Abstract

In this paper, we propose a general mechanism for forming a radial GRIN rod by photocopolymerization in multiple monomer systems and a method of selecting new monomer systems applicable to GRIN. By using the simulation with various monomer systems, it is shown that the index distribution of a plastic GRIN rod can be tightly controlled by the selection of a ternary monomer system and the photocopolymerization condition.

© 1984 Optical Society of America

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References

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  1. Y. Ohtsuka, T. Sugano, Appl. Opt. 22, 413 (1983).
    [CrossRef] [PubMed]
  2. Y. Koike, Y. Ohtsuka, Appl. Opt. 22, 418 (1983).
    [CrossRef] [PubMed]
  3. Japanese Patents (Kokai Tokkyo Koho), 75 83,045; 78 21,937; 82 20,601.
  4. Y. Koike, Y. Kimoto, Y. Ohtsuka, Appl. Opt. 21, 1057 (1982).
    [CrossRef] [PubMed]
  5. C. Walling, E. R. Briggs, J. Am. Chem. Soc. 67, 1774 (1945).
    [CrossRef]
  6. Y. Koike, H. Hatanaka, Y. Ohtsuka, Appl. Opt. 23, 1779 (1984), same issue.
    [CrossRef] [PubMed]
  7. Y. Koike, Y. Kimoto, Y. Ohtsuka, J. Appl. Polym. Sci. 27, 3253 (1982).
    [CrossRef]

1984 (1)

1983 (2)

1982 (2)

Y. Koike, Y. Kimoto, Y. Ohtsuka, J. Appl. Polym. Sci. 27, 3253 (1982).
[CrossRef]

Y. Koike, Y. Kimoto, Y. Ohtsuka, Appl. Opt. 21, 1057 (1982).
[CrossRef] [PubMed]

1945 (1)

C. Walling, E. R. Briggs, J. Am. Chem. Soc. 67, 1774 (1945).
[CrossRef]

Appl. Opt. (4)

J. Am. Chem. Soc. (1)

C. Walling, E. R. Briggs, J. Am. Chem. Soc. 67, 1774 (1945).
[CrossRef]

J. Appl. Polym. Sci. (1)

Y. Koike, Y. Kimoto, Y. Ohtsuka, J. Appl. Polym. Sci. 27, 3253 (1982).
[CrossRef]

Other (1)

Japanese Patents (Kokai Tokkyo Koho), 75 83,045; 78 21,937; 82 20,601.

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Figures (9)

Fig. 1
Fig. 1

Change of copolymer composition with converted P in the MMA–BzA–VB system. Each mark (○, △, +, and ×) represents instantaneous copolymer composition at P = 5k wt. % (k = 1,2, …). MMA/BzA/VB (wt./wt./wt.): A, 3/0/1; B, 2.5/0.5/1; C, 2/1/1; D, 1.5/1.5/1.

Fig. 2
Fig. 2

Refractive index of MMA– BzA–VB copolymer formed at converted P. MMA/BzA/VB (wt./wt./wt.): A, 3/0/1; B, 2.5/0.5/1; C, 2/1/1; D, 1.5/1.5/1.

Fig. 3
Fig. 3

Schematic representation of the photocopolymerization process in the steady state.

Fig. 4
Fig. 4

Formation of the gel phase in a glass tube during the photocopolymerization process.

Fig. 5
Fig. 5

Comparison of the refractive-index distributions between simulations I and II when MMA/AN/VB = 2/1/0.5 (wt./wt./wt.), Pc = 0.25, Pu = 0.6, Pf = 0.8, and Pm = Pc.

Fig. 6
Fig. 6

Variation of Pm with the cross-sectional area of gel phase S.

Fig. 7
Fig. 7

Effect of β on the index distribution of the MMA–BzA–VB GRIN rod when MMA/BzA/VB = 2/1/1 (wt./wt./wt.), Pc = 0.25, Pu = 0.6, and Pf = 0.8. β: A, 0.5; B, 1.0; C, 2.0; D, 4.0.

Fig. 8
Fig. 8

Calculated distribution of copolymer composition for the MMA–BzA–VB GRIN rod when Pc = 0.25, Pu = 0.6, Pf = 0.8, and β = 2.0. MMA/BzA/VB (wt./wt./wt.): (—), 1.5/1.5/1; (- - -) 2/1/1.

Fig. 9
Fig. 9

Calculated index distribution for the MMA–BzA–VB rod. MMA/BzA/VB (wt./wt./wt.): A, 3/0/1; B, 2.5/0.5/1; C, 2/1/1; D, 1.5/1.5/1. n0 is the refractive index at center axis.

Equations (12)

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r i j = k i i / k i j             ( i = 1 , 2 , n j = 1 , 2 , n i j ) .
d [ M i ] d [ M j ] = ( D i i k = 1 n [ M k ] r i k ) / ( D j j k = 1 n [ M k ] r j k ) .
y k = m k d [ M k ] / k = 1 n m k d [ M k ] ,
x k = x k 0 - 0 P y k d P 1 - P ,
n = 1 + 2 φ 1 - φ , φ = k = 1 n ( n k 2 - 1 n k 2 + 2 · m k d [ M k ] ρ p k ) / k = 1 n ( m k d [ M k ] ρ p k ) ,
P m = P c + ( P u - P c ) ( the amount of the gel phase the total amount of the cylinder at P = P f ) β ,
x k = M k / k = 1 n M k , M k i = M k ( i - 1 ) - y k ( i - 1 ) ( Δ W T + Δ W P ) - 1 - P u P u - P m ( i - 1 ) × x k ( i - 1 ) Δ W P + α · [ 1 - P m ( i - 1 ) ] 1 - α P m ( i - 1 ) · x k ( i - 1 ) ( Δ W T + Δ W P + Δ W G )
α = k = 1 n y k ( 1 ρ M k - 1 ρ P k ) / k = 1 n y k ρ M k ,
Q i = Q ( i - 1 ) Δ W P P m ( i - 1 ) P u - P m ( i - 1 ) + Δ W T + α P m ( i - 1 ) 1 - α P m ( i - 1 ) × ( Δ W T + Δ W P + Δ W G ) .
d V = d W P P u - P m [ ( 1 - P u ) k = 1 n x k ρ P k + k = 1 n P c P m y k ρ P k d P m + k = 1 n x k 0 - ( 1 - P c ) x k c ρ P k ] + d W P k = 1 n y k ρ P k ,
Y k = ( 1 - P u ) x k + ( x k 0 - x k c + x k c P c ) + P c P m y k d P m + ( P u - P m ) y k .
( r / R P ) 2 = 1 - S / S P , = 1 - V / V P ,

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