Abstract

We describe a technique for fabricating fast well-corrected cylindrical microlenses for applications such as collimating laser diodes and coupling light into and out of integrated optics devices. The lenses are produced by first grinding a glass preform to a desired cross-sectional shape and then heating and drawing the preform into a fiber of the desired diameter. The heating and drawing operations polish the glass surface and reduce the cross-sectional dimensions but maintain the cross-sectional shape. Diffraction-limited 220-μm focal length immersion lenses with numerical aperture >0.6 have been demonstrated.

© 1991 Optical Society of America

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References

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  1. W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, 1986), pp. 241–246.
  2. N. F. Borrelli, D. L. Morse, R. H. Bellman, W. L. Morgan, “Photolytic Technique for Producing Microlenses in Photosensitive Glass,” Appl. Opt. 24, 2520–2525 (1985).
    [CrossRef] [PubMed]
  3. M. Oikawa, K. Iga, T. Sanada, “A Distributed-Index Planar Microlens made of plastics,” Jpn. J. Appl. Phys. 20, L51–L54 (1981).
    [CrossRef]
  4. L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150–155 (1969).
    [CrossRef]
  5. J. A. Jordon, P. M. Hirsch, L. B. Lesem, D. L. V. Rooy, “Kinoform Lenses,” Appl. Opt. 9, 1883–1887 (1970).
  6. T. M. Baer, D. F. Head, M. Sakamoto, “High Efficiency Diode-Bar Pumped Solid State Laser Using a Tightly Folded Resonator,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper FJ5.
  7. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 112–113.
  8. G. B. Thomas, Calculus and Analytic Geometry (Addison-Wesley, Reading, MA, 1960), pp. 473–490.
  9. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 232–233.
  10. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), pp. 83–87.

1985

1981

M. Oikawa, K. Iga, T. Sanada, “A Distributed-Index Planar Microlens made of plastics,” Jpn. J. Appl. Phys. 20, L51–L54 (1981).
[CrossRef]

1970

1969

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Baer, T. M.

T. M. Baer, D. F. Head, M. Sakamoto, “High Efficiency Diode-Bar Pumped Solid State Laser Using a Tightly Folded Resonator,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper FJ5.

Bellman, R. H.

Borrelli, N. F.

Head, D. F.

T. M. Baer, D. F. Head, M. Sakamoto, “High Efficiency Diode-Bar Pumped Solid State Laser Using a Tightly Folded Resonator,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper FJ5.

Hirsch, P. M.

J. A. Jordon, P. M. Hirsch, L. B. Lesem, D. L. V. Rooy, “Kinoform Lenses,” Appl. Opt. 9, 1883–1887 (1970).

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Iga, K.

M. Oikawa, K. Iga, T. Sanada, “A Distributed-Index Planar Microlens made of plastics,” Jpn. J. Appl. Phys. 20, L51–L54 (1981).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), pp. 83–87.

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Jordon, J. A.

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 112–113.

Lesem, L. B.

J. A. Jordon, P. M. Hirsch, L. B. Lesem, D. L. V. Rooy, “Kinoform Lenses,” Appl. Opt. 9, 1883–1887 (1970).

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Morgan, W. L.

Morse, D. L.

Oikawa, M.

M. Oikawa, K. Iga, T. Sanada, “A Distributed-Index Planar Microlens made of plastics,” Jpn. J. Appl. Phys. 20, L51–L54 (1981).
[CrossRef]

Rooy, D. L. V.

Sakamoto, M.

T. M. Baer, D. F. Head, M. Sakamoto, “High Efficiency Diode-Bar Pumped Solid State Laser Using a Tightly Folded Resonator,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper FJ5.

Sanada, T.

M. Oikawa, K. Iga, T. Sanada, “A Distributed-Index Planar Microlens made of plastics,” Jpn. J. Appl. Phys. 20, L51–L54 (1981).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 232–233.

Thomas, G. B.

G. B. Thomas, Calculus and Analytic Geometry (Addison-Wesley, Reading, MA, 1960), pp. 473–490.

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, 1986), pp. 241–246.

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), pp. 83–87.

Appl. Opt.

IBM J. Res. Dev.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Jpn. J. Appl. Phys.

M. Oikawa, K. Iga, T. Sanada, “A Distributed-Index Planar Microlens made of plastics,” Jpn. J. Appl. Phys. 20, L51–L54 (1981).
[CrossRef]

Other

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, 1986), pp. 241–246.

T. M. Baer, D. F. Head, M. Sakamoto, “High Efficiency Diode-Bar Pumped Solid State Laser Using a Tightly Folded Resonator,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper FJ5.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 112–113.

G. B. Thomas, Calculus and Analytic Geometry (Addison-Wesley, Reading, MA, 1960), pp. 473–490.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 232–233.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), pp. 83–87.

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Figures (9)

Fig. 1
Fig. 1

Dielectric interface that focuses a collimated wave to point f. The optical path for the principal ray along the axis equals the optical path for a parallel ray with height y (dashed line).

Fig. 2
Fig. 2

Spherical aberration-free lens has an elliptical first surface if n1 < n2. Collimated incident light (dashed lines) is focused within the lens onto the second surface.

Fig. 3
Fig. 3

Spherical aberration-free lens has a hyperbolic second surface if n1 > n2. Collimated incident light (dashed lines) is unchanged by the plane first surface and is focused outside the lens by the hyperbolic second surface.

Fig. 4
Fig. 4

Circular lens of radius r and back focal length d. The numerical aperture is found by constructing the tangent (dashed line) from focal point f to the circle.

Fig. 5
Fig. 5

Photo of a preform for an elliptical lens.

Fig. 6
Fig. 6

Photo of the preform stub remaining after drawing into an elliptical lens. The cross section of the broken off tip of the stub is a miniature replica of the preform cross section. In addition, the fire polishing of the stub is evident.

Fig. 7
Fig. 7

SEM photo of an elliptical cylindrical microlens. The lens width is 200 μm.

Fig. 8
Fig. 8

Interferogram of a 200-μm elliptical cylindrical microlens in the double-pass mode. The straight fringes demonstrate diffraction-limited performance over a 150-μm aperture.

Fig. 9
Fig. 9

Interferogram of a simple 200-μm diam cylindrical fiber in the double-pass mode. The straight fringes indicate that diffraction-limited performance is limited to an aperture of ~100 μm.

Equations (16)

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

n 2 f = n 1 x + n 2 ( f - x ) 2 + y 2 ,
( x - a ) 2 a 2 + y 2 b 2 = 1 ,
a 2 = ( f n 2 n 2 + n 1 ) 2 ,
b 2 = f 2 ( ± Δ n n 2 + n 1 )
Δ n n 2 - n 1 .
e 1 b 2 / a 2 = n 1 n 2 ,
f = a ( n 2 + n 1 n 2 ) = a + e a .
A n sin θ ,
A ell = n 2 ( b a ) = n 2 2 - n 1 2 .
A ell = n 2 - 1 ,
θ hyp = arcsin b e a ,
A hyp = n 2 ( b e a ) = n 2 n 1 2 - n 2 2 n 1 .
A hyp = n 2 - 1 n ,
f = n r 2 ( n - 1 ) ,
d = f ( 2 - n ) n = r ( 2 - n ) 2 ( n - 1 ) .
A circ = r r + d = 2 ( n - 1 ) n .

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