Abstract

Diffractive optical beam splitters designed with iterative Fourier transform type algorithms can produce only certain diffraction angles given by the spatial frequencies used for the computations, which are multiples of a certain base spatial frequency. We have developed a design algorithm that overcomes this limitation and can be used to compute binary diffractive elements with arbitrary diffraction angles. The simulated and experimentally measured properties of optical elements producing beam arrays in circular arrangements are presented and discussed.

© 2007 Optical Society of America

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References

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  1. J. E. Jureller, H. Y. Kim, and N. F. Scherer, Opt. Express 14, 3406 (2006).
    [CrossRef] [PubMed]
  2. K. Mangold, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
    [CrossRef] [PubMed]
  3. X. L. Yang, L. Z. Cai, Y. R. Wang, and Q. Liu, Opt. Lett. 28, 453 (2003).
    [CrossRef] [PubMed]
  4. M. Skeren, I. Richter, and P. Fiala, J. Mod. Opt. 49, 18511870 (2002).
  5. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  6. J. Bengtsson, Appl. Opt. 36, 8435 (1997).
    [CrossRef]
  7. S. Bühling and F. Wyrowski, J. Opt. Soc. Am. A 19, 2414 (2002).
    [CrossRef]
  8. S. Krüger, G. Wernicke, A. Langner, H. Gruber, and S. Osten, Proc. SPIE 5457, 627 (2004).
    [CrossRef]

2006 (1)

2004 (1)

S. Krüger, G. Wernicke, A. Langner, H. Gruber, and S. Osten, Proc. SPIE 5457, 627 (2004).
[CrossRef]

2003 (2)

K. Mangold, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef] [PubMed]

X. L. Yang, L. Z. Cai, Y. R. Wang, and Q. Liu, Opt. Lett. 28, 453 (2003).
[CrossRef] [PubMed]

2002 (2)

S. Bühling and F. Wyrowski, J. Opt. Soc. Am. A 19, 2414 (2002).
[CrossRef]

M. Skeren, I. Richter, and P. Fiala, J. Mod. Opt. 49, 18511870 (2002).

1997 (1)

Bechinger, C.

K. Mangold, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef] [PubMed]

Bengtsson, J.

Bühling, S.

Cai, L. Z.

Fiala, P.

M. Skeren, I. Richter, and P. Fiala, J. Mod. Opt. 49, 18511870 (2002).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gruber, H.

S. Krüger, G. Wernicke, A. Langner, H. Gruber, and S. Osten, Proc. SPIE 5457, 627 (2004).
[CrossRef]

Jureller, J. E.

Kim, H. Y.

Krüger, S.

S. Krüger, G. Wernicke, A. Langner, H. Gruber, and S. Osten, Proc. SPIE 5457, 627 (2004).
[CrossRef]

Langner, A.

S. Krüger, G. Wernicke, A. Langner, H. Gruber, and S. Osten, Proc. SPIE 5457, 627 (2004).
[CrossRef]

Leiderer, P.

K. Mangold, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef] [PubMed]

Liu, Q.

Mangold, K.

K. Mangold, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef] [PubMed]

Osten, S.

S. Krüger, G. Wernicke, A. Langner, H. Gruber, and S. Osten, Proc. SPIE 5457, 627 (2004).
[CrossRef]

Richter, I.

M. Skeren, I. Richter, and P. Fiala, J. Mod. Opt. 49, 18511870 (2002).

Scherer, N. F.

Skeren, M.

M. Skeren, I. Richter, and P. Fiala, J. Mod. Opt. 49, 18511870 (2002).

Wang, Y. R.

Wernicke, G.

S. Krüger, G. Wernicke, A. Langner, H. Gruber, and S. Osten, Proc. SPIE 5457, 627 (2004).
[CrossRef]

Wyrowski, F.

Yang, X. L.

Appl. Opt. (1)

J. Mod. Opt. (1)

M. Skeren, I. Richter, and P. Fiala, J. Mod. Opt. 49, 18511870 (2002).

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

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

K. Mangold, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef] [PubMed]

Proc. SPIE (1)

S. Krüger, G. Wernicke, A. Langner, H. Gruber, and S. Osten, Proc. SPIE 5457, 627 (2004).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (3)

Fig. 1
Fig. 1

Computational steps in one iteration of an IFTA design algorithm for diffractive optical elements.

Fig. 2
Fig. 2

Central 100 × 100   pixels of computed beam-splitter transmission functions in grayscale representation of the phase values (upper row) and corresponding sections of the observed far-field diffraction patterns recorded with a CCD camera, containing 36 out of 360 created spots (lower row). The transmission functions are (a) an on-grid design with 64 levels, (b) an off-grid design with 64 levels, and (c) an off-grid design with only 2 levels.

Fig. 3
Fig. 3

Diffraction pattern of a binary 1:10 circular beam splitter measured with a CCD camera.

Equations (5)

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d ( f ) = [ λ f x , λ f y , { 1 λ 2 ( f x 2 + f y 2 ) } ( 1 2 ) ]
{ A S } = SFT ( t E , { f S } ) ,
t S = SFT 1 ( { A S } , { f S } ) ,
{ A N } = DFT ( t E t S ) .
t ̃ E = SFT 1 ( { A ̃ S } , { f S } ) + DFT 1 ( { A ̃ N } ) .

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