Abstract

It is shown theoretically that the method of time delayed incoherent optical feedback ensures control of chaotic dynamics in the vibronic alexandrite laser. The numerical solutions of the laser equations including the optical delayed feedback term are presented and the conditions for stabilization of the laser output are discussed. The possibility of synchronization of two chaotic vibronic lasers is reported when one of them is driven by the output of the other, thus giving the basis for secure communication.

© 2009 OSA

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  1. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64(11), 1196–1199 (1990).
    [CrossRef] [PubMed]
  2. F. T. Arecchi, W. Gadomski, and R. Meucci, “Generation of chaotic dynamics by feedback on a laser,” Phys. Rev. A 34(2), 1617–1620 (1986).
    [CrossRef] [PubMed]
  3. F. T. Arecchi, R. Meucci, and W. Gadomski, “Laser dynamics with competing instabilities,” Phys. Rev. Lett. 58(21), 2205–2208 (1987).
    [CrossRef] [PubMed]
  4. R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by means of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2528–R2531 (1994).
    [CrossRef] [PubMed]
  5. S. Bielawski, D. Derozier, and P. Glorieux, “Controlling unstable periodic orbits by a delayed continuous feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(2), R971–R974 (1994).
    [CrossRef] [PubMed]
  6. R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, “Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68(9), 1259–1262 (1992).
    [CrossRef] [PubMed]
  7. R. Dykstra, D. Y. Tang, and N. R. Heckenberg, “Experimental control of a single-mode laser chaos by using continuous, time-delayed feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(6), 6596–6598 (1998).
    [CrossRef]
  8. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
    [CrossRef]
  9. G. Hek and V. Rottschafer, “Semiconductor laser with filtered optical feedback: bridge between conventional feedback and optical injection”, ENOC-2005, Eindhoven, Netherlands, 7–12 August (2005).
  10. S. Schikora, P. Hövel, H. J. Wünsche, E. Schöll, and F. Henneberger, “All-optical noninvasive control of unstable steady states in a semiconductor laser,” Phys. Rev. Lett. 97(21), 213902 (2006).
    [CrossRef] [PubMed]
  11. M. G. Kovalsky, “On control of Chaos in the Kerr lens mode locked Ti:Sapphire laser,” Opt. Commun. 260(1), 265–270 (2006).
    [CrossRef]
  12. W. Gadomski and B. Ratajska-Gadomska, “Self-pulsations in the phonon assisted lasers,” J. Opt. Soc. Am. B 15(11), 2681–2688 (1998).
    [CrossRef]
  13. W. Gadomski and B. Ratajska-Gadomska, “Homoclinic orbits and chaos in the vibronic short-cavity standing-wave alexandrite laser,” J. Opt. Soc. Am. B 17(2), 188–197 (2000).
    [CrossRef]
  14. W. Gadomski, B. Ratajska-Gadomska, and R. Meucci, “Homoclinic dynamics if the vibronic laser,” Chaos Solitons Fractals 17(2-3), 387–396 (2003).
    [CrossRef]
  15. W. Gadomski and B. Ratajska-Gadomska, “Chaotic dynamics of the vibronic laser” in Recent Advances in Laser Dynamics: Control and Synchronization, A.N. Pisarchik, ed. (Research Signpost, Kerala, India, 2008)
  16. B. Ratajska-Gadomska and W. Gadomski, “Quantum theory of the vibronic solid-state laser,” J. Opt. Soc. Am. B 16(5), 848–860 (1999).
    [CrossRef]
  17. H. Ogilvy, M. J. Withford, R. P. Mildren, J. A. Piper, M. J Withford, R. P Mildren, and J. A Piper, “Investigation of the pump wavelength influence on pulsed laser pumped Alexandrite lasers,” Appl. Phys. B 81(5), 637–644 (2005).
    [CrossRef]
  18. K. Pyragas, “Continuous control of chaos by self-controlling feedback,” Phys. Lett. A 170(6), 421–428 (1992).
    [CrossRef]
  19. J. C. Walling, O. G. Peterson, and R. C. Morris, “Tunable CW Alexandrite Laser,” IEEE J. Quantum Electron. 16(2), 120–121 (1980).
    [CrossRef]
  20. L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Phys. Rev. A 44(4), 2374–2383 (1991).
    [CrossRef] [PubMed]
  21. A. Uchida, S. Yoshimori, M. Shinozuka, T. Ogawa, and F. Kannari, “Chaotic on off keying for secure communications,” Opt. Lett. 26(12), 866–868 (2001).
    [CrossRef]

2006 (2)

S. Schikora, P. Hövel, H. J. Wünsche, E. Schöll, and F. Henneberger, “All-optical noninvasive control of unstable steady states in a semiconductor laser,” Phys. Rev. Lett. 97(21), 213902 (2006).
[CrossRef] [PubMed]

M. G. Kovalsky, “On control of Chaos in the Kerr lens mode locked Ti:Sapphire laser,” Opt. Commun. 260(1), 265–270 (2006).
[CrossRef]

2005 (1)

H. Ogilvy, M. J. Withford, R. P. Mildren, J. A. Piper, M. J Withford, R. P Mildren, and J. A Piper, “Investigation of the pump wavelength influence on pulsed laser pumped Alexandrite lasers,” Appl. Phys. B 81(5), 637–644 (2005).
[CrossRef]

2003 (1)

W. Gadomski, B. Ratajska-Gadomska, and R. Meucci, “Homoclinic dynamics if the vibronic laser,” Chaos Solitons Fractals 17(2-3), 387–396 (2003).
[CrossRef]

2001 (1)

2000 (1)

1999 (1)

1998 (2)

W. Gadomski and B. Ratajska-Gadomska, “Self-pulsations in the phonon assisted lasers,” J. Opt. Soc. Am. B 15(11), 2681–2688 (1998).
[CrossRef]

R. Dykstra, D. Y. Tang, and N. R. Heckenberg, “Experimental control of a single-mode laser chaos by using continuous, time-delayed feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(6), 6596–6598 (1998).
[CrossRef]

1994 (2)

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by means of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2528–R2531 (1994).
[CrossRef] [PubMed]

S. Bielawski, D. Derozier, and P. Glorieux, “Controlling unstable periodic orbits by a delayed continuous feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(2), R971–R974 (1994).
[CrossRef] [PubMed]

1992 (2)

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, “Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68(9), 1259–1262 (1992).
[CrossRef] [PubMed]

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

1991 (1)

L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Phys. Rev. A 44(4), 2374–2383 (1991).
[CrossRef] [PubMed]

1990 (1)

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

1987 (1)

F. T. Arecchi, R. Meucci, and W. Gadomski, “Laser dynamics with competing instabilities,” Phys. Rev. Lett. 58(21), 2205–2208 (1987).
[CrossRef] [PubMed]

1986 (1)

F. T. Arecchi, W. Gadomski, and R. Meucci, “Generation of chaotic dynamics by feedback on a laser,” Phys. Rev. A 34(2), 1617–1620 (1986).
[CrossRef] [PubMed]

1980 (2)

J. C. Walling, O. G. Peterson, and R. C. Morris, “Tunable CW Alexandrite Laser,” IEEE J. Quantum Electron. 16(2), 120–121 (1980).
[CrossRef]

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

Arecchi, F. T.

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by means of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2528–R2531 (1994).
[CrossRef] [PubMed]

F. T. Arecchi, R. Meucci, and W. Gadomski, “Laser dynamics with competing instabilities,” Phys. Rev. Lett. 58(21), 2205–2208 (1987).
[CrossRef] [PubMed]

F. T. Arecchi, W. Gadomski, and R. Meucci, “Generation of chaotic dynamics by feedback on a laser,” Phys. Rev. A 34(2), 1617–1620 (1986).
[CrossRef] [PubMed]

Bielawski, S.

S. Bielawski, D. Derozier, and P. Glorieux, “Controlling unstable periodic orbits by a delayed continuous feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(2), R971–R974 (1994).
[CrossRef] [PubMed]

Carroll, T. L.

L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Phys. Rev. A 44(4), 2374–2383 (1991).
[CrossRef] [PubMed]

Ciofini, M.

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by means of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2528–R2531 (1994).
[CrossRef] [PubMed]

Derozier, D.

S. Bielawski, D. Derozier, and P. Glorieux, “Controlling unstable periodic orbits by a delayed continuous feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(2), R971–R974 (1994).
[CrossRef] [PubMed]

Dykstra, R.

R. Dykstra, D. Y. Tang, and N. R. Heckenberg, “Experimental control of a single-mode laser chaos by using continuous, time-delayed feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(6), 6596–6598 (1998).
[CrossRef]

Gadomski, W.

W. Gadomski, B. Ratajska-Gadomska, and R. Meucci, “Homoclinic dynamics if the vibronic laser,” Chaos Solitons Fractals 17(2-3), 387–396 (2003).
[CrossRef]

W. Gadomski and B. Ratajska-Gadomska, “Homoclinic orbits and chaos in the vibronic short-cavity standing-wave alexandrite laser,” J. Opt. Soc. Am. B 17(2), 188–197 (2000).
[CrossRef]

B. Ratajska-Gadomska and W. Gadomski, “Quantum theory of the vibronic solid-state laser,” J. Opt. Soc. Am. B 16(5), 848–860 (1999).
[CrossRef]

W. Gadomski and B. Ratajska-Gadomska, “Self-pulsations in the phonon assisted lasers,” J. Opt. Soc. Am. B 15(11), 2681–2688 (1998).
[CrossRef]

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by means of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2528–R2531 (1994).
[CrossRef] [PubMed]

F. T. Arecchi, R. Meucci, and W. Gadomski, “Laser dynamics with competing instabilities,” Phys. Rev. Lett. 58(21), 2205–2208 (1987).
[CrossRef] [PubMed]

F. T. Arecchi, W. Gadomski, and R. Meucci, “Generation of chaotic dynamics by feedback on a laser,” Phys. Rev. A 34(2), 1617–1620 (1986).
[CrossRef] [PubMed]

Gills, Z.

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, “Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68(9), 1259–1262 (1992).
[CrossRef] [PubMed]

Glorieux, P.

S. Bielawski, D. Derozier, and P. Glorieux, “Controlling unstable periodic orbits by a delayed continuous feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(2), R971–R974 (1994).
[CrossRef] [PubMed]

Grebogi, C.

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

Heckenberg, N. R.

R. Dykstra, D. Y. Tang, and N. R. Heckenberg, “Experimental control of a single-mode laser chaos by using continuous, time-delayed feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(6), 6596–6598 (1998).
[CrossRef]

Henneberger, F.

S. Schikora, P. Hövel, H. J. Wünsche, E. Schöll, and F. Henneberger, “All-optical noninvasive control of unstable steady states in a semiconductor laser,” Phys. Rev. Lett. 97(21), 213902 (2006).
[CrossRef] [PubMed]

Hövel, P.

S. Schikora, P. Hövel, H. J. Wünsche, E. Schöll, and F. Henneberger, “All-optical noninvasive control of unstable steady states in a semiconductor laser,” Phys. Rev. Lett. 97(21), 213902 (2006).
[CrossRef] [PubMed]

Hunt, E. R.

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, “Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68(9), 1259–1262 (1992).
[CrossRef] [PubMed]

Kannari, F.

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]

Kovalsky, M. G.

M. G. Kovalsky, “On control of Chaos in the Kerr lens mode locked Ti:Sapphire laser,” Opt. Commun. 260(1), 265–270 (2006).
[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]

Maier, T. D.

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, “Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68(9), 1259–1262 (1992).
[CrossRef] [PubMed]

Meucci, R.

W. Gadomski, B. Ratajska-Gadomska, and R. Meucci, “Homoclinic dynamics if the vibronic laser,” Chaos Solitons Fractals 17(2-3), 387–396 (2003).
[CrossRef]

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by means of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2528–R2531 (1994).
[CrossRef] [PubMed]

F. T. Arecchi, R. Meucci, and W. Gadomski, “Laser dynamics with competing instabilities,” Phys. Rev. Lett. 58(21), 2205–2208 (1987).
[CrossRef] [PubMed]

F. T. Arecchi, W. Gadomski, and R. Meucci, “Generation of chaotic dynamics by feedback on a laser,” Phys. Rev. A 34(2), 1617–1620 (1986).
[CrossRef] [PubMed]

Mildren, R. P

H. Ogilvy, M. J. Withford, R. P. Mildren, J. A. Piper, M. J Withford, R. P Mildren, and J. A Piper, “Investigation of the pump wavelength influence on pulsed laser pumped Alexandrite lasers,” Appl. Phys. B 81(5), 637–644 (2005).
[CrossRef]

Mildren, R. P.

H. Ogilvy, M. J. Withford, R. P. Mildren, J. A. Piper, M. J Withford, R. P Mildren, and J. A Piper, “Investigation of the pump wavelength influence on pulsed laser pumped Alexandrite lasers,” Appl. Phys. B 81(5), 637–644 (2005).
[CrossRef]

Morris, R. C.

J. C. Walling, O. G. Peterson, and R. C. Morris, “Tunable CW Alexandrite Laser,” IEEE J. Quantum Electron. 16(2), 120–121 (1980).
[CrossRef]

Murphy, T. W.

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, “Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68(9), 1259–1262 (1992).
[CrossRef] [PubMed]

Ogawa, T.

Ogilvy, H.

H. Ogilvy, M. J. Withford, R. P. Mildren, J. A. Piper, M. J Withford, R. P Mildren, and J. A Piper, “Investigation of the pump wavelength influence on pulsed laser pumped Alexandrite lasers,” Appl. Phys. B 81(5), 637–644 (2005).
[CrossRef]

Ott, E.

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

Pecora, L. M.

L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Phys. Rev. A 44(4), 2374–2383 (1991).
[CrossRef] [PubMed]

Peterson, O. G.

J. C. Walling, O. G. Peterson, and R. C. Morris, “Tunable CW Alexandrite Laser,” IEEE J. Quantum Electron. 16(2), 120–121 (1980).
[CrossRef]

Piper, J. A

H. Ogilvy, M. J. Withford, R. P. Mildren, J. A. Piper, M. J Withford, R. P Mildren, and J. A Piper, “Investigation of the pump wavelength influence on pulsed laser pumped Alexandrite lasers,” Appl. Phys. B 81(5), 637–644 (2005).
[CrossRef]

Piper, J. A.

H. Ogilvy, M. J. Withford, R. P. Mildren, J. A. Piper, M. J Withford, R. P Mildren, and J. A Piper, “Investigation of the pump wavelength influence on pulsed laser pumped Alexandrite lasers,” Appl. Phys. B 81(5), 637–644 (2005).
[CrossRef]

Pyragas, K.

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

Ratajska-Gadomska, B.

Roy, R.

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, “Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68(9), 1259–1262 (1992).
[CrossRef] [PubMed]

Schikora, S.

S. Schikora, P. Hövel, H. J. Wünsche, E. Schöll, and F. Henneberger, “All-optical noninvasive control of unstable steady states in a semiconductor laser,” Phys. Rev. Lett. 97(21), 213902 (2006).
[CrossRef] [PubMed]

Schöll, E.

S. Schikora, P. Hövel, H. J. Wünsche, E. Schöll, and F. Henneberger, “All-optical noninvasive control of unstable steady states in a semiconductor laser,” Phys. Rev. Lett. 97(21), 213902 (2006).
[CrossRef] [PubMed]

Shinozuka, M.

Tang, D. Y.

R. Dykstra, D. Y. Tang, and N. R. Heckenberg, “Experimental control of a single-mode laser chaos by using continuous, time-delayed feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(6), 6596–6598 (1998).
[CrossRef]

Uchida, A.

Walling, J. C.

J. C. Walling, O. G. Peterson, and R. C. Morris, “Tunable CW Alexandrite Laser,” IEEE J. Quantum Electron. 16(2), 120–121 (1980).
[CrossRef]

Withford, M. J

H. Ogilvy, M. J. Withford, R. P. Mildren, J. A. Piper, M. J Withford, R. P Mildren, and J. A Piper, “Investigation of the pump wavelength influence on pulsed laser pumped Alexandrite lasers,” Appl. Phys. B 81(5), 637–644 (2005).
[CrossRef]

Withford, M. J.

H. Ogilvy, M. J. Withford, R. P. Mildren, J. A. Piper, M. J Withford, R. P Mildren, and J. A Piper, “Investigation of the pump wavelength influence on pulsed laser pumped Alexandrite lasers,” Appl. Phys. B 81(5), 637–644 (2005).
[CrossRef]

Wünsche, H. J.

S. Schikora, P. Hövel, H. J. Wünsche, E. Schöll, and F. Henneberger, “All-optical noninvasive control of unstable steady states in a semiconductor laser,” Phys. Rev. Lett. 97(21), 213902 (2006).
[CrossRef] [PubMed]

Yorke, J. A.

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

Yoshimori, S.

Appl. Phys. B (1)

H. Ogilvy, M. J. Withford, R. P. Mildren, J. A. Piper, M. J Withford, R. P Mildren, and J. A Piper, “Investigation of the pump wavelength influence on pulsed laser pumped Alexandrite lasers,” Appl. Phys. B 81(5), 637–644 (2005).
[CrossRef]

Chaos Solitons Fractals (1)

W. Gadomski, B. Ratajska-Gadomska, and R. Meucci, “Homoclinic dynamics if the vibronic laser,” Chaos Solitons Fractals 17(2-3), 387–396 (2003).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. C. Walling, O. G. Peterson, and R. C. Morris, “Tunable CW Alexandrite Laser,” IEEE J. Quantum Electron. 16(2), 120–121 (1980).
[CrossRef]

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

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

M. G. Kovalsky, “On control of Chaos in the Kerr lens mode locked Ti:Sapphire laser,” Opt. Commun. 260(1), 265–270 (2006).
[CrossRef]

Opt. Lett. (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. A (2)

L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Phys. Rev. A 44(4), 2374–2383 (1991).
[CrossRef] [PubMed]

F. T. Arecchi, W. Gadomski, and R. Meucci, “Generation of chaotic dynamics by feedback on a laser,” Phys. Rev. A 34(2), 1617–1620 (1986).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (3)

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by means of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), R2528–R2531 (1994).
[CrossRef] [PubMed]

S. Bielawski, D. Derozier, and P. Glorieux, “Controlling unstable periodic orbits by a delayed continuous feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(2), R971–R974 (1994).
[CrossRef] [PubMed]

R. Dykstra, D. Y. Tang, and N. R. Heckenberg, “Experimental control of a single-mode laser chaos by using continuous, time-delayed feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(6), 6596–6598 (1998).
[CrossRef]

Phys. Rev. Lett. (4)

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

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, “Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68(9), 1259–1262 (1992).
[CrossRef] [PubMed]

F. T. Arecchi, R. Meucci, and W. Gadomski, “Laser dynamics with competing instabilities,” Phys. Rev. Lett. 58(21), 2205–2208 (1987).
[CrossRef] [PubMed]

S. Schikora, P. Hövel, H. J. Wünsche, E. Schöll, and F. Henneberger, “All-optical noninvasive control of unstable steady states in a semiconductor laser,” Phys. Rev. Lett. 97(21), 213902 (2006).
[CrossRef] [PubMed]

Other (2)

W. Gadomski and B. Ratajska-Gadomska, “Chaotic dynamics of the vibronic laser” in Recent Advances in Laser Dynamics: Control and Synchronization, A.N. Pisarchik, ed. (Research Signpost, Kerala, India, 2008)

G. Hek and V. Rottschafer, “Semiconductor laser with filtered optical feedback: bridge between conventional feedback and optical injection”, ENOC-2005, Eindhoven, Netherlands, 7–12 August (2005).

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Figures (3)

Fig. 1.
Fig. 1.

Laser output vs. time in the regime of self-pulsations; a) chaotic dynamics in the absence of the control term ε = 0; b) and c) stabilization of the orbit of the period T = 1.7μs at ε = 5 10-5 and the delay time: (b) τ = T or (c) τ = T/40; d) and e) stabilization of the orbit of the period T = 2.2μs at ε = 5 1031 and the delay time: (d) τ = T or (e) τ = T/5.

Fig. 2.
Fig. 2.

Numerical solutions of Eqs. (2). Laser outputs of two unsynchronized lasers in chaotic regime: a), b), c) and for two synchronized lasers: a), d), e).

Fig. 3.
Fig. 3.

Numerical solutions of Eqs. (2) with time dependent coupling parameter ε(t) : a) signal from the transmitter laser, b) signal from the transmitter laser modulated by encoded message for ε 0 = 1, ∆ε = 0.008, c) signal from the receiver laser synchronized to the signal in (b), d) difference signal between (c) and (a).

Equations (17)

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ddt n3 = Γ3 n3 + K3W W+K30 n0
ddtW=ΓWW2CIW1+CI/ΓP+KW3n3+KW0n0
ddtI(t)=2κI(t)+2CI(t)1+CI(t)/ΓP+BN/ΓP+2εκI(tτ)
ddtN=ΓP(NN(0))KN3n3+KNWW+KN0n0
ΓW=[2γ4+BN+AI0]/2Γ3=γ3+[AI0+3BN]/2
KW3=[3BNAI0 ]/2+γ4γ3K3W=(BNAI0)/2
KW0=(AI0gBN2γ4)/2K30=(AI0+BN)/2
KN3=[3BN+fAI0]/2KNW=(BNfAI0)/2
KN0 =(fAI0+BN)/2
ddtn13=Γ13n13+K31WW1+K310n0
ddtW1=Γ1WW12CI1W11+CI1/ΓP+KW13n13+KW10n0
ddtI1(t)=2κI1(t)+2CI1(t)1+CI1(t)/ΓP+BN1/ΓP
ddtN1=ΓP(N1N(0))KN13n13+KN1WW1+KN10n0
ddtn23=Γ23n23+K32WW2+K320n0
ddtW2=Γ2WW22CI2W21+CI2/ΓP+KW23n23+KW20n0(2f)
ddtI2(t)=2κI2(t)+2CI21+CI2(t)/ΓP+BN2/ΓP+2εκ(I1I2)
ddtN2=ΓP(N2N(0))KN23n23+KN2WW2+KN20n0

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