Abstract

We have investigated the transition route in a gain-modulated intracavity frequency-doubled Nd:YAG laser pumped by a laser diode when a small gain is modulated periodically. Through analysis of the probability distribution and the scaling relationship as the parameters of a laser system are varied, we ascertained that the intermittent laser operation of the intracavity second harmonics is an on–off intermittency. This is what we believe is the first observation of the transition route in a gain-modulated laser system. As further evidence of this transition route, similar intermittent behaviors were obtained in an acousto-optically Q-switched Nd:YAG laser pumped by a laser diode.

© 2003 Optical Society of America

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References

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  1. F. Hollinger, C. Jung, and D. Hennequin, “Single-longitudinal-mode laser as a discrete dynamical system,” J. Opt. Soc. Am. B 2, 218-225 (1985).
    [CrossRef]
  2. D. Dangoisse, P. Glorieux, and D. Hennequin, “Chaos in a CO2 laser with modulated parameters: experiments and numerical simulations,” Phys. Rev. A 36, 4775-4791 (1987).
    [CrossRef] [PubMed]
  3. U. Morgner and F. Mitschke, “Drift instabilities in the pulses from cw mode-locked lasers,” Phys. Rev. E 58, 187-192 (1998).
    [CrossRef]
  4. C. J. Kennedy and J. D. Barry, “Stability of an intracavity frequency-doubled Nd:YAG laser,” IEEE J. Quantum Electron. QE-10, 596-599 (1974).
    [CrossRef]
  5. T. Baer, “Large-amplitude fluctuations due to longitudinal mode coupling in diode-pumped intracavity-doubled Nd:YAG lasers,” J. Opt. Soc. Am. B 3, 1175-1180 (1986).
    [CrossRef]
  6. G. E. James, E. M. Harrell II, and R. Roy, “Intermittency and chaos in intracavity doubled lasers,” Phys. Rev. A 41, 2778-2790 (1990).
    [CrossRef] [PubMed]
  7. C. Bracikowski and R. Roy, “Chaos in a multimode solid state laser system,” Chaos 1, 49-64 (1991).
    [CrossRef] [PubMed]
  8. S. H. Gong and C. M. Kim, “On-off intermittency in the threshold of a continuous-wave Nd:YAG laser,” J. Opt. Soc. Am. B 18, 1285-1287 (2001).
    [CrossRef]
  9. K. V. Volochenko, V. N. Ivanov, D.-S. Lee, S. H. Gong, and C. M. Kim, “On-off intermittency in the threshold of mode locking in a Nd:YAG laser,” J. Opt. Soc. Am. B 19, 198-201 (2001).
    [CrossRef]
  10. H. Fujisaka and T. Yamada, “A new intermittency in coupled dynamical systems,” Prog. Theor. Phys. 74, 918-921 (1985).
    [CrossRef]
  11. N. Platt, E. A. Spiegel, and C. Tresser, “On-off intermittency: a mechanism for bursting,” Phys. Rev. Lett. 70, 279-282 (1993).
    [CrossRef] [PubMed]
  12. J. F. Heagy, N. Platt, and S. M. Hammel, “Characterization of on-off intermittency,” Phys. Rev. E 49, 1140-1150 (1994).
    [CrossRef]
  13. N. Platt, S. M. Hammel, and J. F. Heagy, “Effects of additive noise on on-off intermittency,” Phys. Rev. Lett. 72, 3498-3501 (1994).
    [CrossRef] [PubMed]
  14. P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, “Experimental observation of on-off intermittency,” Phys. Rev. Lett. 73, 1095-1098 (1994).
    [CrossRef] [PubMed]
  15. L. Yu, E. Ott, and Q. Chen, “Transition to chaos for random dynamical systems,” Phys. Rev. Lett. 65, 2935-2938 (1990).
    [CrossRef] [PubMed]
  16. D. J. Gauthier and J. C. Bienfang, “Intermittent loss of synchronization in coupled chaotic oscillators: toward a new criterion for high-quality synchronization,” Phys. Rev. Lett. 77, 1751-1754 (1996).
    [CrossRef] [PubMed]
  17. H. L. Yang and E. J. Ding, “Synchronization of chaotic systems and on-off intermittency,” Phys. Rev. E 54, 1361-1365 (1996).
    [CrossRef]
  18. Y. C. Lai and C. Grebogi, “Intermingled basins and two-state on-off intermittency,” Phys. Rev. E 52, R3313-R3316 (1995).
    [CrossRef]
  19. F. Xie, G. Hu, and Z. Qu, “On-off intermittency in a coupled-map lattice system,” Phys. Rev. E 52, R1265-R1268 (1995).
    [CrossRef]
  20. M. Ding and W. Yang, “Distribution of the first return time in fractional Brownian motion and its application to the study of on-off intermittency,” Phys. Rev. E 52, 207-213 (1995).
    [CrossRef]
  21. S. Rim, D. W. Hwang, I. Kim, and C. M. Kim, “Chaotic transition of random dynamical systems and chaos synchronization by common noises,” Phys. Rev. Lett. 85, 2304–2307 (2000).
    [CrossRef] [PubMed]

2001 (2)

2000 (1)

S. Rim, D. W. Hwang, I. Kim, and C. M. Kim, “Chaotic transition of random dynamical systems and chaos synchronization by common noises,” Phys. Rev. Lett. 85, 2304–2307 (2000).
[CrossRef] [PubMed]

1998 (1)

U. Morgner and F. Mitschke, “Drift instabilities in the pulses from cw mode-locked lasers,” Phys. Rev. E 58, 187-192 (1998).
[CrossRef]

1996 (2)

D. J. Gauthier and J. C. Bienfang, “Intermittent loss of synchronization in coupled chaotic oscillators: toward a new criterion for high-quality synchronization,” Phys. Rev. Lett. 77, 1751-1754 (1996).
[CrossRef] [PubMed]

H. L. Yang and E. J. Ding, “Synchronization of chaotic systems and on-off intermittency,” Phys. Rev. E 54, 1361-1365 (1996).
[CrossRef]

1995 (3)

Y. C. Lai and C. Grebogi, “Intermingled basins and two-state on-off intermittency,” Phys. Rev. E 52, R3313-R3316 (1995).
[CrossRef]

F. Xie, G. Hu, and Z. Qu, “On-off intermittency in a coupled-map lattice system,” Phys. Rev. E 52, R1265-R1268 (1995).
[CrossRef]

M. Ding and W. Yang, “Distribution of the first return time in fractional Brownian motion and its application to the study of on-off intermittency,” Phys. Rev. E 52, 207-213 (1995).
[CrossRef]

1994 (3)

J. F. Heagy, N. Platt, and S. M. Hammel, “Characterization of on-off intermittency,” Phys. Rev. E 49, 1140-1150 (1994).
[CrossRef]

N. Platt, S. M. Hammel, and J. F. Heagy, “Effects of additive noise on on-off intermittency,” Phys. Rev. Lett. 72, 3498-3501 (1994).
[CrossRef] [PubMed]

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, “Experimental observation of on-off intermittency,” Phys. Rev. Lett. 73, 1095-1098 (1994).
[CrossRef] [PubMed]

1993 (1)

N. Platt, E. A. Spiegel, and C. Tresser, “On-off intermittency: a mechanism for bursting,” Phys. Rev. Lett. 70, 279-282 (1993).
[CrossRef] [PubMed]

1991 (1)

C. Bracikowski and R. Roy, “Chaos in a multimode solid state laser system,” Chaos 1, 49-64 (1991).
[CrossRef] [PubMed]

1990 (2)

L. Yu, E. Ott, and Q. Chen, “Transition to chaos for random dynamical systems,” Phys. Rev. Lett. 65, 2935-2938 (1990).
[CrossRef] [PubMed]

G. E. James, E. M. Harrell II, and R. Roy, “Intermittency and chaos in intracavity doubled lasers,” Phys. Rev. A 41, 2778-2790 (1990).
[CrossRef] [PubMed]

1987 (1)

D. Dangoisse, P. Glorieux, and D. Hennequin, “Chaos in a CO2 laser with modulated parameters: experiments and numerical simulations,” Phys. Rev. A 36, 4775-4791 (1987).
[CrossRef] [PubMed]

1986 (1)

1985 (2)

H. Fujisaka and T. Yamada, “A new intermittency in coupled dynamical systems,” Prog. Theor. Phys. 74, 918-921 (1985).
[CrossRef]

F. Hollinger, C. Jung, and D. Hennequin, “Single-longitudinal-mode laser as a discrete dynamical system,” J. Opt. Soc. Am. B 2, 218-225 (1985).
[CrossRef]

1974 (1)

C. J. Kennedy and J. D. Barry, “Stability of an intracavity frequency-doubled Nd:YAG laser,” IEEE J. Quantum Electron. QE-10, 596-599 (1974).
[CrossRef]

Baer, T.

Barry, J. D.

C. J. Kennedy and J. D. Barry, “Stability of an intracavity frequency-doubled Nd:YAG laser,” IEEE J. Quantum Electron. QE-10, 596-599 (1974).
[CrossRef]

Bienfang, J. C.

D. J. Gauthier and J. C. Bienfang, “Intermittent loss of synchronization in coupled chaotic oscillators: toward a new criterion for high-quality synchronization,” Phys. Rev. Lett. 77, 1751-1754 (1996).
[CrossRef] [PubMed]

Bracikowski, C.

C. Bracikowski and R. Roy, “Chaos in a multimode solid state laser system,” Chaos 1, 49-64 (1991).
[CrossRef] [PubMed]

Chen, Q.

L. Yu, E. Ott, and Q. Chen, “Transition to chaos for random dynamical systems,” Phys. Rev. Lett. 65, 2935-2938 (1990).
[CrossRef] [PubMed]

Dangoisse, D.

D. Dangoisse, P. Glorieux, and D. Hennequin, “Chaos in a CO2 laser with modulated parameters: experiments and numerical simulations,” Phys. Rev. A 36, 4775-4791 (1987).
[CrossRef] [PubMed]

Ding, E. J.

H. L. Yang and E. J. Ding, “Synchronization of chaotic systems and on-off intermittency,” Phys. Rev. E 54, 1361-1365 (1996).
[CrossRef]

Ding, M.

M. Ding and W. Yang, “Distribution of the first return time in fractional Brownian motion and its application to the study of on-off intermittency,” Phys. Rev. E 52, 207-213 (1995).
[CrossRef]

Fujisaka, H.

H. Fujisaka and T. Yamada, “A new intermittency in coupled dynamical systems,” Prog. Theor. Phys. 74, 918-921 (1985).
[CrossRef]

Gauthier, D. J.

D. J. Gauthier and J. C. Bienfang, “Intermittent loss of synchronization in coupled chaotic oscillators: toward a new criterion for high-quality synchronization,” Phys. Rev. Lett. 77, 1751-1754 (1996).
[CrossRef] [PubMed]

Glorieux, P.

D. Dangoisse, P. Glorieux, and D. Hennequin, “Chaos in a CO2 laser with modulated parameters: experiments and numerical simulations,” Phys. Rev. A 36, 4775-4791 (1987).
[CrossRef] [PubMed]

Gong, S. H.

Grebogi, C.

Y. C. Lai and C. Grebogi, “Intermingled basins and two-state on-off intermittency,” Phys. Rev. E 52, R3313-R3316 (1995).
[CrossRef]

Hammel, S. M.

J. F. Heagy, N. Platt, and S. M. Hammel, “Characterization of on-off intermittency,” Phys. Rev. E 49, 1140-1150 (1994).
[CrossRef]

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, “Experimental observation of on-off intermittency,” Phys. Rev. Lett. 73, 1095-1098 (1994).
[CrossRef] [PubMed]

N. Platt, S. M. Hammel, and J. F. Heagy, “Effects of additive noise on on-off intermittency,” Phys. Rev. Lett. 72, 3498-3501 (1994).
[CrossRef] [PubMed]

Hammer, P. W.

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, “Experimental observation of on-off intermittency,” Phys. Rev. Lett. 73, 1095-1098 (1994).
[CrossRef] [PubMed]

Harrell II, E. M.

G. E. James, E. M. Harrell II, and R. Roy, “Intermittency and chaos in intracavity doubled lasers,” Phys. Rev. A 41, 2778-2790 (1990).
[CrossRef] [PubMed]

Heagy, J. F.

N. Platt, S. M. Hammel, and J. F. Heagy, “Effects of additive noise on on-off intermittency,” Phys. Rev. Lett. 72, 3498-3501 (1994).
[CrossRef] [PubMed]

J. F. Heagy, N. Platt, and S. M. Hammel, “Characterization of on-off intermittency,” Phys. Rev. E 49, 1140-1150 (1994).
[CrossRef]

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, “Experimental observation of on-off intermittency,” Phys. Rev. Lett. 73, 1095-1098 (1994).
[CrossRef] [PubMed]

Hennequin, D.

D. Dangoisse, P. Glorieux, and D. Hennequin, “Chaos in a CO2 laser with modulated parameters: experiments and numerical simulations,” Phys. Rev. A 36, 4775-4791 (1987).
[CrossRef] [PubMed]

F. Hollinger, C. Jung, and D. Hennequin, “Single-longitudinal-mode laser as a discrete dynamical system,” J. Opt. Soc. Am. B 2, 218-225 (1985).
[CrossRef]

Hollinger, F.

Hu, G.

F. Xie, G. Hu, and Z. Qu, “On-off intermittency in a coupled-map lattice system,” Phys. Rev. E 52, R1265-R1268 (1995).
[CrossRef]

Hwang, D. W.

S. Rim, D. W. Hwang, I. Kim, and C. M. Kim, “Chaotic transition of random dynamical systems and chaos synchronization by common noises,” Phys. Rev. Lett. 85, 2304–2307 (2000).
[CrossRef] [PubMed]

Ivanov, V. N.

James, G. E.

G. E. James, E. M. Harrell II, and R. Roy, “Intermittency and chaos in intracavity doubled lasers,” Phys. Rev. A 41, 2778-2790 (1990).
[CrossRef] [PubMed]

Jung, C.

Kennedy, C. J.

C. J. Kennedy and J. D. Barry, “Stability of an intracavity frequency-doubled Nd:YAG laser,” IEEE J. Quantum Electron. QE-10, 596-599 (1974).
[CrossRef]

Kim, C. M.

Kim, I.

S. Rim, D. W. Hwang, I. Kim, and C. M. Kim, “Chaotic transition of random dynamical systems and chaos synchronization by common noises,” Phys. Rev. Lett. 85, 2304–2307 (2000).
[CrossRef] [PubMed]

Lai, Y. C.

Y. C. Lai and C. Grebogi, “Intermingled basins and two-state on-off intermittency,” Phys. Rev. E 52, R3313-R3316 (1995).
[CrossRef]

Lee, B. D.

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, “Experimental observation of on-off intermittency,” Phys. Rev. Lett. 73, 1095-1098 (1994).
[CrossRef] [PubMed]

Lee, D.-S.

Mitschke, F.

U. Morgner and F. Mitschke, “Drift instabilities in the pulses from cw mode-locked lasers,” Phys. Rev. E 58, 187-192 (1998).
[CrossRef]

Morgner, U.

U. Morgner and F. Mitschke, “Drift instabilities in the pulses from cw mode-locked lasers,” Phys. Rev. E 58, 187-192 (1998).
[CrossRef]

Ott, E.

L. Yu, E. Ott, and Q. Chen, “Transition to chaos for random dynamical systems,” Phys. Rev. Lett. 65, 2935-2938 (1990).
[CrossRef] [PubMed]

Platt, N.

J. F. Heagy, N. Platt, and S. M. Hammel, “Characterization of on-off intermittency,” Phys. Rev. E 49, 1140-1150 (1994).
[CrossRef]

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, “Experimental observation of on-off intermittency,” Phys. Rev. Lett. 73, 1095-1098 (1994).
[CrossRef] [PubMed]

N. Platt, S. M. Hammel, and J. F. Heagy, “Effects of additive noise on on-off intermittency,” Phys. Rev. Lett. 72, 3498-3501 (1994).
[CrossRef] [PubMed]

N. Platt, E. A. Spiegel, and C. Tresser, “On-off intermittency: a mechanism for bursting,” Phys. Rev. Lett. 70, 279-282 (1993).
[CrossRef] [PubMed]

Qu, Z.

F. Xie, G. Hu, and Z. Qu, “On-off intermittency in a coupled-map lattice system,” Phys. Rev. E 52, R1265-R1268 (1995).
[CrossRef]

Rim, S.

S. Rim, D. W. Hwang, I. Kim, and C. M. Kim, “Chaotic transition of random dynamical systems and chaos synchronization by common noises,” Phys. Rev. Lett. 85, 2304–2307 (2000).
[CrossRef] [PubMed]

Roy, R.

C. Bracikowski and R. Roy, “Chaos in a multimode solid state laser system,” Chaos 1, 49-64 (1991).
[CrossRef] [PubMed]

G. E. James, E. M. Harrell II, and R. Roy, “Intermittency and chaos in intracavity doubled lasers,” Phys. Rev. A 41, 2778-2790 (1990).
[CrossRef] [PubMed]

Spiegel, E. A.

N. Platt, E. A. Spiegel, and C. Tresser, “On-off intermittency: a mechanism for bursting,” Phys. Rev. Lett. 70, 279-282 (1993).
[CrossRef] [PubMed]

Tresser, C.

N. Platt, E. A. Spiegel, and C. Tresser, “On-off intermittency: a mechanism for bursting,” Phys. Rev. Lett. 70, 279-282 (1993).
[CrossRef] [PubMed]

Volochenko, K. V.

Xie, F.

F. Xie, G. Hu, and Z. Qu, “On-off intermittency in a coupled-map lattice system,” Phys. Rev. E 52, R1265-R1268 (1995).
[CrossRef]

Yamada, T.

H. Fujisaka and T. Yamada, “A new intermittency in coupled dynamical systems,” Prog. Theor. Phys. 74, 918-921 (1985).
[CrossRef]

Yang, H. L.

H. L. Yang and E. J. Ding, “Synchronization of chaotic systems and on-off intermittency,” Phys. Rev. E 54, 1361-1365 (1996).
[CrossRef]

Yang, W.

M. Ding and W. Yang, “Distribution of the first return time in fractional Brownian motion and its application to the study of on-off intermittency,” Phys. Rev. E 52, 207-213 (1995).
[CrossRef]

Yu, L.

L. Yu, E. Ott, and Q. Chen, “Transition to chaos for random dynamical systems,” Phys. Rev. Lett. 65, 2935-2938 (1990).
[CrossRef] [PubMed]

Chaos (1)

C. Bracikowski and R. Roy, “Chaos in a multimode solid state laser system,” Chaos 1, 49-64 (1991).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

C. J. Kennedy and J. D. Barry, “Stability of an intracavity frequency-doubled Nd:YAG laser,” IEEE J. Quantum Electron. QE-10, 596-599 (1974).
[CrossRef]

J. Opt. Soc. Am. B (4)

Phys. Rev. A (2)

G. E. James, E. M. Harrell II, and R. Roy, “Intermittency and chaos in intracavity doubled lasers,” Phys. Rev. A 41, 2778-2790 (1990).
[CrossRef] [PubMed]

D. Dangoisse, P. Glorieux, and D. Hennequin, “Chaos in a CO2 laser with modulated parameters: experiments and numerical simulations,” Phys. Rev. A 36, 4775-4791 (1987).
[CrossRef] [PubMed]

Phys. Rev. E (6)

U. Morgner and F. Mitschke, “Drift instabilities in the pulses from cw mode-locked lasers,” Phys. Rev. E 58, 187-192 (1998).
[CrossRef]

J. F. Heagy, N. Platt, and S. M. Hammel, “Characterization of on-off intermittency,” Phys. Rev. E 49, 1140-1150 (1994).
[CrossRef]

H. L. Yang and E. J. Ding, “Synchronization of chaotic systems and on-off intermittency,” Phys. Rev. E 54, 1361-1365 (1996).
[CrossRef]

Y. C. Lai and C. Grebogi, “Intermingled basins and two-state on-off intermittency,” Phys. Rev. E 52, R3313-R3316 (1995).
[CrossRef]

F. Xie, G. Hu, and Z. Qu, “On-off intermittency in a coupled-map lattice system,” Phys. Rev. E 52, R1265-R1268 (1995).
[CrossRef]

M. Ding and W. Yang, “Distribution of the first return time in fractional Brownian motion and its application to the study of on-off intermittency,” Phys. Rev. E 52, 207-213 (1995).
[CrossRef]

Phys. Rev. Lett. (6)

S. Rim, D. W. Hwang, I. Kim, and C. M. Kim, “Chaotic transition of random dynamical systems and chaos synchronization by common noises,” Phys. Rev. Lett. 85, 2304–2307 (2000).
[CrossRef] [PubMed]

N. Platt, S. M. Hammel, and J. F. Heagy, “Effects of additive noise on on-off intermittency,” Phys. Rev. Lett. 72, 3498-3501 (1994).
[CrossRef] [PubMed]

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, “Experimental observation of on-off intermittency,” Phys. Rev. Lett. 73, 1095-1098 (1994).
[CrossRef] [PubMed]

L. Yu, E. Ott, and Q. Chen, “Transition to chaos for random dynamical systems,” Phys. Rev. Lett. 65, 2935-2938 (1990).
[CrossRef] [PubMed]

D. J. Gauthier and J. C. Bienfang, “Intermittent loss of synchronization in coupled chaotic oscillators: toward a new criterion for high-quality synchronization,” Phys. Rev. Lett. 77, 1751-1754 (1996).
[CrossRef] [PubMed]

N. Platt, E. A. Spiegel, and C. Tresser, “On-off intermittency: a mechanism for bursting,” Phys. Rev. Lett. 70, 279-282 (1993).
[CrossRef] [PubMed]

Prog. Theor. Phys. (1)

H. Fujisaka and T. Yamada, “A new intermittency in coupled dynamical systems,” Prog. Theor. Phys. 74, 918-921 (1985).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. The Nd:YAG laser is pumped by a laser diode, and its intracavity second harmonic is generated by a KTP nonlinear crystal. The gain of the Nd:YAG laser is modulated by application of periodic current to the laser diode.

Fig. 2
Fig. 2

Experimental output of (a) the laser diode, (b) the diode-pumped Nd:YAG laser, and (c) the intracavity second harmonic of the Nd:YAG laser near threshold of the second harmonic, when a small gain is modulated periodically.

Fig. 3
Fig. 3

Experimental output of the intracavity second harmonic of the Nd:YAG laser. The dc offset and the modulation frequency are 0.46 V and 800 Hz, respectively; the ac amplitudes are (a) 1.225 V, (b) 1.240 V, and (c) 1.250 V.

Fig. 4
Fig. 4

Probability distribution of laminar phases versus laminar length in the intracavity frequency-doubled Nd:YAG laser for two modulation amplitudes: A, 0.68, V and B, 1.0 V. The modulation frequency and the dc offset are 10 kHz and 1.04 V, respectively.

Fig. 5
Fig. 5

Average laminar length, according to modulation amplitude variation δ=|V-Vc|. V is the modulation amplitude and Vc is the point of onset of intermittency. Filled circles, experimental results. Dashed curve, slope of -1.

Fig. 6
Fig. 6

Experimental output of the Q-switched Nd:YAG laser pumped by a laser diode. The currents of the laser diode are (a) 377 mA, (b) 378 mA, and (c) 389 mA.

Fig. 7
Fig. 7

Probability distribution of laminar phases versus laminar length in the acousto-optical Nd:YAG laser. The frequency of the modulator and the current of the laser diode are 10 kHz and 377 mA, respectively.

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