Abstract

We observe the route from laser-off to laser-on in a CO2 laser. On the route, on–off intermittency appears, which is caused by discharge instability near the laser threshold. By analyzing the probability distribution of a laminar phase near the onset of the intermittency, we confirm that what we have observed is on–off intermittency. We reproduce the intermittency through a numerical simulation of the laser rate equations.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Yu, E. Ott, and Q. Chen, “Transition to chaos for random dynamical systems,” Phys. Rev. Lett. 65, 2935–2938 (1990).
    [CrossRef] [PubMed]
  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]
  3. H. L. Yang and E. J. Ding, “Synchronization of chaotic systems and on–off intermittency,” Phys. Rev. E 54, 1361–1365 (1996).
    [CrossRef]
  4. S. Rim, D. U. 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]
  5. E. Ott and J. C. Sommerer, “Blowout bifurcations: the occurrence of riddled basins and on–off intermittency,” Phys. Lett. A 188, 39–47 (1994).
    [CrossRef]
  6. Y. C. Lai and C. Grebogi, “Intermingled basins and two-state on–off intermittency,” Phys. Rev. E 52, R3313–3316 (1995).
    [CrossRef]
  7. P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and N. D. Lee, “Experimental observation of on–off intermittency,” Phys. Rev. Lett. 73, 1095–1098 (1994).
    [CrossRef] [PubMed]
  8. Y. Pomeau and P. Manneville, “Intermittent transition to turbulence in dissipative dynamical systems,” Commun. Math. Phys. 74, 189–198 (1980).
    [CrossRef]
  9. C. M. Kim, O. J. Kwon, E. K. Lee, and H. Lee, “New characteristic relations in type-I intermittency,” Phys. Rev. Lett. 73, 525–528 (1994).
    [CrossRef] [PubMed]
  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 of 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. J. Redondo, E. Roldán, and G. J. de Valcárcel, “On–off intermittency in a Zeeman laser model,” Phys. Lett. A 210, 301–306 (1996).
    [CrossRef]
  15. 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]
  16. K. V. Volodchenko, 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 (2002).
    [CrossRef]
  17. G. U. Kim, H. T. Choo, I. D. Kim, Y. J. Park, S. H. Gong, and C. M. Kim, “Transition through on–off intermittency in Nd:YAG laser systems pumped by a laser diode,” J. Opt. Soc. Am. B 20, 302–306 (2003).
    [CrossRef]
  18. D. J. Biswas, V. Dev, and U. K. Chatterjee, “Experimental observation of oscillatory instabilities and chaos in a gain-modulated single-mode cw CO2 laser,” Phys. Rev. A 35, 456–458 (1987).
    [CrossRef] [PubMed]
  19. C. M. Kim, K. S. Lee, J. M. Kim, S. O. Kwon, C. J. Kim, and J. M. Lee, “Route to chaos through type I intermittency of a gain-modulated CO2 laser caused by the discharge instability at low frequency,” J. Opt. Soc. Am. B 10, 1651–1654 (1993).
    [CrossRef]
  20. K. J. Andrews, P. E. Dyer, and D. J. James, “A rate equation model for the design of TEA CO2 oscillators,” J. Phys. E 8, 493–497 (1975).
    [CrossRef]
  21. A. K. Nath, U. K. Chatterjee, and D. D. Bhawalkar, “Theoretical analysis of the multi-rotational line TEA CO2 laser,” Opt. Quantum Electron. 12, 245–251 (1980).
    [CrossRef]

2003 (1)

2002 (1)

2001 (1)

2000 (1)

S. Rim, D. U. 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]

1996 (3)

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]

J. Redondo, E. Roldán, and G. J. de Valcárcel, “On–off intermittency in a Zeeman laser model,” Phys. Lett. A 210, 301–306 (1996).
[CrossRef]

1995 (1)

Y. C. Lai and C. Grebogi, “Intermingled basins and two-state on–off intermittency,” Phys. Rev. E 52, R3313–3316 (1995).
[CrossRef]

1994 (5)

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

C. M. Kim, O. J. Kwon, E. K. Lee, and H. Lee, “New characteristic relations in type-I intermittency,” Phys. Rev. Lett. 73, 525–528 (1994).
[CrossRef] [PubMed]

E. Ott and J. C. Sommerer, “Blowout bifurcations: the occurrence of riddled basins and on–off intermittency,” Phys. Lett. A 188, 39–47 (1994).
[CrossRef]

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]

1993 (2)

1990 (1)

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

1987 (1)

D. J. Biswas, V. Dev, and U. K. Chatterjee, “Experimental observation of oscillatory instabilities and chaos in a gain-modulated single-mode cw CO2 laser,” Phys. Rev. A 35, 456–458 (1987).
[CrossRef] [PubMed]

1985 (1)

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

1980 (2)

Y. Pomeau and P. Manneville, “Intermittent transition to turbulence in dissipative dynamical systems,” Commun. Math. Phys. 74, 189–198 (1980).
[CrossRef]

A. K. Nath, U. K. Chatterjee, and D. D. Bhawalkar, “Theoretical analysis of the multi-rotational line TEA CO2 laser,” Opt. Quantum Electron. 12, 245–251 (1980).
[CrossRef]

1975 (1)

K. J. Andrews, P. E. Dyer, and D. J. James, “A rate equation model for the design of TEA CO2 oscillators,” J. Phys. E 8, 493–497 (1975).
[CrossRef]

Andrews, K. J.

K. J. Andrews, P. E. Dyer, and D. J. James, “A rate equation model for the design of TEA CO2 oscillators,” J. Phys. E 8, 493–497 (1975).
[CrossRef]

Bhawalkar, D. D.

A. K. Nath, U. K. Chatterjee, and D. D. Bhawalkar, “Theoretical analysis of the multi-rotational line TEA CO2 laser,” Opt. Quantum Electron. 12, 245–251 (1980).
[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]

Biswas, D. J.

D. J. Biswas, V. Dev, and U. K. Chatterjee, “Experimental observation of oscillatory instabilities and chaos in a gain-modulated single-mode cw CO2 laser,” Phys. Rev. A 35, 456–458 (1987).
[CrossRef] [PubMed]

Chatterjee, U. K.

D. J. Biswas, V. Dev, and U. K. Chatterjee, “Experimental observation of oscillatory instabilities and chaos in a gain-modulated single-mode cw CO2 laser,” Phys. Rev. A 35, 456–458 (1987).
[CrossRef] [PubMed]

A. K. Nath, U. K. Chatterjee, and D. D. Bhawalkar, “Theoretical analysis of the multi-rotational line TEA CO2 laser,” Opt. Quantum Electron. 12, 245–251 (1980).
[CrossRef]

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]

Choo, H. T.

de Valcárcel, G. J.

J. Redondo, E. Roldán, and G. J. de Valcárcel, “On–off intermittency in a Zeeman laser model,” Phys. Lett. A 210, 301–306 (1996).
[CrossRef]

Dev, V.

D. J. Biswas, V. Dev, and U. K. Chatterjee, “Experimental observation of oscillatory instabilities and chaos in a gain-modulated single-mode cw CO2 laser,” Phys. Rev. A 35, 456–458 (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]

Dyer, P. E.

K. J. Andrews, P. E. Dyer, and D. J. James, “A rate equation model for the design of TEA CO2 oscillators,” J. Phys. E 8, 493–497 (1975).
[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]

Gong, S. H.

Grebogi, C.

Y. C. Lai and C. Grebogi, “Intermingled basins and two-state on–off intermittency,” Phys. Rev. E 52, R3313–3316 (1995).
[CrossRef]

Hammel, S. M.

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 N. D. Lee, “Experimental observation of on–off intermittency,” Phys. Rev. Lett. 73, 1095–1098 (1994).
[CrossRef] [PubMed]

Hammer, P. W.

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

Heagy, J. F.

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

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]

Hwang, D. U.

S. Rim, D. U. 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, D. J.

K. J. Andrews, P. E. Dyer, and D. J. James, “A rate equation model for the design of TEA CO2 oscillators,” J. Phys. E 8, 493–497 (1975).
[CrossRef]

Kim, C. J.

Kim, C. M.

Kim, G. U.

Kim, I.

S. Rim, D. U. 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]

Kim, I. D.

Kim, J. M.

Kwon, O. J.

C. M. Kim, O. J. Kwon, E. K. Lee, and H. Lee, “New characteristic relations in type-I intermittency,” Phys. Rev. Lett. 73, 525–528 (1994).
[CrossRef] [PubMed]

Kwon, S. O.

Lai, Y. C.

Y. C. Lai and C. Grebogi, “Intermingled basins and two-state on–off intermittency,” Phys. Rev. E 52, R3313–3316 (1995).
[CrossRef]

Lee, D. S.

Lee, E. K.

C. M. Kim, O. J. Kwon, E. K. Lee, and H. Lee, “New characteristic relations in type-I intermittency,” Phys. Rev. Lett. 73, 525–528 (1994).
[CrossRef] [PubMed]

Lee, H.

C. M. Kim, O. J. Kwon, E. K. Lee, and H. Lee, “New characteristic relations in type-I intermittency,” Phys. Rev. Lett. 73, 525–528 (1994).
[CrossRef] [PubMed]

Lee, J. M.

Lee, K. S.

Lee, N. D.

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

Manneville, P.

Y. Pomeau and P. Manneville, “Intermittent transition to turbulence in dissipative dynamical systems,” Commun. Math. Phys. 74, 189–198 (1980).
[CrossRef]

Nath, A. K.

A. K. Nath, U. K. Chatterjee, and D. D. Bhawalkar, “Theoretical analysis of the multi-rotational line TEA CO2 laser,” Opt. Quantum Electron. 12, 245–251 (1980).
[CrossRef]

Ott, E.

E. Ott and J. C. Sommerer, “Blowout bifurcations: the occurrence of riddled basins and on–off intermittency,” Phys. Lett. A 188, 39–47 (1994).
[CrossRef]

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

Park, Y. J.

Platt, N.

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 N. D. Lee, “Experimental observation of on–off intermittency,” Phys. Rev. Lett. 73, 1095–1098 (1994).
[CrossRef] [PubMed]

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

Pomeau, Y.

Y. Pomeau and P. Manneville, “Intermittent transition to turbulence in dissipative dynamical systems,” Commun. Math. Phys. 74, 189–198 (1980).
[CrossRef]

Redondo, J.

J. Redondo, E. Roldán, and G. J. de Valcárcel, “On–off intermittency in a Zeeman laser model,” Phys. Lett. A 210, 301–306 (1996).
[CrossRef]

Rim, S.

S. Rim, D. U. 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]

Roldán, E.

J. Redondo, E. Roldán, and G. J. de Valcárcel, “On–off intermittency in a Zeeman laser model,” Phys. Lett. A 210, 301–306 (1996).
[CrossRef]

Sommerer, J. C.

E. Ott and J. C. Sommerer, “Blowout bifurcations: the occurrence of riddled basins and on–off intermittency,” Phys. Lett. A 188, 39–47 (1994).
[CrossRef]

Spiegel, E. A.

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

Volodchenko, K. V.

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]

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]

Commun. Math. Phys. (1)

Y. Pomeau and P. Manneville, “Intermittent transition to turbulence in dissipative dynamical systems,” Commun. Math. Phys. 74, 189–198 (1980).
[CrossRef]

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

J. Phys. E (1)

K. J. Andrews, P. E. Dyer, and D. J. James, “A rate equation model for the design of TEA CO2 oscillators,” J. Phys. E 8, 493–497 (1975).
[CrossRef]

Opt. Quantum Electron. (1)

A. K. Nath, U. K. Chatterjee, and D. D. Bhawalkar, “Theoretical analysis of the multi-rotational line TEA CO2 laser,” Opt. Quantum Electron. 12, 245–251 (1980).
[CrossRef]

Phys. Lett. A (2)

J. Redondo, E. Roldán, and G. J. de Valcárcel, “On–off intermittency in a Zeeman laser model,” Phys. Lett. A 210, 301–306 (1996).
[CrossRef]

E. Ott and J. C. Sommerer, “Blowout bifurcations: the occurrence of riddled basins and on–off intermittency,” Phys. Lett. A 188, 39–47 (1994).
[CrossRef]

Phys. Rev. A (1)

D. J. Biswas, V. Dev, and U. K. Chatterjee, “Experimental observation of oscillatory instabilities and chaos in a gain-modulated single-mode cw CO2 laser,” Phys. Rev. A 35, 456–458 (1987).
[CrossRef] [PubMed]

Phys. Rev. E (3)

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

Y. C. Lai and C. Grebogi, “Intermingled basins and two-state on–off intermittency,” Phys. Rev. E 52, R3313–3316 (1995).
[CrossRef]

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

Phys. Rev. Lett. (7)

S. Rim, D. U. 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]

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]

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

C. M. Kim, O. J. Kwon, E. K. Lee, and H. Lee, “New characteristic relations in type-I intermittency,” Phys. Rev. Lett. 73, 525–528 (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 of 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]

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 (6)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup.

Fig. 2
Fig. 2

Experimental outputs of on–off intermittency in a gain-modulated CO2 laser when the output voltages from the frequency converter are (a) 35.0 V (2.6 A), (b) 33.0 V (2.3 A), (c) 29.0 V (2.08 A), (d) 27.0 V (1.95 A), and (e) 25.04 V (1.834 A) and (f) is the discharge current shape of (e).

Fig. 3
Fig. 3

Probability distribution of a laminar phase for three values of output voltage from the frequency converter. A, B, C, voltages of 27.1, 24.9, and 24.3 V, respectively.

Fig. 4
Fig. 4

Average laminar phase length depending on the output voltage from the frequency converter on a logarithmic scale. Vc is the critical voltage for laser off, whose value is 23.5 V. We can see a clear -1 slope.

Fig. 5
Fig. 5

Numerical calculation of laser output, exhibiting on–off intermittency by way of random pumping; temporal behavior of photon density in the laser cavity at (a) α=0.55 and (b) α=0.53 (the unit of the y axis is 1017 cm-3); (c) the population difference at α=0.53 (the unit of the y axis is 1013 cm-3); (d) the pumping shape at α=0.53.

Fig. 6
Fig. 6

Numerical calculation of the probability distribution of laser-off length. Circles and triangles, probability distributions of the laser–off length for pumping powers of α=0.53 and α=0.55, respectively; straight line, the slope of -3/2.

Equations (4)

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

n˙1=Wn0-Stq(n1-n2)-Spn1+Kn(N1n0-n1N0),
n˙2=Stq(n1-n2)+Spn1,
N˙1=W1N0-Kn(N1n0-n1N0),
q˙=Stq(n1-n2)-kLq,

Metrics