Liquid crystal half-wave plate lens

1. A diffractive lens, comprising:

immobilized liquid crystals, wherein:

the liquid crystals in a first region are aligned in a first orientation;

the liquid crystals in a second region, located between the first region and a third region and adjacent to the first region and the third region, are aligned in a second orientation that is distinct from the first orientation;

the liquid crystals in the third region, located between the second region and a fourth region and adjacent to the second region and the fourth region, are aligned in the first orientation; and

the liquid crystals in the fourth region, located adjacent to the third region, are aligned in the second orientation, wherein the first region and the third region are spaced apart to cause diffraction of impinging light.

2. The lens of claim 1 , wherein:

the liquid crystals are located between two substrates;

the liquid crystals in the first region are aligned parallel to a first substrate of the two substrates;

the liquid crystals in the second region are aligned perpendicular to the first substrate;

the liquid crystals in the third region are aligned parallel to the first substrate; and

the liquid crystals in the fourth region are aligned perpendicular to the first substrate.

3. The lens of claim 1 , wherein:

the first region has a first refractive index and the second region has a second refractive index so that the difference between the first refractive index and the second refractive index causes a half-wave phase difference for the impinging light.

4. The lens of claim 1 , wherein:

the aligned liquid crystals are configured to focus a portion of light impinging on the lens and disperse a portion of light impinging on the lens.

5. The lens of claim 1 , wherein:

the liquid crystals are located on a substrate; and

spacing between two adjacent regions in which the liquid crystals are aligned in a same orientation is determined based on a distance from a center of the substrate.

6. The lens of claim 1 , wherein:

the liquid crystals are located on a substrate;

two adjacent regions, in which the liquid crystals are aligned in the first orientation, located at a first distance from a center of the substrate are separated by a first spacing;

two adjacent regions, which the liquid crystals are aligned in the first orientation, located at a second distance from the center of the substrate are separated by a second spacing;

the second distance is greater than the first distance; and

the second spacing is less than the first spacing.

7. The lens of claim 1 , wherein:

the aligned liquid crystals in the first region are configured to direct light to a particular focal point;

the aligned liquid crystals in the second region are configured to direct light to the particular focal point;

the aligned liquid crystals in the third region are configured to direct light to the particular focal point; and

the aligned liquid crystals in the fourth region are configured to direct light to the particular focal point.

8. A device, comprising:

the lens of claim 1 ; and

an array of light emitting devices coupled with the lens for outputting light through the lens.

9. The device of claim 8 , wherein the device is a head-mounted display device.

10. The device of claim 8 , wherein:

the lens is configured to receive light output from the array of light emitting devices, wherein:

a portion of light impinging on the first region is directed to a particular focal point;

a portion of light impinging on the second region is directed to the particular focal point;

a portion of light impinging on the third region is directed to the particular focal point; and

a portion of light impinging on the fourth region is directed to the particular focal point.