Abstract

We propose and study both numerically and experimentally a feedback-controlled laser system capable of generating regular bursts with a submicrosecond period. Bursting is obtained in a laser that is controlled by a combination of feedbacks in which the negative feedback loop action is delayed by one cavity round trip with respect to the positive one, and the period is adjusted by relative feedback sensitivity. The proper combination of feedbacks is realized in a Nd:YAG laser with millisecond pumping by means of a single optoelectronic negative feedback unit that utilizes the signal reflected from an intracavity Pockels cell polarizer. Regular bursting (microgroups of picosecond pulses) with controlled periods from 25 to 75 cavity round trips is obtained experimentally. The development of chaotic dynamics displayed by the system at a higher pumping level differs from the Feigenbaum scenario.

© 2009 Optical Society of America

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  1. M. V. Gorbunkov and Yu. V. Shabalin, “Two-loop feedback controlled laser: new possibilities for ultrashort-pulse generation and high-level stabilization,” Proc. SPIE 4751, 463-470(2002).
    [CrossRef]
  2. M. V. Gorbunkov, V. B. Morozov, Yu. V. Shabalin, V. G. Tunkin, and D. V. Yakovlev, “Stabilized picosecond YAG-Nd laser controlled by combination of positive and negative delayed feedbacks,” presented at 12th International Laser Physics Workshop, Hamburg, Germany, 25-29 Aug. 2003 [Book of Abstracts, p. 250].
  3. M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
    [CrossRef]
  4. M. V. Gorbunkov, Yu. Ya. Maslova, Yu. V. Shabalin, and A. V. Vinogradov, “Simulation of regular and chaotic dynamics of a picosecond laser with optoelectronic feedback,” in WDS'07 Proceedings of Contributed Papers: Part III--Physics, J. Safrankova and J. Pavlu, eds. (Matfyzpress, 2007), pp. 140-144.
  5. M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
    [CrossRef]
  6. I. M. Bayanov, V. M. Gordienko, M. G. Zvereva, S. A. Magnitskii, and A. P. Tarasevich, “Highly stable picosecond YAG:Nd3+laser with a negative feedback,” Sov. J. Quantum Electron. 19, 994-996 (1989).
    [CrossRef]
  7. T. A. Murina, E. V. Nilov, N. N. Rozanov, and V. A. Rusov, “Investigation of the stability of a periodic train of pulses emitted by a solid-state laser,” Sov. J. Quantum Electron. 9, 812-815 (1979).
    [CrossRef]
  8. H. G. Schuster, Deterministic Chaos: an Introduction(Physik-Verlag, 1984).
  9. Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory, 2nd ed., Vol. 112 of Applied Mathematical Sciences (Springer1998).
  10. N. A. Loiko and A. M. Samson, “Nonlinear dynamics of laser systems with a delay,” Quantum Electron. 24, 657-672(1994).
    [CrossRef]
  11. V. K. Makukha, V. M. Semibalamut, and V. S. Smirnov, “Generation of ultrashort pulses in a negative-feedback laser,” Sov. J. Quantum Electron. 7, 573-575 (1977).
    [CrossRef]
  12. D. B. Vorchik and M. V. Gorbunkov, “Self mode-locked Nd-YAG laser controlled by fast delayed negative feedback based on reversely biased silicon p-n junction assemblies,” in Physical Foundations of Electronic Laser Engineering Devices, Proceedings of the Moscow Institute of Physics and Technology (Moscow Institute of Physics and Technology, 1995), pp. 4-11.
  13. M. V. Gorbunkov and Yu. V. Shabalin, “Picosecond YAG:Nd3+ laser with self-excitation of gigahertz oscillations in an optoelectronic negative feedback loop,” Bull. Lebedev Phys. Inst. 8, 43-50 (1998).

2005 (2)

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

2002 (1)

M. V. Gorbunkov and Yu. V. Shabalin, “Two-loop feedback controlled laser: new possibilities for ultrashort-pulse generation and high-level stabilization,” Proc. SPIE 4751, 463-470(2002).
[CrossRef]

1998 (1)

M. V. Gorbunkov and Yu. V. Shabalin, “Picosecond YAG:Nd3+ laser with self-excitation of gigahertz oscillations in an optoelectronic negative feedback loop,” Bull. Lebedev Phys. Inst. 8, 43-50 (1998).

1994 (1)

N. A. Loiko and A. M. Samson, “Nonlinear dynamics of laser systems with a delay,” Quantum Electron. 24, 657-672(1994).
[CrossRef]

1989 (1)

I. M. Bayanov, V. M. Gordienko, M. G. Zvereva, S. A. Magnitskii, and A. P. Tarasevich, “Highly stable picosecond YAG:Nd3+laser with a negative feedback,” Sov. J. Quantum Electron. 19, 994-996 (1989).
[CrossRef]

1979 (1)

T. A. Murina, E. V. Nilov, N. N. Rozanov, and V. A. Rusov, “Investigation of the stability of a periodic train of pulses emitted by a solid-state laser,” Sov. J. Quantum Electron. 9, 812-815 (1979).
[CrossRef]

1977 (1)

V. K. Makukha, V. M. Semibalamut, and V. S. Smirnov, “Generation of ultrashort pulses in a negative-feedback laser,” Sov. J. Quantum Electron. 7, 573-575 (1977).
[CrossRef]

Artyukov, I. A.

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

Bayanov, I. M.

I. M. Bayanov, V. M. Gordienko, M. G. Zvereva, S. A. Magnitskii, and A. P. Tarasevich, “Highly stable picosecond YAG:Nd3+laser with a negative feedback,” Sov. J. Quantum Electron. 19, 994-996 (1989).
[CrossRef]

Bessonov, E. G.

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

Fechtchenko, R. M.

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

Gorbunkov, M. V.

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

M. V. Gorbunkov and Yu. V. Shabalin, “Two-loop feedback controlled laser: new possibilities for ultrashort-pulse generation and high-level stabilization,” Proc. SPIE 4751, 463-470(2002).
[CrossRef]

M. V. Gorbunkov and Yu. V. Shabalin, “Picosecond YAG:Nd3+ laser with self-excitation of gigahertz oscillations in an optoelectronic negative feedback loop,” Bull. Lebedev Phys. Inst. 8, 43-50 (1998).

D. B. Vorchik and M. V. Gorbunkov, “Self mode-locked Nd-YAG laser controlled by fast delayed negative feedback based on reversely biased silicon p-n junction assemblies,” in Physical Foundations of Electronic Laser Engineering Devices, Proceedings of the Moscow Institute of Physics and Technology (Moscow Institute of Physics and Technology, 1995), pp. 4-11.

M. V. Gorbunkov, V. B. Morozov, Yu. V. Shabalin, V. G. Tunkin, and D. V. Yakovlev, “Stabilized picosecond YAG-Nd laser controlled by combination of positive and negative delayed feedbacks,” presented at 12th International Laser Physics Workshop, Hamburg, Germany, 25-29 Aug. 2003 [Book of Abstracts, p. 250].

M. V. Gorbunkov, Yu. Ya. Maslova, Yu. V. Shabalin, and A. V. Vinogradov, “Simulation of regular and chaotic dynamics of a picosecond laser with optoelectronic feedback,” in WDS'07 Proceedings of Contributed Papers: Part III--Physics, J. Safrankova and J. Pavlu, eds. (Matfyzpress, 2007), pp. 140-144.

Gordienko, V. M.

I. M. Bayanov, V. M. Gordienko, M. G. Zvereva, S. A. Magnitskii, and A. P. Tarasevich, “Highly stable picosecond YAG:Nd3+laser with a negative feedback,” Sov. J. Quantum Electron. 19, 994-996 (1989).
[CrossRef]

Ishkhanov, B. S.

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

Konyashkin, A. V.

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

Kostryukov, P. V.

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

Kuznetsov, Yu. A.

Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory, 2nd ed., Vol. 112 of Applied Mathematical Sciences (Springer1998).

Loiko, N. A.

N. A. Loiko and A. M. Samson, “Nonlinear dynamics of laser systems with a delay,” Quantum Electron. 24, 657-672(1994).
[CrossRef]

Magnitskii, S. A.

I. M. Bayanov, V. M. Gordienko, M. G. Zvereva, S. A. Magnitskii, and A. P. Tarasevich, “Highly stable picosecond YAG:Nd3+laser with a negative feedback,” Sov. J. Quantum Electron. 19, 994-996 (1989).
[CrossRef]

Makukha, V. K.

V. K. Makukha, V. M. Semibalamut, and V. S. Smirnov, “Generation of ultrashort pulses in a negative-feedback laser,” Sov. J. Quantum Electron. 7, 573-575 (1977).
[CrossRef]

Maslova, Yu. Ya.

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

M. V. Gorbunkov, Yu. Ya. Maslova, Yu. V. Shabalin, and A. V. Vinogradov, “Simulation of regular and chaotic dynamics of a picosecond laser with optoelectronic feedback,” in WDS'07 Proceedings of Contributed Papers: Part III--Physics, J. Safrankova and J. Pavlu, eds. (Matfyzpress, 2007), pp. 140-144.

Mikhailichenko, A. A.

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

Morozov, V. B.

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

M. V. Gorbunkov, V. B. Morozov, Yu. V. Shabalin, V. G. Tunkin, and D. V. Yakovlev, “Stabilized picosecond YAG-Nd laser controlled by combination of positive and negative delayed feedbacks,” presented at 12th International Laser Physics Workshop, Hamburg, Germany, 25-29 Aug. 2003 [Book of Abstracts, p. 250].

Murina, T. A.

T. A. Murina, E. V. Nilov, N. N. Rozanov, and V. A. Rusov, “Investigation of the stability of a periodic train of pulses emitted by a solid-state laser,” Sov. J. Quantum Electron. 9, 812-815 (1979).
[CrossRef]

Nilov, E. V.

T. A. Murina, E. V. Nilov, N. N. Rozanov, and V. A. Rusov, “Investigation of the stability of a periodic train of pulses emitted by a solid-state laser,” Sov. J. Quantum Electron. 9, 812-815 (1979).
[CrossRef]

Olenin, A. N.

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

Poseryaev, A. V.

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

Rozanov, N. N.

T. A. Murina, E. V. Nilov, N. N. Rozanov, and V. A. Rusov, “Investigation of the stability of a periodic train of pulses emitted by a solid-state laser,” Sov. J. Quantum Electron. 9, 812-815 (1979).
[CrossRef]

Rusov, V. A.

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

T. A. Murina, E. V. Nilov, N. N. Rozanov, and V. A. Rusov, “Investigation of the stability of a periodic train of pulses emitted by a solid-state laser,” Sov. J. Quantum Electron. 9, 812-815 (1979).
[CrossRef]

Samson, A. M.

N. A. Loiko and A. M. Samson, “Nonlinear dynamics of laser systems with a delay,” Quantum Electron. 24, 657-672(1994).
[CrossRef]

Schuster, H. G.

H. G. Schuster, Deterministic Chaos: an Introduction(Physik-Verlag, 1984).

Semibalamut, V. M.

V. K. Makukha, V. M. Semibalamut, and V. S. Smirnov, “Generation of ultrashort pulses in a negative-feedback laser,” Sov. J. Quantum Electron. 7, 573-575 (1977).
[CrossRef]

Shabalin, Yu. V.

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

M. V. Gorbunkov and Yu. V. Shabalin, “Two-loop feedback controlled laser: new possibilities for ultrashort-pulse generation and high-level stabilization,” Proc. SPIE 4751, 463-470(2002).
[CrossRef]

M. V. Gorbunkov and Yu. V. Shabalin, “Picosecond YAG:Nd3+ laser with self-excitation of gigahertz oscillations in an optoelectronic negative feedback loop,” Bull. Lebedev Phys. Inst. 8, 43-50 (1998).

M. V. Gorbunkov, V. B. Morozov, Yu. V. Shabalin, V. G. Tunkin, and D. V. Yakovlev, “Stabilized picosecond YAG-Nd laser controlled by combination of positive and negative delayed feedbacks,” presented at 12th International Laser Physics Workshop, Hamburg, Germany, 25-29 Aug. 2003 [Book of Abstracts, p. 250].

M. V. Gorbunkov, Yu. Ya. Maslova, Yu. V. Shabalin, and A. V. Vinogradov, “Simulation of regular and chaotic dynamics of a picosecond laser with optoelectronic feedback,” in WDS'07 Proceedings of Contributed Papers: Part III--Physics, J. Safrankova and J. Pavlu, eds. (Matfyzpress, 2007), pp. 140-144.

Shvedunov, V. I.

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

Smirnov, V. S.

V. K. Makukha, V. M. Semibalamut, and V. S. Smirnov, “Generation of ultrashort pulses in a negative-feedback laser,” Sov. J. Quantum Electron. 7, 573-575 (1977).
[CrossRef]

Tarasevich, A. P.

I. M. Bayanov, V. M. Gordienko, M. G. Zvereva, S. A. Magnitskii, and A. P. Tarasevich, “Highly stable picosecond YAG:Nd3+laser with a negative feedback,” Sov. J. Quantum Electron. 19, 994-996 (1989).
[CrossRef]

Telegin, L. S.

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

Tunkin, V. G.

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

M. V. Gorbunkov, V. B. Morozov, Yu. V. Shabalin, V. G. Tunkin, and D. V. Yakovlev, “Stabilized picosecond YAG-Nd laser controlled by combination of positive and negative delayed feedbacks,” presented at 12th International Laser Physics Workshop, Hamburg, Germany, 25-29 Aug. 2003 [Book of Abstracts, p. 250].

Vinogradov, A. V.

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

M. V. Gorbunkov, Yu. Ya. Maslova, Yu. V. Shabalin, and A. V. Vinogradov, “Simulation of regular and chaotic dynamics of a picosecond laser with optoelectronic feedback,” in WDS'07 Proceedings of Contributed Papers: Part III--Physics, J. Safrankova and J. Pavlu, eds. (Matfyzpress, 2007), pp. 140-144.

Vorchik, D. B.

D. B. Vorchik and M. V. Gorbunkov, “Self mode-locked Nd-YAG laser controlled by fast delayed negative feedback based on reversely biased silicon p-n junction assemblies,” in Physical Foundations of Electronic Laser Engineering Devices, Proceedings of the Moscow Institute of Physics and Technology (Moscow Institute of Physics and Technology, 1995), pp. 4-11.

Yakovlev, D. V.

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

M. V. Gorbunkov, V. B. Morozov, Yu. V. Shabalin, V. G. Tunkin, and D. V. Yakovlev, “Stabilized picosecond YAG-Nd laser controlled by combination of positive and negative delayed feedbacks,” presented at 12th International Laser Physics Workshop, Hamburg, Germany, 25-29 Aug. 2003 [Book of Abstracts, p. 250].

Zvereva, M. G.

I. M. Bayanov, V. M. Gordienko, M. G. Zvereva, S. A. Magnitskii, and A. P. Tarasevich, “Highly stable picosecond YAG:Nd3+laser with a negative feedback,” Sov. J. Quantum Electron. 19, 994-996 (1989).
[CrossRef]

Bull. Lebedev Phys. Inst. (1)

M. V. Gorbunkov and Yu. V. Shabalin, “Picosecond YAG:Nd3+ laser with self-excitation of gigahertz oscillations in an optoelectronic negative feedback loop,” Bull. Lebedev Phys. Inst. 8, 43-50 (1998).

Proc. SPIE (2)

M. V. Gorbunkov and Yu. V. Shabalin, “Two-loop feedback controlled laser: new possibilities for ultrashort-pulse generation and high-level stabilization,” Proc. SPIE 4751, 463-470(2002).
[CrossRef]

M. V. Gorbunkov, V. G. Tunkin, E. G. Bessonov, R. M. Fechtchenko, I. A. Artyukov, Yu. V. Shabalin, P. V. Kostryukov, Yu. Ya. Maslova, A. V. Poseryaev, V. I. Shvedunov, A. V. Vinogradov, A. A. Mikhailichenko, and B. S. Ishkhanov, “Proposal of a compact repetitive dichromatic x-ray generator with millisecond duty cycle for medical applications,” Proc. SPIE 5919, 59190U (2005).
[CrossRef]

Quantum Electron. (2)

M. V. Gorbunkov, A. V. Konyashkin, P. V. Kostryukov, V. B. Morozov, A. N. Olenin, V. A. Rusov, L. S. Telegin, V. G. Tunkin, Yu. V. Shabalin, and D. V. Yakovlev, “Pulsed-diode-pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers,” Quantum Electron. 35, 2-6 (2005).
[CrossRef]

N. A. Loiko and A. M. Samson, “Nonlinear dynamics of laser systems with a delay,” Quantum Electron. 24, 657-672(1994).
[CrossRef]

Sov. J. Quantum Electron. (3)

V. K. Makukha, V. M. Semibalamut, and V. S. Smirnov, “Generation of ultrashort pulses in a negative-feedback laser,” Sov. J. Quantum Electron. 7, 573-575 (1977).
[CrossRef]

I. M. Bayanov, V. M. Gordienko, M. G. Zvereva, S. A. Magnitskii, and A. P. Tarasevich, “Highly stable picosecond YAG:Nd3+laser with a negative feedback,” Sov. J. Quantum Electron. 19, 994-996 (1989).
[CrossRef]

T. A. Murina, E. V. Nilov, N. N. Rozanov, and V. A. Rusov, “Investigation of the stability of a periodic train of pulses emitted by a solid-state laser,” Sov. J. Quantum Electron. 9, 812-815 (1979).
[CrossRef]

Other (5)

H. G. Schuster, Deterministic Chaos: an Introduction(Physik-Verlag, 1984).

Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory, 2nd ed., Vol. 112 of Applied Mathematical Sciences (Springer1998).

M. V. Gorbunkov, Yu. Ya. Maslova, Yu. V. Shabalin, and A. V. Vinogradov, “Simulation of regular and chaotic dynamics of a picosecond laser with optoelectronic feedback,” in WDS'07 Proceedings of Contributed Papers: Part III--Physics, J. Safrankova and J. Pavlu, eds. (Matfyzpress, 2007), pp. 140-144.

M. V. Gorbunkov, V. B. Morozov, Yu. V. Shabalin, V. G. Tunkin, and D. V. Yakovlev, “Stabilized picosecond YAG-Nd laser controlled by combination of positive and negative delayed feedbacks,” presented at 12th International Laser Physics Workshop, Hamburg, Germany, 25-29 Aug. 2003 [Book of Abstracts, p. 250].

D. B. Vorchik and M. V. Gorbunkov, “Self mode-locked Nd-YAG laser controlled by fast delayed negative feedback based on reversely biased silicon p-n junction assemblies,” in Physical Foundations of Electronic Laser Engineering Devices, Proceedings of the Moscow Institute of Physics and Technology (Moscow Institute of Physics and Technology, 1995), pp. 4-11.

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Figures (12)

Fig. 1
Fig. 1

Bifurcation diagram of map (1), r 3 .

Fig. 2
Fig. 2

Dynamics of the logistic map (1): (a) fixed point, (b) two-cycle, (c) four-cycle, (d) chaotic dynamics.

Fig. 3
Fig. 3

Numeric simulation of map (3) dynamics at α = 0.5 : (a) bifurcation diagram in r-parameter space; (b), (c) example of chaotic dynamics at r = 1.61892 (b) train; (c) envelope spectrum, the horizontal scale is a reciprocal round trip.

Fig. 4
Fig. 4

Calculated dynamics period T ( r max ( α ) ) versus relative feedback sensitivity α of map (3): curves are in close agreement in the region of negative argument. The upper dashed curve is an approximation, Eq. (4); the lower solid curve is the exact result, Eq. (A14).

Fig. 5
Fig. 5

Numeric simulation of map (3) dynamics at α = 0.9 : a, bifurcation diagram in r-parameter space; b, example of regular dynamics (41-cycle) at r = 1.11 .

Fig. 6
Fig. 6

(a)  R C circuit and (b) the scheme of discontinuous control in a laser with an optoelectronic feedback unit: the control signal is taken from a Pockels cell polarizer.

Fig. 7
Fig. 7

Self-mode-locking by a fast time-shifted negative optoelectronic feedback loop: temporal variation of laser intensity I ( t ) , photocurrent i ( t ) , modulator control voltage U ( t ) , and modulator transmission P ( t ) .

Fig. 8
Fig. 8

Numerical simulation: laser dynamics at, a, r = 1.03 and, b, r = 1.09 ; energy is normalized to feedback sensitivity. c, Dependence of bursting period T and, d, maximum threshold excess Δ G max for bias voltage U s t .

Fig. 9
Fig. 9

Millisecond lamp pumped Nd:YAG laser designed for submicrosecond scale bursts. AM, active laser medium; P, polarizer; M 1 , M 2 , cavity mirrors; M 3 , M 4 , optical time delay mirrors; Pr, prism; IA, iris aperture; MT, mirror telescope; Li Ta O 3 Pockels cell electro-optical crystals; CC feedback control circuit.

Fig. 10
Fig. 10

Millisecond oscilloscope traces of laser output; signal is proportional to picosecond pulse energy. Pumping energy increases from (a) to (c). Vertical scales are equal.

Fig. 11
Fig. 11

Oscilloscope traces of laser output; signal is proportional to picosecond pulse energy: (a) harmonic modulation, (b) developed regular 0.5 μs burst, (c)  1.7 μs burst regimes.

Fig. 12
Fig. 12

Microsecond time-scale oscilloscope traces of laser output in regular and chaotic regimes and the corresponding Fourier transforms.

Equations (26)

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x n + 1 = r x n ( 1 x n ) ,
x n + 1 = r x n ( 1 x n 1 ) .
x n + 1 = r x n ( 1 α x n x n 1 ) ,
T ( r max ( α ) ) = 2 π α + 1 ,
B n = x n 1 G 2 R x n .
x n + 1 = x n G 2 R P 0 ( 1 ( x n 1 G 2 R x n ) ) .
y n + 1 = y n r ( 1 y n 1 + P 0 r y n ) .
P ( U ) = cos 2 ( U U λ / 4 π 2 ) ,
T ( U ) 2 2 π U λ / 4 U ,
r max ( U ) 1 + π 2 4 ( U U λ / 4 ) .
x n + 1 = f ( x n , x n 1 , ... , x n k )
δ n + 1 = m = 0 k f ( x n , x n 1 , ... , x n k ) x n - m | x s t · δ n m .
δ n + 1 = m = 0 k d m | x s t · δ n m ,
d m = f ( x n , x n 1 , ... , x n k ) x n m .
1 = m = 0 k d m | x s t · δ n m δ n + 1 .
δ n δ n + 1 = 1 λ , δ n m δ n + 1 = 1 λ m + 1 ,
m = 0 k d m λ m + 1 = 1.
x s t = r 1 r ( 1 + α ) .
m = 0 k d m λ m + 1 = d 0 | x s t · 1 λ + d 1 | x s t · 1 λ 2 = 1 ,
d 0 | x s t = r · ( 1 2 x s t α x s t ) = α r + 2 α + 1 1 + α ,
d 1 | x s t = r · x s t = r 1 ( 1 + α ) .
λ 2 λ α r + 2 α + 1 1 + α + r 1 ( 1 + α ) = 0 ,
λ ± = ( α r + 2 α + 1 ) ± ( α r + 2 α + 1 ) 2 4 ( r 1 ) ( 1 + α ) 2 ( 1 + α ) .
r ( α ) = { α + 2 α 3 3 + 4 α 1 α > 3 .
T = 2 π arg ( λ + ) = 2 π arg ( α r + 2 α + 1 + ( α r + 2 α + 1 ) 2 4 ( r 1 ) ( 1 + α ) 2 ( α + 1 ) ) ,
T ( α ) = 2 π α + 1 π α + 1 12 .

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