Abstract

A technique for diffuse beam shaping is presented. The beam shaping is achieved by a single reflection on an element, which consists of many displaced parallel planar reflecting facets. The reflecting facets approximate a designed curved surface. We demonstrate the validity of the method for the conversion of a diffuse Gaussian beam into a uniform one in one of the spatial dimensions.

© 2001 Optical Society of America

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References

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  1. M. T. Eismann, A. M. Tai, J. N. Cederquist, “Iterative design of a holographic beamformer,” Appl. Opt. 28, 2641–2650 (1989).
    [CrossRef] [PubMed]
  2. T. Dresel, M. Beyerlein, J. Schwider, “Design of computer-generated beam-shaping holograms by iterative finite-element mesh adaption,” Appl. Opt. 35, 6865–6874 (1996).
    [CrossRef] [PubMed]
  3. N. Davidson, A. A. Friesem, E. Hasman, “Holographic axilens–high resolution and long focal depth,” Opt. Lett. 16, 523–525 (1991).
    [CrossRef] [PubMed]
  4. E. Hasman, S. Keren, N. Davidson, A. A. Friesem, “Three-dimensional optical metrology with color-coded extended depth of focus,” Opt. Lett. 24, 439–441 (1999).
    [CrossRef]
  5. L. A. Romero, F. M. Dickey, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751–760 (1996).
    [CrossRef]
  6. Y. Chen, D. Li, Y. Sheng, “Beam-shaping element with reduced sensitivity to input variations,” Appl. Opt. 36, 568–571 (1997).
    [CrossRef] [PubMed]
  7. N. Davidson, A. A. Friesem, E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
    [CrossRef]
  8. S. Sinzinger, K.-H. Brenner, J. Moisel, T. Spick, M. Testorf, “Astigmatic gradient-index elements for laser-diode collimation and beam shaping,” Appl. Opt. 34, 6626–6632 (1995).
    [CrossRef] [PubMed]
  9. R. Ozeri, L. Khaykovich, N. Davidson, “Long scattering times in a novel blue-detuned dipole trap,” Phys. Rev. A 59, R1750–R1753 (1999).
    [CrossRef]
  10. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
  11. M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
    [CrossRef] [PubMed]
  12. J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
  13. M. Duparré, M. A. Golub, B. Lüdge, V. S. Pavelyev, V. A. Soifer, G. V. Uspleniev, S. G. Volotovskii, “Investigation of computer-generated diffractive beam shapers for flattening of single-modal CO2 laser beams,” Appl. Opt. 34, 2489–2497 (1995).
    [CrossRef]
  14. J. Bengtsson, “Kinoform-only Gaussian-to-rectangle beam shaper for a semiconductor laser,” Appl. Opt. 35, 3807–3814 (1996).
    [CrossRef] [PubMed]
  15. H. Aagedal, M. Schmid, S. Egner, J. Müller-Quade, T. Beth, F. Wyrowski, “Analytical beam shaping with application to laser-diode arrays,” J. Opt. Soc. Am. A 14, 1549–1553 (1997).
    [CrossRef]
  16. J. W. Ogland, “Mirror system for uniform beam transformation in high-power annular lasers,” Appl. Opt. 17, 2917–2923 (1978).
    [CrossRef] [PubMed]
  17. N. Davidson, A. A. Friesem, E. Hasman, “Reflective and refractive systems for general two-dimensional beam transformations,” Appl. Opt. 33, 815–820 (1994).
    [CrossRef] [PubMed]
  18. M. A. Karim, A. K. Cherri, A. A. Sami Awwal, A. Basit, “Refracting system for annular laser beam transformation,” Appl. Opt. 26, 2446–2449 (1987).
    [CrossRef] [PubMed]
  19. S. K. Case, P. R. Haugen, O. J. Løkberg, “Multifacet holographic optical elements for wave front transformations,” Appl. Opt. 20, 2670–2675 (1981).
    [CrossRef] [PubMed]
  20. N. Davidson, A. A. Friesem, E. Hasman, I. Shariv, “Curved holographic elements for optical coordinate transformations,” Opt. Lett. 16, 1430–1432 (1991).
    [CrossRef] [PubMed]
  21. The propagation distance D actually depends on X, and hence the spread of the different facets is nonuniform. However, for large enough D it is nearly uniform.
  22. N. Davidson, A. A. Friesem, E. Hasman, “Optical coordinate transformations,” Appl. Opt. 31, 1067–1073 (1992).
    [CrossRef] [PubMed]
  23. N. Davidson, A. A. Friesem, E. Hasman, “On the limits of optical interconnects,” Appl. Opt. 31, 5426–5430 (1992).
    [CrossRef] [PubMed]
  24. N. Davidson, A. A. Friesem, “Role of rank in matrix representation of optical interconnects,” J. Opt. Soc. Am. A 10, 1725–1728 (1993).
    [CrossRef]
  25. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
    [CrossRef]

1999 (2)

R. Ozeri, L. Khaykovich, N. Davidson, “Long scattering times in a novel blue-detuned dipole trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[CrossRef]

E. Hasman, S. Keren, N. Davidson, A. A. Friesem, “Three-dimensional optical metrology with color-coded extended depth of focus,” Opt. Lett. 24, 439–441 (1999).
[CrossRef]

1997 (2)

1996 (3)

1995 (2)

1994 (1)

1993 (1)

1992 (3)

1991 (2)

1989 (2)

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

M. T. Eismann, A. M. Tai, J. N. Cederquist, “Iterative design of a holographic beamformer,” Appl. Opt. 28, 2641–2650 (1989).
[CrossRef] [PubMed]

1987 (2)

1981 (1)

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).

1978 (1)

Aagedal, H.

Allebach, J. P.

Basit, A.

Bengtsson, J.

Beth, T.

Beyerlein, M.

Brenner, K.-H.

Case, S. K.

Cederquist, J. N.

Chen, Y.

Cherri, A. K.

Davidson, N.

Dickey, F. M.

Dresel, T.

Duparré, M.

Egner, S.

Eismann, M. T.

Fienup, J. R.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).

Friesem, A. A.

Golub, M. A.

Hasman, E.

Haugen, P. R.

Karim, M. A.

Keren, S.

Khaykovich, L.

R. Ozeri, L. Khaykovich, N. Davidson, “Long scattering times in a novel blue-detuned dipole trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[CrossRef]

Li, D.

Løkberg, O. J.

Lüdge, B.

Moisel, J.

Müller-Quade, J.

Ogland, J. W.

Ozeri, R.

R. Ozeri, L. Khaykovich, N. Davidson, “Long scattering times in a novel blue-detuned dipole trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[CrossRef]

Pavelyev, V. S.

Romero, L. A.

Sami Awwal, A. A.

Schmid, M.

Schwider, J.

Seldowitz, M. A.

Shariv, I.

Sheng, Y.

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

Sinzinger, S.

Soifer, V. A.

Spick, T.

Sweeney, D. W.

Tai, A. M.

Testorf, M.

Turunen, J.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

Uspleniev, G. V.

Vasara, A.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

Volotovskii, S. G.

Westerholm, J.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

Wyrowski, F.

Appl. Opt. (13)

J. W. Ogland, “Mirror system for uniform beam transformation in high-power annular lasers,” Appl. Opt. 17, 2917–2923 (1978).
[CrossRef] [PubMed]

M. A. Karim, A. K. Cherri, A. A. Sami Awwal, A. Basit, “Refracting system for annular laser beam transformation,” Appl. Opt. 26, 2446–2449 (1987).
[CrossRef] [PubMed]

M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
[CrossRef] [PubMed]

M. T. Eismann, A. M. Tai, J. N. Cederquist, “Iterative design of a holographic beamformer,” Appl. Opt. 28, 2641–2650 (1989).
[CrossRef] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “Optical coordinate transformations,” Appl. Opt. 31, 1067–1073 (1992).
[CrossRef] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “On the limits of optical interconnects,” Appl. Opt. 31, 5426–5430 (1992).
[CrossRef] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “Reflective and refractive systems for general two-dimensional beam transformations,” Appl. Opt. 33, 815–820 (1994).
[CrossRef] [PubMed]

Y. Chen, D. Li, Y. Sheng, “Beam-shaping element with reduced sensitivity to input variations,” Appl. Opt. 36, 568–571 (1997).
[CrossRef] [PubMed]

M. Duparré, M. A. Golub, B. Lüdge, V. S. Pavelyev, V. A. Soifer, G. V. Uspleniev, S. G. Volotovskii, “Investigation of computer-generated diffractive beam shapers for flattening of single-modal CO2 laser beams,” Appl. Opt. 34, 2489–2497 (1995).
[CrossRef]

S. Sinzinger, K.-H. Brenner, J. Moisel, T. Spick, M. Testorf, “Astigmatic gradient-index elements for laser-diode collimation and beam shaping,” Appl. Opt. 34, 6626–6632 (1995).
[CrossRef] [PubMed]

J. Bengtsson, “Kinoform-only Gaussian-to-rectangle beam shaper for a semiconductor laser,” Appl. Opt. 35, 3807–3814 (1996).
[CrossRef] [PubMed]

T. Dresel, M. Beyerlein, J. Schwider, “Design of computer-generated beam-shaping holograms by iterative finite-element mesh adaption,” Appl. Opt. 35, 6865–6874 (1996).
[CrossRef] [PubMed]

S. K. Case, P. R. Haugen, O. J. Løkberg, “Multifacet holographic optical elements for wave front transformations,” Appl. Opt. 20, 2670–2675 (1981).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

N. Davidson, A. A. Friesem, E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Eng. (2)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).

Opt. Lett. (3)

Phys. Rev. A (1)

R. Ozeri, L. Khaykovich, N. Davidson, “Long scattering times in a novel blue-detuned dipole trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[CrossRef]

Other (2)

The propagation distance D actually depends on X, and hence the spread of the different facets is nonuniform. However, for large enough D it is nearly uniform.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

One-dimensional surface with the shape of an error function [Z(X) =ERF(2X/ W 0)] and its discrete approximation with N = 22 linear facets at 45° [Z′(X)].

Fig. 2
Fig. 2

Experimental setup for diffuse beam shaping. L1, L2, and L3, lenses; A, aperture; S, screen.

Fig. 3
Fig. 3

Measured intensity of the input and the output beams for the optical setup of Fig. 2: (a) input beam, (b) output beam for a highly collimated input beam (α D = 4 × 10-3 rad), (c) output beam for a diffuse input beam (α D = 0.1 rad).

Fig. 4
Fig. 4

Measured intensity cross sections of Fig. 3(a) (dashed curve) and Fig. 3(c) (continuous curve).

Fig. 5
Fig. 5

Calculated output light intensity cross section for Gaussian-to-uniform beam transformation with N = 22 and dL = 3.5 mm, for (a) Z spread = 1 mm, (b) Z spread = 6 mm, and (c) Z spread = 20 mm.

Fig. 6
Fig. 6

Calculated output light intensity cross section for Gaussian-to-uniform beam transformation with N = 5 and dL = 15.5 mm, for Z spread = 18 mm.

Fig. 7
Fig. 7

Calculated output light intensity cross section for Gaussian-to-uniform beam transformation with N = 50 and dL = 1.5 mm, for Z spread = 3 mm.

Equations (3)

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fX  fZX=fXdX/dZ,
Nopt=ΔXdX=ΔXλ1/2.
Nopt<ΔXαD/λ=M2.

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