Liquid crystal element

1. A liquid crystal element comprising:

a liquid crystal layer;

a plurality of first arcuate electrodes disposed concentrically about an optical axis of the liquid crystal element and configured to apply first voltage to the liquid crystal layer; and

a plurality of second arcuate electrodes disposed concentrically about the optical axis and configured to apply second voltage to the liquid crystal layer, wherein

the liquid crystal element has an electrode placement area in which the first arcuate electrodes and the second arcuate electrodes are disposed,

each of unit electrodes is constituted by one of the first arcuate electrodes and one of the second arcuate electrodes adjacent to each other in a radial direction to the optical axis, the unit electrodes being arranged side by side in the radial direction in the electrode placement area,

the liquid crystal element further comprises high-resistance layers each having a higher electrical resistivity than the first arcuate electrodes and the second arcuate electrodes, the high-resistance layers each being disposed between a corresponding one of the first arcuate electrodes and a corresponding one of the second arcuate electrodes in a plan view,

the liquid crystal element further comprises a core electrode and a center electrode, the core electrode being disposed in a part, of the electrode placement area, through which the optical axis passes, the center electrode forming a potential gradient between the center electrode and the core electrode in the electrode placement area,

a unit electrode of the unit electrodes that is located outside of a specific location in the radial direction has a radius Rn smaller than a radius Un expressed by formula (1) and formula (2), where a subscript n indicates an n-th location from the optical axis, and

the formula (2) includes a radius Sc of the center electrode:

Sn

-

0.1

×

Sn

≤

Un

≤

Sn

+

0.1

×

Sn

(

1

)

Sn

=

(

n

+

1

)

1

2

×

Sc

.

(

2

)

2. The liquid crystal element according to claim 1 , wherein

the electrode placement area includes an annular band-shaped area,

the annular band-shaped area includes a plurality of arcuate band-shaped areas arranged side by side in a circumferential direction about the optical axis,

at least one first arcuate electrode of the first arcuate electrodes and at least one second arcuate electrode of the second arcuate electrodes are disposed in each of the arcuate band-shaped areas.

3. The liquid crystal element according to claim 2 , wherein

the electrode placement area includes a plurality of the annular band-shaped areas,

the annular band-shaped areas are arranged side by side in a radial direction to the optical axis, and

the number of the arcuate band-shaped areas included in an annular band-shaped area, of the annular band-shaped areas, located outward in the radial direction is larger than the number of the arcuate band-shaped areas included in an annular band-shaped area, of the annular band-shaped areas, located inward in the radial direction.

4. The liquid crystal element according to claim 2 , further comprising:

at least one first annular electrode configured to apply the first voltage to the liquid crystal layer; and

at least one second annular electrode configured to apply the second voltage to the liquid crystal layer, wherein

the electrode placement area further includes a circular area located inside of the annular band-shaped area in a radial direction to the optical axis, and

the at least one first annular electrode and the at least one second annular electrode are disposed in the circular area.

5. The liquid crystal element according to claim 4 ,

wherein

the center electrode is disposed inside of the at least one first annular electrode and the at least one second annular electrode in the radial direction,

the at least one first annular electrode and the at least one second annular electrode adjacent to each other in the radial direction constitute a unit electrode, and

out of the unit electrode constituted by the at least one first annular electrode and the at least one second annular electrode and the unit electrodes each constituted by one of the first arcuate electrodes and one of the second arcuate electrodes, a unit electrode located outside of the specific location in the radial direction has a radius Rn smaller than the radius Un expressed by the formula (1) and the formula (2).

6. The liquid crystal element according to claim 2 , wherein

the electrode placement area further includes a non-circular area located outside of the annular band-shaped area in a radial direction to the optical axis, and

at least one first arcuate electrode of the first arcuate electrodes and at least one second arcuate electrode of the second arcuate electrodes are disposed in the non-circular area.

7. The liquid crystal element according to claim 1 , further comprising:

a first radial direction lead wire extending outward in a radial direction to the optical axis; and

a second radial direction lead wire extending outward in the radial direction, wherein

the first radial direction lead wire is connected to one end of a first arcuate electrode of the first arcuate electrodes,

the second radial direction lead wire is connected to one end of a second arcuate electrode of the second arcuate electrodes,

the first radial direction lead wire has a resistance per unit length lower than a resistance per unit length of each of the first arcuate electrodes, and

the second radial direction lead wire has a resistance per unit length lower than a resistance per unit length of each of the second arcuate electrodes.

8. The liquid crystal element according to claim 7 , further comprising

a first circumferential direction lead wire extending in a circumferential direction about the optical axis; and

a second circumferential direction lead wire extending in the circumferential direction, wherein

the first circumferential direction lead wire and the second circumferential direction lead wire are disposed outside of the first arcuate electrodes and the second arcuate electrodes in the radial direction,

one end of the first circumferential direction lead wire is connected to an end of the first radial direction lead wire in the radial direction,

one end of the second circumferential direction lead wire is connected to an end of the second radial direction lead wire in the radial direction,

the first circumferential direction lead wire has a resistance per unit length lower than a resistance per unit length of each of the first arcuate electrodes, and

the second circumferential direction lead wire has a resistance per unit length lower than a resistance per unit length of each of the second arcuate electrodes.

9. The liquid crystal element according to claim 1 , further comprising

a first annular electrode configured to apply the first voltage to the liquid crystal layer; and

a second annular electrode configured to apply the second voltage to the liquid crystal layer, wherein

the electrode placement area includes:

a circular area in which the first annular electrode and the second annular electrode are disposed; and

a non-circular area located outside of the circular area in a radial direction to the optical axis, and

at least one first arcuate electrode of the first arcuate electrodes and at least one second arcuate electrode of the second arcuate electrodes are disposed in the non-circular area.

10. The liquid crystal element according to claim 1 , wherein

the electrode placement area includes a plurality of circumferential direction areas arranged side by side in a circumferential direction about the optical axis,

at least one first arcuate electrode of the first arcuate electrodes and at least one second arcuate electrode of the second arcuate electrodes are disposed in each of the circumferential direction areas, and

the circumferential direction areas include at least two circumferential direction areas that set different focal lengths.

11. The liquid crystal element according to claim 10 ,

the at least two circumferential direction areas cause an astigmatism by setting the different focal lengths.

12. The liquid crystal element according to claim 10 , wherein

paired circumferential direction areas of the circumferential direction areas set substantially the same focal length, the paired circumferential direction areas being located opposite to each other in a radial direction to the optical axis with the optical axis therebetween.

13. The liquid crystal element according to claim 12 , wherein

the number of the circumferential direction areas is an even number,

the number of circumferential direction area sets is an even number, the circumferential direction area sets each being the paired circumferential direction areas, and

the even number of circumferential direction area sets include at least two circumferential direction area sets that set different focal lengths.

14. The liquid crystal element according to claim 10 , wherein

each of the circumferential direction areas has a central angle of less than or equal to 90 degrees.

15. The liquid crystal element according to claim 1 , wherein

the specific location is a location at which a unit electrode, of the unit electrodes, with a width of less than or equal to 200 μm is disposed, and

the width of each of the unit electrodes is a distance between a corresponding one of the first arcuate electrodes and a corresponding one of the second arcuate electrodes in the radial direction.

16. The liquid crystal element according to claim 1 , wherein

a radius Rn of a unit electrode of the unit electrodes that is located inside of the specific location in the radial direction is represented by the radius Un represented by the formula (1) and the formula (2).

17. Eyeglasses comprising

the liquid crystal element according to claim 1 .

18. A head mounted display comprising

the liquid crystal element according to claim 1 .

19. A contact lens comprising

the liquid crystal element according to claim 1 .