Abstract

Plastic GRIN rod and fiber lenses have been fabricated by photocopolymerization of a ternary monomer system, methyl methacrylate–N-vinyl carbazole–vinyl acetate. We now propose the general mechanism for forming radial GRIN in the ternary monomer system using computer simulation. The relationship between the preparation condition and the optical characteristics was clarified. The region having quadratic-index distribution and the numerical aperture were remarkably improved by the ternary monomer system.

© 1983 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

1982

1981

1980

1978

Y. Ohtsuka, Y. Shimizu, Kobunshi Ronbunshu (J. Soc. Polym. Sci. Jpn.) 35, 169 (1978).
[CrossRef]

1973

Y. Ohtsuka, Appl. Phys. Lett. 23, 247 (1973).
[CrossRef]

1970

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

1944

T. Alfrey, G. Goldfinger, J. Chem. Phys. 12, 322 (1944).
[CrossRef]

Alfrey, T.

T. Alfrey, G. Goldfinger, J. Chem. Phys. 12, 322 (1944).
[CrossRef]

Furukawa, M.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Goldfinger, G.

T. Alfrey, G. Goldfinger, J. Chem. Phys. 12, 322 (1944).
[CrossRef]

Kimoto, Y.

Kitano, I.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Koike, Y.

Koizumi, K.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Matsumura, H.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Moore, D. T.

Ohtsuka, Y.

Shimizu, Y.

Y. Ohtsuka, Y. Shimizu, Kobunshi Ronbunshu (J. Soc. Polym. Sci. Jpn.) 35, 169 (1978).
[CrossRef]

Sugano, T.

Terao, Y.

Y. Ohtsuka, T. Sugano, Y. Terao, Appl. Opt. 20, 2319 (1981).
[CrossRef] [PubMed]

Y. Ohtsuka, Y. Terao, J. Appl. Polym. Sci. 26, 2907 (1981).
[CrossRef]

Uchida, T.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Yamazaki, H.

Appl. Opt.

Appl. Phys. Lett.

Y. Ohtsuka, Appl. Phys. Lett. 23, 247 (1973).
[CrossRef]

J. Appl. Polym. Sci.

Y. Ohtsuka, Y. Terao, J. Appl. Polym. Sci. 26, 2907 (1981).
[CrossRef]

J. Chem. Phys.

T. Alfrey, G. Goldfinger, J. Chem. Phys. 12, 322 (1944).
[CrossRef]

J. Jpn. Soc. Appl. Phys. Suppl.

I. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furukawa, J. Jpn. Soc. Appl. Phys. Suppl. 39, 63 (1970).

Kobunshi Ronbunshu (J. Soc. Polym. Sci. Jpn.)

Y. Ohtsuka, Y. Shimizu, Kobunshi Ronbunshu (J. Soc. Polym. Sci. Jpn.) 35, 169 (1978).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Change of instantaneous copolymer composition (arrowhead) and remaining copolymer composition (tail end of arrow) with conversion P = 5k wt. % (k = 0,1,2,…) in MMA–N-VCa–VAc.

Fig. 2
Fig. 2

Change of copolymer composition with conversion P: ⊚, monomer feed composition; ●, composition of copolymer formed at P = 0 wt. %; ○, instantaneous copolymer composition at P = 5k wt. % (k = 1,2,…).

Fig. 3
Fig. 3

Refractive index n of the copolymer formed at conversion P. MMA/N-VCa/VAc (wt./wt./wt.): A, 3/2/0; B, 3/2/0.4; C, 3/2/1; D, 3/2/1.6; E, 3/2/2.

Fig. 4
Fig. 4

Schematic representation of the photocopolymerization process at steady state.

Fig. 5
Fig. 5

Radial distribution of the copolymer composition in the computer simulation for the ternary monomer system. MMA/N-VCa/VAc (wt./wt./wt.): —, 3/2/1; - - -, 3/2/1.4.

Fig. 6
Fig. 6

Refractive-index distribution in the computer simulation. MMA/N-VCa/VAc (wt./wt./wt.): A, 3/2/0; B, 3/2/1; C, 3/2/1.4.

Fig. 7
Fig. 7

Effect of VAc/N-VCa on A′, Rc/Rp, and N.A. when MMA/N-VCa = 3.0 (wt./wt.).

Fig. 8
Fig. 8

Experimental results of the index distribution of LFR. MMA/N-VCa/VAc (wt./wt./wt.): A, 3/1/0.8; B, 3/1/0.5; C, 3/1/0.2; D, 3/1/0.

Fig. 9
Fig. 9

Microphotograph of the image of a 1.6-mm square checkered pattern through the GRIN fiber lens. MMA/N-VCa/VAc (wt./wt./wt.): (a) 3/1/0.2; (b) 3/1/0.5.

Tables (1)

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Table I Physical Properties of the Polymers

Equations (7)

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d x 1 d x 2 = x 1 x 2 · r 1 x 1 + ( m 1 / m 2 ) x 2 x 1 + r 2 ( m 1 / m 2 ) x 2 ,
d x 1 : d x 2 : d x 3 = x 1 ( x 1 r 31 r 21 + m 1 m 2 x 2 r 21 r 32 + m 1 m 3 x 3 r 31 r 23 ) ( x 1 + m 1 m 2 x 2 r 12 + m 1 m 3 x 3 r 13 ) : x 2 ( x 1 r 12 r 31 + m 1 m 2 x 2 r 12 r 32 + m 1 m 3 x 3 r 32 r 13 ) ( x 1 r 21 + m 1 m 2 x 2 + m 1 m 3 x 3 r 23 ) : x 3 ( x 1 r 13 r 21 + m 1 m 2 x 2 r 23 r 12 + m 1 m 3 x 3 r 13 r 23 ) ( x 1 r 31 + m 1 m 2 x 2 r 32 + m 1 m 3 x 3 ) .
x 1 = x 10 0 P ( d x 1 d x 1 + d x 2 + d x 3 ) d P 1 P ,
n = 1 + 2 ϕ 1 ϕ , ϕ = ( n 1 2 1 n 1 2 + 2 · d x 1 ρ 1 + n 2 2 1 n 2 2 + 2 · d x 2 ρ 2 + n 3 2 1 n 3 2 + 2 · d x 3 ρ 3 ) × ( d x 1 ρ 1 + d x 2 ρ 2 + d x 3 ρ 3 ) 1 , }
x 1 ( i + 1 ) = ( 1 + α w i w i ) x 1 i + ( α x 10 d x 1 i d x 1 i + d x 2 i + d x 3 i ) d w 1 + ( α 1 ) ( w i + d w ) P i P c , x 1 ( i + 1 ) = β x 1 i + [ α ( 1 P m i ) 1 α P m i x 1 i d x 1 i d x 1 i + d x 2 i + d x 3 i ] d w β + ( α 1 1 α P m i ) d w P i > P c , β = 1 + α w c w i + w c w i 1 α [ 1 P m ( w ) ] 1 α P m ( w ) d w , }
P i = w i 1 + α w i P i P c , P i = w i + w c w i 1 α P m 1 α P m d w 1 + α w c + w c w i 1 α 1 α P m d w P i > P c . }
n ( r ) = n 0 ( 1 1 2 A r 2 ) = n 0 [ 1 1 2 A ( r R p ) 2 ] ,

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