Abstract

It is demonstrated that, for high-Fresnel-number focusing systems illuminated by certain classes of partially coherent light, it is possible to produce a local minimum of intensity at the geometrical focus. Such an effect is possible even though the average intensity in the entrance plane of the lens is uniform. An explanation is offered for this effect, and potential applications are considered.

© 2003 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  2. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999).
    [CrossRef]
  3. A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
    [CrossRef]
  4. W. Wang, A. T. Friberg, and E. Wolf, J. Opt. Soc. Am. A 14, 491 (1997).
    [CrossRef]
  5. T. D. Visser, G. Gbur, and E. Wolf, Opt. Commun. 213, 13 (2002).
    [CrossRef]
  6. J. Pu and S. Nemoto, Opt. Express 11, 339 (2003), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  7. S. C. Som and S. C. Biswas, Opt. Acta 17, 925 (1970).
    [CrossRef]
  8. F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
    [CrossRef]
  9. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th ed. (Harcourt, Brace Jovanovich, San Diego, Calif., 2001).
  10. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Opt. Lett. 11, 288 (1986).
    [CrossRef]
  11. B. Steinle and H. P. Baltes, J. Opt. Soc. Am. 67, 241 (1977).
  12. G. M. Morris and D. Faklis, Opt. Commun. 62, 5 (1987).
    [CrossRef]

2003 (1)

2002 (1)

T. D. Visser, G. Gbur, and E. Wolf, Opt. Commun. 213, 13 (2002).
[CrossRef]

2001 (1)

A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
[CrossRef]

1997 (1)

W. Wang, A. T. Friberg, and E. Wolf, J. Opt. Soc. Am. A 14, 491 (1997).
[CrossRef]

1987 (2)

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

G. M. Morris and D. Faklis, Opt. Commun. 62, 5 (1987).
[CrossRef]

1986 (1)

1977 (1)

1970 (1)

S. C. Som and S. C. Biswas, Opt. Acta 17, 925 (1970).
[CrossRef]

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th ed. (Harcourt, Brace Jovanovich, San Diego, Calif., 2001).

Ashkin, A.

Baltes, H. P.

Biswas, S. C.

S. C. Som and S. C. Biswas, Opt. Acta 17, 925 (1970).
[CrossRef]

Bjorkholm, J. E.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999).
[CrossRef]

Chu, S.

Dziedzic, J. M.

Faklis, D.

G. M. Morris and D. Faklis, Opt. Commun. 62, 5 (1987).
[CrossRef]

Friberg, A. T.

A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
[CrossRef]

W. Wang, A. T. Friberg, and E. Wolf, J. Opt. Soc. Am. A 14, 491 (1997).
[CrossRef]

Gbur, G.

T. D. Visser, G. Gbur, and E. Wolf, Opt. Commun. 213, 13 (2002).
[CrossRef]

Gori, F.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Mandel, L.

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

Morris, G. M.

G. M. Morris and D. Faklis, Opt. Commun. 62, 5 (1987).
[CrossRef]

Nemoto, S.

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Pu, J.

Som, S. C.

S. C. Som and S. C. Biswas, Opt. Acta 17, 925 (1970).
[CrossRef]

Steinle, B.

Visser, T. D.

T. D. Visser, G. Gbur, and E. Wolf, Opt. Commun. 213, 13 (2002).
[CrossRef]

A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
[CrossRef]

Wang, W.

A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
[CrossRef]

W. Wang, A. T. Friberg, and E. Wolf, J. Opt. Soc. Am. A 14, 491 (1997).
[CrossRef]

Weber, H. J.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th ed. (Harcourt, Brace Jovanovich, San Diego, Calif., 2001).

Wolf, E.

T. D. Visser, G. Gbur, and E. Wolf, Opt. Commun. 213, 13 (2002).
[CrossRef]

A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
[CrossRef]

W. Wang, A. T. Friberg, and E. Wolf, J. Opt. Soc. Am. A 14, 491 (1997).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999).
[CrossRef]

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

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

W. Wang, A. T. Friberg, and E. Wolf, J. Opt. Soc. Am. A 14, 491 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Acta (1)

S. C. Som and S. C. Biswas, Opt. Acta 17, 925 (1970).
[CrossRef]

Opt. Commun. (4)

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

G. M. Morris and D. Faklis, Opt. Commun. 62, 5 (1987).
[CrossRef]

T. D. Visser, G. Gbur, and E. Wolf, Opt. Commun. 213, 13 (2002).
[CrossRef]

A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (3)

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th ed. (Harcourt, Brace Jovanovich, San Diego, Calif., 2001).

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

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Illustration of the focusing arrangement.

Fig. 2
Fig. 2

On-axis intensity distribution for 1/β=3.53 mm, showing a local minimum at focus, with a=10 mm, f=2 m, and λ=500 nm.

Fig. 3
Fig. 3

Intensity in the focal plane for 1/β=3.53 mm, showing a local minimum at focus. All other parameters are as in Fig. 2.

Fig. 4
Fig. 4

(a) On-axis and (b) focal plane intensities for 1/β=20 mm. The curves indicate our numerical calculations, and the circles indicate the classical results for fully coherent fields (from Ref. 2, Sect. 8.8). All other parameters are as in Fig. 2.

Fig. 5
Fig. 5

The normalized form of the correlation function W0r1,r2,ω for the two different values of 1/β, as discussed in the text.

Equations (6)

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

Sr,ω=1λ2WW0r1,r2,ω×exp-ikR1-R2R1R2d2r1d2r2,
Sr,ω=1λf2AW0r1,r2,ω×exp-ikR1-R2d2r1d2r2,
W0r1,r2,ω=S0ωJ0βr2-r1,
fsd2s=1,
W0r1,r2,ω=U02fsexpiks·r2-r1d2s.
fs=k22πβδβ-ks,

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