Abstract

Thermal effects and dynamical hysteresis in VCSELs under dc modulation have been experimentally studied. The results show that the VCSEL turn-on and turn-off currents can display both positive hysteresis and negative hysteresis, depending on the current modulation frequency and on the substrate temperature. Numerical simulations of semiconductor laser rate equations, extended to take into account thermal effects, show a good agreement with the observations.

© 2010 Optical Society of America

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  1. X. Zhao, B. Zhang, L. Christen, D. Parekh, W. Hofmann, M. C. Amann, F. Koyama, A. E. Willner, and C. J. Chang-Hasnain, Opt. Express 17, 13785 (2009).
    [CrossRef] [PubMed]
  2. S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, IEEE J. Quantum Electron. 40, 453 (2004).
    [CrossRef]
  3. Y. Hong, J. Paul, P. S. Paul, and K. A. Shore, IEEE J. Quantum Electron. 44, 30 (2008).
    [CrossRef]
  4. M. S. Torre and C. Masoller, “Dynamical hysteresis and thermal effects in vertical-cavity surface-emitting lasers,” IEEE J. Quantum. Electron. (to be published).
  5. J. R. Tredicce, G. L. Lippi, P. Mandel, B. Charasse, A. Chevalier, and B. Picqué, Am. J. Phys. 72, 799 (2004).
    [CrossRef]
  6. J. Paul, C. Masoller, Y. Hong, P. S. Paul, and K. A. Shore, Opt. Lett. 31, 748 (2006).
    [CrossRef] [PubMed]
  7. D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, and J. R. Tredicce, Opt. Commun. 99, 65 (1993).
    [CrossRef]
  8. S. Sivaprakasam, D. N. Rao, and R. S. Pandher, Opt. Commun. 176, 191 (2000).
    [CrossRef]
  9. C. Chen, P. O. Leisher, A. A. Allerman, K. M. Geib, and K. D. Choquette, IEEE J. Quantum Electron. 42, 1078 (2006).
    [CrossRef]
  10. C. Masoller and M. S. Torre, Opt. Express 16, 21282 (2008).
    [CrossRef] [PubMed]
  11. G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
    [CrossRef]

2009 (1)

2008 (2)

Y. Hong, J. Paul, P. S. Paul, and K. A. Shore, IEEE J. Quantum Electron. 44, 30 (2008).
[CrossRef]

C. Masoller and M. S. Torre, Opt. Express 16, 21282 (2008).
[CrossRef] [PubMed]

2006 (2)

J. Paul, C. Masoller, Y. Hong, P. S. Paul, and K. A. Shore, Opt. Lett. 31, 748 (2006).
[CrossRef] [PubMed]

C. Chen, P. O. Leisher, A. A. Allerman, K. M. Geib, and K. D. Choquette, IEEE J. Quantum Electron. 42, 1078 (2006).
[CrossRef]

2004 (2)

J. R. Tredicce, G. L. Lippi, P. Mandel, B. Charasse, A. Chevalier, and B. Picqué, Am. J. Phys. 72, 799 (2004).
[CrossRef]

S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, IEEE J. Quantum Electron. 40, 453 (2004).
[CrossRef]

2003 (1)

G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
[CrossRef]

2000 (1)

S. Sivaprakasam, D. N. Rao, and R. S. Pandher, Opt. Commun. 176, 191 (2000).
[CrossRef]

1993 (1)

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, and J. R. Tredicce, Opt. Commun. 99, 65 (1993).
[CrossRef]

Albert, J.

G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
[CrossRef]

Allerman, A. A.

C. Chen, P. O. Leisher, A. A. Allerman, K. M. Geib, and K. D. Choquette, IEEE J. Quantum Electron. 42, 1078 (2006).
[CrossRef]

Amann, M. C.

Asplund, C.

S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, IEEE J. Quantum Electron. 40, 453 (2004).
[CrossRef]

Barbay, S.

G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
[CrossRef]

Bromley, D.

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, and J. R. Tredicce, Opt. Commun. 99, 65 (1993).
[CrossRef]

Chang-Hasnain, C. J.

Charasse, B.

J. R. Tredicce, G. L. Lippi, P. Mandel, B. Charasse, A. Chevalier, and B. Picqué, Am. J. Phys. 72, 799 (2004).
[CrossRef]

Chen, C.

C. Chen, P. O. Leisher, A. A. Allerman, K. M. Geib, and K. D. Choquette, IEEE J. Quantum Electron. 42, 1078 (2006).
[CrossRef]

Chevalier, A.

J. R. Tredicce, G. L. Lippi, P. Mandel, B. Charasse, A. Chevalier, and B. Picqué, Am. J. Phys. 72, 799 (2004).
[CrossRef]

Chitica, N.

S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, IEEE J. Quantum Electron. 40, 453 (2004).
[CrossRef]

Choquette, K. D.

C. Chen, P. O. Leisher, A. A. Allerman, K. M. Geib, and K. D. Choquette, IEEE J. Quantum Electron. 42, 1078 (2006).
[CrossRef]

Christen, L.

Christiansson, U.

S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, IEEE J. Quantum Electron. 40, 453 (2004).
[CrossRef]

Danckaert, J.

G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
[CrossRef]

D'Angelo, E. J.

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, and J. R. Tredicce, Opt. Commun. 99, 65 (1993).
[CrossRef]

Geib, K. M.

C. Chen, P. O. Leisher, A. A. Allerman, K. M. Geib, and K. D. Choquette, IEEE J. Quantum Electron. 42, 1078 (2006).
[CrossRef]

Giacomelli, G.

G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
[CrossRef]

Grassi, H.

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, and J. R. Tredicce, Opt. Commun. 99, 65 (1993).
[CrossRef]

Hammar, M.

S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, IEEE J. Quantum Electron. 40, 453 (2004).
[CrossRef]

Hofmann, W.

Hong, Y.

Y. Hong, J. Paul, P. S. Paul, and K. A. Shore, IEEE J. Quantum Electron. 44, 30 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. Hong, P. S. Paul, and K. A. Shore, Opt. Lett. 31, 748 (2006).
[CrossRef] [PubMed]

Koyama, F.

Leisher, P. O.

C. Chen, P. O. Leisher, A. A. Allerman, K. M. Geib, and K. D. Choquette, IEEE J. Quantum Electron. 42, 1078 (2006).
[CrossRef]

Lippi, G. L.

J. R. Tredicce, G. L. Lippi, P. Mandel, B. Charasse, A. Chevalier, and B. Picqué, Am. J. Phys. 72, 799 (2004).
[CrossRef]

Mandel, P.

J. R. Tredicce, G. L. Lippi, P. Mandel, B. Charasse, A. Chevalier, and B. Picqué, Am. J. Phys. 72, 799 (2004).
[CrossRef]

Marin, F.

G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
[CrossRef]

Masoller, C.

C. Masoller and M. S. Torre, Opt. Express 16, 21282 (2008).
[CrossRef] [PubMed]

J. Paul, C. Masoller, Y. Hong, P. S. Paul, and K. A. Shore, Opt. Lett. 31, 748 (2006).
[CrossRef] [PubMed]

M. S. Torre and C. Masoller, “Dynamical hysteresis and thermal effects in vertical-cavity surface-emitting lasers,” IEEE J. Quantum. Electron. (to be published).

Mathis, C.

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, and J. R. Tredicce, Opt. Commun. 99, 65 (1993).
[CrossRef]

Mogg, S.

S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, IEEE J. Quantum Electron. 40, 453 (2004).
[CrossRef]

Nagler, B.

G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
[CrossRef]

Pandher, R. S.

S. Sivaprakasam, D. N. Rao, and R. S. Pandher, Opt. Commun. 176, 191 (2000).
[CrossRef]

Parekh, D.

Paul, J.

Y. Hong, J. Paul, P. S. Paul, and K. A. Shore, IEEE J. Quantum Electron. 44, 30 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. Hong, P. S. Paul, and K. A. Shore, Opt. Lett. 31, 748 (2006).
[CrossRef] [PubMed]

Paul, P. S.

Y. Hong, J. Paul, P. S. Paul, and K. A. Shore, IEEE J. Quantum Electron. 44, 30 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. Hong, P. S. Paul, and K. A. Shore, Opt. Lett. 31, 748 (2006).
[CrossRef] [PubMed]

Peeters, M.

G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
[CrossRef]

Picqué, B.

J. R. Tredicce, G. L. Lippi, P. Mandel, B. Charasse, A. Chevalier, and B. Picqué, Am. J. Phys. 72, 799 (2004).
[CrossRef]

Rao, D. N.

S. Sivaprakasam, D. N. Rao, and R. S. Pandher, Opt. Commun. 176, 191 (2000).
[CrossRef]

Schatz, R.

S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, IEEE J. Quantum Electron. 40, 453 (2004).
[CrossRef]

Shore, K. A.

Y. Hong, J. Paul, P. S. Paul, and K. A. Shore, IEEE J. Quantum Electron. 44, 30 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. Hong, P. S. Paul, and K. A. Shore, Opt. Lett. 31, 748 (2006).
[CrossRef] [PubMed]

Sivaprakasam, S.

S. Sivaprakasam, D. N. Rao, and R. S. Pandher, Opt. Commun. 176, 191 (2000).
[CrossRef]

Sundgren, P.

S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, IEEE J. Quantum Electron. 40, 453 (2004).
[CrossRef]

Torre, M. S.

C. Masoller and M. S. Torre, Opt. Express 16, 21282 (2008).
[CrossRef] [PubMed]

M. S. Torre and C. Masoller, “Dynamical hysteresis and thermal effects in vertical-cavity surface-emitting lasers,” IEEE J. Quantum. Electron. (to be published).

Tredicce, J. R.

J. R. Tredicce, G. L. Lippi, P. Mandel, B. Charasse, A. Chevalier, and B. Picqué, Am. J. Phys. 72, 799 (2004).
[CrossRef]

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, and J. R. Tredicce, Opt. Commun. 99, 65 (1993).
[CrossRef]

Verschaffelt, G.

G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
[CrossRef]

Willner, A. E.

Zhang, B.

Zhao, X.

Am. J. Phys. (1)

J. R. Tredicce, G. L. Lippi, P. Mandel, B. Charasse, A. Chevalier, and B. Picqué, Am. J. Phys. 72, 799 (2004).
[CrossRef]

IEEE J. Quantum Electron. (4)

S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, IEEE J. Quantum Electron. 40, 453 (2004).
[CrossRef]

Y. Hong, J. Paul, P. S. Paul, and K. A. Shore, IEEE J. Quantum Electron. 44, 30 (2008).
[CrossRef]

C. Chen, P. O. Leisher, A. A. Allerman, K. M. Geib, and K. D. Choquette, IEEE J. Quantum Electron. 42, 1078 (2006).
[CrossRef]

G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, IEEE J. Quantum Electron. 39, 1177 (2003).
[CrossRef]

Opt. Commun. (2)

D. Bromley, E. J. D'Angelo, H. Grassi, C. Mathis, and J. R. Tredicce, Opt. Commun. 99, 65 (1993).
[CrossRef]

S. Sivaprakasam, D. N. Rao, and R. S. Pandher, Opt. Commun. 176, 191 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Other (1)

M. S. Torre and C. Masoller, “Dynamical hysteresis and thermal effects in vertical-cavity surface-emitting lasers,” IEEE J. Quantum. Electron. (to be published).

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Figures (4)

Fig. 1
Fig. 1

L–I curve of the VCSEL with 10 kHz modulation frequency for (a) 10 ° C and for (b) 60 ° C substrate temperature. The black curve is for increasing current; the gray curve (red online) is for decreasing current. The insets display details of the threshold currents.

Fig. 2
Fig. 2

Threshold currents as a function of the substrate temperature for various modulation frequencies. The black circles and the gray squares (red online) indicate I on and I off , respectively.

Fig. 3
Fig. 3

Size of the hysteresis cycle, I on I off as a function of the modulation frequency at various values of the substrate temperatures.

Fig. 4
Fig. 4

Numerically calculated size of the hysteresis cycle, I on I off , versus the modulation frequency at three values of the substrate temperatures.

Equations (3)

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E ˙ = 1 2 k ( 1 + j α ) ( g N 1 ) E + β sp γ N ξ ,
N ˙ = γ N ( μ N g N | E | 2 ) ,
T ˙ = γ T ( T T s ) + Z ( N K + 1 ) + P ( μ K + 1 ) 2 ,

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