Abstract

This work demonstrates the suppression of chaos in a Nd:YVO4 laser by biharmonical pump modulation (the first for chaos-inducing and the second for chaos-suppressing). The laser exhibits chaotic behavior when only the first signal is applied for pump modulation and its frequency is adjusted close to the relaxation-oscillation frequency. Adding the second signal with subhamonic and a specific phase difference to the first modulation signal will reshape the modulated waveform of the pump beam to suppress the aforementioned chaotic behavior. The initial phase of the second harmonic perturbation plays an important role in the suppression of chaos. This result is confirmed by numerical simulation.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64(11), 1196–1199 (1990).
    [CrossRef] [PubMed]
  2. T. Kapitaniak, Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics (Academic Press,1996).
  3. 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]
  4. R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by mean of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), 2528–2531 (1994).
    [CrossRef]
  5. K. Otsuka, J.-L. Chern, and J.-S. Lih, “Experimental suppression of chaos in a modulated multimode laser,” Opt. Lett. 22(5), 292–294 (1997).
    [CrossRef] [PubMed]
  6. A. Uchida, T. Sato, and F. Kannari, “Suppression of chaotic oscillations in a microchip laser by injection of a new orbit into the chaotic attractor,” Opt. Lett. 23(6), 460–462 (1998).
    [CrossRef]
  7. P. Colet and Y. Braiman, “Control of chaos in multimode solid state lasers by the use of small periodic perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 200–206 (1996).
    [CrossRef] [PubMed]
  8. R. Chacón, “Geometrical resonance as a chaos eliminating mechanism,” Phys. Rev. Lett. 77(3), 482–485 (1996).
    [CrossRef] [PubMed]
  9. R. Chacón, “Maintenance and suppression of chaos by weak harmonic perturbations: a unified view,” Phys. Rev. Lett. 86(9), 1737–1740 (2001).
    [CrossRef] [PubMed]
  10. V. N. Chizhevsky, R. Corbalán, and A. N. Pisarchik, “Attractor splitting induced by resonant perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(2), 1580–1584 (1997).
    [CrossRef]
  11. I. B. Schwartz, I. Triandaf, R. Meucci, and T. W. Carr, “Open-loop sustained chaos and control: a manifold approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 026213 (2002).
    [CrossRef] [PubMed]
  12. W. Klische, H. R. Telle, and C. O. Weiss, “Chaos in a solid-state laser with a periodically modulated pump,” Opt. Lett. 9(12), 561–563 (1984).
    [CrossRef] [PubMed]
  13. M.-D. Wei, C.-H. Chen, H.-H. Wu, D.-Y. Huang, and C.-H. Chen, “Chaos suppression in the transverse mode degeneracy regime of a pump-modulated Nd:YVO4 laser,” J. Opt. A 11, 045504 (2009).
  14. C.-H. Chen, M.-D. Wei, and W.-F. Hsieh, “Beam-propagation-dominant instability in an axially pumped solid-state laser near degenerate resonator configurations,” J. Opt. Soc. Am. B 18(8), 1076–1083 (2001).
    [CrossRef]

2009 (1)

M.-D. Wei, C.-H. Chen, H.-H. Wu, D.-Y. Huang, and C.-H. Chen, “Chaos suppression in the transverse mode degeneracy regime of a pump-modulated Nd:YVO4 laser,” J. Opt. A 11, 045504 (2009).

2002 (1)

I. B. Schwartz, I. Triandaf, R. Meucci, and T. W. Carr, “Open-loop sustained chaos and control: a manifold approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 026213 (2002).
[CrossRef] [PubMed]

2001 (2)

1998 (1)

1997 (2)

K. Otsuka, J.-L. Chern, and J.-S. Lih, “Experimental suppression of chaos in a modulated multimode laser,” Opt. Lett. 22(5), 292–294 (1997).
[CrossRef] [PubMed]

V. N. Chizhevsky, R. Corbalán, and A. N. Pisarchik, “Attractor splitting induced by resonant perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(2), 1580–1584 (1997).
[CrossRef]

1996 (2)

P. Colet and Y. Braiman, “Control of chaos in multimode solid state lasers by the use of small periodic perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 200–206 (1996).
[CrossRef] [PubMed]

R. Chacón, “Geometrical resonance as a chaos eliminating mechanism,” Phys. Rev. Lett. 77(3), 482–485 (1996).
[CrossRef] [PubMed]

1994 (1)

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by mean of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), 2528–2531 (1994).
[CrossRef]

1992 (1)

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]

1990 (1)

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

1984 (1)

Arecchi, F. T.

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by mean of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), 2528–2531 (1994).
[CrossRef]

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 Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 200–206 (1996).
[CrossRef] [PubMed]

Carr, T. W.

I. B. Schwartz, I. Triandaf, R. Meucci, and T. W. Carr, “Open-loop sustained chaos and control: a manifold approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 026213 (2002).
[CrossRef] [PubMed]

Chacón, R.

R. Chacón, “Maintenance and suppression of chaos by weak harmonic perturbations: a unified view,” Phys. Rev. Lett. 86(9), 1737–1740 (2001).
[CrossRef] [PubMed]

R. Chacón, “Geometrical resonance as a chaos eliminating mechanism,” Phys. Rev. Lett. 77(3), 482–485 (1996).
[CrossRef] [PubMed]

Chen, C.-H.

M.-D. Wei, C.-H. Chen, H.-H. Wu, D.-Y. Huang, and C.-H. Chen, “Chaos suppression in the transverse mode degeneracy regime of a pump-modulated Nd:YVO4 laser,” J. Opt. A 11, 045504 (2009).

M.-D. Wei, C.-H. Chen, H.-H. Wu, D.-Y. Huang, and C.-H. Chen, “Chaos suppression in the transverse mode degeneracy regime of a pump-modulated Nd:YVO4 laser,” J. Opt. A 11, 045504 (2009).

C.-H. Chen, M.-D. Wei, and W.-F. Hsieh, “Beam-propagation-dominant instability in an axially pumped solid-state laser near degenerate resonator configurations,” J. Opt. Soc. Am. B 18(8), 1076–1083 (2001).
[CrossRef]

Chern, J.-L.

Chizhevsky, V. N.

V. N. Chizhevsky, R. Corbalán, and A. N. Pisarchik, “Attractor splitting induced by resonant perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(2), 1580–1584 (1997).
[CrossRef]

Ciofini, M.

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by mean of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), 2528–2531 (1994).
[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 Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 200–206 (1996).
[CrossRef] [PubMed]

Corbalán, R.

V. N. Chizhevsky, R. Corbalán, and A. N. Pisarchik, “Attractor splitting induced by resonant perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(2), 1580–1584 (1997).
[CrossRef]

Gadomski, W.

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by mean of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), 2528–2531 (1994).
[CrossRef]

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]

Grebogi, C.

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

Hsieh, W.-F.

Huang, D.-Y.

M.-D. Wei, C.-H. Chen, H.-H. Wu, D.-Y. Huang, and C.-H. Chen, “Chaos suppression in the transverse mode degeneracy regime of a pump-modulated Nd:YVO4 laser,” J. Opt. A 11, 045504 (2009).

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.

Klische, W.

Lih, J.-S.

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.

I. B. Schwartz, I. Triandaf, R. Meucci, and T. W. Carr, “Open-loop sustained chaos and control: a manifold approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 026213 (2002).
[CrossRef] [PubMed]

R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by mean of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), 2528–2531 (1994).
[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]

Otsuka, K.

Ott, E.

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

Pisarchik, A. N.

V. N. Chizhevsky, R. Corbalán, and A. N. Pisarchik, “Attractor splitting induced by resonant perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(2), 1580–1584 (1997).
[CrossRef]

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]

Sato, T.

Schwartz, I. B.

I. B. Schwartz, I. Triandaf, R. Meucci, and T. W. Carr, “Open-loop sustained chaos and control: a manifold approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 026213 (2002).
[CrossRef] [PubMed]

Telle, H. R.

Triandaf, I.

I. B. Schwartz, I. Triandaf, R. Meucci, and T. W. Carr, “Open-loop sustained chaos and control: a manifold approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 026213 (2002).
[CrossRef] [PubMed]

Uchida, A.

Wei, M.-D.

M.-D. Wei, C.-H. Chen, H.-H. Wu, D.-Y. Huang, and C.-H. Chen, “Chaos suppression in the transverse mode degeneracy regime of a pump-modulated Nd:YVO4 laser,” J. Opt. A 11, 045504 (2009).

C.-H. Chen, M.-D. Wei, and W.-F. Hsieh, “Beam-propagation-dominant instability in an axially pumped solid-state laser near degenerate resonator configurations,” J. Opt. Soc. Am. B 18(8), 1076–1083 (2001).
[CrossRef]

Weiss, C. O.

Wu, H.-H.

M.-D. Wei, C.-H. Chen, H.-H. Wu, D.-Y. Huang, and C.-H. Chen, “Chaos suppression in the transverse mode degeneracy regime of a pump-modulated Nd:YVO4 laser,” J. Opt. A 11, 045504 (2009).

Yorke, J. A.

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

J. Opt. A (1)

M.-D. Wei, C.-H. Chen, H.-H. Wu, D.-Y. Huang, and C.-H. Chen, “Chaos suppression in the transverse mode degeneracy regime of a pump-modulated Nd:YVO4 laser,” J. Opt. A 11, 045504 (2009).

J. Opt. Soc. Am. B (1)

Opt. Lett. (3)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

I. B. Schwartz, I. Triandaf, R. Meucci, and T. W. Carr, “Open-loop sustained chaos and control: a manifold approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 026213 (2002).
[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 mean of weak parametric perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(4), 2528–2531 (1994).
[CrossRef]

P. Colet and Y. Braiman, “Control of chaos in multimode solid state lasers by the use of small periodic perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 200–206 (1996).
[CrossRef] [PubMed]

V. N. Chizhevsky, R. Corbalán, and A. N. Pisarchik, “Attractor splitting induced by resonant perturbations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(2), 1580–1584 (1997).
[CrossRef]

Phys. Rev. Lett. (4)

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]

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

R. Chacón, “Geometrical resonance as a chaos eliminating mechanism,” Phys. Rev. Lett. 77(3), 482–485 (1996).
[CrossRef] [PubMed]

R. Chacón, “Maintenance and suppression of chaos by weak harmonic perturbations: a unified view,” Phys. Rev. Lett. 86(9), 1737–1740 (2001).
[CrossRef] [PubMed]

Other (1)

T. Kapitaniak, Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics (Academic Press,1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

The experimental setup: OL, objective lens; OC, output coupler; PD, photodetector; LD, laser diode; FG1 and FG2, function generator 1 and 2; OSC, oscilloscope; RFSA, RF spectrum analyzer.

Fig. 2
Fig. 2

The time evolutions of output laser and pump laser with various initial phases shown in the left column (a)-(c) and in the right column (d)-(f), respectively, in which pm1 = 15.7% and pm2 = 32.3%.

Fig. 3
Fig. 3

The boundaries of chaos-suppressed regions with various pm1. A periodic intensity was observed inside each region.

Fig. 4
Fig. 4

Numerical results for the boundaries of chaos-suppressed regions with various pm1.

Equations (4)

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

E n + ( r ) = ρ E n ( r ) exp [ σ Δ N n ( r ) d ] ,
E n + 1 ( r ) = 2 π i λ B e i 2 k L E n + ( r ) exp [ i π λ B ( A r 2 + D r 2 ) ] J 0 ( 2 π r r λ B ) r d r ,
Δ N n + 1 ( r ) = Δ N n ( r ) + R n ( r ) Δ t γ Δ N n ( r ) Δ t γ ( | E n ( r ) | 2 / E s 2 ) Δ N n ( r ) Δ t ,
R n ( r ) = R p m ( r ) [ 1 + p m 1 sin ( 2 π f m 1 n t r ) + p m 2 sin ( 2 π f m 2 n t r + φ ) ] .

Metrics