Abstract

For the design and optimization of the fabrication condition of distributed-index planar microlenses, it is necessary to evaluate the N.A., focal length, focused spot, and aberration of a fabricated lens. In this paper, a ray tracing method is improved for this purpose, and properties of planar microlenses are evaluated. An ion concentration matrix is proposed to simplify lens design.

© 1988 Optical Society of America

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References

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  1. M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
    [CrossRef]
  2. K. Iga, S. Misawa, “Distributed-Index Planar Microlens and Stacked Planar Optics: a Review of Progress,” Appl. Opt. 25, 3388 (1986).
    [CrossRef] [PubMed]
  3. G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Küppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), pp. 7.6.1–4.
  4. Y. Koike, Y. Ohtsuka, “Gradient-Index Polymer Materials and Application to Optical Devices,” in Technical Digest, Seventh Topical Meeting on Gradient-Index Optical Imaging Systems, (Optical Society of America, Washington, D.C., 1987), paper ThD1.
  5. K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, “Stacked Planar Optics: an Application of the Planar Microlens,” Appl. Opt. 21, 3456 (1982).
    [CrossRef] [PubMed]
  6. M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlenses Prepared from Ion Exchange Technique,” Jpn. J. Appl. Phys. 20, L296 (1981).
    [CrossRef]
  7. X. Zhu, K. Iga, “Index Profile of a Planar Microlens by Ion Exchange/Diffusion,” Appl. Opt. 25, 3397 (1986).
    [CrossRef] [PubMed]
  8. S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Distributed-Index Planar Microlens,” Jpn. J. Appl. Phys. 21, L589 (1982).
    [CrossRef]
  9. E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), p. 100.

1986 (2)

1982 (2)

S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Distributed-Index Planar Microlens,” Jpn. J. Appl. Phys. 21, L589 (1982).
[CrossRef]

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

1981 (2)

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlenses Prepared from Ion Exchange Technique,” Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
[CrossRef]

Banno, J.

Iga, K.

K. Iga, S. Misawa, “Distributed-Index Planar Microlens and Stacked Planar Optics: a Review of Progress,” Appl. Opt. 25, 3388 (1986).
[CrossRef] [PubMed]

X. Zhu, K. Iga, “Index Profile of a Planar Microlens by Ion Exchange/Diffusion,” Appl. Opt. 25, 3397 (1986).
[CrossRef] [PubMed]

S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Distributed-Index Planar Microlens,” Jpn. J. Appl. Phys. 21, L589 (1982).
[CrossRef]

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

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlenses Prepared from Ion Exchange Technique,” Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

Khoe, G. D.

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Küppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), pp. 7.6.1–4.

Kock, H. G.

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Küppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), pp. 7.6.1–4.

Koike, Y.

Y. Koike, Y. Ohtsuka, “Gradient-Index Polymer Materials and Application to Optical Devices,” in Technical Digest, Seventh Topical Meeting on Gradient-Index Optical Imaging Systems, (Optical Society of America, Washington, D.C., 1987), paper ThD1.

Kokubun, Y.

Küppers, D.

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Küppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), pp. 7.6.1–4.

Luijendijk, J. A.

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Küppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), pp. 7.6.1–4.

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), p. 100.

Misawa, S.

Nishizawa, K.

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlenses Prepared from Ion Exchange Technique,” Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

Ohtsuka, Y.

Y. Koike, Y. Ohtsuka, “Gradient-Index Polymer Materials and Application to Optical Devices,” in Technical Digest, Seventh Topical Meeting on Gradient-Index Optical Imaging Systems, (Optical Society of America, Washington, D.C., 1987), paper ThD1.

Oikawa, M.

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

S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Distributed-Index Planar Microlens,” Jpn. J. Appl. Phys. 21, L589 (1982).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlenses Prepared from Ion Exchange Technique,” Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
[CrossRef]

Sanada, T.

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlenses Prepared from Ion Exchange Technique,” Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

van den Brekel, C. H. J.

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Küppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), pp. 7.6.1–4.

Yamamoto, N.

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlenses Prepared from Ion Exchange Technique,” Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

Zhu, X.

Appl. Opt. (3)

Electron. Lett. (1)

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
[CrossRef]

Jpn. J. Appl. Phys. (2)

S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Distributed-Index Planar Microlens,” Jpn. J. Appl. Phys. 21, L589 (1982).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlenses Prepared from Ion Exchange Technique,” Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

Other (3)

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Küppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), pp. 7.6.1–4.

Y. Koike, Y. Ohtsuka, “Gradient-Index Polymer Materials and Application to Optical Devices,” in Technical Digest, Seventh Topical Meeting on Gradient-Index Optical Imaging Systems, (Optical Society of America, Washington, D.C., 1987), paper ThD1.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), p. 100.

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Figures (5)

Fig. 1
Fig. 1

Ion concentration distribution and that calculated by the concentration matrices.

Fig. 2
Fig. 2

Ray trajectories for a planar microlens made by ion exchange.

Fig. 3
Fig. 3

Focusing properties of lens.

Fig. 4
Fig. 4

Lens properties vs index difference.

Fig. 5
Fig. 5

Focused spot by a planar microlens.

Equations (7)

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d r d z = u n 2 u 2 ,
d u d z = n 2 / r 2 n 2 u 2 .
D = D 0 exp ( k N / N 0 ) ,
τ = D 0 t / r m 2 , ρ = r / r m , ζ = z / r m
N / N 0 = ( 1 , ζ , ζ 2 , ζ 3 ) ( c 00 c 02 c 04 c 06 c 10 c 12 c 14 c 16 c 20 c 22 c 24 c 26 c 30 c 32 c 34 c 36 ) ( 1 ρ 2 ρ 4 ρ 6 ) ,
c i j = ( 1 , k p , k 2 p , k 3 p ) ( b 00 ( i , j ) b 01 ( i , j ) b 02 ( i , j ) b 03 ( i , j ) b 10 ( i , j ) b 11 ( i , j ) b 12 ( i , j ) b 13 ( i , j ) b 20 ( i , j ) b 21 ( i , j ) b 22 ( i , j ) b 23 ( i , j ) b 30 ( i , j ) b 31 ( i , j ) b 32 ( i , j ) b 33 ( i , j ) ) ( 1 τ q τ 2 q τ 3 q ) ,
C = ( 1 0 . 108 0 . 0171 0 . 00172 0 . 254 0 . 192 0 . 0288 0 . 00111 0 . 0202 0 . 188 0 . 012 0 . 001 0 . 0459 0 . 0447 0 . 00157 0 . 000142 ) .

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