Abstract
We employed additive modulation of a laserdiode current to demonstrate dramatic suppression of chaos in the output of a laserdiodepumped multimode Nd:YAG laser. Stable periodic orbits were found to depend on the amplitude and the frequency modulation.
© 1998 Optical Society of America
OCIS Codes
(140.1540) Lasers and laser optics : Chaos
(140.3530) Lasers and laser optics : Lasers, neodymium
Citation
Minhee Kang, Kyuman Cho, ChilMin Kim, SangKun Gil, and JaeChul Lee, "Taming chaos of a laserdiodepumped multimode Nd:YAG laser by small periodic modulation," J. Opt. Soc. Am. B 15, 24102415 (1998)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab1592410
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References

R. Wilbrandt and H. Weber, “Fluctuations in modelocking threshold due to statistics of spontaneous emission,” IEEE J. Quantum Electron. QE11, 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).

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).

D. J. Biaswas and R. G. Harrison, “Experimental evidence of threemode quasiperiodicity and chaos in a single longitudinal, multitransversemode cw CO_{2} 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 multitransversal 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).

M. Shih and P. W. Milonni, “Chaotic twomode lasing,” Opt. Commun. 49, 155 (1984); F. Hollinger and Ch. Jung, “Singlelongitudinalmode laser as a discrete dynamical system,” J. Opt. Soc. Am. B 2, 218 (1985).

B. S. Poh and T. E. Rozzi, “Intrinsic instabilities in narrow stripe geometry lasers caused by lateral current spreading,” IEEE J. Quantum Electron. QE17, 723 (1981); N. J. Halas, S. N. Liu, and N. B. Abraham, “Route to mode locking in a threemode He–Ne 3.39μm 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 vibrorotational CO_{2} laser transitions in a twodimensional 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 CO_{2} laser,” Phys. Rev. Lett. PRLTAO 62, 1274 (1989); W. Klische, C. O. Weiss, and B. Wellegehausen, “Spatiotemporal chaos from a continuous Na_{2} laser,” Phys. Rev. A PLRAAN 39, 919 (1989).

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

E. R. Hunt, “Stabilizing highperiod orbits in a chaotic systemthe diode resonator,” Phys. Rev. Lett. 67, 1953 (1991).

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

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, “Mixedmode oscillations in chemical systems,” J. Chem. Phys. 97, 6191 (1992).

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).

K. Pyragas, “Continuous control of chaos by selfcontrolling feedback,” Phys. Lett. A 170, 421 (1992).

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 phaselocked 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).

A. Azevedo and S. M. Rezende, “Controlling chaos in spinwave 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, “Goaloriented scheme for taming chaos with a weak periodic perturbation experiment in a diode resonator,” Phys. Rev. E PLEEE8 54, 2118 (1996).

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).

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 perturbationinduced intermittency in the dynamics of a lossmodulated CO_{2} 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).

N. Watanabe and K. Karaki, “Inducing periodic oscillations from chaotic oscillations of a compoundcavity 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).

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).

W. Koechner, Solidstate Laser Engineering (SpringerVerlag, Berlin, 1995).

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

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laserexperimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
Grebogi, C.

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64, 1196 (1990).
Hunt, E. R.

E. R. Hunt, “Stabilizing highperiod orbits in a chaotic systemthe diode resonator,” Phys. Rev. Lett. 67, 1953 (1991).
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 laserexperimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
Murphy Jr., T. W.

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laserexperimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
Ott, E.

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64, 1196 (1990).
Pyragas, K.

K. Pyragas, “Continuous control of chaos by selfcontrolling feedback,” Phys. Lett. A 170, 421 (1992).
Roy, R.

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laserexperimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
Yorke, J. A.

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

K. Pyragas, “Continuous control of chaos by selfcontrolling feedback,” Phys. Lett. A 170, 421 (1992).
Phys. Rev. E

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).
Phys. Rev. Lett.

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

E. R. Hunt, “Stabilizing highperiod orbits in a chaotic systemthe diode resonator,” Phys. Rev. Lett. 67, 1953 (1991).

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laserexperimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
Proc. SPIE

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

W. Koechner, Solidstate Laser Engineering (SpringerVerlag, 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 phaselocked 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).

A. Azevedo and S. M. Rezende, “Controlling chaos in spinwave 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, “Goaloriented scheme for taming chaos with a weak periodic perturbation experiment in a diode resonator,” Phys. Rev. E PLEEE8 54, 2118 (1996).

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).

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 perturbationinduced intermittency in the dynamics of a lossmodulated CO_{2} 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).

N. Watanabe and K. Karaki, “Inducing periodic oscillations from chaotic oscillations of a compoundcavity 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).

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, “Mixedmode oscillations in chemical systems,” J. Chem. Phys. 97, 6191 (1992).

R. Wilbrandt and H. Weber, “Fluctuations in modelocking threshold due to statistics of spontaneous emission,” IEEE J. Quantum Electron. QE11, 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).

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).

D. J. Biaswas and R. G. Harrison, “Experimental evidence of threemode quasiperiodicity and chaos in a single longitudinal, multitransversemode cw CO_{2} 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 multitransversal 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).

M. Shih and P. W. Milonni, “Chaotic twomode lasing,” Opt. Commun. 49, 155 (1984); F. Hollinger and Ch. Jung, “Singlelongitudinalmode laser as a discrete dynamical system,” J. Opt. Soc. Am. B 2, 218 (1985).

B. S. Poh and T. E. Rozzi, “Intrinsic instabilities in narrow stripe geometry lasers caused by lateral current spreading,” IEEE J. Quantum Electron. QE17, 723 (1981); N. J. Halas, S. N. Liu, and N. B. Abraham, “Route to mode locking in a threemode He–Ne 3.39μm 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 vibrorotational CO_{2} laser transitions in a twodimensional 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 CO_{2} laser,” Phys. Rev. Lett. PRLTAO 62, 1274 (1989); W. Klische, C. O. Weiss, and B. Wellegehausen, “Spatiotemporal chaos from a continuous Na_{2} laser,” Phys. Rev. A PLRAAN 39, 919 (1989).
1996, Kim, Proc. SPIE

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).
1996, Colet, Phys. Rev. E

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).
1992, Roy, Phys. Rev. Lett.

R. Roy, T. W. Murphy, Jr., T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laserexperimental stabilization of a globally coupled system,” Phys. Rev. Lett. 68, 1259 (1992).
1992, Pyragas, Phys. Lett. A

K. Pyragas, “Continuous control of chaos by selfcontrolling feedback,” Phys. Lett. A 170, 421 (1992).
1991, Hunt, Phys. Rev. Lett.

E. R. Hunt, “Stabilizing highperiod orbits in a chaotic systemthe diode resonator,” Phys. Rev. Lett. 67, 1953 (1991).
1990, Ott, Phys. Rev. Lett.

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