett. 28, 1677–1679 (2003).
[CrossRef] [PubMed]

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Megret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20, 37–44 (2003).
[CrossRef]

M. Sciamanna, C. Masoller, F. Rogister, P. Mégret, N. B. Abraham, and M. Blondel, “Fast pulsing dynamics of a vertical-cavity surface-emitting laser operating in the low-frequency fluctuation regime,” Phys. Rev. A 68, 015805 (2003).
[CrossRef]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543–1545 (2003).
[CrossRef] [PubMed]

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67, 021802 (2003).
[CrossRef]

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68, 033805 (2003).
[CrossRef]

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

A. Scirè, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, “Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

I. V. Koryukin and P. Mandel, “Antiphase dynamics of selectively coupled multimode semiconductor lasers,” IEEE J. Quantum Electron. 39, 1521–1525 (2003).
[CrossRef]

L. Wu and S. Q. Zhu, “Multi-channel communication using chaotic synchronization of multi-mode lasers,” Phys. Lett. A 308, 157–161 (2003).
[CrossRef]

A. Uchida, Y. Liu, and P. Davis, “Characteristics of chaotic masking in synchronized semiconductor lasers,” IEEE J. Quantum Electron. 39, 963–970 (2003).
[CrossRef]

S. Tang and J.-M. Liu, “Effects of message encoding and decoding on synchronized chaotic optical communications,” IEEE J. Quantum Electron. 39, 1468–1475 (2003).
[CrossRef]

J. Paul, S. Sivaprakasam, P. S. Spencer, and K. A. Shore, “Optically modulated chaotic communication scheme with external-cavity length as a key to security,” J. Opt. Soc. Am. B 20, 497–503 (2003).
[CrossRef]

M. W. Lee, J. Paul, S. Sivaprakasam, and K. A. Shore, “Comparison of closed-loop and open-loop feedback schemes of message decoding using chaotic laser diodes,” Opt. Lett. 28, 2168–2170 (2003).
[CrossRef] [PubMed]

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, “Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers,” IEEE J. Quantum Electron. 39, 269–278 (2003).
[CrossRef]

2002 (9)

M. S. Torre, C. Masoller, and P. Mandel, “Transverse-mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A 66, 053817 (2002).
[CrossRef]

M. S. Torre and C. Masoller, “Effects of carrier transport on the transverse-mode selection of index-guided vertical-cavity surface-emitting lasers,” Opt. Commun. 202, 311–318 (2002).
[CrossRef]

E. A. Viktorov and P. Mandel, “Synchronization of two unidirectionally coupled multimode semiconductor lasers,” Phys. Rev. A 65, 015801 (2002).
[CrossRef]

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

A. Locquet, C. Masoller, P. Megret, and M. Blondel, “Comparison of two types of synchronization of external-cavity semiconductor lasers,” Opt. Lett. 27, 31–33 (2002).
[CrossRef]

A. Locquet, C. Masoller, and C. R. Mirasso, “Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 056205 (2002).
[CrossRef]

I. V. Koryukin and P. Mandel, “Two regimes of synchronization in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 026201 (2002).
[CrossRef]

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903 (2002).
[CrossRef] [PubMed]

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

2001 (5)

S. F. Yu, P. Shum, and N. Q. Ngo, “Performance of optical chaotic communication systems using multimode vertical cavity surface emitting lasers,” Opt. Commun. 200, 143–152 (2001).
[CrossRef]

A. Locquet, F. Rogister, M. Sciamanna, P. Mégret, and M. Blondel, “Two types of synchronization in unidirectionally coupled chaotic external-cavity semiconductor lasers,” Phys. Rev. E 64, 045203 (R) (2001).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (R) (2001).
[CrossRef]

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64, 023801 (2001).
[CrossRef]

C. Masoller, “Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback,” Phys. Rev. Lett. 86, 2782–2785 (2001).
[CrossRef] [PubMed]

2000 (3)

H. Fujino and J. Ohtsubo, “Experimental synchronization of chaotic oscillations in external-cavity semiconductor lasers,” Opt. Lett. 25, 625–627 (2000).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62, 011801 (R) (2000).
[CrossRef]

S. Wieczorek, B. Krauskopf, and D. Lenstra, “Mechanisms for multistability in a semiconductor laser with optical injection,” Opt. Commun. 183, 215–226 (2000).
[CrossRef]

1999 (5)

S. Sivaprakasam and K. A. Shore, “Demonstration of optical synchronization of chaotic external-cavity laser diodes,” Opt. Lett. 24, 466–468 (1999).
[CrossRef]

J. K. White and J. V. Moloney, “Multichannel communication using an infinite dimensional spatiotemporal chaotic system,” Phys. Rev. A 59, 2422–2426 (1999).
[CrossRef]

P. S. Spencer and C. R. Mirasso, “Analysis of optical chaos synchronization in frequency-detuned external-cavity VCSELs,” IEEE J. Quantum Electron. 35, 803–809 (1999).
[CrossRef]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16, 2114–2123 (1999).
[CrossRef]

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

1998 (4)

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

J. P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80, 2249–2252 (1998).
[CrossRef]

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E 58, 7208–7213 (1998).
[CrossRef]

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, “Modeling of optical synchronization of chaotic external-cavity VCSELs,” IEEE J. Quantum Electron. 34, 1673–1679 (1998).
[CrossRef]

1997 (2)

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

A. Gavrielides, V. Kovanis, P. M. Varangis, T. Erneux, and G. Lythe, “Coexisting periodic attractors in injection-locked diode lasers,” Quantum Semiclassic. Opt. 9, 785–796 (1997).
[CrossRef]

1996 (1)

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299–301 (1996).
[CrossRef]

1995 (2)

A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting laser diodes,” Opt. Commun. 115, 297–302 (1995).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser-diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

1993 (1)

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547 (1993).
[CrossRef]

1991 (1)

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

1980 (1)

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

Abraham, N. B.

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Megret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20, 37–44 (2003).
[CrossRef]

M. Sciamanna, C. Masoller, F. Rogister, P. Mégret, N. B. Abraham, and M. Blondel, “Fast pulsing dynamics of a vertical-cavity surface-emitting laser operating in the low-frequency fluctuation regime,” Phys. Rev. A 68, 015805 (2003).
[CrossRef]

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

Ackemann, T.

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67, 021802 (2003).
[CrossRef]

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68, 033805 (2003).
[CrossRef]

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16, 2114–2123 (1999).
[CrossRef]

Agrawal, G. P.

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

Ahlers, V.

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E 58, 7208–7213 (1998).
[CrossRef]

Aida, T.

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, “Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers,” IEEE J. Quantum Electron. 39, 269–278 (2003).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (R) (2001).
[CrossRef]

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64, 023801 (2001).
[CrossRef]

Balle, S.

Bandyopadhyay, S.

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

Barland, S.

Blondel, M.

Bohnet, H.

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67, 021802 (2003).
[CrossRef]

Chang-Hasnain, C. J.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Chen, H. F.

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (R) (2001).
[CrossRef]

Colet, P.

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, “Modeling of optical synchronization of chaotic external-cavity VCSELs,” IEEE J. Quantum Electron. 34, 1673–1679 (1998).
[CrossRef]

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299–301 (1996).
[CrossRef]

Dagenais, M.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547 (1993).
[CrossRef]

Danckaert, J.

A. Scirè, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, “Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Davis, P.

A. Uchida, Y. Liu, and P. Davis, “Characteristics of chaotic masking in synchronized semiconductor lasers,” IEEE J. Quantum Electron. 39, 963–970 (2003).
[CrossRef]

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, “Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers,” IEEE J. Quantum Electron. 39, 269–278 (2003).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (R) (2001).
[CrossRef]

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64, 023801 (2001).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62, 011801 (R) (2000).
[CrossRef]

Erneux, T.

A. Gavrielides, V. Kovanis, P. M. Varangis, T. Erneux, and G. Lythe, “Coexisting periodic attractors in injection-locked diode lasers,” Quantum Semiclassic. Opt. 9, 785–796 (1997).
[CrossRef]

Fischer, I.

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64, 023801 (2001).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62, 011801 (R) (2000).
[CrossRef]

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Fujino, H.

Fujiwara, N.

Garcia-Fernandez, P.

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299–301 (1996).
[CrossRef]

Gavrielides, A.

A. Gavrielides, V. Kovanis, P. M. Varangis, T. Erneux, and G. Lythe, “Coexisting periodic attractors in injection-locked diode lasers,” Quantum Semiclassic. Opt. 9, 785–796 (1997).
[CrossRef]

Giudici, M.

Goedgebuer, J. P.

J. P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80, 2249–2252 (1998).
[CrossRef]

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Hong, Y.

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, “Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,” Opt. Lett. 29, 1215–1217 (2004).
[CrossRef] [PubMed]

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

Jiang, S.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547 (1993).
[CrossRef]

Kobayashi, K.

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

Kojima, K.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547 (1993).
[CrossRef]

Koryukin, I. V.

I. V. Koryukin and P. Mandel, “Antiphase dynamics of selectively coupled multimode semiconductor lasers,” IEEE J. Quantum Electron. 39, 1521–1525 (2003).
[CrossRef]

I. V. Koryukin and P. Mandel, “Two regimes of synchronization in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 026201 (2002).
[CrossRef]

Kovanis, V.

A. Gavrielides, V. Kovanis, P. M. Varangis, T. Erneux, and G. Lythe, “Coexisting periodic attractors in injection-locked diode lasers,” Quantum Semiclassic. Opt. 9, 785–796 (1997).
[CrossRef]

Krauskopf, B.

S. Wieczorek, B. Krauskopf, and D. Lenstra, “Mechanisms for multistability in a semiconductor laser with optical injection,” Opt. Commun. 183, 215–226 (2000).
[CrossRef]

Lang, R.

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

Larger, L.

J. P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80, 2249–2252 (1998).
[CrossRef]

Lauterborn, W.

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E 58, 7208–7213 (1998).
[CrossRef]

Law, J. Y.

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

Lee, M. W.

Lenstra, D.

S. Wieczorek, B. Krauskopf, and D. Lenstra, “Mechanisms for multistability in a semiconductor laser with optical injection,” Opt. Commun. 183, 215–226 (2000).
[CrossRef]

Liu, J. M.

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (R) (2001).
[CrossRef]

Liu, J.-M.

S. Tang and J.-M. Liu, “Effects of message encoding and decoding on synchronized chaotic optical communications,” IEEE J. Quantum Electron. 39, 1468–1475 (2003).
[CrossRef]

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, “Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers,” IEEE J. Quantum Electron. 39, 269–278 (2003).
[CrossRef]

Liu, Y.

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, “Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers,” IEEE J. Quantum Electron. 39, 269–278 (2003).
[CrossRef]

A. Uchida, Y. Liu, and P. Davis, “Characteristics of chaotic masking in synchronized semiconductor lasers,” IEEE J. Quantum Electron. 39, 963–970 (2003).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (R) (2001).
[CrossRef]

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64, 023801 (2001).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62, 011801 (R) (2000).
[CrossRef]

Locquet, A.

A. Locquet, C. Masoller, P. Megret, and M. Blondel, “Comparison of two types of synchronization of external-cavity semiconductor lasers,” Opt. Lett. 27, 31–33 (2002).
[CrossRef]

A. Locquet, C. Masoller, and C. R. Mirasso, “Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 056205 (2002).
[CrossRef]

A. Locquet, F. Rogister, M. Sciamanna, P. Mégret, and M. Blondel, “Two types of synchronization in unidirectionally coupled chaotic external-cavity semiconductor lasers,” Phys. Rev. E 64, 045203 (R) (2001).
[CrossRef]

Loiko, N. A.

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68, 033805 (2003).
[CrossRef]

Lythe, G.

A. Gavrielides, V. Kovanis, P. M. Varangis, T. Erneux, and G. Lythe, “Coexisting periodic attractors in injection-locked diode lasers,” Quantum Semiclassic. Opt. 9, 785–796 (1997).
[CrossRef]

Mandel, P.

I. V. Koryukin and P. Mandel, “Antiphase dynamics of selectively coupled multimode semiconductor lasers,” IEEE J. Quantum Electron. 39, 1521–1525 (2003).
[CrossRef]

E. A. Viktorov and P. Mandel, “Synchronization of two unidirectionally coupled multimode semiconductor lasers,” Phys. Rev. A 65, 015801 (2002).
[CrossRef]

M. S. Torre, C. Masoller, and P. Mandel, “Transverse-mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A 66, 053817 (2002).
[CrossRef]

I. V. Koryukin and P. Mandel, “Two regimes of synchronization in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 026201 (2002).
[CrossRef]

Masoller, C.

M. Sciamanna, C. Masoller, F. Rogister, P. Mégret, N. B. Abraham, and M. Blondel, “Fast pulsing dynamics of a vertical-cavity surface-emitting laser operating in the low-frequency fluctuation regime,” Phys. Rev. A 68, 015805 (2003).
[CrossRef]

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Megret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20, 37–44 (2003).
[CrossRef]

A. Locquet, C. Masoller, and C. R. Mirasso, “Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 056205 (2002).
[CrossRef]

A. Locquet, C. Masoller, P. Megret, and M. Blondel, “Comparison of two types of synchronization of external-cavity semiconductor lasers,” Opt. Lett. 27, 31–33 (2002).
[CrossRef]

M. S. Torre, C. Masoller, and P. Mandel, “Transverse-mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A 66, 053817 (2002).
[CrossRef]

M. S. Torre and C. Masoller, “Effects of carrier transport on the transverse-mode selection of index-guided vertical-cavity surface-emitting lasers,” Opt. Commun. 202, 311–318 (2002).
[CrossRef]

C. Masoller, “Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback,” Phys. Rev. Lett. 86, 2782–2785 (2001).
[CrossRef] [PubMed]

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

Megret, P.

Mégret, P.

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543–1545 (2003).
[CrossRef] [PubMed]

M. Sciamanna, C. Masoller, F. Rogister, P. Mégret, N. B. Abraham, and M. Blondel, “Fast pulsing dynamics of a vertical-cavity surface-emitting laser operating in the low-frequency fluctuation regime,” Phys. Rev. A 68, 015805 (2003).
[CrossRef]

A. Locquet, F. Rogister, M. Sciamanna, P. Mégret, and M. Blondel, “Two types of synchronization in unidirectionally coupled chaotic external-cavity semiconductor lasers,” Phys. Rev. E 64, 045203 (R) (2001).
[CrossRef]

Mirasso, C. R.

A. Scirè, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, “Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

A. Locquet, C. Masoller, and C. R. Mirasso, “Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 056205 (2002).
[CrossRef]

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

P. S. Spencer and C. R. Mirasso, “Analysis of optical chaos synchronization in frequency-detuned external-cavity VCSELs,” IEEE J. Quantum Electron. 35, 803–809 (1999).
[CrossRef]

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, “Modeling of optical synchronization of chaotic external-cavity VCSELs,” IEEE J. Quantum Electron. 34, 1673–1679 (1998).
[CrossRef]

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299–301 (1996).
[CrossRef]

Moloney, J. V.

J. K. White and J. V. Moloney, “Multichannel communication using an infinite dimensional spatiotemporal chaotic system,” Phys. Rev. A 59, 2422–2426 (1999).
[CrossRef]

Morgan, R. A.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547 (1993).
[CrossRef]

Mulet, J.

A. Scirè, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, “Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Naumenko, A.

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

Naumenko, A. V.

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68, 033805 (2003).
[CrossRef]

Ngo, N. Q.

S. F. Yu, P. Shum, and N. Q. Ngo, “Performance of optical chaotic communication systems using multimode vertical cavity surface emitting lasers,” Opt. Commun. 200, 143–152 (2001).
[CrossRef]

Ohtsubo, J.

Pan, Z.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547 (1993).
[CrossRef]

Panajotov, K.

Parlitz, U.

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E 58, 7208–7213 (1998).
[CrossRef]

Paul, J.

Perez, T.

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

Porte, H.

J. P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80, 2249–2252 (1998).
[CrossRef]

Rogister, F.

M. Sciamanna, C. Masoller, F. Rogister, P. Mégret, N. B. Abraham, and M. Blondel, “Fast pulsing dynamics of a vertical-cavity surface-emitting laser operating in the low-frequency fluctuation regime,” Phys. Rev. A 68, 015805 (2003).
[CrossRef]

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Megret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20, 37–44 (2003).
[CrossRef]

A. Locquet, F. Rogister, M. Sciamanna, P. Mégret, and M. Blondel, “Two types of synchronization in unidirectionally coupled chaotic external-cavity semiconductor lasers,” Phys. Rev. E 64, 045203 (R) (2001).
[CrossRef]

Roy, R.

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903 (2002).
[CrossRef] [PubMed]

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

Saito, S.

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, “Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers,” IEEE J. Quantum Electron. 39, 269–278 (2003).
[CrossRef]

San Miguel, M.

A. Scirè, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, “Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Sarma, J.

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser-diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting laser diodes,” Opt. Commun. 115, 297–302 (1995).
[CrossRef]

Sciamanna, M.

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543–1545 (2003).
[CrossRef] [PubMed]

M. Sciamanna, C. Masoller, F. Rogister, P. Mégret, N. B. Abraham, and M. Blondel, “Fast pulsing dynamics of a vertical-cavity surface-emitting laser operating in the low-frequency fluctuation regime,” Phys. Rev. A 68, 015805 (2003).
[CrossRef]

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Megret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20, 37–44 (2003).
[CrossRef]

A. Locquet, F. Rogister, M. Sciamanna, P. Mégret, and M. Blondel, “Two types of synchronization in unidirectionally coupled chaotic external-cavity semiconductor lasers,” Phys. Rev. E 64, 045203 (R) (2001).
[CrossRef]

Scirè, A.

A. Scirè, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, “Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers,” Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Shore, K. A.

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, “Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,” Opt. Lett. 29, 1215–1217 (2004).
[CrossRef] [PubMed]

M. W. Lee, J. Paul, S. Sivaprakasam, and K. A. Shore, “Comparison of closed-loop and open-loop feedback schemes of message decoding using chaotic laser diodes,” Opt. Lett. 28, 2168–2170 (2003).
[CrossRef] [PubMed]

J. Paul, S. Sivaprakasam, P. S. Spencer, and K. A. Shore, “Optically modulated chaotic communication scheme with external-cavity length as a key to security,” J. Opt. Soc. Am. B 20, 497–503 (2003).
[CrossRef]

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

S. Sivaprakasam and K. A. Shore, “Demonstration of optical synchronization of chaotic external-cavity laser diodes,” Opt. Lett. 24, 466–468 (1999).
[CrossRef]

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, “Modeling of optical synchronization of chaotic external-cavity VCSELs,” IEEE J. Quantum Electron. 34, 1673–1679 (1998).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting laser diodes,” Opt. Commun. 115, 297–302 (1995).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser-diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

Shum, P.

S. F. Yu, P. Shum, and N. Q. Ngo, “Performance of optical chaotic communication systems using multimode vertical cavity surface emitting lasers,” Opt. Commun. 200, 143–152 (2001).
[CrossRef]

Sivaprakasam, S.

Sondermann, M.

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67, 021802 (2003).
[CrossRef]

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68, 033805 (2003).
[CrossRef]

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

Spencer, P. S.

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, “Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,” Opt. Lett. 29, 1215–1217 (2004).
[CrossRef] [PubMed]

J. Paul, S. Sivaprakasam, P. S. Spencer, and K. A. Shore, “Optically modulated chaotic communication scheme with external-cavity length as a key to security,” J. Opt. Soc. Am. B 20, 497–503 (2003).
[CrossRef]

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

P. S. Spencer and C. R. Mirasso, “Analysis of optical chaos synchronization in frequency-detuned external-cavity VCSELs,” IEEE J. Quantum Electron. 35, 803–809 (1999).
[CrossRef]

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, “Modeling of optical synchronization of chaotic external-cavity VCSELs,” IEEE J. Quantum Electron. 34, 1673–1679 (1998).
[CrossRef]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Takiguchi, Y.

N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, “Observation of the synchronization of chaos in mutually injected vertical-cavity surface-emitting semiconductor lasers,” Opt. Lett. 28, 1677–1679 (2003).
[CrossRef] [PubMed]

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, “Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers,” IEEE J. Quantum Electron. 39, 269–278 (2003).
[CrossRef]

Tang, S.

S. Tang and J.-M. Liu, “Effects of message encoding and decoding on synchronized chaotic optical communications,” IEEE J. Quantum Electron. 39, 1468–1475 (2003).
[CrossRef]

Thienpont, H.

Torre, M. S.

M. S. Torre and C. Masoller, “Effects of carrier transport on the transverse-mode selection of index-guided vertical-cavity surface-emitting lasers,” Opt. Commun. 202, 311–318 (2002).
[CrossRef]

M. S. Torre, C. Masoller, and P. Mandel, “Transverse-mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A 66, 053817 (2002).
[CrossRef]

Tredicce, J. R.

Uchida, A.

A. Uchida, Y. Liu, and P. Davis, “Characteristics of chaotic masking in synchronized semiconductor lasers,” IEEE J. Quantum Electron. 39, 963–970 (2003).
[CrossRef]

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Phys. Rev. A 64, 023801 (2001).
[CrossRef]

Valle, A.

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser-diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting laser diodes,” Opt. Commun. 115, 297–302 (1995).
[CrossRef]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903 (2002).
[CrossRef] [PubMed]

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

Varangis, P. M.

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[CrossRef]

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J. K. White and J. V. Moloney, “Multichannel communication using an infinite dimensional spatiotemporal chaotic system,” Phys. Rev. A 59, 2422–2426 (1999).
[CrossRef]

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A. Gavrielides, V. Kovanis, P. M. Varangis, T. Erneux, and G. Lythe, “Coexisting periodic attractors in injection-locked diode lasers,” Quantum Semiclassic. Opt. 9, 785–796 (1997).
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Figures (11)

Fig. 1
Fig. 1

Complete synchronization when the lasers operate in the in-phase regime. Is=Im=1.95 mA and Ks=Km=1.6 ns-1. (a) Master laser total intensity (ITm=Σ Iim: thick solid curve) and modal intensities (Iim=|Eim|2; LP01, thin solid curve; LP02, dashed curve). (b) Slave laser total and modal intensities. (c) Correlation of the total intensities. (d) Correlation of the LP01 modal intensities.

Fig. 2
Fig. 2

Complete synchronization when the lasers operate in the antiphase regime. Is=Im=3.2 mA and Ks=Km=1.6 ns-1. (a) Master laser total intensity (thick solid curve) and modal intensities (LP01, thin solid curve; LP02, dashed curve; LP03, dot–dash curve). (b) Slave laser total and modal intensities. (c) Correlation of the total intensities. (d) Correlation of the LP01 modal intensities.

Fig. 3
Fig. 3

Injection-locking synchronization when the lasers operate in the in-phase regime. Is=Im=1.95 mA and Ks=100Km=160 ns-1. (a) Master laser total intensity (thick solid curve) and modal intensities (LP01, thin solid curve; LP02, dashed curve). (b) Slave laser total and modal intensities. (c) Correlation of the total intensities. (d) Correlation of the LP01 modal intensities.

Fig. 4
Fig. 4

Injection-locking synchronization when the lasers operate in the antiphase regime. Is=Im=3.2 mA and Ks=100Km=160 ns-1. (a) Master laser total intensity (thick solid curve) and modal intensities (LP01, thin solid curve; LP02, dashed curve; LP03, dot–dash curve). (b) Slave laser total and modal intensities. (c) Correlation of the total intensities. (d) Correlation of the LP01 modal intensities.

Fig. 5
Fig. 5

Dynamics of the slave laser for increasing injection strength. Km=1 ns-1 and τ=1 ns. Ks=(a) 0.1 ns-1, (b) 1 ns-1, (c) 25 ns-1, (d) 50 ns-1, (e) 100 ns-1. Total intensity, thick solid curve; LP01, thin solid curve; LP02, dashed curve; LP03, dot–dash curve.

Fig. 6
Fig. 6

Correlation coefficient of the total intensities (solid curve) and of the LP01 modal intensities (dashed curve) for increasing injection strength. Km=1.6 ns-1. CT and C1 are calculated with a lag time of (a) τc-τ and (b) τc.

Fig. 7
Fig. 7

Correlation coefficient of the total intensities (solid curve) and of the LP01 modal intensities (dashed curve) for increasing injection strength. The lasers have different injection currents. (a) Im=3.2 mA and Is=1.95 mA. (b) Im=1.95 mA and Is=3.2 mA.

Fig. 8
Fig. 8

Correlation of the total intensities (solid curve) and of the LP01 modal intensities (dashed curve) as a function of detuning Ω. Km=1.6 ns-1. (a) Im=Is=1.95 mA, Ks=16 ns-1. (b) Im=Is=1.95 mA, Ks=50 ns-1. (c) Im=Is=3.2 mA, Ks=16 ns-1. (d) Im=Is=3.2 mA, Ks=50 ns-1.

Fig. 9
Fig. 9

Correlation of the total intensities (solid curve) and of the LP01 modal intensities (dashed curve) as a function of detuning Ω. Ks=Km=1.6 ns-1. (a) Im=Is=1.95 mA. (b) Im=Is=3.2 mA.

Fig. 10
Fig. 10

(a) Total and modal intensities of the master laser. Im=1.95 mA and Km=1.6 ns-1. (b) Total and modal intensities of the slave laser when Is=Im, k1s=Km, k2,3s=0. (c) Correlation coefficients. (d) Total and modal intensities of the slave laser when k1s=100Km, k2,3s=0. (e) Correlation coefficients.

Fig. 11
Fig. 11

(a) Total and modal intensities of the master laser. Im=3.2 mA and Km=1.6 ns-1. (b) Total and modal intensities of the slave laser when Is=Im, k1s=Km, k2,3s=0. (c) Correlation coefficients. (d) Total and modal intensities of the slave laser when k1s=100Km, k2,3s=0. (e) Correlation coefficients.

Equations (5)

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deimdt=1+jα2 gim-1τpieim(t)+kimeim(t-τ)×exp(-jωiτ),
deisdt=1+jα2 gis-1τpieis(t)+kiseim(t-τc)×exp[-j(ωi+Ω)τc],
nbm,st=jm,s(r)edb-nbm,sτcap+VQWVb nwm,sτesc-nbm,sτn+D 1r r r nbm,sr,
nwm,st=VbVQW nbm,sτcap-nwm,sτesc-nwm,sτn-g0(nwm,s-nt)×|eim,s|2|ψi|2+D 1r r r nwm,sr.
CT,1(τlag)=[IT,1m(t+τlag)-IT,1m][IT,1s(t)-IT,1s][(IT,1m(t)-IT,1m)2(IT,1s(t)-IT,1s)2]1/2.

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