Abstract

A general, noniterative method for designing diffractive axicons is derived. This new technique clarifies the earlier phenomenological design principle that was used for coherent light and extends it to the domain of partial coherence. The approach is based on the method of stationary phase in fluctuating diffracted wave fields, and it applies to arbitrary axially symmetric radiation of the Schell-model type. It is shown that the general design equation can be solved numerically, in a straightforward way, for any reasonable illumination and image specifications.

© 2001 Optical Society of America

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References

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  1. J. Turunen and F. Wyrowski, eds., Diffractive Optic for Industrial and Commercial Applications (Akademie-Verlag, Berlin, 1997).
  2. S. Yu. Popov and A. T. Friberg, Opt. Lett. 16, 1639 (1998).
    [CrossRef]
  3. J. Turunen, P. Pääkkönen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, and M. Kaivola, J. Mod. Opt. 47, 2467 (2000).
    [CrossRef]
  4. L. M. Soroko, Meso-Optics—Foundations and Applications (World Scientific, Singapore, 1996).
  5. V. Jarutis, R. Paskauskas, and A. Stabinis, Opt. Commun. 184, 105 (2000).
    [CrossRef]
  6. J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
    [CrossRef]
  7. J. Sochacki, A. Kolodziejczyk, Z. Jaroszewicz, and S. Bara, Appl. Opt. 31, 5326 (1992).
    [CrossRef] [PubMed]
  8. Z. Jaroszewicz, Axicons: Design and Propagation Properties, Vol. 5 of Research and Development Treatises (Polish Chapter, SPIE, Warsaw, 1997).
  9. S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, and B. Schnabel, Opt. Commun. 154, 359 (1998).
    [CrossRef]
  10. A. T. Friberg and S. Yu. Popov, J. Opt. Soc. Am. A 16, 1049 (1999).
    [CrossRef]
  11. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), Secs.  4.3.2, 5.3.2, and 5.6.4.
    [CrossRef]
  12. J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Bristol, UK, 1986), Chap.  8.
  13. J. Pu, H. Zhang, S. Nemoto, W. Zhang, and W. Zhang, J. Opt. A 1, 730 (1999).
    [CrossRef]

2000 (3)

J. Turunen, P. Pääkkönen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, and M. Kaivola, J. Mod. Opt. 47, 2467 (2000).
[CrossRef]

V. Jarutis, R. Paskauskas, and A. Stabinis, Opt. Commun. 184, 105 (2000).
[CrossRef]

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

1999 (2)

J. Pu, H. Zhang, S. Nemoto, W. Zhang, and W. Zhang, J. Opt. A 1, 730 (1999).
[CrossRef]

A. T. Friberg and S. Yu. Popov, J. Opt. Soc. Am. A 16, 1049 (1999).
[CrossRef]

1998 (2)

S. Yu. Popov and A. T. Friberg, Opt. Lett. 16, 1639 (1998).
[CrossRef]

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, and B. Schnabel, Opt. Commun. 154, 359 (1998).
[CrossRef]

1992 (1)

Arlt, J.

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

Bara, S.

Dholakia, K.

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

Friberg, A. T.

A. T. Friberg and S. Yu. Popov, J. Opt. Soc. Am. A 16, 1049 (1999).
[CrossRef]

S. Yu. Popov and A. T. Friberg, Opt. Lett. 16, 1639 (1998).
[CrossRef]

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, and B. Schnabel, Opt. Commun. 154, 359 (1998).
[CrossRef]

Honkanen, M.

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, and B. Schnabel, Opt. Commun. 154, 359 (1998).
[CrossRef]

Jaroszewicz, Z.

J. Sochacki, A. Kolodziejczyk, Z. Jaroszewicz, and S. Bara, Appl. Opt. 31, 5326 (1992).
[CrossRef] [PubMed]

Z. Jaroszewicz, Axicons: Design and Propagation Properties, Vol. 5 of Research and Development Treatises (Polish Chapter, SPIE, Warsaw, 1997).

Jarutis, V.

V. Jarutis, R. Paskauskas, and A. Stabinis, Opt. Commun. 184, 105 (2000).
[CrossRef]

Kaivola, M.

J. Turunen, P. Pääkkönen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, and M. Kaivola, J. Mod. Opt. 47, 2467 (2000).
[CrossRef]

Kajava, T.

J. Turunen, P. Pääkkönen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, and M. Kaivola, J. Mod. Opt. 47, 2467 (2000).
[CrossRef]

Kolodziejczyk, A.

Kuittinen, M.

J. Turunen, P. Pääkkönen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, and M. Kaivola, J. Mod. Opt. 47, 2467 (2000).
[CrossRef]

Laakkonen, P.

J. Turunen, P. Pääkkönen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, and M. Kaivola, J. Mod. Opt. 47, 2467 (2000).
[CrossRef]

Lautanen, J.

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, and B. Schnabel, Opt. Commun. 154, 359 (1998).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), Secs.  4.3.2, 5.3.2, and 5.6.4.
[CrossRef]

Nemoto, S.

J. Pu, H. Zhang, S. Nemoto, W. Zhang, and W. Zhang, J. Opt. A 1, 730 (1999).
[CrossRef]

Pääkkönen, P.

J. Turunen, P. Pääkkönen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, and M. Kaivola, J. Mod. Opt. 47, 2467 (2000).
[CrossRef]

Paskauskas, R.

V. Jarutis, R. Paskauskas, and A. Stabinis, Opt. Commun. 184, 105 (2000).
[CrossRef]

Popov, S. Yu.

A. T. Friberg and S. Yu. Popov, J. Opt. Soc. Am. A 16, 1049 (1999).
[CrossRef]

S. Yu. Popov and A. T. Friberg, Opt. Lett. 16, 1639 (1998).
[CrossRef]

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, and B. Schnabel, Opt. Commun. 154, 359 (1998).
[CrossRef]

Pu, J.

J. Pu, H. Zhang, S. Nemoto, W. Zhang, and W. Zhang, J. Opt. A 1, 730 (1999).
[CrossRef]

Schnabel, B.

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, and B. Schnabel, Opt. Commun. 154, 359 (1998).
[CrossRef]

Simonen, J.

J. Turunen, P. Pääkkönen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, and M. Kaivola, J. Mod. Opt. 47, 2467 (2000).
[CrossRef]

Sochacki, J.

Soroko, L. M.

L. M. Soroko, Meso-Optics—Foundations and Applications (World Scientific, Singapore, 1996).

Stabinis, A.

V. Jarutis, R. Paskauskas, and A. Stabinis, Opt. Commun. 184, 105 (2000).
[CrossRef]

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Bristol, UK, 1986), Chap.  8.

Turunen, J.

J. Turunen, P. Pääkkönen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, and M. Kaivola, J. Mod. Opt. 47, 2467 (2000).
[CrossRef]

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, and B. Schnabel, Opt. Commun. 154, 359 (1998).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), Secs.  4.3.2, 5.3.2, and 5.6.4.
[CrossRef]

Zhang, H.

J. Pu, H. Zhang, S. Nemoto, W. Zhang, and W. Zhang, J. Opt. A 1, 730 (1999).
[CrossRef]

Zhang, W.

J. Pu, H. Zhang, S. Nemoto, W. Zhang, and W. Zhang, J. Opt. A 1, 730 (1999).
[CrossRef]

J. Pu, H. Zhang, S. Nemoto, W. Zhang, and W. Zhang, J. Opt. A 1, 730 (1999).
[CrossRef]

Appl. Opt. (1)

J. Mod. Opt. (1)

J. Turunen, P. Pääkkönen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, and M. Kaivola, J. Mod. Opt. 47, 2467 (2000).
[CrossRef]

J. Opt. A (1)

J. Pu, H. Zhang, S. Nemoto, W. Zhang, and W. Zhang, J. Opt. A 1, 730 (1999).
[CrossRef]

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

Opt. Commun. (3)

V. Jarutis, R. Paskauskas, and A. Stabinis, Opt. Commun. 184, 105 (2000).
[CrossRef]

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, and B. Schnabel, Opt. Commun. 154, 359 (1998).
[CrossRef]

Opt. Lett. (1)

S. Yu. Popov and A. T. Friberg, Opt. Lett. 16, 1639 (1998).
[CrossRef]

Other (5)

J. Turunen and F. Wyrowski, eds., Diffractive Optic for Industrial and Commercial Applications (Akademie-Verlag, Berlin, 1997).

L. M. Soroko, Meso-Optics—Foundations and Applications (World Scientific, Singapore, 1996).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), Secs.  4.3.2, 5.3.2, and 5.6.4.
[CrossRef]

J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Bristol, UK, 1986), Chap.  8.

Z. Jaroszewicz, Axicons: Design and Propagation Properties, Vol. 5 of Research and Development Treatises (Polish Chapter, SPIE, Warsaw, 1997).

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Figures (2)

Fig. 1
Fig. 1

Results of simulation of on-axis intensity Iz for an axicon illuminated by a beam of Gaussian intensity of width 5  mm and Gaussian coherence of σg equal to (a) , (b) 10.0  mm, (c) 5.0  mm, (d) 3.0  mm, and (e) 1.5  mm. The axicon is designed to produce a uniform image profile, and the intensities are normalized to unity for the coherent field.

Fig. 2
Fig. 2

Results of numerical simulations of on-axis intensity Iz for an axicon when the incident beam has a Bessel intensity distribution and Gaussian coherence of σg given by (a) , (b) 10.0  mm, (c) 5.0  mm, (d) 3.0  mm, and (e) 1.5  mm. The axicon is optimized to generate an image segment of linearly decreasing intensity.

Equations (8)

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

2πr1ρIinρρdρ=d1zρIaxzdz,
Ispz=k2πz2t2ρIinρg̃inρρ21ϕρ,z.
g̃inρ=2π02πμρ21-cosθ1/2dθ.
zρ=-ρ/φρ,
zρ=ρφρφρ2-1φρ=z2ρρφρ+1zρ,
ρGρ=Fzzρ,
Gρ=k/2πIinρt2ρg˜inρ.
r1ρρGρdρ=d1zρFzdz,

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