Abstract

A 2-D array of 10 × 10 diffractive lenslets was fabricated and tested. Each lenslet has a rectangular aperture and a size of 1.5 mm × 1.5 mm. The focal length of each lenslet is 47 mm. The array was produced by depositing thin films of silicon monoxide on a quartz glass substrate and by using photolithographic techniques. The performance of the lenslets is based on the diffraction of light at a Fresnel zone plate (FZP). The FZP pattern was implemented as a phase structure with eight discrete levels. The diffraction efficiency was measured to be 91%.

© 1990 Optical Society of America

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  1. T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsamura, “Optical Characteristics of a Light-Focusing Fiber Guide and its Applications,” IEEE J. Quantum Electron. QE-6, 606–612 (1970).
    [CrossRef]
  2. L. G. Cohen, M. V. Schneider, “Microlenses for Coupling Junction Lasers to Optical Fibers,” Appl. Opt. 13, 89–94 (1974).
    [CrossRef] [PubMed]
  3. K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, “Stacked Planar Optics: An Application of the Planar Microlens,” Appl. Opt. 21, 3456–3460 (1982).
    [CrossRef] [PubMed]
  4. F. W. Ostermayer, P. A. Kohl, R. H. Burton, C. L. Zipfel, “Photochemical Formation of Integral Lenses on InP/InGaAsP LEDs,” in Proceedings IEEE Conference on Light Emitting Diodes and Photodetectors (1982).
  5. O. Wada, “Ion-Beam Etching of InP and its Applications to the Fabrication of High Radiance InGaAsP/InP Light Emitting Diodes,” J. Electrochem. Soc. 131, 2373–2380 (1983).
    [CrossRef]
  6. N. F. Borrelli, D. L. Morse, “Microlens Arrays Produced by a Photolytic Technique,” Appl. Opt. 27, 476–479 (1988).
    [CrossRef] [PubMed]
  7. Z. D. Popovic, R. A. Sprague, G. A. Neville Connell, “Technique for Monolithic Microlens Fabrication,” Appl. Opt. 27, 1281–1284 (1988).
    [CrossRef] [PubMed]
  8. H. Dammann, “Blazed Synthetic Phase-Only Holograms,” Optik 31, 95–104 (1970).
  9. L. D’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232–235 (1972).
    [CrossRef]
  10. A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, “Fabrication of Planar Optical Phase Elements,” Opt. Commun. 8, 160–162 (1973).
    [CrossRef]
  11. 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]
  12. J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, “Astigmatic Wavefront Correction of a Gain-Guided Laser Diode Array Using Anamorphic Diffractive Microlenses,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82–89 (1988).
  13. J. Jahns, N. Streibl, S. J. Walker, “Multilevel Phase Structures for Array Generations,” OE/LASE ’89, Los Angeles, Jan. 15–20, 1989.
  14. J. Jewell, S. L. McCall, “Microoptic Systems: Essential for Optical Computing,” Topical Meeting on Optical Computing, Salt Lake City, Feb. 27–March 1, 1989.
  15. J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1605 (1989).
    [CrossRef] [PubMed]

1989 (1)

1988 (3)

N. F. Borrelli, D. L. Morse, “Microlens Arrays Produced by a Photolytic Technique,” Appl. Opt. 27, 476–479 (1988).
[CrossRef] [PubMed]

Z. D. Popovic, R. A. Sprague, G. A. Neville Connell, “Technique for Monolithic Microlens Fabrication,” Appl. Opt. 27, 1281–1284 (1988).
[CrossRef] [PubMed]

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, “Astigmatic Wavefront Correction of a Gain-Guided Laser Diode Array Using Anamorphic Diffractive Microlenses,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82–89 (1988).

1987 (1)

1983 (1)

O. Wada, “Ion-Beam Etching of InP and its Applications to the Fabrication of High Radiance InGaAsP/InP Light Emitting Diodes,” J. Electrochem. Soc. 131, 2373–2380 (1983).
[CrossRef]

1982 (2)

F. W. Ostermayer, P. A. Kohl, R. H. Burton, C. L. Zipfel, “Photochemical Formation of Integral Lenses on InP/InGaAsP LEDs,” in Proceedings IEEE Conference on Light Emitting Diodes and Photodetectors (1982).

K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, “Stacked Planar Optics: An Application of the Planar Microlens,” Appl. Opt. 21, 3456–3460 (1982).
[CrossRef] [PubMed]

1974 (1)

1973 (1)

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, “Fabrication of Planar Optical Phase Elements,” Opt. Commun. 8, 160–162 (1973).
[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]

1970 (2)

H. Dammann, “Blazed Synthetic Phase-Only Holograms,” Optik 31, 95–104 (1970).

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsamura, “Optical Characteristics of a Light-Focusing Fiber Guide and its Applications,” IEEE J. Quantum Electron. QE-6, 606–612 (1970).
[CrossRef]

Banno, J.

Borrelli, N. F.

Bundman, P.

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, “Astigmatic Wavefront Correction of a Gain-Guided Laser Diode Array Using Anamorphic Diffractive Microlenses,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82–89 (1988).

Burton, R. H.

F. W. Ostermayer, P. A. Kohl, R. H. Burton, C. L. Zipfel, “Photochemical Formation of Integral Lenses on InP/InGaAsP LEDs,” in Proceedings IEEE Conference on Light Emitting Diodes and Photodetectors (1982).

Cohen, L. G.

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, “Blazed Synthetic Phase-Only Holograms,” Optik 31, 95–104 (1970).

Firester, A. H.

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, “Fabrication of Planar Optical Phase Elements,” Opt. Commun. 8, 160–162 (1973).
[CrossRef]

Furukawa, M.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsamura, “Optical Characteristics of a Light-Focusing Fiber Guide and its Applications,” IEEE J. Quantum Electron. QE-6, 606–612 (1970).
[CrossRef]

Griswold, M. P.

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, “Astigmatic Wavefront Correction of a Gain-Guided Laser Diode Array Using Anamorphic Diffractive Microlenses,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82–89 (1988).

Heller, M. E.

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, “Fabrication of Planar Optical Phase Elements,” Opt. Commun. 8, 160–162 (1973).
[CrossRef]

Hoffman, D. M.

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, “Fabrication of Planar Optical Phase Elements,” Opt. Commun. 8, 160–162 (1973).
[CrossRef]

Huang, A.

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]

Iga, K.

Jahns, J.

J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

J. Jahns, N. Streibl, S. J. Walker, “Multilevel Phase Structures for Array Generations,” OE/LASE ’89, Los Angeles, Jan. 15–20, 1989.

James, E. A.

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, “Fabrication of Planar Optical Phase Elements,” Opt. Commun. 8, 160–162 (1973).
[CrossRef]

Jewell, J.

J. Jewell, S. L. McCall, “Microoptic Systems: Essential for Optical Computing,” Topical Meeting on Optical Computing, Salt Lake City, Feb. 27–March 1, 1989.

Kitano, I.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsamura, “Optical Characteristics of a Light-Focusing Fiber Guide and its Applications,” IEEE J. Quantum Electron. QE-6, 606–612 (1970).
[CrossRef]

Kohl, P. A.

F. W. Ostermayer, P. A. Kohl, R. H. Burton, C. L. Zipfel, “Photochemical Formation of Integral Lenses on InP/InGaAsP LEDs,” in Proceedings IEEE Conference on Light Emitting Diodes and Photodetectors (1982).

Koizumi, K.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsamura, “Optical Characteristics of a Light-Focusing Fiber Guide and its Applications,” IEEE J. Quantum Electron. QE-6, 606–612 (1970).
[CrossRef]

Kokubun, Y.

Leger, J. R.

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, “Astigmatic Wavefront Correction of a Gain-Guided Laser Diode Array Using Anamorphic Diffractive Microlenses,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82–89 (1988).

Matsamura, H.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsamura, “Optical Characteristics of a Light-Focusing Fiber Guide and its Applications,” IEEE J. Quantum Electron. QE-6, 606–612 (1970).
[CrossRef]

McCall, S. L.

J. Jewell, S. L. McCall, “Microoptic Systems: Essential for Optical Computing,” Topical Meeting on Optical Computing, Salt Lake City, Feb. 27–March 1, 1989.

Misawa, S.

Morse, D. L.

Neville Connell, G. A.

Oikawa, M.

Ostermayer, F. W.

F. W. Ostermayer, P. A. Kohl, R. H. Burton, C. L. Zipfel, “Photochemical Formation of Integral Lenses on InP/InGaAsP LEDs,” in Proceedings IEEE Conference on Light Emitting Diodes and Photodetectors (1982).

Popovic, Z. D.

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]

Schneider, M. V.

Scott, M. L.

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, “Astigmatic Wavefront Correction of a Gain-Guided Laser Diode Array Using Anamorphic Diffractive Microlenses,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82–89 (1988).

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]

Sprague, R. A.

Streibl, N.

J. Jahns, N. Streibl, S. J. Walker, “Multilevel Phase Structures for Array Generations,” OE/LASE ’89, Los Angeles, Jan. 15–20, 1989.

Uchida, T.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsamura, “Optical Characteristics of a Light-Focusing Fiber Guide and its Applications,” IEEE J. Quantum Electron. QE-6, 606–612 (1970).
[CrossRef]

Wada, O.

O. Wada, “Ion-Beam Etching of InP and its Applications to the Fabrication of High Radiance InGaAsP/InP Light Emitting Diodes,” J. Electrochem. Soc. 131, 2373–2380 (1983).
[CrossRef]

Walker, S. J.

J. Jahns, N. Streibl, S. J. Walker, “Multilevel Phase Structures for Array Generations,” OE/LASE ’89, Los Angeles, Jan. 15–20, 1989.

Wasa, K.

Yamazaki, O.

Zipfel, C. L.

F. W. Ostermayer, P. A. Kohl, R. H. Burton, C. L. Zipfel, “Photochemical Formation of Integral Lenses on InP/InGaAsP LEDs,” in Proceedings IEEE Conference on Light Emitting Diodes and Photodetectors (1982).

Appl. Opt. (6)

IEEE J. Quantum Electron. (1)

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsamura, “Optical Characteristics of a Light-Focusing Fiber Guide and its Applications,” IEEE J. Quantum Electron. QE-6, 606–612 (1970).
[CrossRef]

J. Electrochem. Soc. (1)

O. Wada, “Ion-Beam Etching of InP and its Applications to the Fabrication of High Radiance InGaAsP/InP Light Emitting Diodes,” J. Electrochem. Soc. 131, 2373–2380 (1983).
[CrossRef]

Opt. Commun. (2)

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

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, “Fabrication of Planar Optical Phase Elements,” Opt. Commun. 8, 160–162 (1973).
[CrossRef]

Optik (1)

H. Dammann, “Blazed Synthetic Phase-Only Holograms,” Optik 31, 95–104 (1970).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, “Astigmatic Wavefront Correction of a Gain-Guided Laser Diode Array Using Anamorphic Diffractive Microlenses,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82–89 (1988).

Proceedings IEEE Conference on Light Emitting Diodes and Photodetectors (1)

F. W. Ostermayer, P. A. Kohl, R. H. Burton, C. L. Zipfel, “Photochemical Formation of Integral Lenses on InP/InGaAsP LEDs,” in Proceedings IEEE Conference on Light Emitting Diodes and Photodetectors (1982).

Other (2)

J. Jahns, N. Streibl, S. J. Walker, “Multilevel Phase Structures for Array Generations,” OE/LASE ’89, Los Angeles, Jan. 15–20, 1989.

J. Jewell, S. L. McCall, “Microoptic Systems: Essential for Optical Computing,” Topical Meeting on Optical Computing, Salt Lake City, Feb. 27–March 1, 1989.

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Figures (13)

Fig. 1
Fig. 1

Fresnel zone pattern (a) and its amplitude transmission as a function of r2 (b).

Fig. 2
Fig. 2

Diffraction of a plane wave at a Fresnel zone plate.

Fig. 3
Fig. 3

Phase profile of a diffractive lens with multiple discrete phase levels.

Fig. 4
Fig. 4

Efficiency of a diffractive lens as a function of the number of phase levels. Note that for L = 1 the efficiency of a binary amplitude FZP is shown for comparison.

Fig. 5
Fig. 5

Focal spectrum of a diffractive lens as a function of the number L of phase levels.

Fig. 6
Fig. 6

Fabrication steps to generate a phase grating using thin film deposition: (a) resist patterning; (b) thin film deposition; (c) lift-off; and (d) resulting phase structure.

Fig. 7
Fig. 7

Fabrication of a phase component with four levels by two successive steps.

Fig. 8
Fig. 8

Section of one of the mask patterns used for the fabrication of the lenslet array shown in Fig. 9.

Fig. 9
Fig. 9

Array of 10 × 10 lenslets on a one inch quartz glass substrate.

Fig. 10
Fig. 10

Center of one lenslet (a) and corner between lenslets (b).

Fig. 11
Fig. 11

Focal spots (a) and intensity profile (b).

Fig. 12
Fig. 12

Magnified view of one spot (a) and intensity profile (b).

Fig. 13
Fig. 13

Measurement of the diffraction efficiency was done by measuring the light intensity Ia without the lenslets being present and, in a second step, the intensity between the focal spots Ib.

Equations (19)

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r m = m r p
g ( x , y ) = g ( x 2 + y 2 ) = g ( r 2 ) = g ( r 2 + j r p 2 ) .
g ( x , y ) = n = - A n exp ( 2 π i n x 2 + y 2 r p 2 ) .
A n = ( 1 / r p 2 ) 0 r p 2 g ( r 2 ) exp ( - 2 π i n r 2 ) d ( r 2 ) .
u ( x , y , z ) = g ( x , y ) 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 [ 2 π i ( n r p 2 + 1 2 λ z ) ( x 2 + y 2 ) ] × exp [ 2 π i ( x x + y y λ z ) ] d x d y .
z n = r p 2 2 λ n ,
u ( x , y , z n ) = A n exp [ i π λ z n ( x 2 + y 2 ) ] δ ( x λ z n , y λ z n ) + m n A m .
u ( x , y , z n ) = A n exp [ i π λ z n ( x 2 + y 2 ) ] sinc ( x w x λ z n , y w x λ z n ) .
g ( r 2 ) = k = 0 N ( L - 1 ) exp ( - 2 π i k L ) rect ( r 2 - k r p 2 / L - r p 2 / 2 L r p 2 / L ) .
A n = 0 1 k = 0 L - 1 exp ( - 2 π i k L ) rect ( r 2 - k / L - 1 / 2 L 1 / L ) exp ( - 2 π i n r 2 ) d ( r 2 ) .
= exp ( i π n L ) sinc ( n / L ) 1 L k = 0 L - 1 exp [ 2 π i k ( n + 1 ) L ] .
k = 0 L - 1 exp [ 2 π i k ( n + 1 ) L ] = { L if n = j L - 1 , j integer 0 else
η = A - 1 2 = sinc 2 ( 1 / L ) = { sin ( π / L ) π / L } 2 .
w = r p L ( N - N - 1 ) .
w = r p 2 L N .
f / n o . = r p 2 / 2 λ 2 N r p = r p 4 N λ .
w = 2 λ f / n o . L .
η = I a - I b I a .

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