Abstract

The system of injection-locked master–slave lasers (MSLs) has been studied. The solutions to the rate equations describing the phase-locked state of MSLs have been given. The equation to test the stability of the phase-locked state of slave lasers has been deduced, and the stabilities of the phase-locked state have been studied under the conditions in which the system operates in the in-phase and out-phase modes, respectively. Finally, other properties of phase-locked MSLs have been investigated.

© 2008 Optical Society of America

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References

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  1. K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).
    [CrossRef]
  2. A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148-1151 (1999).
    [CrossRef]
  3. D. Sukow and D. Gauthier, “Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current,” IEEE J. Quantum Electron. 36, 175-183 (2000).
    [CrossRef]
  4. M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, “Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback,” IEE Proc. Optoelectron. 148, 233-237(2001).
    [CrossRef]
  5. T. Heil, J. Mulet, I. Fischer, C. Mirasso, M. Peil, P. Colet, and W. Elsasser, “ON/OFF phase shift keying for chaos encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38, 1162-1169 (2002).
    [CrossRef]
  6. X. Li, P. Wei, B. Luo, D. Ma, Y. Wang, and N. Li, “Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser,” Chaos Solitons Fractals 27, 1387-1394 (2006).
    [CrossRef]
  7. I. Petitbon and P. Gallion, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron. 24, 148-154 (1988).
    [CrossRef]
  8. C. Henry, N. Olsson, and N. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21, 1152-1156 (1985).
    [CrossRef]
  9. T. Simpson, J. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7, 709-711 (1995).
    [CrossRef]
  10. G. van Tartwijk and G. Agrawal, “Laser instabilities: a modern perspective,” Prog. Quantum Electron. 22, 43-122 (1998).
    [CrossRef]
  11. A. Murakami, “Phase locking and chaos synchronization in injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 39, 438-447 (2003).
    [CrossRef]
  12. S. Hwang and J. Liu, “Dynamical characteristic of an optically injected semiconductor laser,” Opt. Commun. 183, 195-205 (2000).
    [CrossRef]
  13. R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976-983 (1982).
    [CrossRef]
  14. S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J. Liu, “Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling,” IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
    [CrossRef]
  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]
  16. A. Hohl, A. Gavrielides, T. Erneus, and V. Kovanis, “Localized synchronization in two-coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745-4748 (1997).
    [CrossRef]
  17. F. Rogister and M. Blondel, “Dynamics of two mutually delay-coupled semiconductor lasers,” Opt. Commun. 239, 173-180 (2004).
    [CrossRef]
  18. X. Li, W. Pan, B. Luo, and D. Ma, “Nonlinear dynamics of two mutually injected external-cavity semiconductor lasers,” Semicond. Sci. Technol. 21, 25-34 (2006).
    [CrossRef]
  19. A. Uchida, T. Takahashi, S. Kinugawa, and S. Yoshimori, “Dynamics of chaotic oscillations in mutually coupled microchip lasers,” Chaos Solitons Fractals 17, 369-377 (2003).
    [CrossRef]
  20. L. Zhang, R. Dou, and J. Chen, “Analysis of the phase-locked laser diode array with an external cavity,” Semicond. Sci. Technol. 22, 1253-1257 (2007).
    [CrossRef]

2007 (1)

L. Zhang, R. Dou, and J. Chen, “Analysis of the phase-locked laser diode array with an external cavity,” Semicond. Sci. Technol. 22, 1253-1257 (2007).
[CrossRef]

2006 (2)

X. Li, P. Wei, B. Luo, D. Ma, Y. Wang, and N. Li, “Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser,” Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

X. Li, W. Pan, B. Luo, and D. Ma, “Nonlinear dynamics of two mutually injected external-cavity semiconductor lasers,” Semicond. Sci. Technol. 21, 25-34 (2006).
[CrossRef]

2004 (2)

F. Rogister and M. Blondel, “Dynamics of two mutually delay-coupled semiconductor lasers,” Opt. Commun. 239, 173-180 (2004).
[CrossRef]

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J. Liu, “Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling,” IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

2003 (3)

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]

A. Murakami, “Phase locking and chaos synchronization in injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 39, 438-447 (2003).
[CrossRef]

A. Uchida, T. Takahashi, S. Kinugawa, and S. Yoshimori, “Dynamics of chaotic oscillations in mutually coupled microchip lasers,” Chaos Solitons Fractals 17, 369-377 (2003).
[CrossRef]

2002 (1)

T. Heil, J. Mulet, I. Fischer, C. Mirasso, M. Peil, P. Colet, and W. Elsasser, “ON/OFF phase shift keying for chaos encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38, 1162-1169 (2002).
[CrossRef]

2001 (1)

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, “Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback,” IEE Proc. Optoelectron. 148, 233-237(2001).
[CrossRef]

2000 (2)

D. Sukow and D. Gauthier, “Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current,” IEEE J. Quantum Electron. 36, 175-183 (2000).
[CrossRef]

S. Hwang and J. Liu, “Dynamical characteristic of an optically injected semiconductor laser,” Opt. Commun. 183, 195-205 (2000).
[CrossRef]

1999 (1)

A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148-1151 (1999).
[CrossRef]

1998 (1)

G. van Tartwijk and G. Agrawal, “Laser instabilities: a modern perspective,” Prog. Quantum Electron. 22, 43-122 (1998).
[CrossRef]

1997 (1)

A. Hohl, A. Gavrielides, T. Erneus, and V. Kovanis, “Localized synchronization in two-coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745-4748 (1997).
[CrossRef]

1995 (2)

K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).
[CrossRef]

T. Simpson, J. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7, 709-711 (1995).
[CrossRef]

1988 (1)

I. Petitbon and P. Gallion, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron. 24, 148-154 (1988).
[CrossRef]

1985 (1)

C. Henry, N. Olsson, and N. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21, 1152-1156 (1985).
[CrossRef]

1982 (1)

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976-983 (1982).
[CrossRef]

Agrawal, G.

G. van Tartwijk and G. Agrawal, “Laser instabilities: a modern perspective,” Prog. Quantum Electron. 22, 43-122 (1998).
[CrossRef]

Blondel, M.

F. Rogister and M. Blondel, “Dynamics of two mutually delay-coupled semiconductor lasers,” Opt. Commun. 239, 173-180 (2004).
[CrossRef]

Chen, J.

L. Zhang, R. Dou, and J. Chen, “Analysis of the phase-locked laser diode array with an external cavity,” Semicond. Sci. Technol. 22, 1253-1257 (2007).
[CrossRef]

Chiang, M.

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J. Liu, “Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling,” IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

Colet, P.

T. Heil, J. Mulet, I. Fischer, C. Mirasso, M. Peil, P. Colet, and W. Elsasser, “ON/OFF phase shift keying for chaos encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38, 1162-1169 (2002).
[CrossRef]

Dou, R.

L. Zhang, R. Dou, and J. Chen, “Analysis of the phase-locked laser diode array with an external cavity,” Semicond. Sci. Technol. 22, 1253-1257 (2007).
[CrossRef]

Dutta, N.

C. Henry, N. Olsson, and N. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21, 1152-1156 (1985).
[CrossRef]

Elsasser, W.

T. Heil, J. Mulet, I. Fischer, C. Mirasso, M. Peil, P. Colet, and W. Elsasser, “ON/OFF phase shift keying for chaos encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38, 1162-1169 (2002).
[CrossRef]

Erneus, T.

A. Hohl, A. Gavrielides, T. Erneus, and V. Kovanis, “Localized synchronization in two-coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745-4748 (1997).
[CrossRef]

Fischer, A.

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, “Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback,” IEE Proc. Optoelectron. 148, 233-237(2001).
[CrossRef]

Fischer, I.

T. Heil, J. Mulet, I. Fischer, C. Mirasso, M. Peil, P. Colet, and W. Elsasser, “ON/OFF phase shift keying for chaos encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38, 1162-1169 (2002).
[CrossRef]

Fujiwara, N.

Gallion, P.

I. Petitbon and P. Gallion, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron. 24, 148-154 (1988).
[CrossRef]

Gauthier, D.

D. Sukow and D. Gauthier, “Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current,” IEEE J. Quantum Electron. 36, 175-183 (2000).
[CrossRef]

Gavrielides, A.

A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148-1151 (1999).
[CrossRef]

A. Hohl, A. Gavrielides, T. Erneus, and V. Kovanis, “Localized synchronization in two-coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745-4748 (1997).
[CrossRef]

T. Simpson, J. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7, 709-711 (1995).
[CrossRef]

Heil, T.

T. Heil, J. Mulet, I. Fischer, C. Mirasso, M. Peil, P. Colet, and W. Elsasser, “ON/OFF phase shift keying for chaos encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38, 1162-1169 (2002).
[CrossRef]

Henry, C.

C. Henry, N. Olsson, and N. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21, 1152-1156 (1985).
[CrossRef]

Hohl, A.

A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148-1151 (1999).
[CrossRef]

A. Hohl, A. Gavrielides, T. Erneus, and V. Kovanis, “Localized synchronization in two-coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745-4748 (1997).
[CrossRef]

Hwang, S.

S. Hwang and J. Liu, “Dynamical characteristic of an optically injected semiconductor laser,” Opt. Commun. 183, 195-205 (2000).
[CrossRef]

Kinugawa, S.

A. Uchida, T. Takahashi, S. Kinugawa, and S. Yoshimori, “Dynamics of chaotic oscillations in mutually coupled microchip lasers,” Chaos Solitons Fractals 17, 369-377 (2003).
[CrossRef]

Kovanis, V.

A. Hohl, A. Gavrielides, T. Erneus, and V. Kovanis, “Localized synchronization in two-coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745-4748 (1997).
[CrossRef]

Lang, R.

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976-983 (1982).
[CrossRef]

Lenstra, D.

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, “Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback,” IEE Proc. Optoelectron. 148, 233-237(2001).
[CrossRef]

Li, N.

X. Li, P. Wei, B. Luo, D. Ma, Y. Wang, and N. Li, “Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser,” Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

Li, X.

X. Li, P. Wei, B. Luo, D. Ma, Y. Wang, and N. Li, “Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser,” Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

X. Li, W. Pan, B. Luo, and D. Ma, “Nonlinear dynamics of two mutually injected external-cavity semiconductor lasers,” Semicond. Sci. Technol. 21, 25-34 (2006).
[CrossRef]

Liu, J.

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J. Liu, “Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling,” IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

S. Hwang and J. Liu, “Dynamical characteristic of an optically injected semiconductor laser,” Opt. Commun. 183, 195-205 (2000).
[CrossRef]

T. Simpson, J. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7, 709-711 (1995).
[CrossRef]

Luo, B.

X. Li, W. Pan, B. Luo, and D. Ma, “Nonlinear dynamics of two mutually injected external-cavity semiconductor lasers,” Semicond. Sci. Technol. 21, 25-34 (2006).
[CrossRef]

X. Li, P. Wei, B. Luo, D. Ma, Y. Wang, and N. Li, “Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser,” Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

Ma, D.

X. Li, P. Wei, B. Luo, D. Ma, Y. Wang, and N. Li, “Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser,” Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

X. Li, W. Pan, B. Luo, and D. Ma, “Nonlinear dynamics of two mutually injected external-cavity semiconductor lasers,” Semicond. Sci. Technol. 21, 25-34 (2006).
[CrossRef]

Mirasso, C.

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J. Liu, “Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling,” IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

T. Heil, J. Mulet, I. Fischer, C. Mirasso, M. Peil, P. Colet, and W. Elsasser, “ON/OFF phase shift keying for chaos encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38, 1162-1169 (2002).
[CrossRef]

Mulet, J.

T. Heil, J. Mulet, I. Fischer, C. Mirasso, M. Peil, P. Colet, and W. Elsasser, “ON/OFF phase shift keying for chaos encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38, 1162-1169 (2002).
[CrossRef]

Murakami, A.

A. Murakami, “Phase locking and chaos synchronization in injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 39, 438-447 (2003).
[CrossRef]

Ohtsubo, J.

Olsson, N.

C. Henry, N. Olsson, and N. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21, 1152-1156 (1985).
[CrossRef]

Pan, W.

X. Li, W. Pan, B. Luo, and D. Ma, “Nonlinear dynamics of two mutually injected external-cavity semiconductor lasers,” Semicond. Sci. Technol. 21, 25-34 (2006).
[CrossRef]

Peil, M.

T. Heil, J. Mulet, I. Fischer, C. Mirasso, M. Peil, P. Colet, and W. Elsasser, “ON/OFF phase shift keying for chaos encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38, 1162-1169 (2002).
[CrossRef]

Petermann, K.

K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).
[CrossRef]

Petitbon, I.

I. Petitbon and P. Gallion, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron. 24, 148-154 (1988).
[CrossRef]

Rogister, F.

F. Rogister and M. Blondel, “Dynamics of two mutually delay-coupled semiconductor lasers,” Opt. Commun. 239, 173-180 (2004).
[CrossRef]

Simpson, T.

T. Simpson, J. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7, 709-711 (1995).
[CrossRef]

Sukow, D.

D. Sukow and D. Gauthier, “Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current,” IEEE J. Quantum Electron. 36, 175-183 (2000).
[CrossRef]

Takahashi, T.

A. Uchida, T. Takahashi, S. Kinugawa, and S. Yoshimori, “Dynamics of chaotic oscillations in mutually coupled microchip lasers,” Chaos Solitons Fractals 17, 369-377 (2003).
[CrossRef]

Takiguchi, Y.

Tang, S.

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J. Liu, “Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling,” IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

Uchida, A.

A. Uchida, T. Takahashi, S. Kinugawa, and S. Yoshimori, “Dynamics of chaotic oscillations in mutually coupled microchip lasers,” Chaos Solitons Fractals 17, 369-377 (2003).
[CrossRef]

van Tartwijk, G.

G. van Tartwijk and G. Agrawal, “Laser instabilities: a modern perspective,” Prog. Quantum Electron. 22, 43-122 (1998).
[CrossRef]

Vemuri, G.

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, “Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback,” IEE Proc. Optoelectron. 148, 233-237(2001).
[CrossRef]

Vicente, R.

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J. Liu, “Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling,” IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

Wang, Y.

X. Li, P. Wei, B. Luo, D. Ma, Y. Wang, and N. Li, “Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser,” Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

Wei, P.

X. Li, P. Wei, B. Luo, D. Ma, Y. Wang, and N. Li, “Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser,” Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

Yoshimori, S.

A. Uchida, T. Takahashi, S. Kinugawa, and S. Yoshimori, “Dynamics of chaotic oscillations in mutually coupled microchip lasers,” Chaos Solitons Fractals 17, 369-377 (2003).
[CrossRef]

Yousefi, M.

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, “Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback,” IEE Proc. Optoelectron. 148, 233-237(2001).
[CrossRef]

Zhang, L.

L. Zhang, R. Dou, and J. Chen, “Analysis of the phase-locked laser diode array with an external cavity,” Semicond. Sci. Technol. 22, 1253-1257 (2007).
[CrossRef]

Chaos Solitons Fractals (2)

X. Li, P. Wei, B. Luo, D. Ma, Y. Wang, and N. Li, “Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser,” Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

A. Uchida, T. Takahashi, S. Kinugawa, and S. Yoshimori, “Dynamics of chaotic oscillations in mutually coupled microchip lasers,” Chaos Solitons Fractals 17, 369-377 (2003).
[CrossRef]

IEE Proc. Optoelectron. (1)

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, “Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback,” IEE Proc. Optoelectron. 148, 233-237(2001).
[CrossRef]

IEEE J. Quantum Electron. (6)

T. Heil, J. Mulet, I. Fischer, C. Mirasso, M. Peil, P. Colet, and W. Elsasser, “ON/OFF phase shift keying for chaos encrypted communication using external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 38, 1162-1169 (2002).
[CrossRef]

I. Petitbon and P. Gallion, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron. 24, 148-154 (1988).
[CrossRef]

C. Henry, N. Olsson, and N. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21, 1152-1156 (1985).
[CrossRef]

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976-983 (1982).
[CrossRef]

A. Murakami, “Phase locking and chaos synchronization in injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 39, 438-447 (2003).
[CrossRef]

D. Sukow and D. Gauthier, “Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current,” IEEE J. Quantum Electron. 36, 175-183 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J. Liu, “Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling,” IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

T. Simpson, J. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photonics Technol. Lett. 7, 709-711 (1995).
[CrossRef]

Opt. Commun. (2)

S. Hwang and J. Liu, “Dynamical characteristic of an optically injected semiconductor laser,” Opt. Commun. 183, 195-205 (2000).
[CrossRef]

F. Rogister and M. Blondel, “Dynamics of two mutually delay-coupled semiconductor lasers,” Opt. Commun. 239, 173-180 (2004).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

A. Hohl, A. Gavrielides, T. Erneus, and V. Kovanis, “Localized synchronization in two-coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745-4748 (1997).
[CrossRef]

A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148-1151 (1999).
[CrossRef]

Prog. Quantum Electron. (1)

G. van Tartwijk and G. Agrawal, “Laser instabilities: a modern perspective,” Prog. Quantum Electron. 22, 43-122 (1998).
[CrossRef]

Semicond. Sci. Technol. (2)

X. Li, W. Pan, B. Luo, and D. Ma, “Nonlinear dynamics of two mutually injected external-cavity semiconductor lasers,” Semicond. Sci. Technol. 21, 25-34 (2006).
[CrossRef]

L. Zhang, R. Dou, and J. Chen, “Analysis of the phase-locked laser diode array with an external cavity,” Semicond. Sci. Technol. 22, 1253-1257 (2007).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Carrier density N versus phase difference Φ with different positive frequency detuning, respectively. (b) Carrier density N versus phase difference Φ with different negative frequency detuning, respectively.

Fig. 2
Fig. 2

(a) Photon density P versus phase difference Φ with different positive frequency detuning, respectively. (b) Photon density P versus phase difference Φ with different negative frequency detuning, respectively.

Fig. 3
Fig. 3

Photon density P versus carrier density N with different injected photon density N p , respectively.

Fig. 4
Fig. 4

(a) Injected photon density P i versus phase difference Φ with different positive frequency detuning, respectively. (b) Injected photon density P i versus phase difference Φ with different negative frequency detuning, respectively.

Equations (41)

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

d P ( t ) d t = P ( t ) g [ N ( t ) N t ] + 2 τ P ( t ) P i cos [ Φ ( t ) ] ,
d Φ ( t ) d t = ω s ω m + 1 2 β g [ N ( t ) N t ] 1 τ P i P ( t ) sin [ Φ ( t ) ] ,
d N ( t ) d t = N P T e N ( t ) T e { T ph 1 + g [ N ( t ) N t ] } P ( t ) ,
P g [ N N t ] + 2 τ P P i cos ( Φ ) = 0 ,
ω s ω m + 1 2 β g [ N N t ] 1 τ P i P sin ( Φ ) = 0 ,
N P T e N T e { T ph 1 + g [ N N t ] } P = 0.
N = 2 ω g [ β + tan ( Φ ) ] + N t ,
P = N p 2 ω g [ β + tan ( Φ ) ] N t T e { T ph 1 + 2 ω g [ β + tan ( Φ ) ] } .
g ( N N t ) = 2 τ P i P cos ( Φ ) .
P i = P τ ω β cos ( Φ ) + sin ( Φ ) .
T ph 1 + g [ N N t ] > 0 ,
0 < 2 ω g [ β + tan ( Φ ) ] + N t < N p ,
P τ ω β cos ( Φ ) + sin ( Φ ) > 0.
π + γ < Φ < 2 π + η ,
γ = arctan [ 2 ω ( N p N t ) g β ] ,
η = arctan ( 2 ω T ph β ) .
η < Φ < π + γ ,
γ = arctan [ 2 ω ( N p N t ) g β ] ,
η = arctan ( 2 ω T ph β ) .
P ( t ) = W ( t ) ,
W ( t ) = W + δ W ( t ) ,
Φ ( t ) = Φ + δ Φ ( t ) ,
N ( t ) = N + δ N ( t ) .
δ W ˙ ( t ) = a 11 δ W ( t ) + a 12 δ Φ ( t ) + a 13 δ N ( t ) ,
δ Φ ˙ ( t ) = a 21 δ W ( t ) + a 22 δ Φ ( t ) + a 33 δ N ( t ) ,
δ N ˙ ( t ) = a 31 δ W ( t ) + a 32 δ Φ ( t ) + a 33 δ N ( t ) ,
a 11 = 1 2 g ( N N t ) , a 12 = 1 τ P i sin ( Φ ) , a 13 = 1 2 W g , a 21 = 1 τ P i W 2 sin ( Φ ) , a 22 = 1 τ P i W cos ( Φ ) , a 23 = 1 2 β g , a 31 = 2 W [ T ph 1 + g ( N N t ) ] , a 32 = 0 , a 33 = ( T e 1 + g W 2 ) .
δ W ( t ) = X exp ( K t ) ,
δ Φ ( t ) = Y exp ( K t ) ,
δ N ( t ) = Z exp ( K t ) .
[ K δ W ( t ) K δ Φ ( t ) K δ N ( t ) ] = [ a 11 a 12 a 13 a 21 a 22 a 23 a 31 0 a 33 ] [ δ W ( t ) δ Φ ( t ) δ N ( t ) ] .
| a 11 K a 12 a 13 a 21 a 22 K a 23 a 31 0 a 33 K | = 0.
[ 1 2 g ( N N t ) K ] [ 1 τ P i W cos ( Φ ) K ] [ ( T e 1 + g W 2 ) K ] + Q τ β g W P i [ T ph 1 + g ( N N t ) ] sin ( Φ ) + W 2 g [ T ph 1 + g ( N N t ) ] [ 1 τ P i W cos ( Φ ) K ] + Q τ 2 W 2 P i sin 2 ( Φ ) [ ( T e 1 + g W 2 ) K ] = 0.
[ 1 τ P i W K ] × { [ 1 2 g ( N N t ) K ] [ ( T e 1 + g W 2 ) K ] + W 2 g [ T ph 1 + g ( N N t ) ] } = 0.
K 1 = 1 τ P i W .
K 2 ( a 11 + a 33 ) K + a 11 a 33 a 13 a 31 = 0.
K 2 = ( a 11 + a 33 ) + Δ 2 ,
K 3 = ( a 11 + a 33 ) Δ 2 ,
Δ = ( a 11 + a 33 ) 2 4 a 11 a 33 + 4 a 13 a 31 .
[ 1 τ P i W K ] × { [ 1 2 g ( N N t ) K ] [ ( T e 1 + g W 2 ) K ] + W 2 g [ T ph 1 + g ( N N t ) ] } = 0.
K 1 = 1 τ P i W .

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