Abstract

Various microlenses are fabricated on the end of single-mode fibers using a photolithographic technique. The radii of these lenses are in the 2.6–20-μm range. The beam waist and beam waist position of these lenses are measured and compared to theoretical values derived for Gaussian beams under a paraxial ray approximation. Beam spot sizes of <0.75 μm have been achieved at 830 nm.

© 1985 Optical Society of America

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References

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  1. D. Kato, “Light Coupling from a Stripe-Geometry GaAs Diode Laser into an Optical Fiber with Spherical End,” J. Appl. Phys. 44, 2756 (1973).
    [CrossRef]
  2. L. G. Cohen, M. V. Schneider, “Microlenses for Coupling Junction Lasers to Optical Fibers,” Appl. Opt. 13, 298 (1974).
    [CrossRef]
  3. H. Kogelnik, “Imaging of Optical Modes—Resonators with Internal Lenses,” Bell Syst. Tech. J. 44, 455 (1965).
  4. H. Kogelnik, “On the Propagation of Gaussian Beams of Light Through Lenslike Media Including those with a Loss or Gain Variation,” Appl. Opt. 4, 1562 (1965).
    [CrossRef]
  5. A. E. Siegman, An Introduction to Lasers and Masers (1971).
  6. D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703 (1976).
  7. P. D. Bear, “Microlenses for Coupling Single-Mode Fibers to Single-Mode Thin-Film Waveguides,” Appl. Opt. 19, 2906 (1980).
    [CrossRef] [PubMed]
  8. A. H. Firester, M. E. Heller, P. Sheng, “Knife-edge Scanning Measurements of Subwavelength Focused Light Beams,” Appl. Opt. 16, 1971 (1977).
    [CrossRef] [PubMed]

1980

1977

1976

D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703 (1976).

1974

L. G. Cohen, M. V. Schneider, “Microlenses for Coupling Junction Lasers to Optical Fibers,” Appl. Opt. 13, 298 (1974).
[CrossRef]

1973

D. Kato, “Light Coupling from a Stripe-Geometry GaAs Diode Laser into an Optical Fiber with Spherical End,” J. Appl. Phys. 44, 2756 (1973).
[CrossRef]

1965

H. Kogelnik, “Imaging of Optical Modes—Resonators with Internal Lenses,” Bell Syst. Tech. J. 44, 455 (1965).

H. Kogelnik, “On the Propagation of Gaussian Beams of Light Through Lenslike Media Including those with a Loss or Gain Variation,” Appl. Opt. 4, 1562 (1965).
[CrossRef]

Bear, P. D.

Cohen, L. G.

L. G. Cohen, M. V. Schneider, “Microlenses for Coupling Junction Lasers to Optical Fibers,” Appl. Opt. 13, 298 (1974).
[CrossRef]

Firester, A. H.

Heller, M. E.

Kato, D.

D. Kato, “Light Coupling from a Stripe-Geometry GaAs Diode Laser into an Optical Fiber with Spherical End,” J. Appl. Phys. 44, 2756 (1973).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Imaging of Optical Modes—Resonators with Internal Lenses,” Bell Syst. Tech. J. 44, 455 (1965).

H. Kogelnik, “On the Propagation of Gaussian Beams of Light Through Lenslike Media Including those with a Loss or Gain Variation,” Appl. Opt. 4, 1562 (1965).
[CrossRef]

Marcuse, D.

D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703 (1976).

Schneider, M. V.

L. G. Cohen, M. V. Schneider, “Microlenses for Coupling Junction Lasers to Optical Fibers,” Appl. Opt. 13, 298 (1974).
[CrossRef]

Sheng, P.

Siegman, A. E.

A. E. Siegman, An Introduction to Lasers and Masers (1971).

Appl. Opt.

Bell Syst. Tech. J.

H. Kogelnik, “Imaging of Optical Modes—Resonators with Internal Lenses,” Bell Syst. Tech. J. 44, 455 (1965).

D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703 (1976).

J. Appl. Phys.

D. Kato, “Light Coupling from a Stripe-Geometry GaAs Diode Laser into an Optical Fiber with Spherical End,” J. Appl. Phys. 44, 2756 (1973).
[CrossRef]

Other

A. E. Siegman, An Introduction to Lasers and Masers (1971).

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Figures (13)

Fig. 1
Fig. 1

Propagation of the paraxial Gaussian beam through plano-convex lens (thickness, t; refractive index, n; and radius of curvature of lens, R).

Fig. 2
Fig. 2

Minimum spot sizes for thin spherical lenses with various refractive index n(ω1 = 2.5 μm, λ = 0.6328 μm).

Fig. 3
Fig. 3

Minimum spot size positions for thin spherical lenses with various refractive index n(ω1 = 2.5 μm, λ = 0.6328 μm).

Fig. 4
Fig. 4

Minimum spot sizes for thin spherical lenses for various values of wavelength λ(n = 1.55, ω1 = 2.5 μm).

Fig. 5
Fig. 5

Minimum spot size positions for thin spherical lenses for various values of wavelength λ(n = 1.55, ω1 = 2.5 μm).

Fig. 6
Fig. 6

Hemispherical microlenses on the end of the single-mode fiber: (a) thin spherical microlens (thickness = 1.4 μm, diameter = 11.9 μm, radius of curvature = 12.5 μm) (6° tilted); (b) thick microlens (thickness = 3.3 μm, diameter ≃ 11.5 μm).

Fig. 7
Fig. 7

Thickness of thin spherical lens vs exposed energy.

Fig. 8
Fig. 8

Hemispherical-ended long microlens (HLM lens) on the end of single-mode fiber (radius ≃ 3.0 μm, thickness ≃ 7.6 μm).

Fig. 9
Fig. 9

Concave surface ended microlens (diameter ≃ 7.5 μm).

Fig. 10
Fig. 10

Schematic for the spot size measurement.

Fig. 11
Fig. 11

Typical Gaussian shaped spot signal (microlens with 3.5-μm radius of curvature, wavelength for signal = 0.83 μm, and wavelength for interferometer = 0.6328 μm).

Fig. 12
Fig. 12

Minimum spot size dependence on microlens radius. Solid curves and dashed curves are theoretical values for thin micro-lenses and thick microlenses (thickness t = 5 μm): (a) wavelength λ of laser beam is 0.6328 μm; (b) wavelength λ of laser beam is 0.83 μm.

Fig. 13
Fig. 13

Minimum spot size position dependence on microlens radius. Solid curves and dashed curves are theoretical values for thin microlenses and thick microlenses (thickness = 5 μm), respectively. Wavelength λ of the laser beam is 0.83 μm.

Equations (9)

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1 q ( z ) = 1 R ( z ) j [ λ π ω ( z ) 2 ] .
q 2 = A q 1 + B C q 1 + D ,
( A B C D ) = ( 1 0 1 f 1 ) ( 1 t n 0 1 ) = ( 1 t n 1 f t n f + 1 ) ,
1 q 1 = 0 i λ π ω 1 2 .
Z 2 = t n ( t n f 1 ) + Z 1 2 f ( 1 t n f ) 2 + ( Z 1 f ) 2 ,
ω 2 = ω 1 1 [ ( 1 t n f ) 2 + ( Z 1 f ) 2 ] 1 / 2 ,
Z R = Z 1 ( 1 t n f ) 2 + ( Z 1 f ) 2 ,
Z 1 = π ω 1 2 λ , f = R n 1 ( R < 0 ) .
ω 1 a = 0 . 65 + 1 . 691 V 3 / 2 + 2 . 879 V 6 ,

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