Optical waveguide using polymer composed of silsesquioxane derivative

1. An optical waveguide comprising a polymer obtained by using a silsesquioxane derivative represented by the formula (1-0)

wherein R 0 independently represents:

hydrogen,

alkyl having 1 to 40 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or cycloalkenylene,

aryl in which hydrogen may optionally be replaced by halogen, or by alkyl having 1 to 20 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or phenylene, or

arylalkyl in which hydrogen in the aryl may optionally be replaced by halogen or alkyl having 1 to 20 carbon atoms, and hydrogen in the alkylene of the arylalkyl may optionally be replaced by fluorine, and —CH 2 — in the alkylene of the arylalkyl may optionally be replaced by —O—, —CH═CH—, or cycloalkylene, and

Y is a group represented by the formula (a) or (b)

wherein X in each of the formulae (a) and (b) independently represents a group selected from hydrogen, chlorine, a group defined in the same way as R 0 , or a group having any one of —CH═CH—, —C≡C—, —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, —NH 2 , —CN, and —O—, and at least one of X is a reactive group selected from the above-defined group, and

Z in the formula (b) represents a single bond, —O—, or —CH 2 —.

2. The optical waveguide according to claim 1 , wherein the reactive group is hydrogen bound to Si, chlorine bound to Si, or a group having any one of —CH═CH—, —C≡C—, —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, and —NH 2 .

3. The optical waveguide according to claim 1 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-0) with a compound having a group capable of reacting with the reactive group in the silsesquioxane derivative

wherein R 0 independently represents

hydrogen,

alkyl having 1 to 40 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or cycloalkenylene,

aryl in which hydrogen may optionally be replaced by halogen, or by alkyl having 1 to 20 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may be replaced by —O—, —CH═CH—, cycloalkylene, or phenylene, or

arylalkyl in which hydrogen in the aryl may optionally be replaced by halogen or alkyl having 1 to 20 carbon atoms, and hydrogen in the alkylene of the arylalkyl may optionally be replaced by fluorine, and —CH 2 — in the alkylene of the arylalkyl may optionally be replaced by —O—, —CH═CH—, or cycloalkylene, and

Y is a group represented by the formula (a) or (b)

wherein X in each of the formulae (a) and (b) independently represents a group selected from hydrogen, chlorine, a group defined in the same way as R 0 , or a group having any one of —CH═CH—, —C≡C—, —OH, —COOH, —COO—, 2-oxapropane-1,3 -dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, —NH 2 , —CN, and —O—, and at least one of X is a reactive group selected from the above-defined group, and

Z in the formula (b) represents a single bond, —O—, or —CH 2 —.

4. The optical waveguide according to claim 3 , wherein the reactive group is hydrogen bound to Si, chlorine bound to Si, or a group having any one of —CH═CH—, —C≡C—, —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, and —NH 2 .

5. The optical waveguide according to claim 3 , wherein:

R 0 independently represents

an alkyl having 1 to 8 carbon atoms in which hydrogen may optionally be replaced by fluorine, and —CH 2 — may optionally be replaced by —O— or cycloalkylene,

naphthyl,

phenyl in which hydrogen may optionally be replaced by halogen, methyl, or methoxy, or

phenylalkyl in which hydrogen of the benzene ring may optionally be replaced by halogen, alkyl having 1 to 4 carbon atoms or methoxy, and the alkylene in the phenylalkyl has 1 to 8 carbon atoms, and —CH 2 — in the alkylene in the phenylalkyl may optionally be replaced by —O— or cycloalkylene;

in each of the formulae (a) and (b), at least one of X is a reactive group selected from hydrogen bound to Si, chlorine bound to Si, and a group having any one of —CH═CH—, —C≡C—, —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, and —NH 2 , and

the remaining X is a group defined in the same way as R 0 ; and

Z in the formula (b) represents —O—.

6. The optical waveguide according to claim 3 , wherein:

all of the R 0 are the same group selected from

alkyl having 1 to 8 carbon atoms, in which hydrogen may optionally be replaced by fluorine, and —CH 2 — may optionally be replaced by —O— or a cycloalkylene,

naphthyl,

phenyl in which hydrogen may optionally be replaced by halogen, methyl, or methoxy, and

phenylalkyl in which hydrogen of the benzene ring may optionally be replaced by halogen, alkyl having 1 to 4 carbon atoms or methoxy, and alkylene in the phenylalkyl has 1 to 8 carbon atoms, and —CH 2 — in the alkylene in the phenylalkyl may optionally be replaced by —O— or cycloalkylene;

in each of the formulae (a) and (b), one of the X is a reactive group selected from hydrogen bound to Si, chlorine bound to Si, and a group having any one of —CH═CH—, —C≡C—, —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, and —NH 2 , and the remaining X is a group defined in the same way as R 0 ; and

Z in the formula (b) represents —O—.

7. The optical waveguide according to claim 3 , wherein:

all of the R 0 are the same group selected from unsubstituted phenyl, cyclopentyl, and cyclohexyl;

in each of the formulae (a) and (b), one of the X is a reactive group selected from hydrogen bound to Si, chlorine bound to Si, and a group having any one of —CH═CH—, —C≡C—, —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, and —NH 2 , and

the remaining X is a group defined in the same way as R 0 ; and

Z in the formula (b) represents —O—.

8. The optical waveguide according to claim 3 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-1) with a compound having at least two Si—H groups

wherein R independently represents

hydrogen,

alkyl having 1 to 40 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or cycloalkenylene,

aryl in which hydrogen may optionally be replaced by halogen, or by alkyl having 1 to 20 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or phenylene, or

arylalkyl in which hydrogen in the aryl may optionally be replaced by halogen or alkyl having 1 to 20 carbon atoms, and hydrogen in the alkylene of the arylalkyl may optionally be replaced by fluorine, and —CH 2 — in the alkylene of the arylalkyl may optionally be replaced by —O—, —CH═CH—, or cycloalkylene, and

Y 1 is a group represented by the formula (a-1) or (b-1)

wherein, in each of the formulae (a-1) and (b-1), at least one of the X 11 is alkenyl-containing group, and the remaining X 11 independently represents a hydrogen, a group defined in the same way as R, or a group having any one of —OH, —COOH, —COO—, 2 -oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, —NH 2 , —CN, and —O—, and

Z in the formula (b-1) represents a single bond, —O—, or —CH 2 —.

9. The optical waveguide according to claim 8 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-1) with at least one of the compounds selected from the group consisting of a silsesquioxane derivative represented by the formula (1-2), a compound represented by the formula (2-1), a compound represented by the formula (3-1), a compound represented by the formula (4-1), a compound represented by the formula (5-1), and a compound represented by the formula (6-1)

wherein, in the formula (1-1), R independently represents

hydrogen,

alkyl having 1 to 40 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or cycloalkenylene,

aryl in which hydrogen may optionally be replaced by halogen, or with alkyl having 1 to 20 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or phenylene, or

arylalkyl in which hydrogen in the aryl may optionally be replaced by halogen or alkyl having 1 to 20 carbon atoms, and hydrogen in the alkylene of the arylalkyl may optionally be replaced by fluorine, and —CH 2 — in the alkylene of the arylalkyl may optionally be replaced by —O—, —CH═CH—, or cycloalkylene, and

Y 1 is a group represented by the formula (a-1) or (b-1)

wherein, in each of the formulae (a-1) and (b-1), at least one of X 11 is an alkenyl-containing group, and the remaining X 11 independently represents hydrogen, a group defined in the same way as R, or a group having any one of —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, —NH 2 , —CN, and —O—,

Z in the formula (b-1) represents a single bond, —O—, or —CH 2 —

wherein, in the formula (1-2), R is a group defined in the same way as the R in the formula (1-1), and Y 2 is a group represented by the formula (a-2) or the formula (b-2)

wherein, in each of the formulae (a-2) and (b-2), at least one of X 12 is hydrogen, and the remaining X 12 independently represents chlorine, a group defined in the same way as R, or a group having any one of —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, —NH 2 , —CN, and —O—

Z in the formula (b-2) represents a single bond, —O—, or —CH 2 —

wherein, in the formula (2-1), R 1 is a group defined in the same way as R in the formula (1-1), at least two of X 21 is hydrogen, and the remaining X 21 is R 1

wherein, in the formula (3-1), R 1 is a group defined in the same way as R in the formula (1-1), and L represents a single bond, —O—, —CH 2 —, —(CH 2 ) 2 —, —(CH 2 ) 3 —, —(CH 2 ) 4 —, 1,4-phenylene, 4,4′-diphenylene, 4,4′-oxy-1,1′-diphenylene, or a group represented by the formula (c); in the formula (c), R 2 is a group defined in the same way as R 1 , and m represents an integer of 1 to 30

wherein, in the formula (4-1), R 2 is a group defined in the same way as R 1 in the formula (2-1), at least two of X 21 are hydrogen, the remaining X 21 is a group defined in the same group as R in the formula (1-1), e represents 0 or 1, and n represents an integer of 3 to 30

wherein, in the formula (5-1), each of R and R 1 is a group defined in the same way as R in the formula (1-1), at least two of X 31 are hydrogen, and the remaining X 31 is R 1

wherein, in the formula (6-1), each of R and R 1 represents a group defined in the same way as R in the formula (1-1), at least two of the X 31 are hydrogen, and the remaining X 31 is R 1 .

10. The optical waveguide according to claim 9 , wherein:

in each of the formulae (a-1) and (b-1) in the formula (1-1), at least one of X 11 is an alkenyl-containing group, and the remaining X 11 is chlorine or a group defined in the same way as R in the formula (1-1); and

in each of the formulae (a-2) and (b-2) in the formula (1-2), at least one of X 12 is hydrogen, and the remaining X 12 is chlorine or a group defined in the same way as R in the formula (1-1).

11. The optical waveguide according to claim 9 , wherein:

R in the formula (1-1) independently represents

alkyl having 1 to 8 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O— or cycloalkylene,

naphthyl,

phenyl in which hydrogen may optionally be replaced by halogen, methyl or methoxy, or

phenylalkyl in which hydrogen of the benzene ring may optionally be replaced by halogen, an alkyl group having 1 to 4 carbon atoms, or methoxy, and the alkylene in the phenylalkyl has 1 to 8 carbon atoms, and —CH 2 — in the alkylene in the phenylalkyl may optionally be replaced by —O— or cycloalkylene;

in each of the formulae (a-1) and (b-1) in the formula (1-1), at least one of the X 11 is an alkenyl-containing group, and the remaining X 11 is a group defined in the same way as R in the formula (1-1);

in each of the formulae (a-2) and (b-2) in the formula (1-2), at least one of X 12 is hydrogen, and the remaining X 12 is a group defined in the same way as R in the formula (1-2); and

Z in each of the formulae (b-1) and (b-2) represents —O—.

12. The optical waveguide according to claim 9 , wherein:

all of the R in the formula (1-1) are the same group selected from

alkyl having 1 to 8 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O— or cycloalkylene,

naphthyl,

phenyl in which hydrogen may optionally be replaced by halogen, methyl, or methoxy, and

phenylalkyl in which hydrogen of the benzene ring may optionally be replaced by halogen, alkyl having 1 to 4 carbon atoms, or methoxy, and alkylene in the phenylalkyl has 1 to 8 carbon atoms, and —CH 2 — in the alkylene in the phenylalkyl may optionally be replaced by —O— or cycloalkylene;

in each of the formulae (a-1) and (b-1) in the formula (1-1), one of the X 11 is alkenyl-containing group, and the remaining X 11 is a group defined in the same way as R in the formula (1-1);

in each of the formulae (a-2) and (b-2) in the formula (1-2), one of the X 12 is hydrogen, and the remaining X 12 is a group defined in the same way as R in the formula (1-2); and

Z in each of the formulae (b-1) and (b-2) represents —O—.

13. The optical waveguide according to claim 9 , wherein:

all of the R in the formula (1-1) are the same group selected from unsubstituted phenyl, cyclopentyl, and cyclohexyl;

in each of the formulae (a-1) and (b-1) in the formula (1-1), at least one of X 11 is an alkenyl-containing group, and the remaining X 11 is an alkyl having 1 to 8 carbon atoms, or unsubstituted phenyl, cyclopentyl, or cyclohexyl;

in each of the formulae (a-2) and (b-2) in the formula (1-2), at least one of the X 12 is hydrogen, and the remaining X 12 is an alkyl having 1 to 8 carbon atoms, or unsubstituted phenyl, cyclopentyl, or cyclohexyl;

Z in each of the formulae (b-1) and (b-2) in the formulae (1-1) and (1-2) represents —O—;

in each of the formulae (2-1), (3-1), (5-1), and (6-1), R 1 is an alkyl having 1 to 8 carbon atoms, or unsubstituted phenyl, cyclopentyl, or cyclohexyl;

in the formula (2-1), at least two of the X 21 are hydrogen, and the remaining X 21 is R 1 ; and

in the formula (4-1), at least two of the X 21 is hydrogen, and the remaining X 21 is a group defined in the same way as R in the formula (1-1).

14. The optical waveguide according to claim 9 , wherein:

all of the R in the formula (1-1) are the same group selected from unsubstituted phenyl, cyclopentyl, and cyclohexyl;

in each of the formulae (a-1) and (b-1) in the formula (1-1), at least one of X 11 is vinyl, aryl, or styryl, and the remaining X 11 is alkyl having 1 to 8 carbon atoms, or unsubstituted phenyl, cyclopentyl, or cyclohexyl;

in each of the formulae (a-2) and (b-2) in the formula (1-2), at least one of X 12 is hydrogen, and the remaining X 12 is alkyl having 1 to 8 carbon atoms, or unsubstituted phenyl, cyclopentyl, or cyclohexyl;

Z in each of the formulae (b-1) and (b-2) represents —O—;

in each of the formulae (2-1), (3-1), (5-1), and (6-1), R 1 is alkyl having 1 to 8 carbon atoms, or unsubstituted phenyl, cyclopentyl, or cyclohexyl;

in the formula (2-1), at least two of the X 21 is hydrogen, and the remaining X 21 is R 1 ; and

in the formula (4-1), at least two of the X 21 is hydrogen, and the remaining X 21 is a group defined in the same way as R in the formula (1-1).

15. The optical waveguide according to claim 9 , wherein:

all of the R in the formula (1-1) are unsubstituted phenyl;

in each of the formulae (a-1) and (b-1), at least one of the X 11 is vinyl, aryl, or styryl, and the remaining X 11 is alkyl having 1 to 4 carbon atoms or unsubstituted phenyl;

in each of the formulae (a-2) and (b-2), at least one of X 12 is hydrogen, and the remaining X 12 is alkyl having 1 to 4 carbon atoms or unsubstituted phenyl;

in each of the formulae (2-1), (3-1), (5-1), and (6-1), R 1 is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl;

in the formula (2-1), at least two of the X 21 is hydrogen, and the remaining X 21 is R 1 ; and

in the formula (4-1), at least two of the X 21 is hydrogen, and the remaining X 21 is a group defined in the same way as R in the formula (1-1).

16. The optical waveguide according to claim 3 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-2) with a compound having at least two alkenyl-containing groups or a compound having a carbon-carbon triple bond

wherein, in the formula (1-2), R independently represents

hydrogen,

alkyl having 1 to 40 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or cycloalkenylene,

aryl in which hydrogen may optionally be replaced by halogen, or by alkyl having 1 to 20 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or phenylene, or

arylalkyl in which hydrogen in the aryl may optionally be replaced by halogen or alkyl having 1 to 20 carbon atoms, and hydrogen in the alkylene of the arylalkyl may optionally be replaced by fluorine, and —CH 2 — in the alkylene of the arylalkyl may optionally be replaced by —O—, —CH═CH—, or cycloalkylene, and

Y 2 is a group represented by the formula (a-2) or (b-2)

 wherein, in each of the formulae (a-2) and (b-2), at least one of the X 12 is hydrogen, and the remaining X 12 independently represents hydrogen, a group defined in the same way as R, or a group having any one of —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, —NH 2 , —CN, and —O—

Z in the formula (b-2) represents a single bond, —O—, or —CH 2 —.

17. The optical waveguide according to claim 16 , comprising of a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-2) with at least one of the compounds selected from the group consisting of a compound represented by the formula (2-2), a compound represented by the formula (3-2), a compound represented by the formula (4-2), a compound represented by the formula (5-2), a compound represented by the formula (6-2), a compound represented by the formula (d-1), a compound represented by the formula (d-2), a compound represented by the formula (d-3), and a compound represented by the formula (d-4)

wherein, in the formula (1-2), R independently represents

hydrogen,

alkyl having 1 to 40 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or cycloalkenylene,

aryl in which hydrogen may optionally be replaced by halogen, or by alkyl having 1 to 20 carbon atoms in which hydrogen may optionally be replaced by fluorine and optional —CH 2 — may be replaced by —O—, —CH═CH—, cycloalkylene, or phenylene, or

arylalkyl in which hydrogen in the aryl may optionally be replaced by halogen or alkyl having 1 to 20 carbon atoms, and hydrogen in the alkylene of the arylalkyl may optionally be replaced by fluorine, and —CH 2 — in the alkylene of the arylalkyl may optionally be replaced by —O—, —CH═CH—, or cycloalkylene, and

Y 2 is a group represented by the formula (a-2) or (b-2)

wherein, in each of the formulae (a-2) and (b-2), at least one of X 12 is hydrogen, and the remaining X 12 independently represents chlorine, a group defined in the same way as R, or a group having any one of —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, —NH 2 , —CN, and —O—, and

Z in the formula (b-2) represents a single bond, —O—, or —CH 2 —

wherein, in the formula (2-2), R 1 is a group defined in the same way as R in the formula (1-2), at least two X 22 are an alkenyl-containing group or a group having a carbon-carbon triple bond, and the remaining X 22 is R 1

wherein, in the formula (3-2), R 1 is a group defined in the same way as R in the formula (1-2), X 22 is alykenyl-containing group, and L represents a single bond, —O—, —CH 2 —, —(CH 2 ) 2 —, —(CH 2 ) 3 —, —(CH 2 ) 4 —, 1,4-phenylene, 4,4′-diphenylene, 4,4′-oxy-1,1′-diphenylene, or a group represented by the formula (c)

wherein, in the formula (c), R 2 is a group defined in the same way as R 1 , and m represents an integer of 1 to 30

wherein, in the formula (4-2), R 2 is a group defined in the same way as R 1 in the formula (2-2), at least two of the X 22 is an alkenyl-containing group, the remaining X 22 is a group defined in the same way as R in the formula (1-2), e represents 0 or 1, and n represents an integer of 3 to 30

wherein, in the formula (5-2), each of R and R 1 is a group defined in the same way as R in the formula (1-2), at least two of the X 32 is an alkenyl-containing group, and the remaining X 32 is R 1

wherein, in the formula (6-2), each of R and R 1 is a group defined in the same way as R in the formula (1-2), at least two of the X 32 is an alkenyl-containing group, and the remaining X 32 is R 1

H 2 C═CH—R 3 —CH═CH 2   (d-1)

HC≡C—R 3 —C≡CH  (d-2)

R 4 —C≡C—R 4   (d-3)

R 4 —C≡C—C≡C—R 4   (d-4)

wherein, in each of the formulae (d-1), (d-2), (d-3) and (d-4),

R 3 represents

alkyl having 1 to 40 carbon atoms in which —CH 2 —may optionally be replaced by —O— or —COO—, or

phenyl in which hydrogen may optionally be replaced by halogen or an alkyl having 1 to 4 carbon atoms,

R 4 represents

an alkyl having 1 to 8 carbon atoms in which —CH 2 — may optionally be replaced by —O— or —COO—, or

phenyl in which hydrogen may optionally be replaced by halogen or an alkyl having 1 to 4 carbon atoms.

18. The optical waveguide according to claim 17 , wherein:

in each of the formulae (a-2) and (b-2) in the formula (1-2), at least one of X 12 is hydrogen, and the remaining X 12 is chlorine or the same group as R in the formula (1-2).

19. The optical waveguide according to claim 17 , wherein:

R in the formula (1-2) independently represents.

alkyl having 1 to 8 carbon atoms in which hydrogen may optionally be replaced by fluorine, and —CH 2 — may optionally be replaced by —O— or cycloalkylene,

naphthyl,

phenyl in which hydrogen may optionally be replaced by halogen, methyl, or methoxy, or

phenylalkyl in which hydrogen of the benzene ring may optionally be replaced by halogen, alkyl having 1 to 4 carbon atoms, or methoxy, and alkylene in the phenylalkyl has 1 to 8 carbon atoms, and —CH 2 — in the alkylene in the phenylalkyl may optionally be replaced by —O— or cycloalkylene;

in each of the formulae (a-2) and (b-2), at least one of X 12 is hydrogen, and the remaining X 12 is a group defined in the same way as R in the formula (1-2); and

Z in the formula (b-2) represents —O—.

20. The optical waveguide according to claim 17 , wherein:

all of the R in the formula (1-2) are the same group selected from

alkyl having 1 to 8 carbon atoms in which hydrogen may optionally be replaced by fluorine, and —CH 2 — may optionally be replaced by —O— or cycloalkylene,

naphthyl,

phenyl in which hydrogen may optionally be replaced by halogen, methyl, or methoxy, or

phenylalkyl in which hydrogen of the benzene ring may optionally be replaced by halogen, an alkyl group having 1 to 4 carbon atoms, or methoxy, and alkylene in the phenylalkyl has 1 to 8 carbon atoms, and —CH 2 — in the alkylene in the phenylalkyl may optionally be replaced by —O— or a cycloalkylene;

in each of the formulae (a-2) and (b-2), at least one of X 12 is hydrogen, and the remaining X 12 is a group defined in the same way as R in the formula (1-2); and

Z in the formula (b-2) represents —O—.

21. The optical waveguide according to claim 17 , wherein:

all of the R in the formula (1-2) are the same group selected from unsubstituted phenyl, cyclopentyl, and cyclohexyl;

in each of the formulae (a-2) and (b-2), at least one of X 12 is hydrogen, and the remaining X 12 is an alkyl having 1 to 8 carbon atoms, or unsubstituted phenyl, cyclopentyl, or cyclohexyl;

Z in the formula (b-2) represents —O—; and

in each of the formulae (2-2), (3-2), (5-2), and (6-2), R 1 is an alkyl having 1 to 8 carbon atoms, or unsubstituted phenyl, cyclopentyl, or cyclohexyl.

22. The optical waveguide according to claim 17 , wherein:

all of the R in the formula (1-2) are the same group selected from unsubstituted phenyl, cyclopentyl, and cyclohexyl;

in each of the formulae (a-2) and (b-2), at least one of X 12 is hydrogen, and the remaining X 12 is an alkyl having 1 to 8 carbon atoms, or unsubstituted phenyl, cyclopentyl, or cyclohexyl;

Z in the formula (b-2) represents —O—;

in each of the formulae (2-2), (3-2), (5-2), and (6-2), R 1 is an alkyl having 1 to 8 carbon atoms, or unsubstituted phenyl, cyclopentyl, or cyclohexyl;

in the formula (2-2), at least two X 22 are vinyl, aryl or styryl, and the remaining X 22 is R 1 ;

in the formula (3-2), X 22 is vinyl, aryl or styryl;

in the formula (4-2), at least two X 22 are vinyl, aryl or styryl, and the remaining X 22 is a group defined in the same way as R in the formula (1-2); and

in each of the formulae (5-2) and (6-2), at least two of the X 32 are vinyl, aryl or styryl, and the remaining X 32 is R 1 .

23. The optical waveguide according to claim 17 , wherein:

all of the R in the formula (1-2) are unsubstituted phenyl;

in each of the formulae (a-2) and (b-2), at least one of X 12 is hydrogen, and the remaining X 12 is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl;

Z in the formula (b-2) represents —O—;

in each of the formulae (2-2), (3-2), (5-2), and (6-2), R 1 is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl;

in the formula (2-2), at least two X 22 are a vinyl, allyl, or styryl, and the remaining X 22 is R 1 ;

in the formula (3-2), X 22 is a vinyl, allyl, or styryl;

in the formula (4-2), at least two X 22 are a vinyl, allyl, or styryl, and the remaining X 22 is an unsubstituted phenyl; and

in each of the formulae (5-2) and (6-2), at least two of the X 32 are a vinyl, allyl, or styryl, and the remaining X 32 is R 1 .

24. The optical waveguide according to claim 3 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-4) with a compound having at least two groups capable of reacting with the reactive group in the silsesquioxane derivative

wherein, in the formula (1-4), R 0 independently represents

hydrogen,

alkyl having 1 to 40 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or cycloalkenylene,

aryl in which hydrogen may optionally be replaced by halogen, or with alkyl having 1 to 20 carbon atoms in which hydrogen may optionally be replaced by fluorine and —CH 2 — may optionally be replaced by —O—, —CH═CH—, cycloalkylene, or phenylene, or

arylalkyl in which hydrogen in the aryl may optionally be replaced by halogen or alkyl having 1 to 20 carbon atoms, and hydrogen in the alkylene of the arylalkyl may optionally be replaced by fluorine, and —CH 2 — in the alkylene of the arylalkyl may optionally be replaced by —O—, —CH═CH—, or cycloalkylene, and

Y 4 is a group represented by the formula (a-4) or (b-4)

wherein, in each of the formulae (a-4) and (b-4), X 4 independently represents a chlorine, a group defined in the way as R 0 , or a group having any one of —CH═CH—, —C≡C—, —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, —NH 2 , —CN, and —O—, and at least one of the X 4 is a reactive group selected from chlorine bound to Si, and a group having any one of —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, and —NH 2 , and

Z in the formula (b-4) represents a single bond, —O—, or —CH 2 —.

25. The optical waveguide according to claim 24 , wherein:

in the formula (1-4), R 0 independently represents

alkyl having 1 to 8 carbon atoms in which hydrogen may be replaced by fluorine, and —CH 2 — may optionally be replaced by —O— or a cycloalkylene,

naphthyl,

phenyl in which hydrogen may optionally be replaced by halogen, methyl, or methoxy, or

phenylalkyl in which hydrogen of the benzene ring may optionally be replaced by halogen, an alkyl having 1 to 4 carbon atoms, or methoxy, and alkylene in the phenylalkyl has 1 to 8 carbon atoms, and —CH 2 — in the alkylene in the phenylalkyl may optionally be replaced by —O— or cycloalkylene;

in each of the formulae (a-4) and (b-4), at least one of X 4 is a reactive group selected from chlorine bound to Si, and a group having any one of —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4 -epoxycyclohexyl, —SH, —NH—, and —NH 2 , and the remaining X 4 is a group defined in the same way as R 0 in the formula (1-4); and

Z in the formula (b-4) represents —O—.

26. The optical waveguide according to claim 24 , wherein:

in the formula (1-4), all of the R 0 are the same group selected from

alkyl having 1 to 8 carbon atoms in which hydrogen may optionally be replaced by fluorine, and —CH 2 — may optionally be replaced by —O— or cycloalkylene,

naphthyl,

phenyl in which hydrogen may optionally be replaced by halogen, methyl, or methoxy, and

phenylalkyl in which hydrogen of the benzene ring may optionally be replaced by halogen, an alkyl having 1 to 4 carbon atoms or methoxy, and alkylene in the phenylalkyl has 1 to 8 carbon atoms, and —CH 2 — in the alkylene in the phenylalkyl may optionally be replaced by —O— or cycloalkylene;

in each of the formulae (a-4) and (b-4), at least one of X 4 is a reactive group selected from chlorine bound to Si, and a group having any one of —OH, —COOH, —COO—, 2-oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4 -epoxycyclohexyl, —SH, —NH—, and —NH 2 , and the remaining X 4 is a group defined in the same way as R 0 in the formula (1-4); and

Z in the formula (b-4) represents —O—.

27. The optical waveguide according to claim 24 , wherein:

all of the R 0 are the same group selected from unsubstituted phenyl, cyclopentyl, and cyclohexyl;

in each of the formulae (a-4) and (b-4), one of X 4 is a group selected from chlorine bound to Si, and a group having any one of —OH, —COOH, —COO—, 2 -oxapropane-1,3-dioyl, oxilanyl, oxilanylene, oxetanyl, oxetanylene, 3,4-epoxycyclohexyl, —SH, —NH—, and —NH 2 , and the remaining X 4 is a group defined in the same way as R 0 in the formula (1-4); and

Z in the formula (b-4) represents —O—.

28. The optical waveguide according to claim 24 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-4) in which Y 4 is a group represented by the formula (a-2) with a compound represented by the formula (8-2)

X 12 in the formula (a-2) is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl

wherein, in the formula (8-2), R 1 is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl, and R 3 is a phenyl, naphthalene, or anthracene.

29. The optical waveguide according to claim 24 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-4) in which Y 4 is a group represented by the formula (a-3) with a carboxylic acid or an epoxy

wherein, in the formula (a-3), R 4 is a divalent organic group having 1 to 20 carbon atoms, and X 13 is an alkyl having 1 to 4 carbon atoms or an unsubstituted phenyl.

30. The optical waveguide according to claim 24 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-4) in which Y 4 is a group represented by the formula (a-4) with diamine

wherein, in the formula (a-4), R 4 is a divalent organic group having 1 to 20 carbon atoms, and X 14 is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl.

31. The optical waveguide according to claim 24 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-4) in which Y 4 is a group represented by the formula (a-3) with a silsesquioxane derivative represented by the formula (1-4) in which Y 4 is a group represented by the formula (a-4)

wherein, in the formula (a-3), R 4 is a divalent organic group having 1 to 20 carbon atoms, and X 13 is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl

wherein, in the formula (a-4), R 4 is a divalent organic group having 1 to 20 carbon atoms, and X 14 is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl.

32. The optical waveguide according to claim 24 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-4) in which Y 4 is a group represented by the formula (a-4) with a silsesquioxane derivative represented by the formula (1-4) in which Y 4 is a group represented by the formula (a-5)

wherein, in the formula (a-4), R 4 is a divalent organic group having 1 to 20 carbon atoms, and X 14 is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl

X 15 in the formula (a-5) is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl.

33. The optical waveguide according to claim 24 , comprising a polymer obtained by reacting a silsesquioxane derivative represented by the formula (1-4) in which Y 4 is a group represented by the formula (a-4) with a compound represented by the formula (9-1)

wherein, in the formula (a-4), R 4 is a divalent organic group having 1 to 20 carbon atoms, and X 14 is an alkyl having 1 to 4 carbon atoms or unsubstituted phenyl

wherein, in the formula (9-1), all of the R 5 are alkyl having 1 to 20 carbon atoms, alkenyl having 2 to 20 carbon atoms, or aryl having 6 to 20 carbon atoms, in which —CH 2 — may optionally be replaced by —O—, and optional hydrogen may be replaced by halogen

R 6 is a single bond or a divalent organic group having 1 to 15 carbon atoms, and R 7 is a trivalent organic group having 1 to 15 carbon atoms.