Abstract

We study synchronization in chaotic oscillations of counterpropagating waves in a solid-state ring laser with a periodically modulated pump. The new phenomenon of spontaneous switching of in-phase- and anti-phase chaotic synchronization has been discovered in a numerical experiment.

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References

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  1. L.M. Pecora, T.L. Carrol, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).<BR>
    [CrossRef] [PubMed]
  2. L.M. Pecora, T.L. Carrol, "Driving systems with chaotic signals," Phys. Rev. A 44, 2374-2383 (1991).<BR>
    [CrossRef] [PubMed]
  3. I.I. Blekhman, P.S. Landa, M.G. Rosenblum, "Synchronization and chaotization in interacting dynamical
    [CrossRef]
  4. H.G. Winful, L. Rahman, "Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers," Phys. Rev. Lett. 65, 1575-1577 (1990).<BR>
    [CrossRef] [PubMed]
  5. R. Roy, K.S. Thornburg, "Experimental synchronization of chaotic lasers," Phys. Rev. Lett. 72, 2009-2011 (1994).<BR>
    [CrossRef] [PubMed]
  6. T. Sugawara, M. Tachikawa, T. Tsukamoto, V. Shimizu, "Observation of synchronization in laser chaos," Phys. Rev. Lett. 72 , 3502-3504 (1994).<BR>
    [CrossRef] [PubMed]
  7. V. Annovazzi-Lodi, S. Donati, A. Scire, "Synchronization of chaotic injected-laser systems and its application to optical cryptography," IEEE J. Quantum Electron., 32, 953-959 (1996).<BR>
    [CrossRef]
  8. C.R. Mirasso, P. Colet, P. Garcia-Fernandez "Synchronization of chaotic semiconductor lasers: application to encoded communications," IEEE Photonics Technol. Lett. 8, 299-301 (1996).<BR>
    [CrossRef]
  9. L. Rahman, G. Li, F. Tian, "Remoute synchronization of high-frequency chaotic signals in semiconductor lasers for secure communications," Opt. Commun. 138, 91-94 (1997) .<BR>
    [CrossRef]
  10. V. Annovazzi-Lodi, S. Donati, A. Scire, "Synchronization of chaotic lasers by optical feedback for cryptographic applications," IEEE J. Quantum Electron. 33, 1449-1454 (1997).<BR>
    [CrossRef]
  11. A. Pikovsky, M. Rosenblum, J.Kurths, "Synchronization in a population of globally coupled chaotic oscillators, Europhys. Lett. 34, 165-170 (1996).<BR>
    [CrossRef]
  12. G.V.Osipov, A. Pikovsky, M. Rosenblum, J.Kurths, "Phase synchronization effects in a lattice of nonidentical Rossler oscillators," Phys. Rev. E 55, 2353-2361 (1997).<BR>
    [CrossRef]
  13. U.Parlitz, L.Junge, W.Lauterborn, L.Kocarev, "Experimental observation of phase synchronization," Phys. Rev. E 54, 2115-2117 (1996).<BR>
    [CrossRef]
  14. D.N.Klimenko, N.V.Kravtsov, E.G.Lariontsev, V.V. Firsov, "Synchronization of dynamic chaos in counterpropagating ring-laser waves," Quantum Electron. 27, 631-634 (1997).<BR>
    [CrossRef]
  15. W. Klische, H.R. Telle, C.O. Weiss, "Chaos in a solid-state laser with a periodically modulated pump," Opt. Lett. 9, 561-564 (1984)<BR>
    [CrossRef] [PubMed]
  16. G.P. Puccioni, A. Poggi, W. Gadomski, J.R. Tredicce, F.T. Arecchi, "Measurement of the formation and evolution of a strange attractor in a laser," Phys. Rev. Lett. 55, 339-342 (1985).<BR>
    [CrossRef] [PubMed]
  17. J.R. Tredicce, F.T. Arecchi, G.P. Puccioni, A. Poggi, W. Gadomski, "Dynamic behavior and onset of low-dimensional chaos in a modulated homogeneously broadened single-mode laser," Phys. Rev. A 34, 2073-2081 (1986).<BR>
    [CrossRef] [PubMed]
  18. F. Papoff, D. Dangoisse, E. Poite-Hanoteau, P. Glorieux, "Chaotic transients in a CO2 laser with modulated parameters: critical slowing-down and crisis-unduced intermittency," Opt. Commun. 67, 358-362 (1988) .<BR>
    [CrossRef]
  19. N.G. Solari, E. Eschnazi, R. Gilmore, J.R. Tredicce, "Influence of coexisting attractors on the dynamics of a laser system," Opt. Commun. 64, 49-53 (1987) .<BR>
    [CrossRef]
  20. I.I..Zolotoverkh, D.N.Klimenko, E.G.Lariontsev, "Influence of periodic loss modulation on the dynamics of self-modulation oscillations in a solid-state ring laser," Quantum Electron. 26, 609-613 (1996).<BR>
    [CrossRef]
  21. I.I..Zolotoverkh, D.N.Klimenko, N.V.Kravtsov, E.G.Lariontsev, V.V. Firsov, "Parametric processes and multistability in a ring chip laser with periodic pump modulation," Quantum Electron. 26, 914-918 (1996)<BR>
    [CrossRef]

Other

L.M. Pecora, T.L. Carrol, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).<BR>
[CrossRef] [PubMed]

L.M. Pecora, T.L. Carrol, "Driving systems with chaotic signals," Phys. Rev. A 44, 2374-2383 (1991).<BR>
[CrossRef] [PubMed]

I.I. Blekhman, P.S. Landa, M.G. Rosenblum, "Synchronization and chaotization in interacting dynamical
[CrossRef]

H.G. Winful, L. Rahman, "Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers," Phys. Rev. Lett. 65, 1575-1577 (1990).<BR>
[CrossRef] [PubMed]

R. Roy, K.S. Thornburg, "Experimental synchronization of chaotic lasers," Phys. Rev. Lett. 72, 2009-2011 (1994).<BR>
[CrossRef] [PubMed]

T. Sugawara, M. Tachikawa, T. Tsukamoto, V. Shimizu, "Observation of synchronization in laser chaos," Phys. Rev. Lett. 72 , 3502-3504 (1994).<BR>
[CrossRef] [PubMed]

V. Annovazzi-Lodi, S. Donati, A. Scire, "Synchronization of chaotic injected-laser systems and its application to optical cryptography," IEEE J. Quantum Electron., 32, 953-959 (1996).<BR>
[CrossRef]

C.R. Mirasso, P. Colet, P. Garcia-Fernandez "Synchronization of chaotic semiconductor lasers: application to encoded communications," IEEE Photonics Technol. Lett. 8, 299-301 (1996).<BR>
[CrossRef]

L. Rahman, G. Li, F. Tian, "Remoute synchronization of high-frequency chaotic signals in semiconductor lasers for secure communications," Opt. Commun. 138, 91-94 (1997) .<BR>
[CrossRef]

V. Annovazzi-Lodi, S. Donati, A. Scire, "Synchronization of chaotic lasers by optical feedback for cryptographic applications," IEEE J. Quantum Electron. 33, 1449-1454 (1997).<BR>
[CrossRef]

A. Pikovsky, M. Rosenblum, J.Kurths, "Synchronization in a population of globally coupled chaotic oscillators, Europhys. Lett. 34, 165-170 (1996).<BR>
[CrossRef]

G.V.Osipov, A. Pikovsky, M. Rosenblum, J.Kurths, "Phase synchronization effects in a lattice of nonidentical Rossler oscillators," Phys. Rev. E 55, 2353-2361 (1997).<BR>
[CrossRef]

U.Parlitz, L.Junge, W.Lauterborn, L.Kocarev, "Experimental observation of phase synchronization," Phys. Rev. E 54, 2115-2117 (1996).<BR>
[CrossRef]

D.N.Klimenko, N.V.Kravtsov, E.G.Lariontsev, V.V. Firsov, "Synchronization of dynamic chaos in counterpropagating ring-laser waves," Quantum Electron. 27, 631-634 (1997).<BR>
[CrossRef]

W. Klische, H.R. Telle, C.O. Weiss, "Chaos in a solid-state laser with a periodically modulated pump," Opt. Lett. 9, 561-564 (1984)<BR>
[CrossRef] [PubMed]

G.P. Puccioni, A. Poggi, W. Gadomski, J.R. Tredicce, F.T. Arecchi, "Measurement of the formation and evolution of a strange attractor in a laser," Phys. Rev. Lett. 55, 339-342 (1985).<BR>
[CrossRef] [PubMed]

J.R. Tredicce, F.T. Arecchi, G.P. Puccioni, A. Poggi, W. Gadomski, "Dynamic behavior and onset of low-dimensional chaos in a modulated homogeneously broadened single-mode laser," Phys. Rev. A 34, 2073-2081 (1986).<BR>
[CrossRef] [PubMed]

F. Papoff, D. Dangoisse, E. Poite-Hanoteau, P. Glorieux, "Chaotic transients in a CO2 laser with modulated parameters: critical slowing-down and crisis-unduced intermittency," Opt. Commun. 67, 358-362 (1988) .<BR>
[CrossRef]

N.G. Solari, E. Eschnazi, R. Gilmore, J.R. Tredicce, "Influence of coexisting attractors on the dynamics of a laser system," Opt. Commun. 64, 49-53 (1987) .<BR>
[CrossRef]

I.I..Zolotoverkh, D.N.Klimenko, E.G.Lariontsev, "Influence of periodic loss modulation on the dynamics of self-modulation oscillations in a solid-state ring laser," Quantum Electron. 26, 609-613 (1996).<BR>
[CrossRef]

I.I..Zolotoverkh, D.N.Klimenko, N.V.Kravtsov, E.G.Lariontsev, V.V. Firsov, "Parametric processes and multistability in a ring chip laser with periodic pump modulation," Quantum Electron. 26, 914-918 (1996)<BR>
[CrossRef]

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Figures (2)

Fig.1
Fig.1

Time-dependence of ReE1 (a), ReE2 (b), and |E|2 - (1), hcos(ωpt) - (2) (c) for the chaotic oscillations in a modulated SSRL. The results were obtained by numerically integrating the system of equations (1) with ωp/2π=50 kHz, h=0.24.

Fig.2.
Fig.2.

Projections of the chaotic pulsations on the planes of variables (ReE1, ImE1) (a), (ReE1 , ReE2) (b), and (ImE1, ImE2) (c). The results were obtained by numerically integrating the system of equations (1) with ωp/2π=50 kHz, h=0.24.

Equations (5)

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

d E 1,2 d t = 1 2 ω Q E 1,2 + i m 2 E 2,1 + σ l 2 T ( N 0 E 1,2 + N E 2,1 ) ,
T 1 d N 0 d t = N t h ( 1 + η eff ) N 0 ( 1 + à ( E 1 2 + E 2 2 ) ) à N + E 1 E 2 * à N E 1 * E 2 ,
T 1 d N + d t = N + ( 1 + à ( E 1 2 + E 2 2 ) ) à N 0 E 1 E 2 * ,
N 0 = 1 L 0 L N d z , N ± = 1 L 0 L N e ± i 2 k z d z , N = N + * ,
η eff = η + h cos ( ω p t ) ,

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