Abstract

Planar technology has been used to make a microlens array monolithically. By selectively diffusing a dopant into the planar substrate a distributed-index planar microlens has been realized. The monomer exchange technique for the plastic substrate and ion exchange and electromigration techniques for the glass substrate are used. In particular a 2-D planar microlens array was fabricated in a glass substrate. Each microlens was 1.2 mm in diameter and the focal length was 9.4 mm. The focused spot of the collimated He–Ne laser beam was as small as 17 μmϕ.

© 1982 Optical Society of America

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References

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  1. K. Iga, Appl. Opt. 19, 1039 (1980).
    [CrossRef] [PubMed]
  2. M. Saruwatari, T. Sugie, Electron. Lett. 16, 955 (1980).
    [CrossRef]
  3. J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, 1975).
  4. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  5. T. Imamura, Physics and Green’s Function (wanami, Tokyo, 1978), in Japanese.
  6. E. W. Marchand, Gradient Index Optics (Academic, New York, 1978).
  7. Y. Ohtsuka, Appl. Phys. Lett. 23, 247 (1973).
    [CrossRef]
  8. K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
    [CrossRef]
  9. K. Iga, N. Yamamoto, Appl. Opt. 16, 1305 (1977).
    [CrossRef] [PubMed]
  10. I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, in Proceedings, First Conference Solid State DevicesTokyo, 1969); O. Buturi, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).
  11. H. Kawanishi, Y. Suematsu, Trans. IECE Jpn. E60, 231 (1977).
  12. J. Koyama, H. Nishihara, Opto-Electronics Engineering (Corona, Tokyo, 1978), in Japanese.
  13. T. Izawa, H. Nakagome, Appl. Phys. Lett. 21, 584 (1972).
    [CrossRef]

1980 (2)

K. Iga, Appl. Opt. 19, 1039 (1980).
[CrossRef] [PubMed]

M. Saruwatari, T. Sugie, Electron. Lett. 16, 955 (1980).
[CrossRef]

1977 (2)

K. Iga, N. Yamamoto, Appl. Opt. 16, 1305 (1977).
[CrossRef] [PubMed]

H. Kawanishi, Y. Suematsu, Trans. IECE Jpn. E60, 231 (1977).

1975 (1)

K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[CrossRef]

1973 (1)

Y. Ohtsuka, Appl. Phys. Lett. 23, 247 (1973).
[CrossRef]

1972 (1)

T. Izawa, H. Nakagome, Appl. Phys. Lett. 21, 584 (1972).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Crank, J.

J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, 1975).

Furukawa, M.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, in Proceedings, First Conference Solid State DevicesTokyo, 1969); O. Buturi, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Iga, K.

Imamura, T.

T. Imamura, Physics and Green’s Function (wanami, Tokyo, 1978), in Japanese.

Izawa, T.

T. Izawa, H. Nakagome, Appl. Phys. Lett. 21, 584 (1972).
[CrossRef]

Kawanishi, H.

H. Kawanishi, Y. Suematsu, Trans. IECE Jpn. E60, 231 (1977).

Kitano, I.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, in Proceedings, First Conference Solid State DevicesTokyo, 1969); O. Buturi, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Koizumi, K.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, in Proceedings, First Conference Solid State DevicesTokyo, 1969); O. Buturi, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Koyama, J.

J. Koyama, H. Nishihara, Opto-Electronics Engineering (Corona, Tokyo, 1978), in Japanese.

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978).

Matsumura, H.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, in Proceedings, First Conference Solid State DevicesTokyo, 1969); O. Buturi, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Nakagome, H.

T. Izawa, H. Nakagome, Appl. Phys. Lett. 21, 584 (1972).
[CrossRef]

Nishihara, H.

J. Koyama, H. Nishihara, Opto-Electronics Engineering (Corona, Tokyo, 1978), in Japanese.

Ohtsuka, Y.

Y. Ohtsuka, Appl. Phys. Lett. 23, 247 (1973).
[CrossRef]

Sakayori, T.

K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[CrossRef]

Saruwatari, M.

M. Saruwatari, T. Sugie, Electron. Lett. 16, 955 (1980).
[CrossRef]

Suematsu, Y.

H. Kawanishi, Y. Suematsu, Trans. IECE Jpn. E60, 231 (1977).

Sugie, T.

M. Saruwatari, T. Sugie, Electron. Lett. 16, 955 (1980).
[CrossRef]

Uchida, T.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, in Proceedings, First Conference Solid State DevicesTokyo, 1969); O. Buturi, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Yamamoto, N.

Yokomori, K.

K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

T. Izawa, H. Nakagome, Appl. Phys. Lett. 21, 584 (1972).
[CrossRef]

Y. Ohtsuka, Appl. Phys. Lett. 23, 247 (1973).
[CrossRef]

K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[CrossRef]

Electron. Lett. (1)

M. Saruwatari, T. Sugie, Electron. Lett. 16, 955 (1980).
[CrossRef]

Trans. IECE Jpn. (1)

H. Kawanishi, Y. Suematsu, Trans. IECE Jpn. E60, 231 (1977).

Other (6)

J. Koyama, H. Nishihara, Opto-Electronics Engineering (Corona, Tokyo, 1978), in Japanese.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, in Proceedings, First Conference Solid State DevicesTokyo, 1969); O. Buturi, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, 1975).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

T. Imamura, Physics and Green’s Function (wanami, Tokyo, 1978), in Japanese.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978).

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Figures (9)

Fig. 1
Fig. 1

Structure of distributed-index planar microlens array.

Fig. 2
Fig. 2

Light ray trajectory in a distributed-index medium made by diffusion from a small hemispherical source.

Fig. 3
Fig. 3

Estimated light ray trajectories at various normalized diffusion times.

Fig. 4
Fig. 4

Plastic planar microlens. Magnified letters can be seen at the center where there has been a 3.6-mmϕ disk mask.

Fig. 5
Fig. 5

Method of measuring the focal length. Collimated light is incident on the back surface, and the distance from the front surface to the focused point is measured as a focal length.

Fig. 6
Fig. 6

Real images made by the planar microlens array.

Fig. 7
Fig. 7

Experimental setup to measure the focused spot diameter against the aperture radius.

Fig. 8
Fig. 8

Spot diameter of focused light vs aperture diameter. The plane wave from a He–Ne laser was used as the light source.

Fig. 9
Fig. 9

Airylike focused spot of a planar microlens fabricated by the electromigration technique.

Tables (1)

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Table I Summary of Fabrication Times

Equations (10)

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u ( r ; t ) = u 0 r m r erfc ( r - r m 2 D t ) ,
K = grad log n ( r ) ,
u ( r ˜ , z ˜ ; τ ) = J 0 0 1 0 2 π r ˜ d r ˜ d θ G ( r ˜ , θ , z ˜ , r ˜ , θ , z ˜ ; τ ) ,
G ( r ˜ , θ , z ˜ , r ˜ , θ , z ˜ ; τ ) = r m · erfc ( R ˜ / τ ) 2 π 3 / 2 D · R ˜ ,
R ˜ = ( r ˜ 2 - 2 r ˜ r ˜ cos θ + r ˜ 2 + z ˜ 2 ) .
r ¨ + 1 n 2 ( 1 + r ˙ 2 ) r ˙ z ( ½ n 2 ) - 1 n 2 ( 1 + r ˙ 2 ) r ( ½ n 2 ) = 0 ,
u ( r ˜ , z ˜ ; τ ) = J 0 [ 0 0 2 π r ˜ d r ˜ d θ G ( r ˜ , θ , z ˜ , r ˜ , θ , z ˜ ; ξ ) - 0 1 0 2 π r ˜ d r ˜ d θ G ( r ˜ , θ , z ˜ , r ˜ , θ , z ˜ ; τ ) ] .
D s = 2.44 f 2 r a λ ,
D s = 1.22 λ N . A . ,
N . A . = 1.22 D s λ = 0.05.

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