Abstract

We employed additive modulation of a laser-diode current to demonstrate dramatic suppression of chaos in the output of a laser-diode-pumped multimode Nd:YAG laser. Stable periodic orbits were found to depend on the amplitude and the frequency modulation.

© 1998 Optical Society of America

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  1. R. Wilbrandt and H. Weber, “Fluctuations in mode-locking threshold due to statistics of spontaneous emission,” IEEE J. Quantum Electron. QE-11, 186 (1975); K. Kaufmann and G. Marowsky, Appl. Phys. 11, 47 (1976); C. O. Weiss and H. King, “Oscillation period doubling chaos in a laser,” Opt. Commun. OPCOB8 44, 58 (1982); C. O. Weiss, A. Godone, and A. Olafsson, “Routes to chaotic emission in a cw He–Ne laser,” Phys. Rev. A PLRAAN 28, 892 (1983).
    [CrossRef]
  2. L. A. Lugiato, G.-L. Oppo, M. A. Pernigo, J. R. Tredicce, L. M. Narducci, and D. K. Bandy, “Spontaneously spatial pattern formation in lasers and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: the experimental side,” Opt. Commun. 65, 3124 (1990); M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Parti, A. J. Kent, G.-L. Oppo, A. B. Coates, C. O. Weiss, G. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A PLRAAN 49, 1427 (1994); A. B. Coates, C. O. Weiss, G. Green, E. J. D’Angelo, J. R. Tredicce, M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Prati, A. J. Kent, and G.-L. Oppo, “Dynamical transverse laser patterns. II. Experiments,” Phys. Rev. A PLRAAN 49, 1452 (1994); M. Brambilla, F. Battiped, L. A. Lugiato, V. Penna, F. Parti, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A PLRAAN 43, 5090 (1991).
    [CrossRef] [PubMed]
  3. D. J. Biaswas and R. G. Harrison, “Experimental evidence of three-mode quasi-periodicity and chaos in a single longitudinal, multi-transverse-mode cw CO2 laser,” Phys. Rev. A 32, 3835 (1985); R. Hauck, F. Hollinger, and H. Weber, “Chaotic and periodic emission of high power solid state lasers,” Opt. Commun. 47, 141 (1983); M.-L. Shih, P. W. Milonni, and J. R. Ackerhalt, “Modeling chaos in the secondary beat frequency,” J. Opt. Soc. Am. B JOBPDE 2, 130 (1985); F. Hollinger, Ch. Jung, and H. Weber, “Quasiperiodicity versus chaos in high power solid state lasers in multi-transversal mode operation,” Opt. Commun. OPCOB8 75, 85 (1990); C. Tamm, “Frequency locking of two transverse optical modes of a laser,” Phys. Rev. A PLRAAN 38, 5960 (1988).
    [CrossRef] [PubMed]
  4. M. Shih and P. W. Milonni, “Chaotic two-mode lasing,” Opt. Commun. 49, 155 (1984); F. Hollinger and Ch. Jung, “Single-longitudinal-mode laser as a discrete dynamical system,” J. Opt. Soc. Am. B 2, 218 (1985).
    [CrossRef]
  5. B. S. Poh and T. E. Rozzi, “Intrinsic instabilities in narrow stripe geometry lasers caused by lateral current spreading,” IEEE J. Quantum Electron. QE-17, 723 (1981); N. J. Halas, S. N. Liu, and N. B. Abraham, “Route to mode locking in a three-mode He–Ne 3.39-μm laser including chaos in the secondary beat frequency,” Phys. Rev. A 28, 2915 (1983); G.-L. Oppo, J. R. Tredicce, and L. M. Narducci, “Dynamics of vibro-rotational CO2 laser transitions in a two-dimensional phase space,” Opt. Commun. OPCOB8 69, 393 (1989); J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. PRLTAO 62, 1274 (1989); W. Klische, C. O. Weiss, and B. Wellegehausen, “Spatiotemporal chaos from a continuous Na2 laser,” Phys. Rev. A PLRAAN 39, 919 (1989).
    [CrossRef] [PubMed]
  6. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64, 1196 (1990).
    [CrossRef] [PubMed]
  7. E. R. Hunt, “Stabilizing high-period orbits in a chaotic system-the diode resonator,” Phys. Rev. Lett. 67, 1953 (1991).
    [CrossRef] [PubMed]
  8. R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laser-experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
    [CrossRef] [PubMed]
  9. V. Petrov, V. Gáspár, J. Masere, and K. Showalter, “Controlling chaos in the Belousov–Zhabotinsky reaction,” Nature (London) 361, 240 (1993); V. Petrov, S. K. Scott, and K. Showalter, “Mixed-mode oscillations in chemical systems,” J. Chem. Phys. 97, 6191 (1992).
    [CrossRef]
  10. J. M. Kim, K. S. Kim, C. J. Kim, and C. M. Kim, in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. S. Chang, J. H. Lee, S. Y. Lee, and C. H. Nam, eds., Proc. SPIE 2778, 806–807 (1996).
  11. K. Pyragas, “Continuous control of chaos by self-controlling feedback,” Phys. Lett. A 170, 421 (1992).
    [CrossRef]
  12. R. Lima and M. Pettini, “Suppression of chaos by resonant parametric perturbations,” Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, “Taming chaotic dynamics with weak periodic perturbations,” Phys. Rev. Lett. 66, 2545 (1991); S. T. Vohra, L. Fabing, and F. Bucholtz, “Suppressed and induced chaos by near resonant perturbation of bifurcations,” Phys. Rev. Lett. PRLTAO 75, 65 (1995); M. Salerno, “Suppression of phase-locked chaos in long Josephson junctions by biharmonic microwave fields,” Phys. Rev. B PRBMDO 44, 2720 (1991); G. Filatrella, G. Rotoli, and M. Salerno, “Suppression of chaos in the perturbed sine–Gordon system by weak periodic signals,” Phys. Lett. A PYLAAG 178, 81 (1993); R. Chacon and J. D. Bejarano, “Routes to suppressing chaos by weak periodic perturbations,” Phys. Rev. Lett. PRLTAO 71, 3103 (1993); R. Chacon, “Inhibition of chaos in Hamiltonian systems by periodic pulses,” Phys. Rev. E PLEEE8 50, 750 (1994); R.-R. Hsu, H.-T. Su, J.-L. Chern, and C.-C. Chen, “Conditions to control chaotic dynamics by weak periodic perturbation,” Phys. Rev. Lett. PRLTAO 78, 2936 (1997).
    [CrossRef] [PubMed]
  13. A. Azevedo and S. M. Rezende, “Controlling chaos in spin-wave instabilities,” Phys. Rev. Lett. 66, 1342 (1991); W. X. Ding, H. Q. She, W. Huang, and C. X. Yu, “Controlling chaos in a discharge plasma,” Phys. Rev. Lett. 72, 96 (1994); L. Fronzoni, M. Giocondo, and M. Pettini, “Experimental evidence of suppression of chaos by resonant parametric perturbations,” Phys. Rev. A PLRAAN 43, 6483 (1991); H.-J. Li and J.-L. Chern, “Goal-oriented scheme for taming chaos with a weak periodic perturbation experiment in a diode resonator,” Phys. Rev. E PLEEE8 54, 2118 (1996).
    [CrossRef] [PubMed]
  14. Y. D. Liu and J. R. Rios Leite, “Control of Lorenz chaos,” Phys. Lett. A 185, 35 (1994); R. Vilaseca, A. Kul’minskii, and R. Corbalán, “Tracking unstable steady states by large periodic modulation of control parameter in a nonlinear system,” Phys. Rev. E 54, 82 (1996).
    [CrossRef]
  15. R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by means of weak parametric perturbations,” Phys. Rev. E 49, R2528 (1994); V. N. Chizhevsky and R. Corbalán, “Experimental observation of perturbation-induced intermittency in the dynamics of a loss-modulated CO2 Laser,” Phys. Rev. E 54, 4576 (1996); M. Ciofini, R. Meucci, and F. T. Arecchi, “Experimental control of chaos in a laser,” Phys. Rev. E PLEEE8 52, 94 (1995).
    [CrossRef]
  16. N. Watanabe and K. Karaki, “Inducing periodic oscillations from chaotic oscillations of a compound-cavity laser diode with sinusoidally modulated drive,” Opt. Lett. 20, 1032 (1995); “Improvement of interference fringes of a laser diode interferometer by controlling chaos with sinusoidally modulated injection,” Opt. Lett. 21, 1256 (1996).
    [CrossRef] [PubMed]
  17. P. Colet and Y. Braiman, “Control of chaos in multimode solid state lasers by the use of small periodic perturbations,” Phys. Rev. E 53, 200 (1996).
    [CrossRef]
  18. W. Koechner, Solid-state Laser Engineering (Springer-Verlag, Berlin, 1995).
  19. H. G. Schuster, Deterministic Chaos (VCH Verlagesellschaft, MbH, Weinheim, 1994).

1996 (2)

J. M. Kim, K. S. Kim, C. J. Kim, and C. M. Kim, in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. S. Chang, J. H. Lee, S. Y. Lee, and C. H. Nam, eds., Proc. SPIE 2778, 806–807 (1996).

P. Colet and Y. Braiman, “Control of chaos in multimode solid state lasers by the use of small periodic perturbations,” Phys. Rev. E 53, 200 (1996).
[CrossRef]

1992 (2)

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laser-experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

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

1991 (1)

E. R. Hunt, “Stabilizing high-period orbits in a chaotic system-the diode resonator,” Phys. Rev. Lett. 67, 1953 (1991).
[CrossRef] [PubMed]

1990 (1)

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

Braiman, Y.

P. Colet and Y. Braiman, “Control of chaos in multimode solid state lasers by the use of small periodic perturbations,” Phys. Rev. E 53, 200 (1996).
[CrossRef]

Colet, P.

P. Colet and Y. Braiman, “Control of chaos in multimode solid state lasers by the use of small periodic perturbations,” Phys. Rev. E 53, 200 (1996).
[CrossRef]

Gills, Z.

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laser-experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Grebogi, C.

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

Hunt, E. R.

E. R. Hunt, “Stabilizing high-period orbits in a chaotic system-the diode resonator,” Phys. Rev. Lett. 67, 1953 (1991).
[CrossRef] [PubMed]

Kim, C. J.

J. M. Kim, K. S. Kim, C. J. Kim, and C. M. Kim, in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. S. Chang, J. H. Lee, S. Y. Lee, and C. H. Nam, eds., Proc. SPIE 2778, 806–807 (1996).

Kim, C. M.

J. M. Kim, K. S. Kim, C. J. Kim, and C. M. Kim, in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. S. Chang, J. H. Lee, S. Y. Lee, and C. H. Nam, eds., Proc. SPIE 2778, 806–807 (1996).

Kim, J. M.

J. M. Kim, K. S. Kim, C. J. Kim, and C. M. Kim, in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. S. Chang, J. H. Lee, S. Y. Lee, and C. H. Nam, eds., Proc. SPIE 2778, 806–807 (1996).

Kim, K. S.

J. M. Kim, K. S. Kim, C. J. Kim, and C. M. Kim, in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. S. Chang, J. H. Lee, S. Y. Lee, and C. H. Nam, eds., Proc. SPIE 2778, 806–807 (1996).

Maier, T. D.

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laser-experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Murphy Jr., T. W.

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laser-experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Ott, E.

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

Pyragas, K.

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

Roy, R.

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laser-experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Yorke, J. A.

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

Phys. Lett. A (1)

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

Phys. Rev. E (1)

P. Colet and Y. Braiman, “Control of chaos in multimode solid state lasers by the use of small periodic perturbations,” Phys. Rev. E 53, 200 (1996).
[CrossRef]

Phys. Rev. Lett. (3)

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

E. R. Hunt, “Stabilizing high-period orbits in a chaotic system-the diode resonator,” Phys. Rev. Lett. 67, 1953 (1991).
[CrossRef] [PubMed]

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laser-experimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Proc. SPIE (1)

J. M. Kim, K. S. Kim, C. J. Kim, and C. M. Kim, in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. S. Chang, J. H. Lee, S. Y. Lee, and C. H. Nam, eds., Proc. SPIE 2778, 806–807 (1996).

Other (13)

W. Koechner, Solid-state Laser Engineering (Springer-Verlag, Berlin, 1995).

H. G. Schuster, Deterministic Chaos (VCH Verlagesellschaft, MbH, Weinheim, 1994).

R. Lima and M. Pettini, “Suppression of chaos by resonant parametric perturbations,” Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, “Taming chaotic dynamics with weak periodic perturbations,” Phys. Rev. Lett. 66, 2545 (1991); S. T. Vohra, L. Fabing, and F. Bucholtz, “Suppressed and induced chaos by near resonant perturbation of bifurcations,” Phys. Rev. Lett. PRLTAO 75, 65 (1995); M. Salerno, “Suppression of phase-locked chaos in long Josephson junctions by biharmonic microwave fields,” Phys. Rev. B PRBMDO 44, 2720 (1991); G. Filatrella, G. Rotoli, and M. Salerno, “Suppression of chaos in the perturbed sine–Gordon system by weak periodic signals,” Phys. Lett. A PYLAAG 178, 81 (1993); R. Chacon and J. D. Bejarano, “Routes to suppressing chaos by weak periodic perturbations,” Phys. Rev. Lett. PRLTAO 71, 3103 (1993); R. Chacon, “Inhibition of chaos in Hamiltonian systems by periodic pulses,” Phys. Rev. E PLEEE8 50, 750 (1994); R.-R. Hsu, H.-T. Su, J.-L. Chern, and C.-C. Chen, “Conditions to control chaotic dynamics by weak periodic perturbation,” Phys. Rev. Lett. PRLTAO 78, 2936 (1997).
[CrossRef] [PubMed]

A. Azevedo and S. M. Rezende, “Controlling chaos in spin-wave instabilities,” Phys. Rev. Lett. 66, 1342 (1991); W. X. Ding, H. Q. She, W. Huang, and C. X. Yu, “Controlling chaos in a discharge plasma,” Phys. Rev. Lett. 72, 96 (1994); L. Fronzoni, M. Giocondo, and M. Pettini, “Experimental evidence of suppression of chaos by resonant parametric perturbations,” Phys. Rev. A PLRAAN 43, 6483 (1991); H.-J. Li and J.-L. Chern, “Goal-oriented scheme for taming chaos with a weak periodic perturbation experiment in a diode resonator,” Phys. Rev. E PLEEE8 54, 2118 (1996).
[CrossRef] [PubMed]

Y. D. Liu and J. R. Rios Leite, “Control of Lorenz chaos,” Phys. Lett. A 185, 35 (1994); R. Vilaseca, A. Kul’minskii, and R. Corbalán, “Tracking unstable steady states by large periodic modulation of control parameter in a nonlinear system,” Phys. Rev. E 54, 82 (1996).
[CrossRef]

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by means of weak parametric perturbations,” Phys. Rev. E 49, R2528 (1994); V. N. Chizhevsky and R. Corbalán, “Experimental observation of perturbation-induced intermittency in the dynamics of a loss-modulated CO2 Laser,” Phys. Rev. E 54, 4576 (1996); M. Ciofini, R. Meucci, and F. T. Arecchi, “Experimental control of chaos in a laser,” Phys. Rev. E PLEEE8 52, 94 (1995).
[CrossRef]

N. Watanabe and K. Karaki, “Inducing periodic oscillations from chaotic oscillations of a compound-cavity laser diode with sinusoidally modulated drive,” Opt. Lett. 20, 1032 (1995); “Improvement of interference fringes of a laser diode interferometer by controlling chaos with sinusoidally modulated injection,” Opt. Lett. 21, 1256 (1996).
[CrossRef] [PubMed]

V. Petrov, V. Gáspár, J. Masere, and K. Showalter, “Controlling chaos in the Belousov–Zhabotinsky reaction,” Nature (London) 361, 240 (1993); V. Petrov, S. K. Scott, and K. Showalter, “Mixed-mode oscillations in chemical systems,” J. Chem. Phys. 97, 6191 (1992).
[CrossRef]

R. Wilbrandt and H. Weber, “Fluctuations in mode-locking threshold due to statistics of spontaneous emission,” IEEE J. Quantum Electron. QE-11, 186 (1975); K. Kaufmann and G. Marowsky, Appl. Phys. 11, 47 (1976); C. O. Weiss and H. King, “Oscillation period doubling chaos in a laser,” Opt. Commun. OPCOB8 44, 58 (1982); C. O. Weiss, A. Godone, and A. Olafsson, “Routes to chaotic emission in a cw He–Ne laser,” Phys. Rev. A PLRAAN 28, 892 (1983).
[CrossRef]

L. A. Lugiato, G.-L. Oppo, M. A. Pernigo, J. R. Tredicce, L. M. Narducci, and D. K. Bandy, “Spontaneously spatial pattern formation in lasers and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: the experimental side,” Opt. Commun. 65, 3124 (1990); M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Parti, A. J. Kent, G.-L. Oppo, A. B. Coates, C. O. Weiss, G. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A PLRAAN 49, 1427 (1994); A. B. Coates, C. O. Weiss, G. Green, E. J. D’Angelo, J. R. Tredicce, M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Prati, A. J. Kent, and G.-L. Oppo, “Dynamical transverse laser patterns. II. Experiments,” Phys. Rev. A PLRAAN 49, 1452 (1994); M. Brambilla, F. Battiped, L. A. Lugiato, V. Penna, F. Parti, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A PLRAAN 43, 5090 (1991).
[CrossRef] [PubMed]

D. J. Biaswas and R. G. Harrison, “Experimental evidence of three-mode quasi-periodicity and chaos in a single longitudinal, multi-transverse-mode cw CO2 laser,” Phys. Rev. A 32, 3835 (1985); R. Hauck, F. Hollinger, and H. Weber, “Chaotic and periodic emission of high power solid state lasers,” Opt. Commun. 47, 141 (1983); M.-L. Shih, P. W. Milonni, and J. R. Ackerhalt, “Modeling chaos in the secondary beat frequency,” J. Opt. Soc. Am. B JOBPDE 2, 130 (1985); F. Hollinger, Ch. Jung, and H. Weber, “Quasiperiodicity versus chaos in high power solid state lasers in multi-transversal mode operation,” Opt. Commun. OPCOB8 75, 85 (1990); C. Tamm, “Frequency locking of two transverse optical modes of a laser,” Phys. Rev. A PLRAAN 38, 5960 (1988).
[CrossRef] [PubMed]

M. Shih and P. W. Milonni, “Chaotic two-mode lasing,” Opt. Commun. 49, 155 (1984); F. Hollinger and Ch. Jung, “Single-longitudinal-mode laser as a discrete dynamical system,” J. Opt. Soc. Am. B 2, 218 (1985).
[CrossRef]

B. S. Poh and T. E. Rozzi, “Intrinsic instabilities in narrow stripe geometry lasers caused by lateral current spreading,” IEEE J. Quantum Electron. QE-17, 723 (1981); N. J. Halas, S. N. Liu, and N. B. Abraham, “Route to mode locking in a three-mode He–Ne 3.39-μm laser including chaos in the secondary beat frequency,” Phys. Rev. A 28, 2915 (1983); G.-L. Oppo, J. R. Tredicce, and L. M. Narducci, “Dynamics of vibro-rotational CO2 laser transitions in a two-dimensional phase space,” Opt. Commun. OPCOB8 69, 393 (1989); J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. PRLTAO 62, 1274 (1989); W. Klische, C. O. Weiss, and B. Wellegehausen, “Spatiotemporal chaos from a continuous Na2 laser,” Phys. Rev. A PLRAAN 39, 919 (1989).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup.

Fig. 2
Fig. 2

Power spectra of the laser output when the LD current is (a) 390 mA, (b) 400 mA, (c) 450 mA.

Fig. 3
Fig. 3

(a) Temporal behavior of the chaotic output of the laser when the additive current is zero with stabilized outputs of (b) period 1T at 87.80 kHz of additive current frequency, (c) period 2T at 46.10 kHz, (d) period 3T at 30.60 kHz, (e) period 4T at 12.31 kHz, (f) period 5T at 18.60 kHz, and (g) a suppressed output at 100.43 kHz. In (b)–(g) the added sinusoidal current is 25 mA.

Fig. 4
Fig. 4

(a) Corresponding frequency spectra of Fig. 3(b) at 87.80 kHz, (b) Fig. 3(c) at 46.10 kHz, (c) Fig. 3(d) at 30.60 kHz, (d) Fig. 3(e) at 12.31 kHz, and (e) Fig. 3(f) at 18.60 kHz.

Fig. 5
Fig. 5

Phase diagrams of regions stabilized by a small additive signal. Regions (1), (2), (3), (4), and (7) represent the locking ranges for stable orbits with periods 4T, 5T, 3T, 2T, and 1T, respectively. Regions (5) and (6) represent locking ranges of quasi-periodicity. Vertical dashed–dotted lines represent the fundamental (fr) and the subharmonic relaxation-oscillation (fr/n) frequencies (n=2, 3, 4, 5, 8). Chaotic output is suppressed in the region labeled “suppressed.”

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