Abstract

We propose the use of a truncated ball lens in a collimating system to transform a spherical wave from a highly divergent source into a plane wave. The proposed scheme, which incorporates a hyperbolic lens, is discussed, and the overall system is found to have a large acceptance angle and to be free of spherical aberration. Diffraction and polarization effects are neglected, as well as skew rays.

© 2004 Optical Society of America

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References

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  1. R. Iiinsky, “Gradient-index meniscus lens free of spherical aberration,” J. Opt. A Pure Appl. Opt. 2, 449–451 (2000).
    [CrossRef]
  2. H. M. Presby, C. A. Edwards, “Near 100% efficient fibre microlenses,” Electron. Lett. 28, 582–584 (1992).
    [CrossRef]
  3. A. E. Christopher, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
    [CrossRef]
  4. B. E. A. Saleh, M. C. Teich, Fundamental of Photonics (Wiley, New York, 1991).
    [CrossRef]

2000

R. Iiinsky, “Gradient-index meniscus lens free of spherical aberration,” J. Opt. A Pure Appl. Opt. 2, 449–451 (2000).
[CrossRef]

1993

A. E. Christopher, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

1992

H. M. Presby, C. A. Edwards, “Near 100% efficient fibre microlenses,” Electron. Lett. 28, 582–584 (1992).
[CrossRef]

Christopher, A. E.

A. E. Christopher, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

Dragone, C.

A. E. Christopher, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

Edwards, C. A.

H. M. Presby, C. A. Edwards, “Near 100% efficient fibre microlenses,” Electron. Lett. 28, 582–584 (1992).
[CrossRef]

Iiinsky, R.

R. Iiinsky, “Gradient-index meniscus lens free of spherical aberration,” J. Opt. A Pure Appl. Opt. 2, 449–451 (2000).
[CrossRef]

Presby, H. M.

A. E. Christopher, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

H. M. Presby, C. A. Edwards, “Near 100% efficient fibre microlenses,” Electron. Lett. 28, 582–584 (1992).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamental of Photonics (Wiley, New York, 1991).
[CrossRef]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamental of Photonics (Wiley, New York, 1991).
[CrossRef]

Electron. Lett.

H. M. Presby, C. A. Edwards, “Near 100% efficient fibre microlenses,” Electron. Lett. 28, 582–584 (1992).
[CrossRef]

J. Lightwave Technol.

A. E. Christopher, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

J. Opt. A Pure Appl. Opt.

R. Iiinsky, “Gradient-index meniscus lens free of spherical aberration,” J. Opt. A Pure Appl. Opt. 2, 449–451 (2000).
[CrossRef]

Other

B. E. A. Saleh, M. C. Teich, Fundamental of Photonics (Wiley, New York, 1991).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Ideal geometrical profile of a hyperbolic lens.

Fig. 2
Fig. 2

(a) Divergence angle of the light source, 2θ m ′. (b) The divergence angle is reduced from 2θ m ′ to 2θ m if a truncated ball lens with refractive index n 3 is integrated or placed close to the light source at O.

Fig. 3
Fig. 3

Proposed collimating system that consists of a truncated ball lens and a hyperbolic lens.

Fig. 4
Fig. 4

Modified ball lens with a concave spherical surface.

Tables (1)

Tables Icon

Table 1 Input and Output Divergence Angles for the Truncated Ball Lenses with Plane Input Aperture and Concave Spherical Surfacea

Equations (14)

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z+aa2-rb2=1,
a2=n0n1+n02f2, b2=n1-n0n1+n0f2.
θa=arctanb/a.
 ndl=constant,
Ln3=n3x2+y2+n0R2-y2+R2-L+x21/2
Ln3-n0R2=n3x2+y2-n0y2+R2-L+x21/2,
η2x2+y2=y2+R21-1η+x2,
R2η+12=y2+x-R21ηη+12
R02=y2+x-d2,
1η4-1tan θa,
1η2-1tan θa.
f=n1+n01+V2Vn1-n0 W0,
V=tan θmη2+η2-1tan2 θm1/2
f=s+R01+η,

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