Abstract

We establish the equation of distribution of the refractive index of Maxwell fish-eye spherical lenses and report fabrication of Maxwell fish-eye spherical lenses using optical glasses. The distribution profiles are discussed for the process of ion exchanging, and the experimental results accord with the theoretical analysis.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. S. Ilyas and M. Gal, "Gradient refractive index planar microlens in Si using porous silicon," Appl. Phys. Lett. 89, 211123-211125 (2006).
    [CrossRef]
  8. B. Messerschmidt, B. L. Mclntyre, and S. N. Houde-Walter, "Desired concentration-dependent ion exchange for micro-optic lenses," Appl. Opt. 35, 5670-5676 (1996).
    [CrossRef] [PubMed]
  9. L. D. Seng and G. Y. Jun, Physics Foundation of Gradient Refractive Index (National Defence Industry Press, 1991) (in Chinese).
  10. Y. L. Hao, L. W. Jin, and W. X. Zhao "Research on low chromatic aberration GRIN rod lens manufacturing technology," Opt. Technol. 30, 603-605 (2004) (in Chinese).

2006

H. Lv and A. Liu, "Research on coupling efficiencies of ball lenses," Opt. Precision Eng. 14, 386-390 (2006) (in Chinese).

S. Ilyas and M. Gal, "Gradient refractive index planar microlens in Si using porous silicon," Appl. Phys. Lett. 89, 211123-211125 (2006).
[CrossRef]

2005

2004

Y. L. Hao, L. W. Jin, and W. X. Zhao "Research on low chromatic aberration GRIN rod lens manufacturing technology," Opt. Technol. 30, 603-605 (2004) (in Chinese).

1996

1994

1986

1854

J. C. Maxwell, "On the general laws of optical instruments," Q. J. Pure Appl. Math. 2, 233-247 (1854).

Appl. Opt.

Appl. Phys. Lett.

S. Ilyas and M. Gal, "Gradient refractive index planar microlens in Si using porous silicon," Appl. Phys. Lett. 89, 211123-211125 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Precision Eng.

H. Lv and A. Liu, "Research on coupling efficiencies of ball lenses," Opt. Precision Eng. 14, 386-390 (2006) (in Chinese).

Opt. Technol.

Y. L. Hao, L. W. Jin, and W. X. Zhao "Research on low chromatic aberration GRIN rod lens manufacturing technology," Opt. Technol. 30, 603-605 (2004) (in Chinese).

Q. J. Pure Appl. Math.

J. C. Maxwell, "On the general laws of optical instruments," Q. J. Pure Appl. Math. 2, 233-247 (1854).

Other

Y. Koike and Y. Ohtsuka, "Precise nondestructive method of measuring refractive-index distribution of spherical GRIN lens by interferometry," in Technical Digest, Topical Meeting on Gradient Index Optical Imaging Systems, Palermo, Italy (1985), paper H1.

L. D. Seng and G. Y. Jun, Physics Foundation of Gradient Refractive Index (National Defence Industry Press, 1991) (in Chinese).

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Figures (3)

Fig. 1
Fig. 1

Photos of MFSLs of diameter 1.6 mm .

Fig. 2
Fig. 2

Diffusion coefficient D into glass versus radius of r of a MFSL of diameter 1.6 mm .

Fig. 3
Fig. 3

Interferogram and refractive-index profiles of a 1.6 mm diameter MFSL at 6, 7, 8, 9, 10, and 11 days. The ideal curve is according to Eq. (7); the fitting data curve is the experimental curve according to the interferogram; the bottom curve is the fitting curve for the experimental data.

Equations (12)

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n ( r ) = n 0 [ 1 + ( r a ) 2 ] 1 ,
n ( r ) = n 0 ( 1 A r 2 ) ,
n t = D ( 2 n x 2 + 2 n y 2 + 2 n y 2 ) .
1 D n t = 1 r 2 r ( r 2 n n ) ,
n = n 1 + 2 ( n 0 n 1 ) k ( 1 ) k + 1 exp [ ( k π r 0 ) D t ] [ sin ( k π r 0 ) ( k π r r 0 ) ] .
n = n 1 + 2 ( n 0 n ) exp [ π 2 ( D t r 0 2 ) ] ( 1 ( π r ) 2 6 r 0 2 + ( π r ) 4 120 r 0 4 ) .
n = n 0 ( 1 ( n 0 n 1 ) ( π r ) 2 6 n 0 r 0 2 + ( n 0 n 1 ) ( π r ) 4 120 n 0 r 0 4 ) .
n = n 0 ( 1 A r 2 ) .
D = r 2 π 2 t ln [ 2 ( 1 1 6 g 2 h 2 ) ] ,
Δ n 21 = n ( r 2 ) n ( r 1 ) = ( k 2 k 1 ) λ t 0 ,
n ( r m ) = n ( 0 ) Δ n m , m 1 Δ n m 1 , m 2 Δ n 2 , 1 Δ n 1 , 0 .
n ( r m ) = n ( 0 ) Δ k m , 0 = n ( 0 ) ( k m k 0 ) λ t 0 .

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