Abstract

We demonstrate that a full polarization analysis in terms of the Stokes vector parameters is necessary to determine the polarization state of light emitted by vertical-cavity surface-emitting lasers (VCSELs). For three selected representative VCSEL devices, we measured the injection current dependence of the three Stokes parameters and compared these results with linearly selected polarization P-I curves, clearly demonstrating that a complete polarization analysis is required to unveil the full polarization behavior.

© 2012 Optical Society of America

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  1. M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
    [CrossRef]
  2. A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, IEEE J. Quantum Electron. 34, 700 (1998).
    [CrossRef]
  3. F. M. di Sopra, M. Brunner, and R. Hövel, IEEE J. Quantum Electron. 14, 1034 (2002).
  4. C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
    [CrossRef]
  5. S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, Opt. Lett. 24, 1121 (1999).
    [CrossRef]
  6. R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, A. von Gulen, L. Weegels, K. H. Gulden, and M. Moser, Appl. Phys. Lett. 71, 2599 (1997).
    [CrossRef]
  7. M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, Phys. Rev. A 56, 845 (1997).
    [CrossRef]
  8. M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, Phys. Rev. A 57, 2080 (1998).
    [CrossRef]
  9. J. M. Ostermann, P. Debernardi, C. Jalics, A. Kroner, M. C. Riedl, and R. Michalzik, Opt. Commun. 246, 511 (2005).
    [CrossRef]
  10. A. Molitor, M. Blazek, J. M. Ostermann, R. Michalzik, P. Debernardi, and W. Elsäßer, IEEE J. Quantum Electron. 46, 554 (2010).
    [CrossRef]
  11. A. Molitor, M. Blazek, and W. Elsäßer, Opt. Lett. 36, 3777 (2011).
    [CrossRef]
  12. P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsäßer, IEEE J. Quantum Electron. 38, 73 (2002).
    [CrossRef]
  13. T. Ackemann and M. Sondermann, Appl. Phys. Lett. 78, 3574 (2001).
    [CrossRef]
  14. J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
    [CrossRef]
  15. M. B. Willemson, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 84, 4337 (2000).
    [CrossRef]
  16. H. G. Berry, G. Gabrielse, and A. E. Livingston, Appl. Opt. 16, 3200 (1977).
    [CrossRef]
  17. B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, Am. J. Phys. 75, 163 (2007).
    [CrossRef]
  18. N. C. Gerhardt and M. R. Hofmann, Adv. Opt. Technol. 2012, 268949 (2012).
    [CrossRef]

2012 (1)

N. C. Gerhardt and M. R. Hofmann, Adv. Opt. Technol. 2012, 268949 (2012).
[CrossRef]

2011 (1)

2010 (1)

A. Molitor, M. Blazek, J. M. Ostermann, R. Michalzik, P. Debernardi, and W. Elsäßer, IEEE J. Quantum Electron. 46, 554 (2010).
[CrossRef]

2007 (1)

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, Am. J. Phys. 75, 163 (2007).
[CrossRef]

2005 (1)

J. M. Ostermann, P. Debernardi, C. Jalics, A. Kroner, M. C. Riedl, and R. Michalzik, Opt. Commun. 246, 511 (2005).
[CrossRef]

2002 (2)

F. M. di Sopra, M. Brunner, and R. Hövel, IEEE J. Quantum Electron. 14, 1034 (2002).

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsäßer, IEEE J. Quantum Electron. 38, 73 (2002).
[CrossRef]

2001 (2)

T. Ackemann and M. Sondermann, Appl. Phys. Lett. 78, 3574 (2001).
[CrossRef]

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

2000 (1)

M. B. Willemson, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 84, 4337 (2000).
[CrossRef]

1999 (1)

1998 (2)

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, Phys. Rev. A 57, 2080 (1998).
[CrossRef]

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, IEEE J. Quantum Electron. 34, 700 (1998).
[CrossRef]

1997 (3)

R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, A. von Gulen, L. Weegels, K. H. Gulden, and M. Moser, Appl. Phys. Lett. 71, 2599 (1997).
[CrossRef]

M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, Phys. Rev. A 56, 845 (1997).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

1995 (1)

M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
[CrossRef]

1977 (1)

Abraham, N. B.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Ackemann, T.

T. Ackemann and M. Sondermann, Appl. Phys. Lett. 78, 3574 (2001).
[CrossRef]

Balle, S.

Barrett, D.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, Am. J. Phys. 75, 163 (2007).
[CrossRef]

Bava, G. P.

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsäßer, IEEE J. Quantum Electron. 38, 73 (2002).
[CrossRef]

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

Berry, H. G.

Blazek, M.

A. Molitor, M. Blazek, and W. Elsäßer, Opt. Lett. 36, 3777 (2011).
[CrossRef]

A. Molitor, M. Blazek, J. M. Ostermann, R. Michalzik, P. Debernardi, and W. Elsäßer, IEEE J. Quantum Electron. 46, 554 (2010).
[CrossRef]

Brunner, M.

F. M. di Sopra, M. Brunner, and R. Hövel, IEEE J. Quantum Electron. 14, 1034 (2002).

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

Collett, E.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, Am. J. Phys. 75, 163 (2007).
[CrossRef]

Debernardi, P.

A. Molitor, M. Blazek, J. M. Ostermann, R. Michalzik, P. Debernardi, and W. Elsäßer, IEEE J. Quantum Electron. 46, 554 (2010).
[CrossRef]

J. M. Ostermann, P. Debernardi, C. Jalics, A. Kroner, M. C. Riedl, and R. Michalzik, Opt. Commun. 246, 511 (2005).
[CrossRef]

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsäßer, IEEE J. Quantum Electron. 38, 73 (2002).
[CrossRef]

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

Degen, C.

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsäßer, IEEE J. Quantum Electron. 38, 73 (2002).
[CrossRef]

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

di Sopra, F. M.

F. M. di Sopra, M. Brunner, and R. Hövel, IEEE J. Quantum Electron. 14, 1034 (2002).

Elsäßer, W.

A. Molitor, M. Blazek, and W. Elsäßer, Opt. Lett. 36, 3777 (2011).
[CrossRef]

A. Molitor, M. Blazek, J. M. Ostermann, R. Michalzik, P. Debernardi, and W. Elsäßer, IEEE J. Quantum Electron. 46, 554 (2010).
[CrossRef]

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsäßer, IEEE J. Quantum Electron. 38, 73 (2002).
[CrossRef]

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

Feng, Q.

M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
[CrossRef]

Fischer, I.

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsäßer, IEEE J. Quantum Electron. 38, 73 (2002).
[CrossRef]

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

Fraher, B.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, Am. J. Phys. 75, 163 (2007).
[CrossRef]

Fratta, L.

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

Gabrielse, G.

Gahl, A.

Gerhardt, N. C.

N. C. Gerhardt and M. R. Hofmann, Adv. Opt. Technol. 2012, 268949 (2012).
[CrossRef]

Gulden, K.

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

Gulden, K. H.

R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, A. von Gulen, L. Weegels, K. H. Gulden, and M. Moser, Appl. Phys. Lett. 71, 2599 (1997).
[CrossRef]

Hendriks, R. F. M.

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, Phys. Rev. A 57, 2080 (1998).
[CrossRef]

R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, A. von Gulen, L. Weegels, K. H. Gulden, and M. Moser, Appl. Phys. Lett. 71, 2599 (1997).
[CrossRef]

Hofmann, M. R.

N. C. Gerhardt and M. R. Hofmann, Adv. Opt. Technol. 2012, 268949 (2012).
[CrossRef]

Hövel, R.

F. M. di Sopra, M. Brunner, and R. Hövel, IEEE J. Quantum Electron. 14, 1034 (2002).

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

Jalics, C.

J. M. Ostermann, P. Debernardi, C. Jalics, A. Kroner, M. C. Riedl, and R. Michalzik, Opt. Commun. 246, 511 (2005).
[CrossRef]

Jansen van Doorn, A. K.

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, IEEE J. Quantum Electron. 34, 700 (1998).
[CrossRef]

M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, Phys. Rev. A 56, 845 (1997).
[CrossRef]

Kroner, A.

J. M. Ostermann, P. Debernardi, C. Jalics, A. Kroner, M. C. Riedl, and R. Michalzik, Opt. Commun. 246, 511 (2005).
[CrossRef]

Livingston, A. E.

Martin-Regalado, J.

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, Opt. Lett. 24, 1121 (1999).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Michalzik, R.

A. Molitor, M. Blazek, J. M. Ostermann, R. Michalzik, P. Debernardi, and W. Elsäßer, IEEE J. Quantum Electron. 46, 554 (2010).
[CrossRef]

J. M. Ostermann, P. Debernardi, C. Jalics, A. Kroner, M. C. Riedl, and R. Michalzik, Opt. Commun. 246, 511 (2005).
[CrossRef]

Molitor, A.

A. Molitor, M. Blazek, and W. Elsäßer, Opt. Lett. 36, 3777 (2011).
[CrossRef]

A. Molitor, M. Blazek, J. M. Ostermann, R. Michalzik, P. Debernardi, and W. Elsäßer, IEEE J. Quantum Electron. 46, 554 (2010).
[CrossRef]

Moloney, J. V.

M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
[CrossRef]

Moser, M.

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, A. von Gulen, L. Weegels, K. H. Gulden, and M. Moser, Appl. Phys. Lett. 71, 2599 (1997).
[CrossRef]

Ostermann, J. M.

A. Molitor, M. Blazek, J. M. Ostermann, R. Michalzik, P. Debernardi, and W. Elsäßer, IEEE J. Quantum Electron. 46, 554 (2010).
[CrossRef]

J. M. Ostermann, P. Debernardi, C. Jalics, A. Kroner, M. C. Riedl, and R. Michalzik, Opt. Commun. 246, 511 (2005).
[CrossRef]

Prati, F.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Riedl, M. C.

J. M. Ostermann, P. Debernardi, C. Jalics, A. Kroner, M. C. Riedl, and R. Michalzik, Opt. Commun. 246, 511 (2005).
[CrossRef]

San Miguel, M.

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, Opt. Lett. 24, 1121 (1999).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
[CrossRef]

Schaefer, B.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, Am. J. Phys. 75, 163 (2007).
[CrossRef]

Smyth, R.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, Am. J. Phys. 75, 163 (2007).
[CrossRef]

Sondermann, M.

T. Ackemann and M. Sondermann, Appl. Phys. Lett. 78, 3574 (2001).
[CrossRef]

Tolkachova, E.

Tredicce, J. R.

van Exter, M. P.

M. B. Willemson, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 84, 4337 (2000).
[CrossRef]

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, IEEE J. Quantum Electron. 34, 700 (1998).
[CrossRef]

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, Phys. Rev. A 57, 2080 (1998).
[CrossRef]

M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, Phys. Rev. A 56, 845 (1997).
[CrossRef]

R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, A. von Gulen, L. Weegels, K. H. Gulden, and M. Moser, Appl. Phys. Lett. 71, 2599 (1997).
[CrossRef]

von Gulen, A.

R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, A. von Gulen, L. Weegels, K. H. Gulden, and M. Moser, Appl. Phys. Lett. 71, 2599 (1997).
[CrossRef]

Weegels, L.

R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, A. von Gulen, L. Weegels, K. H. Gulden, and M. Moser, Appl. Phys. Lett. 71, 2599 (1997).
[CrossRef]

Willemson, M. B.

M. B. Willemson, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 84, 4337 (2000).
[CrossRef]

Woerdman, J. P.

M. B. Willemson, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 84, 4337 (2000).
[CrossRef]

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, Phys. Rev. A 57, 2080 (1998).
[CrossRef]

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, IEEE J. Quantum Electron. 34, 700 (1998).
[CrossRef]

R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, A. von Gulen, L. Weegels, K. H. Gulden, and M. Moser, Appl. Phys. Lett. 71, 2599 (1997).
[CrossRef]

M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, Phys. Rev. A 56, 845 (1997).
[CrossRef]

Adv. Opt. Technol. (1)

N. C. Gerhardt and M. R. Hofmann, Adv. Opt. Technol. 2012, 268949 (2012).
[CrossRef]

Am. J. Phys. (1)

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, Am. J. Phys. 75, 163 (2007).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

T. Ackemann and M. Sondermann, Appl. Phys. Lett. 78, 3574 (2001).
[CrossRef]

R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, A. von Gulen, L. Weegels, K. H. Gulden, and M. Moser, Appl. Phys. Lett. 71, 2599 (1997).
[CrossRef]

IEEE J. Quantum Electron. (5)

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, IEEE J. Quantum Electron. 34, 700 (1998).
[CrossRef]

F. M. di Sopra, M. Brunner, and R. Hövel, IEEE J. Quantum Electron. 14, 1034 (2002).

A. Molitor, M. Blazek, J. M. Ostermann, R. Michalzik, P. Debernardi, and W. Elsäßer, IEEE J. Quantum Electron. 46, 554 (2010).
[CrossRef]

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsäßer, IEEE J. Quantum Electron. 38, 73 (2002).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Opt. Commun. (1)

J. M. Ostermann, P. Debernardi, C. Jalics, A. Kroner, M. C. Riedl, and R. Michalzik, Opt. Commun. 246, 511 (2005).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (4)

M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
[CrossRef]

C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. P. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden, Phys. Rev. A 63, 023817 (2001).
[CrossRef]

M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, Phys. Rev. A 56, 845 (1997).
[CrossRef]

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, Phys. Rev. A 57, 2080 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

M. B. Willemson, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 84, 4337 (2000).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematical drawing of the experimental setup showing the VCSEL with the crystalline axes [110] and [110]. The emitted light is collimated by a lens, passes a combination of a quarter-wave plate with revolvable fast axis and a polarizer with fixed transmission axis and is finally detected by a photo detector. The inset shows a representative set of measured data (black crosses) together with a fit to the measured data (red line) to extract the Stokes parameters.

Fig. 2.
Fig. 2.

Polarization resolved P-I curves of a 3 μm device in comparison with the Stokes parameters both as a function of pump current: Total optical power (black curve) together with the optical power of the linear horizontal polarization (blue dotted curve) and the vertical linear polarization (red dashed curve) (top). Stokes parameters S1 (red pluses), S2 (blue crosses), S3 (green circles) and the DOP (magenta squares) (bottom). The errors of the Stokes parameters, mainly caused by the fitting process are on the order of 10%, and they are not depicted for the sake of clarity.

Fig. 3.
Fig. 3.

Polarization resolved P-I curves of a 4 μm device compared to the Stokes parameters, both as a function of pump current.

Fig. 4.
Fig. 4.

Polarization resolved P-I curves of a 10 μm device compared to the Stokes parameters, both as a function of pump current.

Equations (2)

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

S=Mp*Mwp*S.
S0(β)=S0S1*1/2*(1+cos(4β))+S2*1/2*(sin(4β))+S3*(sin(2β)).

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