Abstract

The amplitude and the phase of a multimode vertical-cavity surface-emitting laser (VCSEL) are recovered by a simple tomographic procedure based on the ambiguity function. The results are of considerable importance for any field of optics in which VCSELs are employed.

© 2002 Optical Society of America

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References

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  1. T. E. Gureyev, A. Roberts, and K. A. Nugent, J. Opt. Soc. Am. A 12, 1942 (1995).
    [CrossRef]
  2. H.-F. Shih, T.-P. Yang, M. O. Freeman, J.-K. Wang, H.-F. Yau, and D.-R. Hua, Jpn. J. Appl. Phys. 38, 1750 (1999).
    [CrossRef]
  3. D. Dragoman, Prog. Opt. 37, 1 (1997).
    [CrossRef]
  4. M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
    [CrossRef] [PubMed]
  5. M. Beck, M. G. Raymer, L. A. Walmsley, and V. Wong, Opt. Lett. 18, 2041 (1993).
    [CrossRef]
  6. D. F. McAlister, M. Beck, L. Clarke, A. Mayer, and M. G. Raymer, Opt. Lett. 20, 1181 (1995).
    [CrossRef] [PubMed]
  7. D. Dragoman, M. Dragoman, and K.-H. Brenner, Appl. Opt. 39, 2912 (2000).
    [CrossRef]
  8. K.-H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 44, 323 (1983).
    [CrossRef]
  9. R. H. Clarke, J. Opt. Soc. A 3, 1224 (1986).
    [CrossRef]
  10. J. Ojeda-Castaneda, L. R. Berriel-Valdos, and E. Montes, Appl. Opt. 4, 790 (1998).
  11. J. Tu and S. Tamura, Phys. Rev. E 55, 1946 (1997).
    [CrossRef]

2000 (1)

1999 (1)

H.-F. Shih, T.-P. Yang, M. O. Freeman, J.-K. Wang, H.-F. Yau, and D.-R. Hua, Jpn. J. Appl. Phys. 38, 1750 (1999).
[CrossRef]

1998 (1)

J. Ojeda-Castaneda, L. R. Berriel-Valdos, and E. Montes, Appl. Opt. 4, 790 (1998).

1997 (2)

J. Tu and S. Tamura, Phys. Rev. E 55, 1946 (1997).
[CrossRef]

D. Dragoman, Prog. Opt. 37, 1 (1997).
[CrossRef]

1995 (2)

1994 (1)

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

1993 (1)

1986 (1)

R. H. Clarke, J. Opt. Soc. A 3, 1224 (1986).
[CrossRef]

1983 (1)

K.-H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Beck, M.

Berriel-Valdos, L. R.

J. Ojeda-Castaneda, L. R. Berriel-Valdos, and E. Montes, Appl. Opt. 4, 790 (1998).

Brenner, K.-H.

D. Dragoman, M. Dragoman, and K.-H. Brenner, Appl. Opt. 39, 2912 (2000).
[CrossRef]

K.-H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Clarke, L.

Clarke, R. H.

R. H. Clarke, J. Opt. Soc. A 3, 1224 (1986).
[CrossRef]

Dragoman, D.

Dragoman, M.

Freeman, M. O.

H.-F. Shih, T.-P. Yang, M. O. Freeman, J.-K. Wang, H.-F. Yau, and D.-R. Hua, Jpn. J. Appl. Phys. 38, 1750 (1999).
[CrossRef]

Gureyev, T. E.

Hua, D.-R.

H.-F. Shih, T.-P. Yang, M. O. Freeman, J.-K. Wang, H.-F. Yau, and D.-R. Hua, Jpn. J. Appl. Phys. 38, 1750 (1999).
[CrossRef]

Lohmann, A. W.

K.-H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Mayer, A.

McAlister, D. F.

Montes, E.

J. Ojeda-Castaneda, L. R. Berriel-Valdos, and E. Montes, Appl. Opt. 4, 790 (1998).

Nugent, K. A.

Ojeda-Castaneda, J.

J. Ojeda-Castaneda, L. R. Berriel-Valdos, and E. Montes, Appl. Opt. 4, 790 (1998).

K.-H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Raymer, M. G.

Roberts, A.

Shih, H.-F.

H.-F. Shih, T.-P. Yang, M. O. Freeman, J.-K. Wang, H.-F. Yau, and D.-R. Hua, Jpn. J. Appl. Phys. 38, 1750 (1999).
[CrossRef]

Tamura, S.

J. Tu and S. Tamura, Phys. Rev. E 55, 1946 (1997).
[CrossRef]

Tu, J.

J. Tu and S. Tamura, Phys. Rev. E 55, 1946 (1997).
[CrossRef]

Walmsley, L. A.

Wang, J.-K.

H.-F. Shih, T.-P. Yang, M. O. Freeman, J.-K. Wang, H.-F. Yau, and D.-R. Hua, Jpn. J. Appl. Phys. 38, 1750 (1999).
[CrossRef]

Wong, V.

Yang, T.-P.

H.-F. Shih, T.-P. Yang, M. O. Freeman, J.-K. Wang, H.-F. Yau, and D.-R. Hua, Jpn. J. Appl. Phys. 38, 1750 (1999).
[CrossRef]

Yau, H.-F.

H.-F. Shih, T.-P. Yang, M. O. Freeman, J.-K. Wang, H.-F. Yau, and D.-R. Hua, Jpn. J. Appl. Phys. 38, 1750 (1999).
[CrossRef]

Appl. Opt. (2)

J. Ojeda-Castaneda, L. R. Berriel-Valdos, and E. Montes, Appl. Opt. 4, 790 (1998).

D. Dragoman, M. Dragoman, and K.-H. Brenner, Appl. Opt. 39, 2912 (2000).
[CrossRef]

J. Opt. Soc. A (1)

R. H. Clarke, J. Opt. Soc. A 3, 1224 (1986).
[CrossRef]

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

H.-F. Shih, T.-P. Yang, M. O. Freeman, J.-K. Wang, H.-F. Yau, and D.-R. Hua, Jpn. J. Appl. Phys. 38, 1750 (1999).
[CrossRef]

Opt. Commun. (1)

K.-H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. E (1)

J. Tu and S. Tamura, Phys. Rev. E 55, 1946 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Prog. Opt. (1)

D. Dragoman, Prog. Opt. 37, 1 (1997).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Intensity distribution of the VCSEL in the reference plane.

Fig. 2
Fig. 2

Real part of the AF obtained from intensity samples taken at various propagation planes.

Fig. 3
Fig. 3

(a) Recovered amplitude profile A (solid curve) versus experimental amplitude profile in the reference plane (dotted curve). (b) Recovered phase profile (solid curve) and the best-fit parabola (dotted curve).

Equations (5)

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

AFx,q;z=φx+x/2;zφ*x-x/2;z×exp-ixqdx,
AFDx-Bq,-Cx+Aq;z=AFx,q;0.
xqz=ABCDxq0.
Ix,zexp-ixq/Adx=AFx=-Bq/A,q;0.
φxφ*0=AFx,qexpixq/2dq.

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