Abstract

Two-dimensional arrays of mutually coherent optical beams are needed in holographic interconnections for both recording and reading gratings. We analyze the use and limitations of binary phase Fresnel lenses to generate beams for these applications. Two known techniques of ion beam milling and thin film deposition are compared to fabricate such lens arrays in SiO2 and Si3N4. Each lens in the 8 × 8 arrays has a 1.2-mm square aperture with a focal length of 20 mm. Diffraction of a single argon-ion beam into an 8 × 8 array of highly uniform coherent focused beams (with 12-μm spot size) was achieved by the lenses with an efficiency of ~30% (41% theoretical limit).

© 1991 Optical Society of America

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References

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  1. D. Z. Anderson, D. M. Lininger, “Dynamic Optical Interconnects: Volume Holograms as Optical Two-Port Operators,” Appl. Opt. 26, 5031–5038 (1987).
    [CrossRef] [PubMed]
  2. H. Lee, “Volume Holographic Global and Local Interconnecting Patterns with Maximal Capacity and Minimal First-Order Crosstalk,” Appl. Opt. 28, 5312–5316 (1989).
    [CrossRef] [PubMed]
  3. A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic Holographic Interconnects with Analog Weights in Photorefractive Crystals,” Opt. Eng. 29, 215–224 (1990).
    [CrossRef]
  4. H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  5. M. R. Taghizadeh, J. I. B. Wilson, “Optimization and Fabrication of Grating Beamsplitters in Silicon Nitride,” Appl. Phys. Lett. 54, 1492–1494 (1989).
    [CrossRef]
  6. 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).
    [CrossRef]
  7. L. D’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232–235 (1972).
    [CrossRef]
  8. G. J. Swanson, W. B. Veldkamp, “Binary Lenses for Use at 10.6 Micrometers,” Opt. Eng. 24, 791–795 (1985).
    [CrossRef]
  9. T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Rectangular-Apertured Micro-Fresnel Lens Arrays Fabricated by Electron-Beam Lithography,” Appl. Opt. 26, 587–591 (1987).
    [CrossRef] [PubMed]
  10. T. Shiono, K. Setsune, “Blazed Reflection Micro-Fresnel Lenses Fabricated by Electron-Beam Writing and Dry Development,” Opt. Lett. 15, 84–86 (1990).
    [CrossRef] [PubMed]
  11. J. Jahns, S. J. Walker, “Two-Dimensional Array of Diffractive Microlenses Fabricated by Thin Film Deposition,” Appl. Opt. 29, 931–936 (1990).
    [CrossRef] [PubMed]
  12. F. A. Jenkins, H. E. White, Fundamentals of Physical Optics (McGraw-Hill, New York, 1937).
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

1990 (3)

1989 (3)

H. Lee, “Volume Holographic Global and Local Interconnecting Patterns with Maximal Capacity and Minimal First-Order Crosstalk,” Appl. Opt. 28, 5312–5316 (1989).
[CrossRef] [PubMed]

M. R. Taghizadeh, J. I. B. Wilson, “Optimization and Fabrication of Grating Beamsplitters 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).
[CrossRef]

1987 (2)

1985 (1)

G. J. Swanson, W. B. Veldkamp, “Binary Lenses for Use at 10.6 Micrometers,” Opt. Eng. 24, 791–795 (1985).
[CrossRef]

1972 (1)

L. D’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

1971 (1)

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Anderson, D. Z.

D’Auria, L.

L. D’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

Dammann, H.

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–315 (1971).
[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).
[CrossRef]

Goodman, J. W.

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

Gortler, K.

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Habiby, S. F.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic Holographic Interconnects with Analog Weights in Photorefractive Crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

Hubbard, W. M.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic Holographic Interconnects with Analog Weights in Photorefractive Crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

Huignard, J. P.

L. D’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

Jahns, J.

J. Jahns, S. J. Walker, “Two-Dimensional Array of Diffractive Microlenses Fabricated by Thin Film Deposition,” Appl. Opt. 29, 931–936 (1990).
[CrossRef] [PubMed]

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).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Physical Optics (McGraw-Hill, New York, 1937).

Lee, H.

Lininger, D. M.

Marrakchi, A.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic Holographic Interconnects with Analog Weights in Photorefractive Crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

Patel, J. S.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic Holographic Interconnects with Analog Weights in Photorefractive Crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

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).
[CrossRef]

Roy, A. M.

L. D’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

Setsune, K.

Shiono, T.

Spitz, E.

L. D’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

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).
[CrossRef]

Swanson, G. J.

G. J. Swanson, W. B. Veldkamp, “Binary Lenses for Use at 10.6 Micrometers,” Opt. Eng. 24, 791–795 (1985).
[CrossRef]

Taghizadeh, M. R.

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

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, “Binary Lenses for Use at 10.6 Micrometers,” Opt. Eng. 24, 791–795 (1985).
[CrossRef]

Walker, S. J.

J. Jahns, S. J. Walker, “Two-Dimensional Array of Diffractive Microlenses Fabricated by Thin Film Deposition,” Appl. Opt. 29, 931–936 (1990).
[CrossRef] [PubMed]

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).
[CrossRef]

Wasa, K.

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Physical Optics (McGraw-Hill, New York, 1937).

Wilson, J. I. B.

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

Yamazaki, O.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

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

Opt. Commun. (2)

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

L. D’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

Opt. Eng. (3)

G. J. Swanson, W. B. Veldkamp, “Binary Lenses for Use at 10.6 Micrometers,” Opt. Eng. 24, 791–795 (1985).
[CrossRef]

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic Holographic Interconnects with Analog Weights in Photorefractive Crystals,” Opt. Eng. 29, 215–224 (1990).
[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).
[CrossRef]

Opt. Lett. (1)

Other (2)

F. A. Jenkins, H. E. White, Fundamentals of Physical Optics (McGraw-Hill, New York, 1937).

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

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of PISCES.

Fig. 2
Fig. 2

(a) Schematic diagram of a binary amplitude/phase Fresnel lens. In the amplitude lens every other zone is opaque, while in the phase lens they are all transparent with an induced π phase shift between the neighboring zones. (b) The phase shift induced by a binary phase Fresnel lens as a function of R2. The period of this function is 2 R 1 2. The amplitude of the transmittance function is unity.

Fig. 3
Fig. 3

Electron-beam generated mask used for patterning BP-FLAs on both SiO2 and Si3N4. The array consists of 8 × 8 square aperture elements, each 1.2 mm wide.

Fig. 4
Fig. 4

Sequence for patterning and selective ion beam milling technique for fabricating BP-FLAs on SiO2.

Fig. 5
Fig. 5

Scanning electron micrograph (55×) of a BP-FLA fabricated on SiO2 as described in the text. The array consists of 8 × 8 elements, each with a 1.2-mm square aperture. The graininess is an artifact of the microscope.

Fig. 6
Fig. 6

Scanning electron micrograph (286×) of a BP-FL fabricated on SiO2 shows highly uniform surfaces. The graininess is an artifact of the microscope.

Fig. 7
Fig. 7

Sequence for the patterning and plasma etching technique for fabricating BP-FLAs on plasma-CVD Si3N4.

Fig. 8
Fig. 8

Optical micrograph (56×) of a BP-FLA fabricated on Si3N4. The array consists of 8 × 8 elements, each with a 1.2-mm square aperture.

Fig. 9
Fig. 9

Scanning electron micrograph (2800×) of a section of the Si3N4 BP-FL. The only visible nonuniformity results from a 0.5-μm step size used for patterning the original mask.

Fig. 10
Fig. 10

An 8 × 8 array of beams focused at 20 mm when the beam from an argon-ion laser was diffracted from the BP-FLA fabricated on SiO2.

Fig. 11
Fig. 11

Scan of the intensity across four generated spots revealing uniformity. The maximum intensity variation is ~6%.

Fig. 12
Fig. 12

Diffraction pattern at the focal plane of a single BP-FL: (a) SiO2, (b) Si3N4. The patterns are characteristic of the diffraction from square apertures and are identical for both lens types.

Equations (14)

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R m 2 = m R 1 2 ,
t ( R 2 ) = n = a n exp ( i π n R 2 R 1 2 ) ,
a n = 1 2 R 1 2 0 2 R 1 2 t ( R 2 ) exp ( i π n R 2 R 1 2 ) d ( R 2 ) .
U ( x , y , z ) = t ( R 2 ) exp ( i π λ z [ ( x x ) 2 + ( y y ) 2 ] ) d x d y ,
U ( x , y , z ) = n = a n exp ( i π λ z ( x 2 + y 2 ) ) exp [ i π ( x 2 + y 2 ) × ( n R 1 2 + 1 λ z ) ] exp [ 2 i π λ z ( x x + y y ) ] d x d y .
z n = R 1 2 n λ , n = 0 , ± 1 , ± 2 , ± 3 ,
U ( x , y , z n ) = a n exp ( i π λ z n ( x 2 + y 2 ) ) sin c ( x L x λ z n , y L y λ z n ) + q n b q .
t ( R 2 ) = m = 0 M / 2 [ exp ( i ϕ ) rect [ R 2 2 m R 1 2 R 1 2 / 2 R 1 2 ] + rect ( R 2 2 m R 1 2 3 R 1 2 / 2 R 1 2 ) ] .
a n = 1 2 exp ( i π n 2 ) [ 1 + exp ( i π n ) ] sin c n 2 .
[ 1 + exp ( i π n ) ] = { 2 , n = ± ( 2 j + 1 ) j = 0 , 1 , 2 , . 0 , otherwise .
f n = R 1 2 n λ , n = ± 1 , ± 3 , ± 5 , .
I n = sin c 2 n 2 = ( sin n π 2 n π 2 ) 2 , n = ± 1 , ± 3 , ± 5 , .
d = λ 2 Δ n ,
S n = 2 λ z n L x .

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