Abstract

We show the advantages of controlling the unstable dynamics of a semiconductor laser subject to conventional optical feedback by means of a second filtered feedback branch. We give an overview of the analytical solutions of the double cavity feedback and show numerically that the region of stabilization is much larger when using a second branch with filtered feedback than when using a conventional feedback one.

© 2009 OSA

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  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 437(7066), 343–346 (2005).
    [CrossRef]
  2. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64(11), 1196–1199 (1990).
    [CrossRef]
  3. K. Pyragas, “Continuous control of chaos by self-controlling feedback,” Phys. Lett. A 170(6), 421–428 (1992).
    [CrossRef]
  4. E. Schöll and K. Pyragas, “Tunable semiconductor oscillator based on self-control of chaos in the dynamic hall effect,” Europhys. Lett. 24(3), 159–164 (1993).
    [CrossRef]
  5. C. Lourenço and A. Babloyantz, “Control of chaos in networks with delay: A model for synchronization of cortical tissue,” Neural Comput. 6(6), 1141–1154 (1994).
    [CrossRef]
  6. F. R. Ruiz-Oliveras and A. N. Pisarchik, “Phase-locking phenomenon in a semiconductor laser with external cavities,” Opt. Express 14(26), 12859–12867 (2006).
    [CrossRef]
  7. H. Erzgräber, D. Lenstra, B. Krauskopf, A. P. Fischer, and G. Vemuri, “Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: experiment and theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026212 (2007).
    [CrossRef]
  8. 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(5-6), 233–237 (2001).
    [CrossRef]
  9. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
    [CrossRef]
  10. B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
    [CrossRef]
  11. M. Wolfrum and D. Turaev, “Instabilities of lasers with moderately delayed optical feedback,” Opt. Commun. 212(1-3), 127–138 (2002).
    [CrossRef]
  12. V. Z. Tronciu, H.-J. Wünsche, M. Wolfrum, and M. Radziunas, “Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046205 (2006).
    [CrossRef]
  13. V. Z. Tronciu, I. V. Ermakov, P. Colet, and C. R. Mirasso, “Chaotic dynamics of a semiconductor laser with double cavity feedback: Applications to phase shift keying modulation,” Opt. Commun. 281(18), 4747–4752 (2008).
    [CrossRef]

2008 (1)

V. Z. Tronciu, I. V. Ermakov, P. Colet, and C. R. Mirasso, “Chaotic dynamics of a semiconductor laser with double cavity feedback: Applications to phase shift keying modulation,” Opt. Commun. 281(18), 4747–4752 (2008).
[CrossRef]

2007 (1)

H. Erzgräber, D. Lenstra, B. Krauskopf, A. P. Fischer, and G. Vemuri, “Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: experiment and theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026212 (2007).
[CrossRef]

2006 (2)

F. R. Ruiz-Oliveras and A. N. Pisarchik, “Phase-locking phenomenon in a semiconductor laser with external cavities,” Opt. Express 14(26), 12859–12867 (2006).
[CrossRef]

V. Z. Tronciu, H.-J. Wünsche, M. Wolfrum, and M. Radziunas, “Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046205 (2006).
[CrossRef]

2005 (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 437(7066), 343–346 (2005).
[CrossRef]

2002 (1)

M. Wolfrum and D. Turaev, “Instabilities of lasers with moderately delayed optical feedback,” Opt. Commun. 212(1-3), 127–138 (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(5-6), 233–237 (2001).
[CrossRef]

1994 (1)

C. Lourenço and A. Babloyantz, “Control of chaos in networks with delay: A model for synchronization of cortical tissue,” Neural Comput. 6(6), 1141–1154 (1994).
[CrossRef]

1993 (1)

E. Schöll and K. Pyragas, “Tunable semiconductor oscillator based on self-control of chaos in the dynamic hall effect,” Europhys. Lett. 24(3), 159–164 (1993).
[CrossRef]

1992 (1)

K. Pyragas, “Continuous control of chaos by self-controlling feedback,” Phys. Lett. A 170(6), 421–428 (1992).
[CrossRef]

1990 (1)

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64(11), 1196–1199 (1990).
[CrossRef]

1984 (1)

B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
[CrossRef]

1980 (1)

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

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 437(7066), 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 437(7066), 343–346 (2005).
[CrossRef]

Babloyantz, A.

C. Lourenço and A. Babloyantz, “Control of chaos in networks with delay: A model for synchronization of cortical tissue,” Neural Comput. 6(6), 1141–1154 (1994).
[CrossRef]

Colet, P.

V. Z. Tronciu, I. V. Ermakov, P. Colet, and C. R. Mirasso, “Chaotic dynamics of a semiconductor laser with double cavity feedback: Applications to phase shift keying modulation,” Opt. Commun. 281(18), 4747–4752 (2008).
[CrossRef]

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 437(7066), 343–346 (2005).
[CrossRef]

Ermakov, I. V.

V. Z. Tronciu, I. V. Ermakov, P. Colet, and C. R. Mirasso, “Chaotic dynamics of a semiconductor laser with double cavity feedback: Applications to phase shift keying modulation,” Opt. Commun. 281(18), 4747–4752 (2008).
[CrossRef]

Erzgräber, H.

H. Erzgräber, D. Lenstra, B. Krauskopf, A. P. Fischer, and G. Vemuri, “Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: experiment and theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026212 (2007).
[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(5-6), 233–237 (2001).
[CrossRef]

Fischer, A. P.

H. Erzgräber, D. Lenstra, B. Krauskopf, A. P. Fischer, and G. Vemuri, “Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: experiment and theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026212 (2007).
[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 437(7066), 343–346 (2005).
[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 437(7066), 343–346 (2005).
[CrossRef]

Grebogi, C.

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64(11), 1196–1199 (1990).
[CrossRef]

Kobayashi, K.

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

Krauskopf, B.

H. Erzgräber, D. Lenstra, B. Krauskopf, A. P. Fischer, and G. Vemuri, “Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: experiment and theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026212 (2007).
[CrossRef]

Lang, R.

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

Larger, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef]

Lenstra, D.

H. Erzgräber, D. Lenstra, B. Krauskopf, A. P. Fischer, and G. Vemuri, “Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: experiment and theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026212 (2007).
[CrossRef]

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(5-6), 233–237 (2001).
[CrossRef]

Lourenço, C.

C. Lourenço and A. Babloyantz, “Control of chaos in networks with delay: A model for synchronization of cortical tissue,” Neural Comput. 6(6), 1141–1154 (1994).
[CrossRef]

Mirasso, C. R.

V. Z. Tronciu, I. V. Ermakov, P. Colet, and C. R. Mirasso, “Chaotic dynamics of a semiconductor laser with double cavity feedback: Applications to phase shift keying modulation,” Opt. Commun. 281(18), 4747–4752 (2008).
[CrossRef]

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 437(7066), 343–346 (2005).
[CrossRef]

Olesen, H.

B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
[CrossRef]

Osmundsen, J. H.

B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
[CrossRef]

Ott, E.

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64(11), 1196–1199 (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 437(7066), 343–346 (2005).
[CrossRef]

Pisarchik, A. N.

Pyragas, K.

E. Schöll and K. Pyragas, “Tunable semiconductor oscillator based on self-control of chaos in the dynamic hall effect,” Europhys. Lett. 24(3), 159–164 (1993).
[CrossRef]

K. Pyragas, “Continuous control of chaos by self-controlling feedback,” Phys. Lett. A 170(6), 421–428 (1992).
[CrossRef]

Radziunas, M.

V. Z. Tronciu, H.-J. Wünsche, M. Wolfrum, and M. Radziunas, “Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046205 (2006).
[CrossRef]

Ruiz-Oliveras, F. R.

Schöll, E.

E. Schöll and K. Pyragas, “Tunable semiconductor oscillator based on self-control of chaos in the dynamic hall effect,” Europhys. Lett. 24(3), 159–164 (1993).
[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 437(7066), 343–346 (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 437(7066), 343–346 (2005).
[CrossRef]

Tromborg, B.

B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
[CrossRef]

Tronciu, V. Z.

V. Z. Tronciu, I. V. Ermakov, P. Colet, and C. R. Mirasso, “Chaotic dynamics of a semiconductor laser with double cavity feedback: Applications to phase shift keying modulation,” Opt. Commun. 281(18), 4747–4752 (2008).
[CrossRef]

V. Z. Tronciu, H.-J. Wünsche, M. Wolfrum, and M. Radziunas, “Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046205 (2006).
[CrossRef]

Turaev, D.

M. Wolfrum and D. Turaev, “Instabilities of lasers with moderately delayed optical feedback,” Opt. Commun. 212(1-3), 127–138 (2002).
[CrossRef]

Vemuri, G.

H. Erzgräber, D. Lenstra, B. Krauskopf, A. P. Fischer, and G. Vemuri, “Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: experiment and theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026212 (2007).
[CrossRef]

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(5-6), 233–237 (2001).
[CrossRef]

Wolfrum, M.

V. Z. Tronciu, H.-J. Wünsche, M. Wolfrum, and M. Radziunas, “Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046205 (2006).
[CrossRef]

M. Wolfrum and D. Turaev, “Instabilities of lasers with moderately delayed optical feedback,” Opt. Commun. 212(1-3), 127–138 (2002).
[CrossRef]

Wünsche, H.-J.

V. Z. Tronciu, H.-J. Wünsche, M. Wolfrum, and M. Radziunas, “Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046205 (2006).
[CrossRef]

Yorke, J. A.

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64(11), 1196–1199 (1990).
[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(5-6), 233–237 (2001).
[CrossRef]

Europhys. Lett. (1)

E. Schöll and K. Pyragas, “Tunable semiconductor oscillator based on self-control of chaos in the dynamic hall effect,” Europhys. Lett. 24(3), 159–164 (1993).
[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(5-6), 233–237 (2001).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

B. Tromborg, J. H. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20(9), 1023–1032 (1984).
[CrossRef]

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 437(7066), 343–346 (2005).
[CrossRef]

Neural Comput. (1)

C. Lourenço and A. Babloyantz, “Control of chaos in networks with delay: A model for synchronization of cortical tissue,” Neural Comput. 6(6), 1141–1154 (1994).
[CrossRef]

Opt. Commun. (2)

M. Wolfrum and D. Turaev, “Instabilities of lasers with moderately delayed optical feedback,” Opt. Commun. 212(1-3), 127–138 (2002).
[CrossRef]

V. Z. Tronciu, I. V. Ermakov, P. Colet, and C. R. Mirasso, “Chaotic dynamics of a semiconductor laser with double cavity feedback: Applications to phase shift keying modulation,” Opt. Commun. 281(18), 4747–4752 (2008).
[CrossRef]

Opt. Express (1)

Phys. Lett. A (1)

K. Pyragas, “Continuous control of chaos by self-controlling feedback,” Phys. Lett. A 170(6), 421–428 (1992).
[CrossRef]

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

V. Z. Tronciu, H.-J. Wünsche, M. Wolfrum, and M. Radziunas, “Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046205 (2006).
[CrossRef]

H. Erzgräber, D. Lenstra, B. Krauskopf, A. P. Fischer, and G. Vemuri, “Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: experiment and theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026212 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64(11), 1196–1199 (1990).
[CrossRef]

Supplementary Material (21)

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