Abstract

We consider the fabrication of high-quality interferogram-type diffractive optical elements with conventional photolithographic techniques and compare the results with those achievable with electron-beam lithography. The fringes associated with the phase transfer function of the binary phase holographic interferogram are approximated with rectangles, which can be realized at submicron accuracy using a pattern generator and step-and-repeat camera. The effects of the rectangle quantization are analyzed both numerically and experimentally with the aid of diffraction patterns produced by simple focusing elements. Both resolution and diffraction efficiency of the best holograms approach their theoretical values.

© 1989 Optical Society of America

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References

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  1. W-H. Lee, “Computer-Generated Holograms: Techniques and Applications,” Prog. Opt. 16, 119 (1978).
    [CrossRef]
  2. K. A. Winick, J. R. Fienup, “Optimum Holographic Elements Recorded with Nonspherical Wave Fronts,” J. Opt. Soc. Am. 73, 208 (1983).
    [CrossRef]
  3. M. R. Feldman, C. C. Guest, “Computer Generated Holographic Optical Elements for Optical Interconnection of Very Large Scale Integrated Circuits,” Appl. Opt. 26, 4377 (1987).
    [CrossRef] [PubMed]
  4. H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505 (1977).
    [CrossRef]
  5. W-H. Lee, “Method for Converting a Gaussian Laser Beam into a Uniform Beam,” Opt. Commun. 36, 469 (1981).
    [CrossRef]
  6. A. J. Macgovern, J. C. Wyant, “Computer Generated Holograms for Testing Optical Elements,” Appl. Opt. 10, 619 (1971).
    [CrossRef] [PubMed]
  7. D. Casasent, “Computer-Generated Holograms in Pattern Recognition,” Opt. Eng. 24, 724 (1985).
    [CrossRef]
  8. A. J. Lee, D. P. Casasent, “Computer Generated Hologram Recording Using a Laser Printer,” Appl. Opt. 26, 136 (1987).
    [CrossRef] [PubMed]
  9. E. Hasman, A. A. Friesem, M. Nagler, R. Fogel, “Holographic Optical Elements for the Far IR Radiation,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 152.
  10. S. Arnold, “Electron Beam Fabrication of Computer-Generated Holograms,” Opt. Eng. 24, 803 (1985).
    [CrossRef]
  11. H. Buczek, J. M. Teijido, “Application of Electron-Beam Lithography at CSEM for Fabricating Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 46 (1988).
  12. J. Lague, “Fabrication of Binary Optics Using Electron Beam Lithography,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 95 (1988).
  13. J. Fagerholm, J. Turunen, E. Byckling, “Optimization of Holographic Optical Systems by Damped Least Squares and Wavefront Matching Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, 20 (1988).
  14. J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and Fabrication of Grating Beamsplitters,” J. Phys. D 21, 5102 (1988); see also J. Turunen, A. Vasara, G. Jin, “Optimization and Photolithographic Fabrication of Computer-Generated Holographic Beamsplitters,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 158.
    [CrossRef]
  15. C. L. Chen, T. R. Osborne, “Quantization Effects on the Fields of Electron-Beam Generated Cylindrical Zone Plates,” Appl. Opt. 26, 2342 (1987).
    [CrossRef] [PubMed]
  16. P. Burggraaf, “Stepper Lens Options for VLSI,” Semicond. Int. 11, 44 (Feb.1988).
  17. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  18. NAG Reference Manual, Numerical Algorithms Group Mark II.
  19. J. N. Cederquist, J. R. Fienup, A. M. Tai, “CGH Fabrication Techniques and Facilities,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 40 (1988).
  20. M. Nakase, “Potential of Optical Lithography,” Opt. Eng. 26, 319 (1987).
    [CrossRef]

1988

H. Buczek, J. M. Teijido, “Application of Electron-Beam Lithography at CSEM for Fabricating Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 46 (1988).

J. Lague, “Fabrication of Binary Optics Using Electron Beam Lithography,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 95 (1988).

J. Fagerholm, J. Turunen, E. Byckling, “Optimization of Holographic Optical Systems by Damped Least Squares and Wavefront Matching Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, 20 (1988).

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and Fabrication of Grating Beamsplitters,” J. Phys. D 21, 5102 (1988); see also J. Turunen, A. Vasara, G. Jin, “Optimization and Photolithographic Fabrication of Computer-Generated Holographic Beamsplitters,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 158.
[CrossRef]

P. Burggraaf, “Stepper Lens Options for VLSI,” Semicond. Int. 11, 44 (Feb.1988).

J. N. Cederquist, J. R. Fienup, A. M. Tai, “CGH Fabrication Techniques and Facilities,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 40 (1988).

1987

1985

S. Arnold, “Electron Beam Fabrication of Computer-Generated Holograms,” Opt. Eng. 24, 803 (1985).
[CrossRef]

D. Casasent, “Computer-Generated Holograms in Pattern Recognition,” Opt. Eng. 24, 724 (1985).
[CrossRef]

1983

1981

W-H. Lee, “Method for Converting a Gaussian Laser Beam into a Uniform Beam,” Opt. Commun. 36, 469 (1981).
[CrossRef]

1978

W-H. Lee, “Computer-Generated Holograms: Techniques and Applications,” Prog. Opt. 16, 119 (1978).
[CrossRef]

1977

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505 (1977).
[CrossRef]

1971

Arnold, S.

S. Arnold, “Electron Beam Fabrication of Computer-Generated Holograms,” Opt. Eng. 24, 803 (1985).
[CrossRef]

Buczek, H.

H. Buczek, J. M. Teijido, “Application of Electron-Beam Lithography at CSEM for Fabricating Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 46 (1988).

Burggraaf, P.

P. Burggraaf, “Stepper Lens Options for VLSI,” Semicond. Int. 11, 44 (Feb.1988).

Byckling, E.

J. Fagerholm, J. Turunen, E. Byckling, “Optimization of Holographic Optical Systems by Damped Least Squares and Wavefront Matching Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, 20 (1988).

Casasent, D.

D. Casasent, “Computer-Generated Holograms in Pattern Recognition,” Opt. Eng. 24, 724 (1985).
[CrossRef]

Casasent, D. P.

Cederquist, J. N.

J. N. Cederquist, J. R. Fienup, A. M. Tai, “CGH Fabrication Techniques and Facilities,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 40 (1988).

Chen, C. L.

Dammann, H.

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505 (1977).
[CrossRef]

Fagerholm, J.

J. Fagerholm, J. Turunen, E. Byckling, “Optimization of Holographic Optical Systems by Damped Least Squares and Wavefront Matching Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, 20 (1988).

Feldman, M. R.

Fienup, J. R.

J. N. Cederquist, J. R. Fienup, A. M. Tai, “CGH Fabrication Techniques and Facilities,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 40 (1988).

K. A. Winick, J. R. Fienup, “Optimum Holographic Elements Recorded with Nonspherical Wave Fronts,” J. Opt. Soc. Am. 73, 208 (1983).
[CrossRef]

Fogel, R.

E. Hasman, A. A. Friesem, M. Nagler, R. Fogel, “Holographic Optical Elements for the Far IR Radiation,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 152.

Friesem, A. A.

E. Hasman, A. A. Friesem, M. Nagler, R. Fogel, “Holographic Optical Elements for the Far IR Radiation,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 152.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Guest, C. C.

Hasman, E.

E. Hasman, A. A. Friesem, M. Nagler, R. Fogel, “Holographic Optical Elements for the Far IR Radiation,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 152.

Jin, G.

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and Fabrication of Grating Beamsplitters,” J. Phys. D 21, 5102 (1988); see also J. Turunen, A. Vasara, G. Jin, “Optimization and Photolithographic Fabrication of Computer-Generated Holographic Beamsplitters,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 158.
[CrossRef]

Klotz, E.

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505 (1977).
[CrossRef]

Lague, J.

J. Lague, “Fabrication of Binary Optics Using Electron Beam Lithography,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 95 (1988).

Lee, A. J.

Lee, W-H.

W-H. Lee, “Method for Converting a Gaussian Laser Beam into a Uniform Beam,” Opt. Commun. 36, 469 (1981).
[CrossRef]

W-H. Lee, “Computer-Generated Holograms: Techniques and Applications,” Prog. Opt. 16, 119 (1978).
[CrossRef]

Macgovern, A. J.

Nagler, M.

E. Hasman, A. A. Friesem, M. Nagler, R. Fogel, “Holographic Optical Elements for the Far IR Radiation,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 152.

Nakase, M.

M. Nakase, “Potential of Optical Lithography,” Opt. Eng. 26, 319 (1987).
[CrossRef]

Osborne, T. R.

Salin, A.

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and Fabrication of Grating Beamsplitters,” J. Phys. D 21, 5102 (1988); see also J. Turunen, A. Vasara, G. Jin, “Optimization and Photolithographic Fabrication of Computer-Generated Holographic Beamsplitters,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 158.
[CrossRef]

Tai, A. M.

J. N. Cederquist, J. R. Fienup, A. M. Tai, “CGH Fabrication Techniques and Facilities,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 40 (1988).

Teijido, J. M.

H. Buczek, J. M. Teijido, “Application of Electron-Beam Lithography at CSEM for Fabricating Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 46 (1988).

Turunen, J.

J. Fagerholm, J. Turunen, E. Byckling, “Optimization of Holographic Optical Systems by Damped Least Squares and Wavefront Matching Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, 20 (1988).

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and Fabrication of Grating Beamsplitters,” J. Phys. D 21, 5102 (1988); see also J. Turunen, A. Vasara, G. Jin, “Optimization and Photolithographic Fabrication of Computer-Generated Holographic Beamsplitters,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 158.
[CrossRef]

Vasara, A.

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and Fabrication of Grating Beamsplitters,” J. Phys. D 21, 5102 (1988); see also J. Turunen, A. Vasara, G. Jin, “Optimization and Photolithographic Fabrication of Computer-Generated Holographic Beamsplitters,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 158.
[CrossRef]

Westerholm, J.

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and Fabrication of Grating Beamsplitters,” J. Phys. D 21, 5102 (1988); see also J. Turunen, A. Vasara, G. Jin, “Optimization and Photolithographic Fabrication of Computer-Generated Holographic Beamsplitters,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 158.
[CrossRef]

Winick, K. A.

Wyant, J. C.

Appl. Opt.

J. Opt. Soc. Am.

J. Phys. D

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and Fabrication of Grating Beamsplitters,” J. Phys. D 21, 5102 (1988); see also J. Turunen, A. Vasara, G. Jin, “Optimization and Photolithographic Fabrication of Computer-Generated Holographic Beamsplitters,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 158.
[CrossRef]

Opt. Acta

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505 (1977).
[CrossRef]

Opt. Commun.

W-H. Lee, “Method for Converting a Gaussian Laser Beam into a Uniform Beam,” Opt. Commun. 36, 469 (1981).
[CrossRef]

Opt. Eng.

D. Casasent, “Computer-Generated Holograms in Pattern Recognition,” Opt. Eng. 24, 724 (1985).
[CrossRef]

S. Arnold, “Electron Beam Fabrication of Computer-Generated Holograms,” Opt. Eng. 24, 803 (1985).
[CrossRef]

M. Nakase, “Potential of Optical Lithography,” Opt. Eng. 26, 319 (1987).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

J. N. Cederquist, J. R. Fienup, A. M. Tai, “CGH Fabrication Techniques and Facilities,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 40 (1988).

H. Buczek, J. M. Teijido, “Application of Electron-Beam Lithography at CSEM for Fabricating Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 46 (1988).

J. Lague, “Fabrication of Binary Optics Using Electron Beam Lithography,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 95 (1988).

J. Fagerholm, J. Turunen, E. Byckling, “Optimization of Holographic Optical Systems by Damped Least Squares and Wavefront Matching Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, 20 (1988).

Prog. Opt.

W-H. Lee, “Computer-Generated Holograms: Techniques and Applications,” Prog. Opt. 16, 119 (1978).
[CrossRef]

Semicond. Int.

P. Burggraaf, “Stepper Lens Options for VLSI,” Semicond. Int. 11, 44 (Feb.1988).

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

NAG Reference Manual, Numerical Algorithms Group Mark II.

E. Hasman, A. A. Friesem, M. Nagler, R. Fogel, “Holographic Optical Elements for the Far IR Radiation,” in Abstracts, OPTICS-ECOOSA ’88, Birmingham, U.K. (22–25 Mar. 1988), p. 152.

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Figures (9)

Fig. 1
Fig. 1

Criterion for determination of length L of a rectangle: δ/d is equal to a predetermined constant.

Fig. 2
Fig. 2

Determination of position S (and width w) of a rectangle; the shaded and dotted areas must be equal.

Fig. 3
Fig. 3

Structure of an F:50 (λ = 633 nm) off-axis focusing element with allowable local phase error ΔΦ/2π = 1/6.

Fig. 4
Fig. 4

Diffraction pattern of the structure shown in Fig. 3. The scales are in meters.

Fig. 5
Fig. 5

Structure of an F:50 off-axis focusing element with randomness in the length of the first rectangle of every fringe.

Fig. 6
Fig. 6

Diffraction pattern of the structure shown in Fig. 5.

Fig. 7
Fig. 7

Structure of an F:50 off-axis focusing element with allowable local phase error ΔΦ/2π = 1/40.

Fig. 8
Fig. 8

Diffraction pattern of the structure shown in Fig. 7.

Fig. 9
Fig. 9

Measured profile of the diffraction pattern of the structure shown in Fig. 7.

Equations (5)

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

d ( x 0 , y 0 ) = 2 π Φ ( x , y ) ( x 0 , y 0 ) - 1 .
L = [ α d ( α d + 2 R ) ] 1 / 2 .
D = R [ - ( 2 R L arctan L 2 R ) 1 / 2 ] .
α = 12 Δ Φ / 2 π .
η = η 0 [ 1 - 18.5 ( Δ Φ / 2 π ) 2 ] % .

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