Abstract

We present an experimental analysis of the effect of a rf amplitude modulation of the injection current in a distributed-feedback diode laser at 1.55 μm near the first period-doubling bifurcation. First experimental results of a virtual Hopf phenomenon were observed when two moving bumps with Lorentzian shapes appeared in the spectrum before the onset of the first period-doubling bifurcation occurred. We characterized this observation by increasing the amplitude of the current modulation of the diode laser until period-doubling bifurcation took place. The shape and position in the spectrum of these Lorentzian bumps were studied by the noise precursors theory, which predicts that the presence of noise will act as a virtual Hopf precursor in systems undergoing a period-doubling bifurcation.

© 2001 Optical Society of America

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  1. K. A. Shore, Solid-State Electron. 30, 59 (1987).
    [CrossRef]
  2. J. Sacher, D. Baums, P. Panknin, W. Elsasser, and E. O. Gobel, Phys. Rev. A 45, 1893 (1992).
    [CrossRef] [PubMed]
  3. T. Mukai and K. Otswka, Phys. Rev. Lett. 55, 1711 (1985).
    [CrossRef] [PubMed]
  4. J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
    [CrossRef]
  5. H. F. Liu and W. F. Ngai, IEEE J. Quantum Electron. 29, 1668 (1993).
    [CrossRef]
  6. H. Lamela, G. Carpintero, and P. Acedo, IEEE J. Quantum Electron. 34, 491 (1998).
    [CrossRef]
  7. H. Grothe, W. Harth, and P. Russer, Electron. Lett. 12, 522 (1976).
    [CrossRef]
  8. K. Wiesenfeld, Phys. Rev. A 33, 4026 (1986).
    [CrossRef] [PubMed]
  9. Y. H. Kao and H. T. Lin, IEEE J. Quantum Electron. 29, 1617 (1993).
    [CrossRef]
  10. Y. H. Kao and H. T. Lin, Phys. Rev. A 48, 2292 (1993).
    [CrossRef] [PubMed]
  11. K. Wiesenfeld, Phys. Rev. A 32, 1744 (1986).
    [CrossRef]
  12. K. Wiesenfeld, in Period Doubling Bifurcations: What Good Are They?, F. Moss and P. V. C. Madintok, eds. (Cambridge U. Press, Cambrige, 1989), pp. 145–168.
  13. Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
    [CrossRef]
  14. L. Chusseau, E. Hemery, and J. M. Lourtioz, Appl. Phys. Lett. 55, 822 (1989).
    [CrossRef]

1998 (1)

H. Lamela, G. Carpintero, and P. Acedo, IEEE J. Quantum Electron. 34, 491 (1998).
[CrossRef]

1993 (3)

H. F. Liu and W. F. Ngai, IEEE J. Quantum Electron. 29, 1668 (1993).
[CrossRef]

Y. H. Kao and H. T. Lin, IEEE J. Quantum Electron. 29, 1617 (1993).
[CrossRef]

Y. H. Kao and H. T. Lin, Phys. Rev. A 48, 2292 (1993).
[CrossRef] [PubMed]

1992 (2)

J. Sacher, D. Baums, P. Panknin, W. Elsasser, and E. O. Gobel, Phys. Rev. A 45, 1893 (1992).
[CrossRef] [PubMed]

J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

1989 (1)

L. Chusseau, E. Hemery, and J. M. Lourtioz, Appl. Phys. Lett. 55, 822 (1989).
[CrossRef]

1987 (1)

K. A. Shore, Solid-State Electron. 30, 59 (1987).
[CrossRef]

1986 (2)

K. Wiesenfeld, Phys. Rev. A 33, 4026 (1986).
[CrossRef] [PubMed]

K. Wiesenfeld, Phys. Rev. A 32, 1744 (1986).
[CrossRef]

1985 (2)

Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

T. Mukai and K. Otswka, Phys. Rev. Lett. 55, 1711 (1985).
[CrossRef] [PubMed]

1976 (1)

H. Grothe, W. Harth, and P. Russer, Electron. Lett. 12, 522 (1976).
[CrossRef]

Acedo, P.

H. Lamela, G. Carpintero, and P. Acedo, IEEE J. Quantum Electron. 34, 491 (1998).
[CrossRef]

Baums, D.

J. Sacher, D. Baums, P. Panknin, W. Elsasser, and E. O. Gobel, Phys. Rev. A 45, 1893 (1992).
[CrossRef] [PubMed]

Carpintero, G.

H. Lamela, G. Carpintero, and P. Acedo, IEEE J. Quantum Electron. 34, 491 (1998).
[CrossRef]

Chen, Y. C.

Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

Chusseau, L.

L. Chusseau, E. Hemery, and J. M. Lourtioz, Appl. Phys. Lett. 55, 822 (1989).
[CrossRef]

Elsasser, W.

J. Sacher, D. Baums, P. Panknin, W. Elsasser, and E. O. Gobel, Phys. Rev. A 45, 1893 (1992).
[CrossRef] [PubMed]

Gobel, E. O.

J. Sacher, D. Baums, P. Panknin, W. Elsasser, and E. O. Gobel, Phys. Rev. A 45, 1893 (1992).
[CrossRef] [PubMed]

Grothe, H.

H. Grothe, W. Harth, and P. Russer, Electron. Lett. 12, 522 (1976).
[CrossRef]

Harth, W.

H. Grothe, W. Harth, and P. Russer, Electron. Lett. 12, 522 (1976).
[CrossRef]

Hemery, E.

L. Chusseau, E. Hemery, and J. M. Lourtioz, Appl. Phys. Lett. 55, 822 (1989).
[CrossRef]

Kao, Y. H.

Y. H. Kao and H. T. Lin, Phys. Rev. A 48, 2292 (1993).
[CrossRef] [PubMed]

Y. H. Kao and H. T. Lin, IEEE J. Quantum Electron. 29, 1617 (1993).
[CrossRef]

Lamela, H.

H. Lamela, G. Carpintero, and P. Acedo, IEEE J. Quantum Electron. 34, 491 (1998).
[CrossRef]

Lin, H. T.

Y. H. Kao and H. T. Lin, Phys. Rev. A 48, 2292 (1993).
[CrossRef] [PubMed]

Y. H. Kao and H. T. Lin, IEEE J. Quantum Electron. 29, 1617 (1993).
[CrossRef]

Liu, H. F.

H. F. Liu and W. F. Ngai, IEEE J. Quantum Electron. 29, 1668 (1993).
[CrossRef]

Liu, J. M.

Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

Lourtioz, J. M.

L. Chusseau, E. Hemery, and J. M. Lourtioz, Appl. Phys. Lett. 55, 822 (1989).
[CrossRef]

Mark, J.

J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Mork, J.

J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Mukai, T.

T. Mukai and K. Otswka, Phys. Rev. Lett. 55, 1711 (1985).
[CrossRef] [PubMed]

Ngai, W. F.

H. F. Liu and W. F. Ngai, IEEE J. Quantum Electron. 29, 1668 (1993).
[CrossRef]

Otswka, K.

T. Mukai and K. Otswka, Phys. Rev. Lett. 55, 1711 (1985).
[CrossRef] [PubMed]

Panknin, P.

J. Sacher, D. Baums, P. Panknin, W. Elsasser, and E. O. Gobel, Phys. Rev. A 45, 1893 (1992).
[CrossRef] [PubMed]

Russer, P.

H. Grothe, W. Harth, and P. Russer, Electron. Lett. 12, 522 (1976).
[CrossRef]

Sacher, J.

J. Sacher, D. Baums, P. Panknin, W. Elsasser, and E. O. Gobel, Phys. Rev. A 45, 1893 (1992).
[CrossRef] [PubMed]

Shore, K. A.

K. A. Shore, Solid-State Electron. 30, 59 (1987).
[CrossRef]

Tromborg, B.

J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Wiesenfeld, K.

K. Wiesenfeld, Phys. Rev. A 33, 4026 (1986).
[CrossRef] [PubMed]

K. Wiesenfeld, Phys. Rev. A 32, 1744 (1986).
[CrossRef]

K. Wiesenfeld, in Period Doubling Bifurcations: What Good Are They?, F. Moss and P. V. C. Madintok, eds. (Cambridge U. Press, Cambrige, 1989), pp. 145–168.

Winful, H. G.

Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

Appl. Phys. Lett. (2)

Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

L. Chusseau, E. Hemery, and J. M. Lourtioz, Appl. Phys. Lett. 55, 822 (1989).
[CrossRef]

Electron. Lett. (1)

H. Grothe, W. Harth, and P. Russer, Electron. Lett. 12, 522 (1976).
[CrossRef]

IEEE J. Quantum Electron. (4)

J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

H. F. Liu and W. F. Ngai, IEEE J. Quantum Electron. 29, 1668 (1993).
[CrossRef]

H. Lamela, G. Carpintero, and P. Acedo, IEEE J. Quantum Electron. 34, 491 (1998).
[CrossRef]

Y. H. Kao and H. T. Lin, IEEE J. Quantum Electron. 29, 1617 (1993).
[CrossRef]

Phys. Rev. A (4)

Y. H. Kao and H. T. Lin, Phys. Rev. A 48, 2292 (1993).
[CrossRef] [PubMed]

K. Wiesenfeld, Phys. Rev. A 32, 1744 (1986).
[CrossRef]

J. Sacher, D. Baums, P. Panknin, W. Elsasser, and E. O. Gobel, Phys. Rev. A 45, 1893 (1992).
[CrossRef] [PubMed]

K. Wiesenfeld, Phys. Rev. A 33, 4026 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

T. Mukai and K. Otswka, Phys. Rev. Lett. 55, 1711 (1985).
[CrossRef] [PubMed]

Solid-State Electron. (1)

K. A. Shore, Solid-State Electron. 30, 59 (1987).
[CrossRef]

Other (1)

K. Wiesenfeld, in Period Doubling Bifurcations: What Good Are They?, F. Moss and P. V. C. Madintok, eds. (Cambridge U. Press, Cambrige, 1989), pp. 145–168.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for rf modulation of injection current amplitude applied to a diode laser.

Fig. 2
Fig. 2

Spectrum of the onset of the first period-doubling bifurcation in modulated diode lasers. The appearance of a double peak in the spectrum of fm/2 is observed in (a); in (b) the onset of period-doubling bifurcation is presented.

Fig. 3
Fig. 3

Evolution of the moving Lorentzian bumps corresponding to Figs.  2(a) and 2(b), where the amplitude modulation coupled to the diode laser is increased with rf power from (a) 9.43, (b) 10.26, (c) 10.9, (d) 12, (e) 12.6  dBm.

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