Abstract

We report on the numerical observation of short-duration low-frequency pulsations in class-B solid-state lasers subject to delayed feedback. The period of these pulsations is much larger than either the delay induced by the feedback or the relaxation oscillation period of the laser without feedback. A link is established between the low-frequency pulsations and the low-frequency fluctuations observed in semiconductor lasers subject to coherent optical feedback.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
    [CrossRef]
  2. C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
    [CrossRef]
  3. F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 37, L325–L328 (1998).
    [CrossRef]
  4. F. Kuwashima, T. Ichikawa, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 38, 6321–6326 (1999).
    [CrossRef]
  5. F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 40, 601–608 (2001).
    [CrossRef]
  6. F. T. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617–1620 (1986).
    [CrossRef] [PubMed]
  7. G. Giacomelli, M. Calzavara, and F. T. Arecchi, Opt. Commun. 74, 97–101 (1989).
    [CrossRef]
  8. E. V. Grigorieva, S. Kaschenko, N. A. Loiko, and A. M. Samson, Physica D 59, 297–319 (1992).
    [CrossRef]
  9. K. Otsuka and J. L. Chern, Opt. Lett. 16, 1759–1761 (1991).
    [CrossRef] [PubMed]
  10. D. Pieroux, T. Erneux, T. Luzyanina, and K. Engelborghs, Phys. Rev. E 63, 036211 (2001).
    [CrossRef]
  11. D. E. McCumber, Phys. Rev. 141, 306 (1966).
    [CrossRef]
  12. D. Pieroux and P. Mandel are preparing a manuscript to be called “On the dynamics of a complex delay differential equation with cubic nonlinearity.”
  13. E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations, 2nd ed. (Springer, Berlin, 1992), Vol. 1.

2001 (2)

F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 40, 601–608 (2001).
[CrossRef]

D. Pieroux, T. Erneux, T. Luzyanina, and K. Engelborghs, Phys. Rev. E 63, 036211 (2001).
[CrossRef]

1999 (1)

F. Kuwashima, T. Ichikawa, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 38, 6321–6326 (1999).
[CrossRef]

1998 (1)

F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 37, L325–L328 (1998).
[CrossRef]

1992 (1)

E. V. Grigorieva, S. Kaschenko, N. A. Loiko, and A. M. Samson, Physica D 59, 297–319 (1992).
[CrossRef]

1991 (1)

1989 (1)

G. Giacomelli, M. Calzavara, and F. T. Arecchi, Opt. Commun. 74, 97–101 (1989).
[CrossRef]

1986 (1)

F. T. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617–1620 (1986).
[CrossRef] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

1977 (1)

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

1966 (1)

D. E. McCumber, Phys. Rev. 141, 306 (1966).
[CrossRef]

Arecchi, F. T.

G. Giacomelli, M. Calzavara, and F. T. Arecchi, Opt. Commun. 74, 97–101 (1989).
[CrossRef]

F. T. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617–1620 (1986).
[CrossRef] [PubMed]

Calzavara, M.

G. Giacomelli, M. Calzavara, and F. T. Arecchi, Opt. Commun. 74, 97–101 (1989).
[CrossRef]

Chern, J. L.

Engelborghs, K.

D. Pieroux, T. Erneux, T. Luzyanina, and K. Engelborghs, Phys. Rev. E 63, 036211 (2001).
[CrossRef]

Erneux, T.

D. Pieroux, T. Erneux, T. Luzyanina, and K. Engelborghs, Phys. Rev. E 63, 036211 (2001).
[CrossRef]

Gadomski, W.

F. T. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617–1620 (1986).
[CrossRef] [PubMed]

Giacomelli, G.

G. Giacomelli, M. Calzavara, and F. T. Arecchi, Opt. Commun. 74, 97–101 (1989).
[CrossRef]

Grigorieva, E. V.

E. V. Grigorieva, S. Kaschenko, N. A. Loiko, and A. M. Samson, Physica D 59, 297–319 (1992).
[CrossRef]

Hairer, E.

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations, 2nd ed. (Springer, Berlin, 1992), Vol. 1.

Ichikawa, T.

F. Kuwashima, T. Ichikawa, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 38, 6321–6326 (1999).
[CrossRef]

Iwasawa, H.

F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 40, 601–608 (2001).
[CrossRef]

F. Kuwashima, T. Ichikawa, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 38, 6321–6326 (1999).
[CrossRef]

F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 37, L325–L328 (1998).
[CrossRef]

Kaschenko, S.

E. V. Grigorieva, S. Kaschenko, N. A. Loiko, and A. M. Samson, Physica D 59, 297–319 (1992).
[CrossRef]

Kitazima, I.

F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 40, 601–608 (2001).
[CrossRef]

F. Kuwashima, T. Ichikawa, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 38, 6321–6326 (1999).
[CrossRef]

F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 37, L325–L328 (1998).
[CrossRef]

Kobayashi, K.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Kuwashima, F.

F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 40, 601–608 (2001).
[CrossRef]

F. Kuwashima, T. Ichikawa, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 38, 6321–6326 (1999).
[CrossRef]

F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 37, L325–L328 (1998).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Loiko, N. A.

E. V. Grigorieva, S. Kaschenko, N. A. Loiko, and A. M. Samson, Physica D 59, 297–319 (1992).
[CrossRef]

Luzyanina, T.

D. Pieroux, T. Erneux, T. Luzyanina, and K. Engelborghs, Phys. Rev. E 63, 036211 (2001).
[CrossRef]

Mandel, P.

D. Pieroux and P. Mandel are preparing a manuscript to be called “On the dynamics of a complex delay differential equation with cubic nonlinearity.”

McCumber, D. E.

D. E. McCumber, Phys. Rev. 141, 306 (1966).
[CrossRef]

Meucci, R.

F. T. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617–1620 (1986).
[CrossRef] [PubMed]

Nørsett, S. P.

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations, 2nd ed. (Springer, Berlin, 1992), Vol. 1.

Otsuka, K.

Pieroux, D.

D. Pieroux, T. Erneux, T. Luzyanina, and K. Engelborghs, Phys. Rev. E 63, 036211 (2001).
[CrossRef]

D. Pieroux and P. Mandel are preparing a manuscript to be called “On the dynamics of a complex delay differential equation with cubic nonlinearity.”

Risch, C.

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Samson, A. M.

E. V. Grigorieva, S. Kaschenko, N. A. Loiko, and A. M. Samson, Physica D 59, 297–319 (1992).
[CrossRef]

Voumard, C.

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Wanner, G.

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations, 2nd ed. (Springer, Berlin, 1992), Vol. 1.

IEEE J. Quantum Electron. (1)

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

J. Appl. Phys. (1)

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Jpn. J. Appl. Phys. (3)

F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 37, L325–L328 (1998).
[CrossRef]

F. Kuwashima, T. Ichikawa, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 38, 6321–6326 (1999).
[CrossRef]

F. Kuwashima, I. Kitazima, and H. Iwasawa, Jpn. J. Appl. Phys. 40, 601–608 (2001).
[CrossRef]

Opt. Commun. (1)

G. Giacomelli, M. Calzavara, and F. T. Arecchi, Opt. Commun. 74, 97–101 (1989).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

D. E. McCumber, Phys. Rev. 141, 306 (1966).
[CrossRef]

Phys. Rev. A (1)

F. T. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617–1620 (1986).
[CrossRef] [PubMed]

Phys. Rev. E (1)

D. Pieroux, T. Erneux, T. Luzyanina, and K. Engelborghs, Phys. Rev. E 63, 036211 (2001).
[CrossRef]

Physica D (1)

E. V. Grigorieva, S. Kaschenko, N. A. Loiko, and A. M. Samson, Physica D 59, 297–319 (1992).
[CrossRef]

Other (2)

D. Pieroux and P. Mandel are preparing a manuscript to be called “On the dynamics of a complex delay differential equation with cubic nonlinearity.”

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations, 2nd ed. (Springer, Berlin, 1992), Vol. 1.

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 (3)

Fig. 1
Fig. 1

LFPs obtained by integration of the reduced Eq. (4). (b), (c), and (d) are magnifications of, respectively, (a), (b), and (c). (a) Slowest time scale corresponding to the LFPs. The period between two pulses is 275 delay times. (b)–(c) Medium time scale corresponding to oscillations whose period is comparable with the delay. (d) Fastest time scale corresponding to relaxation oscillations. As the relaxation mechanism is eliminated from the reduced model, this time trace is almost constant. Note that, because of the existence of two very different time scales, the oscillations seen in (b) and (c) are indistinguishable in (a). Parameters: ωrτ=2213.5943, Θ=7, and η=1.09813.

Fig. 2
Fig. 2

LFPs obtained by integration of the full Eqs. (1) and (2). (b), (c), and (d) are magnifications of, respectively, (a), (b), and (c). The magnification factors are identical to those of Fig. 1. (a) Slowest time scale corresponding to the LFPs. The period between two pulses is 260 delay times. (b) and (c) Medium time scale corresponding to oscillations whose period is comparable with the delay. (d) Fastest time scale corresponding to relaxation oscillations. Note that, because of the existence of three very different time scales, the oscillations seen in (d) are indistinguishable in (a)–(c), and those seen in (b) and (c) are indistinguishable in (a). Parameters: T=105, P=1, τ=7 105, and κ=2.206 10-5.

Fig. 3
Fig. 3

Time trace illustrating LFPs. Laser with [(a) and (b)] optoelectronic feedback acting on the pump and [(c) and (d)] incoherent optical feedback. (a)–(c) Full model. (b)–(d) Reduced model. (a) κ=6.93 10-3, (b) η=1.0941, (c) κ=7 10-3, and (d) η=1.1015. Other parameters are as in Figs. 1 and 2.

Equations (12)

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

dIdt=N-1-κIt-τI,
TdNdt=P+1-N-NI.
ItP1+6ξωr1/2Aξωr2t×expiωrt+c.c.,
dAdσ=-1+iA2A-η exp-iωrτAσ-Θ,
dEdt=1+iαp-E2E+ηexp-iΩEt-1,
η=-secωΘ+ωrτ,ρ2=-ω-tanωΘ+ωrτ,
dIdt=N-1I,
TdNdt=P+1-N-NI+κIt-τ,
dAdσ=-1+iη˜+iA2A+iη˜ exp-iωrτAσ-Θ,
dIdt=N-1I,
TdNdt=P+1-N-NI+κIt-τ,
dAdσ=-1-iη˜+iA2A-iη˜ exp-iωrτAσ-Θ,

Metrics