Abstract

Recently we observed a strong reduction of spatial coherence of the emission of large-aperture vertical-cavity surface-emitting lasers when they are driven by microsecond electrical pulses [Opt. Express 13, 9337 (2005)]. We study the influence of this partial spatial coherence on the propagation characteristics. The spatial decoherence manifests itself in the formation of a Gaussian far-field intensity distribution. We measure the transverse pulse profile from near to far field and see that the shape-invariant far-field regime starts after 140μm in the pulsed regime as opposed to several centimeters in continuous wave operation. This value matches quantitatively calculations made with a novel partially coherent propagation model without any free fitting parameters.

© 2006 Optical Society of America

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  1. S. Hegarty, G. Huyet, J. McInerney, and K. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
    [CrossRef]
  2. K. Huang, Y. Chen, and L. Lai, Phys. Rev. Lett. 89, 224102 (2002).
    [CrossRef] [PubMed]
  3. W. Nakwaski, Opt. Quantum Electron. 28, 335 (1996).
    [CrossRef]
  4. M. Peeters, G. Verschaffelt, H. Thienpont, S. K. Mandre, I. Fischer, and M. Grabherr, Opt. Express 13, 9337 (2005).
    [CrossRef] [PubMed]
  5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  6. J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
    [CrossRef]
  7. S. A. Kemme, R. K. Kostuk, and C. K. Y. Chun, IEEE Photonics Technol. Lett. 9, 554 (1997).
    [CrossRef]
  8. F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).
    [CrossRef]
  9. F. Gori, Opt. Acta 27, 1025 (1980).
    [CrossRef]
  10. P. Vahimaa and J. TurunenOpt. Express 14, 1376 (2006).
    [CrossRef] [PubMed]
  11. F. Gori, Opt. Lett. 30, 2840 (2005).
    [CrossRef] [PubMed]

2006 (1)

2005 (2)

2002 (1)

K. Huang, Y. Chen, and L. Lai, Phys. Rev. Lett. 89, 224102 (2002).
[CrossRef] [PubMed]

1999 (1)

S. Hegarty, G. Huyet, J. McInerney, and K. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

1997 (1)

S. A. Kemme, R. K. Kostuk, and C. K. Y. Chun, IEEE Photonics Technol. Lett. 9, 554 (1997).
[CrossRef]

1996 (1)

W. Nakwaski, Opt. Quantum Electron. 28, 335 (1996).
[CrossRef]

1995 (2)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
[CrossRef]

1980 (1)

F. Gori, Opt. Acta 27, 1025 (1980).
[CrossRef]

1978 (1)

F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).
[CrossRef]

Benware, B.

J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
[CrossRef]

Chen, Y.

K. Huang, Y. Chen, and L. Lai, Phys. Rev. Lett. 89, 224102 (2002).
[CrossRef] [PubMed]

Chilla, J. L. A.

J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
[CrossRef]

Choquette, K.

S. Hegarty, G. Huyet, J. McInerney, and K. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

Chun, C. K. Y.

S. A. Kemme, R. K. Kostuk, and C. K. Y. Chun, IEEE Photonics Technol. Lett. 9, 554 (1997).
[CrossRef]

Feld, S.

J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
[CrossRef]

Fischer, I.

Gori, F.

F. Gori, Opt. Lett. 30, 2840 (2005).
[CrossRef] [PubMed]

F. Gori, Opt. Acta 27, 1025 (1980).
[CrossRef]

F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).
[CrossRef]

Grabherr, M.

Hegarty, S.

S. Hegarty, G. Huyet, J. McInerney, and K. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

Huang, K.

K. Huang, Y. Chen, and L. Lai, Phys. Rev. Lett. 89, 224102 (2002).
[CrossRef] [PubMed]

Huyet, G.

S. Hegarty, G. Huyet, J. McInerney, and K. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

Kemme, S. A.

S. A. Kemme, R. K. Kostuk, and C. K. Y. Chun, IEEE Photonics Technol. Lett. 9, 554 (1997).
[CrossRef]

Kostuk, R. K.

S. A. Kemme, R. K. Kostuk, and C. K. Y. Chun, IEEE Photonics Technol. Lett. 9, 554 (1997).
[CrossRef]

Lai, L.

K. Huang, Y. Chen, and L. Lai, Phys. Rev. Lett. 89, 224102 (2002).
[CrossRef] [PubMed]

Leibenguth, R.

J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Mandre, S. K.

McInerney, J.

S. Hegarty, G. Huyet, J. McInerney, and K. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

Nakwaski, W.

W. Nakwaski, Opt. Quantum Electron. 28, 335 (1996).
[CrossRef]

Palma, C.

F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).
[CrossRef]

Peeters, M.

Rocca, J. J.

J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
[CrossRef]

Stanko, P.

J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
[CrossRef]

Thienpont, H.

Turunen, J.

Vahimaa, P.

Verschaffelt, G.

Watson, M. E.

J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
[CrossRef]

Wilmsen, C.

J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

IEEE Photonics Technol. Lett. (2)

J. L. A. Chilla, B. Benware, M. E. Watson, P. Stanko, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, IEEE Photonics Technol. Lett. 7, 449 (1995).
[CrossRef]

S. A. Kemme, R. K. Kostuk, and C. K. Y. Chun, IEEE Photonics Technol. Lett. 9, 554 (1997).
[CrossRef]

Opt. Acta (1)

F. Gori, Opt. Acta 27, 1025 (1980).
[CrossRef]

Opt. Commun. (1)

F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

W. Nakwaski, Opt. Quantum Electron. 28, 335 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

S. Hegarty, G. Huyet, J. McInerney, and K. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[CrossRef]

K. Huang, Y. Chen, and L. Lai, Phys. Rev. Lett. 89, 224102 (2002).
[CrossRef] [PubMed]

Other (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

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Figures (2)

Fig. 1
Fig. 1

Top, power emitted by the VCSEL in cw operation (dashed curve) and peak power in pulsed operation (solid curve). Pulse duration, 1 μ s ; duty cycle, 2%. Bottom, visibility in cw operation (dashed interpolation, ×) and in pulsed operation (solid interpolation +).

Fig. 2
Fig. 2

Normalized contour plots of the intensity profile in several regimes. Insets, two-dimensional near- and far-field distributions: (a) cw operation at an injection current of 70 mA . (b) Pulsed operation; pulse peak height, 300 mA . (c) Calculated profile evolution for (b) obtained with Eq. (3), starting from the measured near-field distribution.

Equations (4)

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W ( r 1 , r 2 ) = W ( r ¯ , Δ r ) = S ( r ¯ ) μ ( Δ r ) ,
μ ( Δ r ) = exp [ ( Δ r ) 2 2 σ 2 ] ,
W ( x 1 , y 1 , x 2 , y 2 ) = m A n A S ( x m , y n ) exp [ ( x 1 m Δ ) 2 σ 2 ] exp [ ( x 2 m Δ ) 2 σ 2 ] exp [ ( y 1 n Δ ) 2 σ 2 ] exp [ ( y 2 n Δ ) 2 σ 2 ] ,
z z FF = R min ( σ , 2 R ) 2 λ = 21 μ m .

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