Abstract

We report on the design and fabrication of fully 2-D surface relief diffraction elements that can split a single collimated beam into many beams in an arbitrary intensity distribution. These splitters were designed by computer using simulated annealing, and made into phase gratings by electron-beam lithography followed by plasma etching into quartz glass. Both two and four phase level gratings have been fabricated, allowing a wide range of uniform and weighted spot patterns to be generated. These grating elements have a measured diffraction efficiency of over 74%, with the beam intensity ratios accurate to within 1% of their target values.

© 1991 Optical Society of America

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References

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  1. F. B. M. Cormick, “Generation of Large Spot Arrays from a Single Laser Beam by Multiple Imaging with Binary Phase Gratings,” Opt. Eng. 28, 299–304 (1989).
  2. N. M. Barnes et al., “High Speed Opto-Electronic Neural Network,” Postdeadline Session International Conference on Optical Computing, (Kobe, Japan, 1990).
  3. N. M. Barnes et al., “High Speed Opto-Electronic Neural Network,” Electron. Lett. 26, 1110–1113 (1990).
    [CrossRef]
  4. D. Prongue, H. P. Herzig, “Design and Fabrication of HOE for Clock Distribution in Integrated Circuits,” IEE Conference on Holographic Systems, Components and Applications, (Bath, U.K., 1989).
  5. M. C. Hutley, “Optical Techniques for the Generation of Microlens Arrays,” J. Mod. Opt. 37, 253–265 (1990).
    [CrossRef]
  6. K. M. Flood, J. M. Finlan, “Collimation of Diode Laser Arrays Using Etched Cylindrical Computer Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 186–190 (1989).
  7. H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
    [CrossRef]
  8. M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasera, J. Westerholm, “Optimization and Fabrication of Grating Beam-splitters in Silicon Nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
    [CrossRef]
  9. J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann Gratings for Laser Beam Shaping,” Opt. Eng. 28, 1267–1275 (1989).
  10. J. N. Mait, “Design of Dammann Gratings for Two-Dimensional, Nonseparable, Noncentrosymmetric Responses,” Opt. Lett. 14, 196–198 (1990).
    [CrossRef]
  11. H. Akahori, “Spectrum Leveling by an Iterative Algorithm with a Dummy Area for Synthesizing the Kinoform,” Appl. Opt. 25, 802–811 (1986).
    [CrossRef] [PubMed]
  12. F. Wyrowski, O. Bryndahl, “Iterative Fourier-Transform Algorithm Applied to Computer Holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
    [CrossRef]
  13. F. Wyrowski, O. Bryndahl, “Digital Holograms for Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 126–130 (1989).
  14. M. R. Feldman, C. C. Guest, “Iterative Encoding of High-Efficiency Holograms for Generation of Spot Arrays,” Opt. Lett. 14, 479–481 (1989).
    [CrossRef] [PubMed]
  15. S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
    [CrossRef] [PubMed]
  16. S. M. Arnold, “Electron Beam Fabrication of Computer Generated Holograms,” Opt. Eng. 24, 803–807 (1985).
  17. K. M. Flood, J. M. Finlan, “Multiple-Phase Level Computer Generated Holograms Etched in Fused Silica,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 91–96 (1989).
  18. J. Jahns, N. Streibl, S. J. Walker, “Multiple Phase Structures for Array Generation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 198–203 (1989).

1990 (3)

N. M. Barnes et al., “High Speed Opto-Electronic Neural Network,” Electron. Lett. 26, 1110–1113 (1990).
[CrossRef]

M. C. Hutley, “Optical Techniques for the Generation of Microlens Arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

J. N. Mait, “Design of Dammann Gratings for Two-Dimensional, Nonseparable, Noncentrosymmetric Responses,” Opt. Lett. 14, 196–198 (1990).
[CrossRef]

1989 (8)

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasera, J. Westerholm, “Optimization and Fabrication of Grating Beam-splitters in Silicon Nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann Gratings for Laser Beam Shaping,” Opt. Eng. 28, 1267–1275 (1989).

K. M. Flood, J. M. Finlan, “Collimation of Diode Laser Arrays Using Etched Cylindrical Computer Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 186–190 (1989).

F. B. M. Cormick, “Generation of Large Spot Arrays from a Single Laser Beam by Multiple Imaging with Binary Phase Gratings,” Opt. Eng. 28, 299–304 (1989).

F. Wyrowski, O. Bryndahl, “Digital Holograms for Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 126–130 (1989).

M. R. Feldman, C. C. Guest, “Iterative Encoding of High-Efficiency Holograms for Generation of Spot Arrays,” Opt. Lett. 14, 479–481 (1989).
[CrossRef] [PubMed]

K. M. Flood, J. M. Finlan, “Multiple-Phase Level Computer Generated Holograms Etched in Fused Silica,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 91–96 (1989).

J. Jahns, N. Streibl, S. J. Walker, “Multiple Phase Structures for Array Generation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 198–203 (1989).

1988 (1)

1986 (1)

1985 (1)

S. M. Arnold, “Electron Beam Fabrication of Computer Generated Holograms,” Opt. Eng. 24, 803–807 (1985).

1983 (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

1977 (1)

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Akahori, H.

Arnold, S. M.

S. M. Arnold, “Electron Beam Fabrication of Computer Generated Holograms,” Opt. Eng. 24, 803–807 (1985).

Barnes, N. M.

N. M. Barnes et al., “High Speed Opto-Electronic Neural Network,” Electron. Lett. 26, 1110–1113 (1990).
[CrossRef]

N. M. Barnes et al., “High Speed Opto-Electronic Neural Network,” Postdeadline Session International Conference on Optical Computing, (Kobe, Japan, 1990).

Bryndahl, O.

F. Wyrowski, O. Bryndahl, “Digital Holograms for Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 126–130 (1989).

F. Wyrowski, O. Bryndahl, “Iterative Fourier-Transform Algorithm Applied to Computer Holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
[CrossRef]

Cormick, F. B. M.

F. B. M. Cormick, “Generation of Large Spot Arrays from a Single Laser Beam by Multiple Imaging with Binary Phase Gratings,” Opt. Eng. 28, 299–304 (1989).

Dammann, H.

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Downs, M. M.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann Gratings for Laser Beam Shaping,” Opt. Eng. 28, 1267–1275 (1989).

Feldman, M. R.

Finlan, J. M.

K. M. Flood, J. M. Finlan, “Collimation of Diode Laser Arrays Using Etched Cylindrical Computer Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 186–190 (1989).

K. M. Flood, J. M. Finlan, “Multiple-Phase Level Computer Generated Holograms Etched in Fused Silica,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 91–96 (1989).

Flood, K. M.

K. M. Flood, J. M. Finlan, “Collimation of Diode Laser Arrays Using Etched Cylindrical Computer Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 186–190 (1989).

K. M. Flood, J. M. Finlan, “Multiple-Phase Level Computer Generated Holograms Etched in Fused Silica,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 91–96 (1989).

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Guest, C. C.

Herzig, H. P.

D. Prongue, H. P. Herzig, “Design and Fabrication of HOE for Clock Distribution in Integrated Circuits,” IEE Conference on Holographic Systems, Components and Applications, (Bath, U.K., 1989).

Hutley, M. C.

M. C. Hutley, “Optical Techniques for the Generation of Microlens Arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

Jahns, J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann Gratings for Laser Beam Shaping,” Opt. Eng. 28, 1267–1275 (1989).

J. Jahns, N. Streibl, S. J. Walker, “Multiple Phase Structures for Array Generation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 198–203 (1989).

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Klotz, E.

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Mait, J. N.

Prise, M. E.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann Gratings for Laser Beam Shaping,” Opt. Eng. 28, 1267–1275 (1989).

Prongue, D.

D. Prongue, H. P. Herzig, “Design and Fabrication of HOE for Clock Distribution in Integrated Circuits,” IEE Conference on Holographic Systems, Components and Applications, (Bath, U.K., 1989).

Streibl, N.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann Gratings for Laser Beam Shaping,” Opt. Eng. 28, 1267–1275 (1989).

J. Jahns, N. Streibl, S. J. Walker, “Multiple Phase Structures for Array Generation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 198–203 (1989).

Taghizadeh, M. R.

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasera, J. Westerholm, “Optimization and Fabrication of Grating Beam-splitters in Silicon Nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

Turunen, J.

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasera, J. Westerholm, “Optimization and Fabrication of Grating Beam-splitters in Silicon Nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

Vasera, A.

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasera, J. Westerholm, “Optimization and Fabrication of Grating Beam-splitters in Silicon Nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Walker, S. J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann Gratings for Laser Beam Shaping,” Opt. Eng. 28, 1267–1275 (1989).

J. Jahns, N. Streibl, S. J. Walker, “Multiple Phase Structures for Array Generation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 198–203 (1989).

Westerholm, J.

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasera, J. Westerholm, “Optimization and Fabrication of Grating Beam-splitters in Silicon Nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

Wilson, J. I. B.

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasera, J. Westerholm, “Optimization and Fabrication of Grating Beam-splitters in Silicon Nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

Wyrowski, F.

F. Wyrowski, O. Bryndahl, “Digital Holograms for Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 126–130 (1989).

F. Wyrowski, O. Bryndahl, “Iterative Fourier-Transform Algorithm Applied to Computer Holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. R. Taghizadeh, J. I. B. Wilson, J. Turunen, A. Vasera, J. Westerholm, “Optimization and Fabrication of Grating Beam-splitters in Silicon Nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
[CrossRef]

Electron. Lett. (1)

N. M. Barnes et al., “High Speed Opto-Electronic Neural Network,” Electron. Lett. 26, 1110–1113 (1990).
[CrossRef]

J. Mod. Opt. (1)

M. C. Hutley, “Optical Techniques for the Generation of Microlens Arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

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

Opt. Acta (1)

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Opt. Eng. (3)

S. M. Arnold, “Electron Beam Fabrication of Computer Generated Holograms,” Opt. Eng. 24, 803–807 (1985).

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann Gratings for Laser Beam Shaping,” Opt. Eng. 28, 1267–1275 (1989).

F. B. M. Cormick, “Generation of Large Spot Arrays from a Single Laser Beam by Multiple Imaging with Binary Phase Gratings,” Opt. Eng. 28, 299–304 (1989).

Opt. Lett. (2)

Proc. Soc. Photo-Opt. Instrum. Eng. (4)

F. Wyrowski, O. Bryndahl, “Digital Holograms for Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 126–130 (1989).

K. M. Flood, J. M. Finlan, “Multiple-Phase Level Computer Generated Holograms Etched in Fused Silica,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 91–96 (1989).

J. Jahns, N. Streibl, S. J. Walker, “Multiple Phase Structures for Array Generation,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 198–203 (1989).

K. M. Flood, J. M. Finlan, “Collimation of Diode Laser Arrays Using Etched Cylindrical Computer Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 186–190 (1989).

Science (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Other (2)

N. M. Barnes et al., “High Speed Opto-Electronic Neural Network,” Postdeadline Session International Conference on Optical Computing, (Kobe, Japan, 1990).

D. Prongue, H. P. Herzig, “Design and Fabrication of HOE for Clock Distribution in Integrated Circuits,” IEE Conference on Holographic Systems, Components and Applications, (Bath, U.K., 1989).

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Figures (7)

Fig. 1
Fig. 1

Optical arrangement for a Fourier transform beam splitter hologram.

Fig. 2
Fig. 2

(a) Single cell of a binary phase Fourier plane hologram to produce sixteen spots in a 4 × 4 square array. Theoretical efficiency 73%. The black areas denote π phase shift and the white areas denote 0 phase shift. (b) As for (a) but with a theoretical efficiency of 78%. © 1989 British Telecommunications PLC.

Fig. 3
Fig. 3

Schematic diagram of the processing steps after electron beam lithography.

Fig. 4
Fig. 4

Photograph of an eight spot pattern produced by a beam splitter hologram in visible light.

Fig. 5
Fig. 5

(a) Measurements of the spot intensities, at a wavelength of 1.5 μm, from the sixteen spot splitter design shown in Fig. 2(b). This element had not been AR coated. (b) As for (a), except that the element had been AR coated.

Fig. 6
Fig. 6

Measurements of the spot intensities, at a wavelength of 1.5 μm, from a twelve spot weighted intensity beams splitter. The element had been AR coated.

Fig. 7
Fig. 7

Vidicon camera image at 1.5 μm of the weighted spot pattern from a four-level phase hologram.

Equations (5)

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

Δ s = f λ L ,
a k l = 1 N 2 m = 0 m = N - 1 n = 0 n = N - 1 t m n exp ( 2 π i ( m k + n l ) N ) ,
Δ a k l = ( t m n - t m n ) N 2 exp ( - 2 π i ( m k + n l ) N ) ,
C = ( k , l ) target spots ( a k l - b k l ) 4 ,
η = k , l target spots b k l 2 .

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