Abstract

The refractive-index distribution patterns obtainable by the photocopolymerization of ternary monomer systems were predicted with the help of the mechanism for forming a radial gradient index reported by Ohtsuka and Koike. On the basis of this prediction, we successfully fabricated a convex lens, a concave lens, and a fiber with the W-shaped index distribution expected of an optical fiber with low modal dispersion. It was theoretically and experimentally confirmed that the index distribution of the rod by the photocopolymerization of a ternary monomer system could be widely controlled.

© 1985 Optical Society of America

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References

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  1. Y. Ohtsuka, Y. Terao, “Studies on the Light-Focusing Plastic Rod. IX. Chemical Composition of the Copolymer RodDiethylene Glycol Bis(allyl Carbonate) with 2,2,3,3-Tetrafluo-ropropyl Methacrylate,” J. Appl. Polym. Sci. 26, 2907 (1981).
    [CrossRef]
  2. Y. Ohtsuka, T. Sugano, “Studies on the Light-Focusing Plastic Rod. 14: GRIN rod of CR-39-trifluoroethyl Methacrylate Copolymer by a Vapor-Phase Transfer Process,” Appl. Opt. 22, 413 (1983).
    [CrossRef] [PubMed]
  3. Y. Koike, Y. Kimoto, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. XIII. Photocopolymerization of Methyl Methacrylate–Vinyl Esters of Aromatic Carboxylic Acid,” J. Appl. Polym. Sci. 27, 3253 (1982).
    [CrossRef]
  4. Y. Ohtsuka, Y. Koike, “Studies on the Light-Focusing Plastic Rod. 16: Mechanism of Gradient-Index Formation in Photocopolymerization of Multiple Monomer Systems,” Appl. Opt. 23, 1774 (1984).
    [CrossRef] [PubMed]
  5. Y. Koike, H. Hatanaka, Y. Ohtsuka, “Studies on Light-Focusing Plastic Rod. 17: Plastic GRIN Rod Lens Prepared by Photocopolymerization of a Ternary Monomer Systems,” Appl. Opt. 23, 1779 (1984).
    [CrossRef] [PubMed]
  6. Japanese Patents (Kokal Tokkyo Koho), 75 83, 045; 78 21, 937; 82 20, 601.
  7. Y. Koike, Y. Kimoto, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. 12: The GRIN Fiber Lens of Methyl Methacrylate-vinyl Phenylacetate Copolymer,” Appl. Opt 21, 1057 (1982).
    [CrossRef] [PubMed]
  8. J. Brandrup, E. H. Immergut, Polymer Handbook (Wiley-Interscience, New York, 1975), p. II-387.
  9. Y. Ohtsuka, Y. Koike, “Determination of the Refractive-Index Profile of Light-Focusing Rods: Accuracy of a Method Using Interphako Interference Microscopy,” Appl. Opt. 19, 2866 (1980).
    [CrossRef] [PubMed]
  10. Registered trade name Carl Zeiss, Jena, East Germany.

1984

1983

1982

Y. Koike, Y. Kimoto, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. XIII. Photocopolymerization of Methyl Methacrylate–Vinyl Esters of Aromatic Carboxylic Acid,” J. Appl. Polym. Sci. 27, 3253 (1982).
[CrossRef]

Y. Koike, Y. Kimoto, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. 12: The GRIN Fiber Lens of Methyl Methacrylate-vinyl Phenylacetate Copolymer,” Appl. Opt 21, 1057 (1982).
[CrossRef] [PubMed]

1981

Y. Ohtsuka, Y. Terao, “Studies on the Light-Focusing Plastic Rod. IX. Chemical Composition of the Copolymer RodDiethylene Glycol Bis(allyl Carbonate) with 2,2,3,3-Tetrafluo-ropropyl Methacrylate,” J. Appl. Polym. Sci. 26, 2907 (1981).
[CrossRef]

1980

Brandrup, J.

J. Brandrup, E. H. Immergut, Polymer Handbook (Wiley-Interscience, New York, 1975), p. II-387.

Hatanaka, H.

Immergut, E. H.

J. Brandrup, E. H. Immergut, Polymer Handbook (Wiley-Interscience, New York, 1975), p. II-387.

Kimoto, Y.

Y. Koike, Y. Kimoto, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. 12: The GRIN Fiber Lens of Methyl Methacrylate-vinyl Phenylacetate Copolymer,” Appl. Opt 21, 1057 (1982).
[CrossRef] [PubMed]

Y. Koike, Y. Kimoto, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. XIII. Photocopolymerization of Methyl Methacrylate–Vinyl Esters of Aromatic Carboxylic Acid,” J. Appl. Polym. Sci. 27, 3253 (1982).
[CrossRef]

Koike, Y.

Ohtsuka, Y.

Y. Koike, H. Hatanaka, Y. Ohtsuka, “Studies on Light-Focusing Plastic Rod. 17: Plastic GRIN Rod Lens Prepared by Photocopolymerization of a Ternary Monomer Systems,” Appl. Opt. 23, 1779 (1984).
[CrossRef] [PubMed]

Y. Ohtsuka, Y. Koike, “Studies on the Light-Focusing Plastic Rod. 16: Mechanism of Gradient-Index Formation in Photocopolymerization of Multiple Monomer Systems,” Appl. Opt. 23, 1774 (1984).
[CrossRef] [PubMed]

Y. Ohtsuka, T. Sugano, “Studies on the Light-Focusing Plastic Rod. 14: GRIN rod of CR-39-trifluoroethyl Methacrylate Copolymer by a Vapor-Phase Transfer Process,” Appl. Opt. 22, 413 (1983).
[CrossRef] [PubMed]

Y. Koike, Y. Kimoto, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. 12: The GRIN Fiber Lens of Methyl Methacrylate-vinyl Phenylacetate Copolymer,” Appl. Opt 21, 1057 (1982).
[CrossRef] [PubMed]

Y. Koike, Y. Kimoto, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. XIII. Photocopolymerization of Methyl Methacrylate–Vinyl Esters of Aromatic Carboxylic Acid,” J. Appl. Polym. Sci. 27, 3253 (1982).
[CrossRef]

Y. Ohtsuka, Y. Terao, “Studies on the Light-Focusing Plastic Rod. IX. Chemical Composition of the Copolymer RodDiethylene Glycol Bis(allyl Carbonate) with 2,2,3,3-Tetrafluo-ropropyl Methacrylate,” J. Appl. Polym. Sci. 26, 2907 (1981).
[CrossRef]

Y. Ohtsuka, Y. Koike, “Determination of the Refractive-Index Profile of Light-Focusing Rods: Accuracy of a Method Using Interphako Interference Microscopy,” Appl. Opt. 19, 2866 (1980).
[CrossRef] [PubMed]

Sugano, T.

Terao, Y.

Y. Ohtsuka, Y. Terao, “Studies on the Light-Focusing Plastic Rod. IX. Chemical Composition of the Copolymer RodDiethylene Glycol Bis(allyl Carbonate) with 2,2,3,3-Tetrafluo-ropropyl Methacrylate,” J. Appl. Polym. Sci. 26, 2907 (1981).
[CrossRef]

Appl. Opt

Y. Koike, Y. Kimoto, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. 12: The GRIN Fiber Lens of Methyl Methacrylate-vinyl Phenylacetate Copolymer,” Appl. Opt 21, 1057 (1982).
[CrossRef] [PubMed]

Appl. Opt.

J. Appl. Polym. Sci.

Y. Ohtsuka, Y. Terao, “Studies on the Light-Focusing Plastic Rod. IX. Chemical Composition of the Copolymer RodDiethylene Glycol Bis(allyl Carbonate) with 2,2,3,3-Tetrafluo-ropropyl Methacrylate,” J. Appl. Polym. Sci. 26, 2907 (1981).
[CrossRef]

Y. Koike, Y. Kimoto, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. XIII. Photocopolymerization of Methyl Methacrylate–Vinyl Esters of Aromatic Carboxylic Acid,” J. Appl. Polym. Sci. 27, 3253 (1982).
[CrossRef]

Other

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

J. Brandrup, E. H. Immergut, Polymer Handbook (Wiley-Interscience, New York, 1975), p. II-387.

Registered trade name Carl Zeiss, Jena, East Germany.

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Figures (8)

Fig. 1
Fig. 1

Changes in the remaining monomer composition (arrow tail) and composition of the copolymer formed at each monomer composition (arrowhead) with P = 5k wt. % (k = 1,2, …) in the BzMA–AN–VAc system. A double circle expresses the monomer feed composition.

Fig. 2
Fig. 2

Classification of ternary monomer system.

Fig. 3
Fig. 3

Refractive index of MMA–AN–VB (Type I) copolymer formed at conversion P. MMA/AN/VB (wt./wt./wt.): A, 1/0/1; B, 1/1/3; C, 1/1.5/3; D, 1/2/3.

Fig. 4
Fig. 4

Refractive index of BzMA–VAc–VPAc copolymer (Type V) formed at conversion P. BzMA/VAc/VPAc (wt./wt./wt): A, 1/1/1; B, 3/1/1; C, 7/1/1.

Fig. 5
Fig. 5

Refractive index of MAt–MMA–EA copolymer (Type VI) formed at conversion P. MAt/MMA/EA (wt./wt./wt.): A, 1/1/1; B, 1/2/1;C, 1/2/2.

Fig. 6
Fig. 6

Calculated index distribution of BzMA–VAc–VPAc GRIN rod (Type V). BzMA/VAc/VPAc = 2/1/1 (wt./wt./wt.). Pc = 0.25, Pu = 0.60, Pf = 0.80, and β = 2.

Fig. 7
Fig. 7

Calculated-index distributions of GRIN rods (Type VI): A, BzMA/AN/VAc = 3/3/2 (wt./wt./wt.); B, MAt/MMA/EA = 1/1/1 (wt./wt./wt.).

Fig. 8
Fig. 8

Index distributions of the GRIN rods fabricated in each type. Type I, MMA–AN–VB; Type III, MMA–N–VCa–VAc; Type V, BzMA–VAc–VPAc; Type VI, BzMA–AN–VAc; A, BzMA–MMA–VAc–VPAc.

Tables (2)

Tables Icon

Table I Ternary Monomer System

Tables Icon

Table II Values of Q, e, and rij of Ternary Monomer Systems in Table I

Equations (7)

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M i · + M i k i j M i M i · M i · + M j k i j M i M j · ( Polymer radical ) ( Monomer ) ( Polymer radical )
r i j = k i j k i j ( i = 1,2 , , n j = 1,2 , , n i j ) .
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 r i j = n ( n 1 ) .
r 12 > 1 r 13 > 1 r 23 > 1 , r 21 < 1 r 31 < 1 r 32 < 1 .
r i j = Q i Q j exp [ e i ( e i e j ) ] , r j i = Q j Q i exp [ e j ( e j e i ) ] , }

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