Abstract

A model of a semiconductor laser with weak-to-moderate optical feedback generalizing Lang–Kobayashi equations to the case of incoherent feedback is presented. It is shown that the transition from coherent to incoherent feedback through increasing spontaneous noise leads to replacement of dynamic chaos by almost stationary lasing with slightly fluctuating intensity. In the case of incoherent feedback, the proposed model has fluctuating solutions only, so it is impossible to build a purely dynamic model of the semiconductor laser with incoherent feedback.

© 2014 Optical Society of America

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References

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  1. J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2007).
  2. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821–824 (1990).
    [CrossRef]
  3. P. Colet and R. Roy, “Digital communication with synchronized chaotic lasers,” Opt. Lett. 19, 2056–2058 (1994).
    [CrossRef]
  4. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
    [CrossRef]
  5. T. Morikawa, Y. Mitsuhashi, J. Shimada, and Y. Kojima, “Return-beam-induced oscillations in self-coupled semiconductor lasers,” Electron. Lett. 12, 435–436 (1976).
    [CrossRef]
  6. C. Risch and C. Voumard, “Self-pulsation in the output intensity and spectrum of GaAs-AlGaAs cw diode lasers coupled to a frequency-selective external optical cavity,” J. Appl. Phys. 48, 2083–2085 (1977).
    [CrossRef]
  7. I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76, 220–223 (1996).
    [CrossRef]
  8. K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 480–489 (1995).
    [CrossRef]
  9. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [CrossRef]
  10. H. Yasaka, Y. Yoshikuni, and H. Kawaguchi, “FM noise and spectral linewidth reduction by incoherent optical negative feedback,” IEEE J. Quantum Electron. 27, 193–204 (1991).
    [CrossRef]
  11. K. Otsuka and J. L. Chen, “High-speed picosecond pulse generation in semiconductor lasers with incoherent optical feedback,” Opt. Lett. 16, 1759–1761 (1991).
    [CrossRef]
  12. J. L. Chen, K. Otsuka, and F. Ishiyama, “Coexistence of two attractors in lasers with delayed incoherent optical feedback,” Opt. Commun. 96, 259–266 (1993).
    [CrossRef]
  13. F. Ishiyama, “Bistability of quasi periodicity and period doubling in a delay-induced system,” J. Opt. Soc. Am. B 16, 2202–2206 (1999).
    [CrossRef]
  14. R. Ju and P. S. Spencer, “Dynamical regimes in semiconductor lasers subject to incoherent optical feedback,” J. Lightwave Technol. 23, 2513–2523 (2005).
    [CrossRef]
  15. R. Ju, Y. Hong, and P. S. Spencer, “Semiconductor lasers subject to polarisation rotated optical feedback,” IEE Proc.—Optoelectron. 153, 131–137 (2006).
  16. J. Houlihan, G. Huyet, and J. G. McInerney, “Dynamics of a semiconductor laser with incoherent optical feedback,” Opt. Commun. 199, 175–179 (2001).
    [CrossRef]
  17. T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
    [CrossRef]
  18. M. Lax, Fluctuation and Coherence Phenomena in Classical and Quantum Physics (Gordon and Breach, 1968).
  19. P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53, 4429–4434 (1996).
    [CrossRef]
  20. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
    [CrossRef]
  21. C. H. Henry, “Theory of the phase noise and power spectrum of a single mode injection laser,” IEEE J. Quantum Electron. 19, 1391–1397 (1983).
    [CrossRef]
  22. E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, 1987).
  23. R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: the TISEAN package,” Chaos 9, 413–435 (1999).
    [CrossRef]
  24. I. V. Koryukin, “Dynamics of a single-mode semiconductor laser with incoherent optical feedback,” arXiv:1310.7358 (2013).

2006 (1)

R. Ju, Y. Hong, and P. S. Spencer, “Semiconductor lasers subject to polarisation rotated optical feedback,” IEE Proc.—Optoelectron. 153, 131–137 (2006).

2005 (2)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

R. Ju and P. S. Spencer, “Dynamical regimes in semiconductor lasers subject to incoherent optical feedback,” J. Lightwave Technol. 23, 2513–2523 (2005).
[CrossRef]

2003 (1)

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

2001 (1)

J. Houlihan, G. Huyet, and J. G. McInerney, “Dynamics of a semiconductor laser with incoherent optical feedback,” Opt. Commun. 199, 175–179 (2001).
[CrossRef]

1999 (2)

R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: the TISEAN package,” Chaos 9, 413–435 (1999).
[CrossRef]

F. Ishiyama, “Bistability of quasi periodicity and period doubling in a delay-induced system,” J. Opt. Soc. Am. B 16, 2202–2206 (1999).
[CrossRef]

1996 (2)

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53, 4429–4434 (1996).
[CrossRef]

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76, 220–223 (1996).
[CrossRef]

1995 (1)

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

1994 (1)

1993 (1)

J. L. Chen, K. Otsuka, and F. Ishiyama, “Coexistence of two attractors in lasers with delayed incoherent optical feedback,” Opt. Commun. 96, 259–266 (1993).
[CrossRef]

1991 (2)

H. Yasaka, Y. Yoshikuni, and H. Kawaguchi, “FM noise and spectral linewidth reduction by incoherent optical negative feedback,” IEEE J. Quantum Electron. 27, 193–204 (1991).
[CrossRef]

K. Otsuka and J. L. Chen, “High-speed picosecond pulse generation in semiconductor lasers with incoherent optical feedback,” Opt. Lett. 16, 1759–1761 (1991).
[CrossRef]

1990 (1)

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821–824 (1990).
[CrossRef]

1983 (1)

C. H. Henry, “Theory of the phase noise and power spectrum of a single mode injection laser,” IEEE J. Quantum Electron. 19, 1391–1397 (1983).
[CrossRef]

1982 (1)

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

1980 (1)

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

1977 (1)

C. Risch and C. Voumard, “Self-pulsation in the output intensity and spectrum of GaAs-AlGaAs cw diode lasers coupled to a frequency-selective external optical cavity,” J. Appl. Phys. 48, 2083–2085 (1977).
[CrossRef]

1976 (1)

T. Morikawa, Y. Mitsuhashi, J. Shimada, and Y. Kojima, “Return-beam-induced oscillations in self-coupled semiconductor lasers,” Electron. Lett. 12, 435–436 (1976).
[CrossRef]

Aida, T.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Alsing, P. M.

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53, 4429–4434 (1996).
[CrossRef]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

Argyris, A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

Carroll, T. L.

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821–824 (1990).
[CrossRef]

Chen, J. L.

J. L. Chen, K. Otsuka, and F. Ishiyama, “Coexistence of two attractors in lasers with delayed incoherent optical feedback,” Opt. Commun. 96, 259–266 (1993).
[CrossRef]

K. Otsuka and J. L. Chen, “High-speed picosecond pulse generation in semiconductor lasers with incoherent optical feedback,” Opt. Lett. 16, 1759–1761 (1991).
[CrossRef]

Colet, P.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

P. Colet and R. Roy, “Digital communication with synchronized chaotic lasers,” Opt. Lett. 19, 2056–2058 (1994).
[CrossRef]

Davis, P.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Elsasser, W.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76, 220–223 (1996).
[CrossRef]

Erneux, T.

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53, 4429–4434 (1996).
[CrossRef]

Fischer, I.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76, 220–223 (1996).
[CrossRef]

García-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

Gavrielides, A.

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53, 4429–4434 (1996).
[CrossRef]

Gobel, E.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76, 220–223 (1996).
[CrossRef]

Hairer, E.

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, 1987).

Hegger, R.

R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: the TISEAN package,” Chaos 9, 413–435 (1999).
[CrossRef]

Heil, T.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Henry, C. H.

C. H. Henry, “Theory of the phase noise and power spectrum of a single mode injection laser,” IEEE J. Quantum Electron. 19, 1391–1397 (1983).
[CrossRef]

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

Hong, Y.

R. Ju, Y. Hong, and P. S. Spencer, “Semiconductor lasers subject to polarisation rotated optical feedback,” IEE Proc.—Optoelectron. 153, 131–137 (2006).

Houlihan, J.

J. Houlihan, G. Huyet, and J. G. McInerney, “Dynamics of a semiconductor laser with incoherent optical feedback,” Opt. Commun. 199, 175–179 (2001).
[CrossRef]

Huyet, G.

J. Houlihan, G. Huyet, and J. G. McInerney, “Dynamics of a semiconductor laser with incoherent optical feedback,” Opt. Commun. 199, 175–179 (2001).
[CrossRef]

Ishiyama, F.

F. Ishiyama, “Bistability of quasi periodicity and period doubling in a delay-induced system,” J. Opt. Soc. Am. B 16, 2202–2206 (1999).
[CrossRef]

J. L. Chen, K. Otsuka, and F. Ishiyama, “Coexistence of two attractors in lasers with delayed incoherent optical feedback,” Opt. Commun. 96, 259–266 (1993).
[CrossRef]

Ju, R.

R. Ju, Y. Hong, and P. S. Spencer, “Semiconductor lasers subject to polarisation rotated optical feedback,” IEE Proc.—Optoelectron. 153, 131–137 (2006).

R. Ju and P. S. Spencer, “Dynamical regimes in semiconductor lasers subject to incoherent optical feedback,” J. Lightwave Technol. 23, 2513–2523 (2005).
[CrossRef]

Kantz, H.

R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: the TISEAN package,” Chaos 9, 413–435 (1999).
[CrossRef]

Kawaguchi, H.

H. Yasaka, Y. Yoshikuni, and H. Kawaguchi, “FM noise and spectral linewidth reduction by incoherent optical negative feedback,” IEEE J. Quantum Electron. 27, 193–204 (1991).
[CrossRef]

Kobayashi, K.

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

Kojima, Y.

T. Morikawa, Y. Mitsuhashi, J. Shimada, and Y. Kojima, “Return-beam-induced oscillations in self-coupled semiconductor lasers,” Electron. Lett. 12, 435–436 (1976).
[CrossRef]

Koryukin, I. V.

I. V. Koryukin, “Dynamics of a single-mode semiconductor laser with incoherent optical feedback,” arXiv:1310.7358 (2013).

Kovanis, V.

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53, 4429–4434 (1996).
[CrossRef]

Lang, R.

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

Larger, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

Lax, M.

M. Lax, Fluctuation and Coherence Phenomena in Classical and Quantum Physics (Gordon and Breach, 1968).

Lenstra, D.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76, 220–223 (1996).
[CrossRef]

Levine, A. M.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76, 220–223 (1996).
[CrossRef]

McInerney, J. G.

J. Houlihan, G. Huyet, and J. G. McInerney, “Dynamics of a semiconductor laser with incoherent optical feedback,” Opt. Commun. 199, 175–179 (2001).
[CrossRef]

Mirasso, C. R.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

Mitsuhashi, Y.

T. Morikawa, Y. Mitsuhashi, J. Shimada, and Y. Kojima, “Return-beam-induced oscillations in self-coupled semiconductor lasers,” Electron. Lett. 12, 435–436 (1976).
[CrossRef]

Morikawa, T.

T. Morikawa, Y. Mitsuhashi, J. Shimada, and Y. Kojima, “Return-beam-induced oscillations in self-coupled semiconductor lasers,” Electron. Lett. 12, 435–436 (1976).
[CrossRef]

Norsett, S. P.

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, 1987).

Ohtsubo, J.

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2007).

Otsuka, K.

J. L. Chen, K. Otsuka, and F. Ishiyama, “Coexistence of two attractors in lasers with delayed incoherent optical feedback,” Opt. Commun. 96, 259–266 (1993).
[CrossRef]

K. Otsuka and J. L. Chen, “High-speed picosecond pulse generation in semiconductor lasers with incoherent optical feedback,” Opt. Lett. 16, 1759–1761 (1991).
[CrossRef]

Pecora, L. M.

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821–824 (1990).
[CrossRef]

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

Petermann, K.

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

Risch, C.

C. Risch and C. Voumard, “Self-pulsation in the output intensity and spectrum of GaAs-AlGaAs cw diode lasers coupled to a frequency-selective external optical cavity,” J. Appl. Phys. 48, 2083–2085 (1977).
[CrossRef]

Roy, R.

Schreiber, T.

R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: the TISEAN package,” Chaos 9, 413–435 (1999).
[CrossRef]

Shimada, J.

T. Morikawa, Y. Mitsuhashi, J. Shimada, and Y. Kojima, “Return-beam-induced oscillations in self-coupled semiconductor lasers,” Electron. Lett. 12, 435–436 (1976).
[CrossRef]

Shore, K. A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

Spencer, P. S.

R. Ju, Y. Hong, and P. S. Spencer, “Semiconductor lasers subject to polarisation rotated optical feedback,” IEE Proc.—Optoelectron. 153, 131–137 (2006).

R. Ju and P. S. Spencer, “Dynamical regimes in semiconductor lasers subject to incoherent optical feedback,” J. Lightwave Technol. 23, 2513–2523 (2005).
[CrossRef]

Syvridis, D.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

Uchida, A.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

van Tartwijk, G. H. M.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76, 220–223 (1996).
[CrossRef]

Voumard, C.

C. Risch and C. Voumard, “Self-pulsation in the output intensity and spectrum of GaAs-AlGaAs cw diode lasers coupled to a frequency-selective external optical cavity,” J. Appl. Phys. 48, 2083–2085 (1977).
[CrossRef]

Wanner, G.

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, 1987).

Yasaka, H.

H. Yasaka, Y. Yoshikuni, and H. Kawaguchi, “FM noise and spectral linewidth reduction by incoherent optical negative feedback,” IEEE J. Quantum Electron. 27, 193–204 (1991).
[CrossRef]

Yoshikuni, Y.

H. Yasaka, Y. Yoshikuni, and H. Kawaguchi, “FM noise and spectral linewidth reduction by incoherent optical negative feedback,” IEEE J. Quantum Electron. 27, 193–204 (1991).
[CrossRef]

Chaos (1)

R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: the TISEAN package,” Chaos 9, 413–435 (1999).
[CrossRef]

Electron. Lett. (1)

T. Morikawa, Y. Mitsuhashi, J. Shimada, and Y. Kojima, “Return-beam-induced oscillations in self-coupled semiconductor lasers,” Electron. Lett. 12, 435–436 (1976).
[CrossRef]

IEE Proc.—Optoelectron. (1)

R. Ju, Y. Hong, and P. S. Spencer, “Semiconductor lasers subject to polarisation rotated optical feedback,” IEE Proc.—Optoelectron. 153, 131–137 (2006).

IEEE J. Quantum Electron. (4)

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

H. Yasaka, Y. Yoshikuni, and H. Kawaguchi, “FM noise and spectral linewidth reduction by incoherent optical negative feedback,” IEEE J. Quantum Electron. 27, 193–204 (1991).
[CrossRef]

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

C. H. Henry, “Theory of the phase noise and power spectrum of a single mode injection laser,” IEEE J. Quantum Electron. 19, 1391–1397 (1983).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

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

J. Appl. Phys. (1)

C. Risch and C. Voumard, “Self-pulsation in the output intensity and spectrum of GaAs-AlGaAs cw diode lasers coupled to a frequency-selective external optical cavity,” J. Appl. Phys. 48, 2083–2085 (1977).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
[CrossRef]

Opt. Commun. (2)

J. L. Chen, K. Otsuka, and F. Ishiyama, “Coexistence of two attractors in lasers with delayed incoherent optical feedback,” Opt. Commun. 96, 259–266 (1993).
[CrossRef]

J. Houlihan, G. Huyet, and J. G. McInerney, “Dynamics of a semiconductor laser with incoherent optical feedback,” Opt. Commun. 199, 175–179 (2001).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[CrossRef]

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53, 4429–4434 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76, 220–223 (1996).
[CrossRef]

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821–824 (1990).
[CrossRef]

Other (4)

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2007).

M. Lax, Fluctuation and Coherence Phenomena in Classical and Quantum Physics (Gordon and Breach, 1968).

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, 1987).

I. V. Koryukin, “Dynamics of a single-mode semiconductor laser with incoherent optical feedback,” arXiv:1310.7358 (2013).

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Figures (5)

Fig. 1.
Fig. 1.

Time-dependent solution of model (3) for P=103, η=0.01. (a) Laser intensity and (b) averaged laser intensity for coherent feedback ρ=0 (LFF); (c) laser intensity for incoherent feedback ρ=0.05. The averaging time for plot (b) is 2 ns.

Fig. 2.
Fig. 2.

Transition from coherent to incoherent feedback with an increase in spontaneous emission rate. (a)–(d) Behavior of the phase difference between internal and feedback field; (e)–(h) correlation function of this phase difference. P=103, η=0.01, (a), (e) ρ=0; (b), (f) ρ=2×104; (c), (g) ρ=4×104; (b), (f) ρ=0.05.

Fig. 3.
Fig. 3.

Power spectral density of the laser intensity and correlation dimension for (a), (c) coherent feedback ρ=0 (LFF) and (b), (d) incoherent feedback ρ=0.05. Other parameters as in Fig. 1. Embedding dimension varies from 1 to 8 for different plots in (c), (d).

Fig. 4.
Fig. 4.

Time-dependent solution of model (3) for P=0.3, η=0.0075. (a), (c) Laser intensity for coherent feedback ρ=0 (DRO); (b), (d) laser intensity for incoherent feedback ρ=0.05.

Fig. 5.
Fig. 5.

Power spectral density of the laser intensity and correlation dimension for (a), (c) coherent feedback ρ=0 (DRO) and (b), (d) incoherent feedback ρ=0.05. Other parameters as in Fig. 4. The embedding dimension varies from 1 to 8 for different plots in (c), (d).

Equations (6)

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dE(t)dt=(1+iα)N(t)E(t)+ηE(tτ)eiΩτ+FE(t),TdN(t)dt=PN(t)(1+2N(t))|E(t)|2+FN(t),
FA(t)=0andFA(t)FB(t)=2DABδ(tt).
dI(t)dt=2N(t)I(t)+2ηI(t)I(tτ)cos[φ(tτ)φ(t)+Ωτ]+FI(t),dφ(t)dt=αN(t)+ηI(t)/I(tτ)sin[φ(tτ)φ(t)+Ωτ]+Fφ(t),TdN(t)dt=PN(t)(1+2N(t))I(t)+FN(t).
Δφi=sin(θi)/I,ΔIi=1+2Icos(θi),ΔNi=1,
Δφi=ρsin(θi)/I,ΔIi=ρ(1+2Icos(θi)),ΔNi=ρ2,
τcoh=4IRsp(1+α2),

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