Abstract

Research into 2-D arrayed planar microlenses (0.2–2 mm in diameter) is reviewed. A planar microlens with N.A. = 0.54 has been obtained. Coupling of optical fibers and other applications of stacked planar optics are presented.

© 1986 Optical Society of America

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References

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  1. M. Oikawa, K. Iga, T. Sanada, “A Distributed-Index Planar Microlens Made of Plastics,” Jpn. J. Appl. Phys. 20, L51 (1981).
    [Crossref]
  2. M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlens Prepared from Ion Exchange Technique,” Jpn. J. Appl. Phys. 20, L296 (1981).
    [Crossref]
  3. M. Oikawa, K. Iga, “Distributed-Index Planar Microlens,” Appl. Opt. 21, 1052 (1982).
    [Crossref] [PubMed]
  4. 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), p. 7.6.
  5. N. F. Borrelli, D. L. Morse, “Planar Gradient Index Structures,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), p. D1.
  6. M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452 (1981).
    [Crossref]
  7. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, 1966).
  8. S. P. Morgan, “General Solution of the Luneburg Lens Problem,” J. Appl. Phys. 29, 1358 (1958).
    [Crossref]
  9. S. Misawa, M. Oikawa, K. Iga, “Maximum and Effective N.A. of Planar Microlens,” Appl. Opt. 23, 1784 (1984).
    [Crossref] [PubMed]
  10. I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” in First Conference, Solid State Devices, Tokyo, Japan (1969); “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” J. Jpn Soc. Appl. Phys. 39, 63 (1970).
  11. Y. Kokubun, K. Iga, “Index Profiling of Distributed-Index Lenses by a Shearing Interference Method,” Appl. Opt. 21, 1030 (1982).
    [Crossref] [PubMed]
  12. S. Misawa, M. Oikawa, K. Iga, “Measurement of Numerical Aperture of Planar Microlens by Far Field Pattern Method,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1984), paper ThE-D4.
  13. S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Distributed-Index Planar Microlens,” Jpn. J. Appl. Phys. 21, L589 (1982).
    [Crossref]
  14. S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Planar Microlens,” Optics (in Japanese) 12, 464 (1983).
  15. M. Oikawa, K. Iga, S. Misawa, Y. Kokubun, “Improved Distributed-Index Planar Microlens and its Applications to 2-D Lightwave Components,” Appl. Opt. 22, 441 (1983).
    [Crossref] [PubMed]
  16. Y. Kokubun, T. Usui, M. Oikawa, K. Iga, “Wave Aberration Testing System for Micro-Lenses by Shearing Interference Method,” Jpn. J. Appl. Phys. 23, 101 (1984).
    [Crossref]
  17. K. Iga, S. Misawa, X. F. Zhu, L. K. Phua, “Planar Microlens Array for Electrooptic Applications,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper FA4.
  18. H. Kesseler, Handbuch der Physik, Vol. 15, X. Geiger, K. Scheel, Eds. (Springer-Verlag, New York, 1927).
  19. 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]
  20. M. Oikawa, K. Iga, S. Misawa, “Optical Tap Array Using Distributed-Index Planar Microlens,” Electron. Lett. 18, L316 (1981).
    [Crossref]
  21. M. Oikawa, K. Iga, “Stacked Array Components with Distributed-Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), paper H2.
  22. M. Oikawa, K. Iga, S. Misawa, “2-D Branching Component Array with Distributed-Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1984), paper THE-D3.
  23. M. Oikawa, K. Iga, “Simplified Ray Matrix of Distributed Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), paper A4.

1984 (2)

Y. Kokubun, T. Usui, M. Oikawa, K. Iga, “Wave Aberration Testing System for Micro-Lenses by Shearing Interference Method,” Jpn. J. Appl. Phys. 23, 101 (1984).
[Crossref]

S. Misawa, M. Oikawa, K. Iga, “Maximum and Effective N.A. of Planar Microlens,” Appl. Opt. 23, 1784 (1984).
[Crossref] [PubMed]

1983 (2)

1982 (4)

1981 (4)

M. Oikawa, K. Iga, S. Misawa, “Optical Tap Array Using Distributed-Index Planar Microlens,” Electron. Lett. 18, L316 (1981).
[Crossref]

M. Oikawa, K. Iga, T. Sanada, “A Distributed-Index Planar Microlens Made of Plastics,” Jpn. J. Appl. Phys. 20, L51 (1981).
[Crossref]

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlens 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]

1958 (1)

S. P. Morgan, “General Solution of the Luneburg Lens Problem,” J. Appl. Phys. 29, 1358 (1958).
[Crossref]

Banno, J.

Borrelli, N. F.

N. F. Borrelli, D. L. Morse, “Planar Gradient Index Structures,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), p. D1.

Furukawa, M.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” in First Conference, Solid State Devices, Tokyo, Japan (1969); “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” J. Jpn Soc. Appl. Phys. 39, 63 (1970).

Iga, K.

S. Misawa, M. Oikawa, K. Iga, “Maximum and Effective N.A. of Planar Microlens,” Appl. Opt. 23, 1784 (1984).
[Crossref] [PubMed]

Y. Kokubun, T. Usui, M. Oikawa, K. Iga, “Wave Aberration Testing System for Micro-Lenses by Shearing Interference Method,” Jpn. J. Appl. Phys. 23, 101 (1984).
[Crossref]

S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Planar Microlens,” Optics (in Japanese) 12, 464 (1983).

M. Oikawa, K. Iga, S. Misawa, Y. Kokubun, “Improved Distributed-Index Planar Microlens and its Applications to 2-D Lightwave Components,” Appl. Opt. 22, 441 (1983).
[Crossref] [PubMed]

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]

Y. Kokubun, K. Iga, “Index Profiling of Distributed-Index Lenses by a Shearing Interference Method,” Appl. Opt. 21, 1030 (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, “Distributed-Index Planar Microlens,” Appl. Opt. 21, 1052 (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, “A Distributed-Index Planar Microlens Made of Plastics,” Jpn. J. Appl. Phys. 20, L51 (1981).
[Crossref]

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

M. Oikawa, K. Iga, S. Misawa, “Optical Tap Array Using Distributed-Index Planar Microlens,” Electron. Lett. 18, L316 (1981).
[Crossref]

M. Oikawa, K. Iga, “Stacked Array Components with Distributed-Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), paper H2.

M. Oikawa, K. Iga, S. Misawa, “2-D Branching Component Array with Distributed-Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1984), paper THE-D3.

M. Oikawa, K. Iga, “Simplified Ray Matrix of Distributed Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), paper A4.

K. Iga, S. Misawa, X. F. Zhu, L. K. Phua, “Planar Microlens Array for Electrooptic Applications,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper FA4.

S. Misawa, M. Oikawa, K. Iga, “Measurement of Numerical Aperture of Planar Microlens by Far Field Pattern Method,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1984), paper ThE-D4.

Kesseler, H.

H. Kesseler, Handbuch der Physik, Vol. 15, X. Geiger, K. Scheel, Eds. (Springer-Verlag, New York, 1927).

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), p. 7.6.

Kitano, I.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” in First Conference, Solid State Devices, Tokyo, Japan (1969); “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” J. Jpn Soc. Appl. Phys. 39, 63 (1970).

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), p. 7.6.

Koizumi, K.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” in First Conference, Solid State Devices, Tokyo, Japan (1969); “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” J. Jpn Soc. Appl. Phys. 39, 63 (1970).

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), p. 7.6.

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), p. 7.6.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, 1966).

Matsumura, H.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” in First Conference, Solid State Devices, Tokyo, Japan (1969); “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” J. Jpn Soc. Appl. Phys. 39, 63 (1970).

Misawa, S.

S. Misawa, M. Oikawa, K. Iga, “Maximum and Effective N.A. of Planar Microlens,” Appl. Opt. 23, 1784 (1984).
[Crossref] [PubMed]

S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Planar Microlens,” Optics (in Japanese) 12, 464 (1983).

M. Oikawa, K. Iga, S. Misawa, Y. Kokubun, “Improved Distributed-Index Planar Microlens and its Applications to 2-D Lightwave Components,” Appl. Opt. 22, 441 (1983).
[Crossref] [PubMed]

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, S. Misawa, “Optical Tap Array Using Distributed-Index Planar Microlens,” Electron. Lett. 18, L316 (1981).
[Crossref]

M. Oikawa, K. Iga, S. Misawa, “2-D Branching Component Array with Distributed-Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1984), paper THE-D3.

K. Iga, S. Misawa, X. F. Zhu, L. K. Phua, “Planar Microlens Array for Electrooptic Applications,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper FA4.

S. Misawa, M. Oikawa, K. Iga, “Measurement of Numerical Aperture of Planar Microlens by Far Field Pattern Method,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1984), paper ThE-D4.

Morgan, S. P.

S. P. Morgan, “General Solution of the Luneburg Lens Problem,” J. Appl. Phys. 29, 1358 (1958).
[Crossref]

Morse, D. L.

N. F. Borrelli, D. L. Morse, “Planar Gradient Index Structures,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), p. D1.

Nishizawa, K.

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

Oikawa, M.

S. Misawa, M. Oikawa, K. Iga, “Maximum and Effective N.A. of Planar Microlens,” Appl. Opt. 23, 1784 (1984).
[Crossref] [PubMed]

Y. Kokubun, T. Usui, M. Oikawa, K. Iga, “Wave Aberration Testing System for Micro-Lenses by Shearing Interference Method,” Jpn. J. Appl. Phys. 23, 101 (1984).
[Crossref]

M. Oikawa, K. Iga, S. Misawa, Y. Kokubun, “Improved Distributed-Index Planar Microlens and its Applications to 2-D Lightwave Components,” Appl. Opt. 22, 441 (1983).
[Crossref] [PubMed]

S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Planar Microlens,” Optics (in Japanese) 12, 464 (1983).

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, “Distributed-Index Planar Microlens,” Appl. Opt. 21, 1052 (1982).
[Crossref] [PubMed]

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, S. Misawa, “Optical Tap Array Using Distributed-Index Planar Microlens,” Electron. Lett. 18, L316 (1981).
[Crossref]

M. Oikawa, K. Iga, T. Sanada, “A Distributed-Index Planar Microlens Made of Plastics,” Jpn. J. Appl. Phys. 20, L51 (1981).
[Crossref]

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, “Array of Distributed-Index Planar Microlens 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]

S. Misawa, M. Oikawa, K. Iga, “Measurement of Numerical Aperture of Planar Microlens by Far Field Pattern Method,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1984), paper ThE-D4.

M. Oikawa, K. Iga, “Stacked Array Components with Distributed-Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), paper H2.

M. Oikawa, K. Iga, S. Misawa, “2-D Branching Component Array with Distributed-Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1984), paper THE-D3.

M. Oikawa, K. Iga, “Simplified Ray Matrix of Distributed Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), paper A4.

Phua, L. K.

K. Iga, S. Misawa, X. F. Zhu, L. K. Phua, “Planar Microlens Array for Electrooptic Applications,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper FA4.

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, “A Distributed-Index Planar Microlens Made of Plastics,” Jpn. J. Appl. Phys. 20, L51 (1981).
[Crossref]

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

Uchida, T.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” in First Conference, Solid State Devices, Tokyo, Japan (1969); “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” J. Jpn Soc. Appl. Phys. 39, 63 (1970).

Usui, T.

Y. Kokubun, T. Usui, M. Oikawa, K. Iga, “Wave Aberration Testing System for Micro-Lenses by Shearing Interference Method,” Jpn. J. Appl. Phys. 23, 101 (1984).
[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), p. 7.6.

Yamamoto, N.

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

Zhu, X. F.

K. Iga, S. Misawa, X. F. Zhu, L. K. Phua, “Planar Microlens Array for Electrooptic Applications,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper FA4.

Appl. Opt. (5)

Electron. Lett. (2)

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, S. Misawa, “Optical Tap Array Using Distributed-Index Planar Microlens,” Electron. Lett. 18, L316 (1981).
[Crossref]

J. Appl. Phys. (1)

S. P. Morgan, “General Solution of the Luneburg Lens Problem,” J. Appl. Phys. 29, 1358 (1958).
[Crossref]

Jpn. J. Appl. Phys. (4)

M. Oikawa, K. Iga, T. Sanada, “A Distributed-Index Planar Microlens Made of Plastics,” Jpn. J. Appl. Phys. 20, L51 (1981).
[Crossref]

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

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

Y. Kokubun, T. Usui, M. Oikawa, K. Iga, “Wave Aberration Testing System for Micro-Lenses by Shearing Interference Method,” Jpn. J. Appl. Phys. 23, 101 (1984).
[Crossref]

Optics (in Japanese) (1)

S. Misawa, M. Oikawa, K. Iga, “Ray Tracing in a Planar Microlens,” Optics (in Japanese) 12, 464 (1983).

Other (10)

K. Iga, S. Misawa, X. F. Zhu, L. K. Phua, “Planar Microlens Array for Electrooptic Applications,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper FA4.

H. Kesseler, Handbuch der Physik, Vol. 15, X. Geiger, K. Scheel, Eds. (Springer-Verlag, New York, 1927).

M. Oikawa, K. Iga, “Stacked Array Components with Distributed-Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), paper H2.

M. Oikawa, K. Iga, S. Misawa, “2-D Branching Component Array with Distributed-Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1984), paper THE-D3.

M. Oikawa, K. Iga, “Simplified Ray Matrix of Distributed Index Planar Microlens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), paper A4.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” in First Conference, Solid State Devices, Tokyo, Japan (1969); “A Light-Focusing Fiber Guide Prepared by Ion-Exchange Techniques,” J. Jpn Soc. Appl. Phys. 39, 63 (1970).

S. Misawa, M. Oikawa, K. Iga, “Measurement of Numerical Aperture of Planar Microlens by Far Field Pattern Method,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1984), paper ThE-D4.

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, 1966).

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), p. 7.6.

N. F. Borrelli, D. L. Morse, “Planar Gradient Index Structures,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Kobe, Japan (1983), p. D1.

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Figures (21)

Fig. 1
Fig. 1

Distributed index planar microlens.

Fig. 2
Fig. 2

(a) Hemispherical microlens; (b) stacked spherical microlens.

Fig. 3
Fig. 3

Maximally available N.A. when the maximum index difference is given. The solid lines are an exact calculation; and the broken lines are an approximation using Eqs. (10) and (15). The ao-25-19-3388-i001 indicates the effective N.A. of a single lens obtained by measurement, and ao-25-19-3388-i002 shows the N.A. of a stacked lens. These are calculated at n2 = 1.537.

Fig. 4
Fig. 4

Index profiles giving low aberration for a hemispherical lens.

Fig. 5
Fig. 5

Index profiles giving low aberration for a stacked lens.

Fig. 6
Fig. 6

(a) Conventional electromigration method; (b) transverse electromigration method.

Fig. 7
Fig. 7

Fringe pattern of the fabricated planar microlens obtained by the shearing interference method.

Fig. 8
Fig. 8

Three-dimensional representation of measured index profile of the fabricated lens.

Fig. 9
Fig. 9

Ray trajectories of the fabricated planar microlens for parallel incidence.

Fig. 10
Fig. 10

Comparison between the index profiles of a fabricated lens and those of the hemispherical Luneburg lens. The two solid lines represent the measured index profile of the fabricated lens for axial and radial directions. The broken line is that of a hemispherical Luneburg lens with the same index difference.

Fig. 11
Fig. 11

Focused spot by a stacked planar microlens. A He–Ne laser beam (λ = 0.63 μm) was used as a light source.

Fig. 12
Fig. 12

Wave aberration of a planar microlens with low aberration.

Fig. 13
Fig. 13

Relationship between N.A. and diameter of fabricated planar microlenses. The ao-25-19-3388-i001 indicates the measured effective N.A. of a single lens, and ao-25-19-3388-i002 shows the N.A. of a stacked lens; the lens was fabricated by ion exchange.

Fig. 14
Fig. 14

Measurement system of the N.A. by far-field pattern.

Fig. 15
Fig. 15

(a) Ray trajectories of rear incidence and corresponding N.A. expressed by the intensity of the far-field pattern. (b) Ray trajectories of front incidence and the N.A. same as (a).

Fig. 16
Fig. 16

Concept of stacked planar optics.

Fig. 17
Fig. 17

Structure of a 2 × 2 fiber-to-fiber coupler array.

Fig. 18
Fig. 18

Characteristic of coupling loss for single-mode fiber coupling.

Fig. 19
Fig. 19

Structure of a branching component array with beam splitter.

Fig. 20
Fig. 20

Structure of a 2 × 3 branching component array.

Fig. 21
Fig. 21

Structure of a focusing beam splitter.

Equations (17)

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n ( r ) = n 2 exp [ 2 ω ( ρ , f / a ) ] ,
r = a ρ exp [ - 2 ω ( ρ , f / a ) ] .
n ( r ) = n 2 exp [ ω ( ρ , f / a ) ] ,
r = a ρ exp [ - ω ( ρ , f / a ) ] ,
ω ( ρ , f / a ) = 1 π ρ 1 sin - 1 ( t a / f ) t 2 - ρ 2 d t .
n ( 0 ) = n 2 exp [ 2 π 0 1 sin - 1 ( t a / f ) t d t ] = n 2 exp { 2 π [ a f + 1 2 · 3 2 ( a f ) 3 + ] } n 2 exp ( 2 a / π f ) .
Δ = [ n ( 0 ) - n 2 ] / n 2 exp ( 2 a / π f ) - 1.
f 2 a / { π [ n ( 0 ) / n 2 ] } = 2 a / [ π ln ( 1 + Δ ) ] ,
N . A . = n 2 a / f ( π / 2 ) n 2 ln [ n ( 0 ) / n 2 ] = ( π / 2 ) n 2 ln ( 1 + Δ ) .
N . A . ( π / 2 ) n 2 Δ .
n ( 0 ) n 2 exp ( a / π f ) ,
Δ = [ n ( 0 ) - n 2 ] / n 2 exp ( a / π f ) - 1 ,
f a / { π ln [ n ( 0 ) / n 2 ] } = a / [ π ln ( 1 + Δ ) ] ,
N . A . = n 2 a / f π n 2 ln [ n ( 0 ) / n 2 ] = π n 2 ln ( 1 + Δ ) .
N . A . π n 2 Δ .
n 2 ( r , z ) = n 2 ( 0 ) [ 1 , ( g z ) 2 , ( g z ) 4 , ( g z ) 6 ] × [ 1 - 1 ν 04 ν 06 ν 20 ν 22 ν 24 ν 26 ν 40 ν 42 ν 44 ν 46 ν 60 ν 62 ν 64 ν 66 ] [ 1 ( g r ) 2 ( g r ) 4 ( g r ) 6 ] ( in the distributed index region ) = n 2 2 ( in the substrate ) ,
N . A . = l 2 / [ 2 l 1 2 + ( l 2 / 2 ) 2 ] .

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