Abstract

It is made clear theoretically and experimentally how the 3-D index distribution in a planar microlens is formed in the fabrication process. The combination of both drift and thermal diffusion of ions plays an important role in achieving an index profile for low aberration. The lens dimension and migration time are determined mainly by ion drift aided by the electric field. A very strong concentration dependency exists in the diffusion coefficient and this brings about an upward convex index shape up to the periphery resulting in full utilization of the index difference.

© 1984 Optical Society of America

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References

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  1. M. Oikawa, K. Iga, Appl. Opt. 21, 1052 (1982).
    [CrossRef] [PubMed]
  2. M. Oikawa, K. Iga, S. Misawa, Electron. Lett. 18, 8, 316 (1981).
  3. K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, Appl. Opt. 21, 3456 (1982).
    [CrossRef] [PubMed]
  4. M. Oikawa, K. Iga, S. Misawa, K. Kokubun, Appl. Opt. 22, 441 (1983).
    [CrossRef] [PubMed]
  5. M. Oikawa, K. Iga, T. Sanada, Electron. Lett. 17, 452 (1981).
    [CrossRef]
  6. T. Izawa, H. Nakagome, Appl. Phys. Lett. 21, 584 (1972).
    [CrossRef]
  7. Y. Kokubun, K. Iga, Appl. Opt. 21, 1030 (1982).
    [CrossRef] [PubMed]
  8. S. Misawa, M. Oikawa, K. Iga, 4th Topical Meeting on Gradient-Index Optical Imaging Systems, D2, Kobe, Japan (1983),Appl. Opt. 23, 1792 (1984).

1983 (1)

1982 (3)

1981 (2)

M. Oikawa, K. Iga, S. Misawa, Electron. Lett. 18, 8, 316 (1981).

M. Oikawa, K. Iga, T. Sanada, Electron. Lett. 17, 452 (1981).
[CrossRef]

1972 (1)

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

Banno, J.

Iga, K.

M. Oikawa, K. Iga, S. Misawa, K. Kokubun, Appl. Opt. 22, 441 (1983).
[CrossRef] [PubMed]

M. Oikawa, K. Iga, Appl. Opt. 21, 1052 (1982).
[CrossRef] [PubMed]

K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, Appl. Opt. 21, 3456 (1982).
[CrossRef] [PubMed]

Y. Kokubun, K. Iga, Appl. Opt. 21, 1030 (1982).
[CrossRef] [PubMed]

M. Oikawa, K. Iga, T. Sanada, Electron. Lett. 17, 452 (1981).
[CrossRef]

M. Oikawa, K. Iga, S. Misawa, Electron. Lett. 18, 8, 316 (1981).

S. Misawa, M. Oikawa, K. Iga, 4th Topical Meeting on Gradient-Index Optical Imaging Systems, D2, Kobe, Japan (1983),Appl. Opt. 23, 1792 (1984).

Izawa, T.

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

Kokubun, K.

Kokubun, Y.

Misawa, S.

M. Oikawa, K. Iga, S. Misawa, K. Kokubun, Appl. Opt. 22, 441 (1983).
[CrossRef] [PubMed]

K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, Appl. Opt. 21, 3456 (1982).
[CrossRef] [PubMed]

M. Oikawa, K. Iga, S. Misawa, Electron. Lett. 18, 8, 316 (1981).

S. Misawa, M. Oikawa, K. Iga, 4th Topical Meeting on Gradient-Index Optical Imaging Systems, D2, Kobe, Japan (1983),Appl. Opt. 23, 1792 (1984).

Nakagome, H.

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

Oikawa, M.

M. Oikawa, K. Iga, S. Misawa, K. Kokubun, Appl. Opt. 22, 441 (1983).
[CrossRef] [PubMed]

M. Oikawa, K. Iga, Appl. Opt. 21, 1052 (1982).
[CrossRef] [PubMed]

K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, Appl. Opt. 21, 3456 (1982).
[CrossRef] [PubMed]

M. Oikawa, K. Iga, S. Misawa, Electron. Lett. 18, 8, 316 (1981).

M. Oikawa, K. Iga, T. Sanada, Electron. Lett. 17, 452 (1981).
[CrossRef]

S. Misawa, M. Oikawa, K. Iga, 4th Topical Meeting on Gradient-Index Optical Imaging Systems, D2, Kobe, Japan (1983),Appl. Opt. 23, 1792 (1984).

Sanada, T.

M. Oikawa, K. Iga, T. Sanada, Electron. Lett. 17, 452 (1981).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

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

Electron. Lett. (2)

M. Oikawa, K. Iga, S. Misawa, Electron. Lett. 18, 8, 316 (1981).

M. Oikawa, K. Iga, T. Sanada, Electron. Lett. 17, 452 (1981).
[CrossRef]

Other (1)

S. Misawa, M. Oikawa, K. Iga, 4th Topical Meeting on Gradient-Index Optical Imaging Systems, D2, Kobe, Japan (1983),Appl. Opt. 23, 1792 (1984).

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Figures (3)

Fig. 1
Fig. 1

(a) Model of electromigration process. (b) Simplified spherical model.

Fig. 2
Fig. 2

Electromigration time vs lens size.

Fig. 3
Fig. 3

Ion concentration profile compared to radial/depth distance (spherical model/measured).

Equations (7)

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

J = q μ E N - q D grad N ,
N / t = - μ E · grad N + div ( D grad N ) .
N / t = - μ ( r m V s / r 2 ) N / r .
E = r m V s / r 2 ,
N ( r , t ) = N 0 h [ t - ( r 3 - r m 3 ) / ( 3 μ r m V s ) ] ,
r = ( 3 μ r m V s t e + r m 3 ) 1 / 3
D ( N 0 ) = μ K T / q ,

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