Variable-pitch liquid crystal diffraction grating

1. An apparatus comprising:

a waveguide display assembly of a wearable device, wherein the waveguide display assembly comprises a variable-pitch diffraction grating having a planar liquid-crystal structure comprising a plurality of liquid crystals;

a plurality of electrodes coupled to the planar liquid-crystal structure such that:

when a first plurality of voltages are applied to at least some of the plurality of electrodes, the plurality of liquid crystals are oriented such that the planar liquid-crystal structure operates as a diffraction grating having a first pitch that diffracts a first color of light at a first angle; and

when a second using plurality of voltages are applied to at least some of the plurality of electrodes, the plurality of liquid crystals are oriented such that the planar liquid-crystal structure operates as a diffraction grating having a second pitch different from the first pitch that diffracts a second color of light at substantially the first angle, wherein the second color of light is different than the first color of light; and

at least one projector that is optically coupled to the waveguide assembly and that switches from emitting monochromatic light of the first color to emitting monochromatic light of the second color such that, when the variable-pitch diffraction grating directs light of the first and second colors toward an eye of a user of the wearable device, the monochromatic light of the first and second colors is perceived as a single polychromatic image.

2. The apparatus of claim 1 , wherein, when a third plurality of voltages are applied to at least some of the plurality of electrodes, the plurality of liquid crystals are oriented such that the planar liquid-crystal structure operates as a diffraction grating having a third pitch different from the first pitch and the second pitch.

3. The apparatus of claim 2 , wherein:

the first pitch and the first color of light correspond to a wavelength of a red light;

the second pitch and the second color of light correspond to a wavelength of a green light; and

the third pitch and a third color of light correspond to a wavelength of a blue light.

4. The apparatus of claim 3 , wherein:

the plurality of electrodes are spaced evenly along a surface of the planar liquid-crystal structure;

alternating positive and negative voltages are applied to every seventh electrode of the plurality of electrodes to create the first pitch;

alternating positive and negative voltages are applied to every sixth electrode of the plurality of electrodes to create the second pitch; and

alternating positive and negative voltages are applied to every fifth electrode of the plurality of electrodes to create the third pitch.

5. The apparatus of claim 1 , wherein:

the first plurality of voltages comprise alternating positive and negative voltages such that a first distance along the planar liquid-crystal structure between consecutive ones of the positive and negative voltages is equal to the first pitch; and

the second plurality of voltages comprise alternating positive and negative voltages such that a second distance along the planar liquid-crystal structure between consecutive ones of the positive and negative voltages is equal to the second pitch.

6. The apparatus of claim 5 , wherein the first plurality of voltages further comprise a ground voltage applied between consecutive ones of the positive and negative voltages.

7. The apparatus of claim 1 , wherein the plurality of electrodes comprise indium tin oxide.

8. The apparatus of claim 1 , wherein the plurality of liquid crystals comprise a plurality of nematic liquid crystals.

9. The apparatus of claim 1 , wherein the plurality of liquid crystals comprise a plurality of cholesteric liquid crystals.

10. The apparatus of claim 1 , wherein the planar liquid-crystal structure operates as a reflective diffraction grating.

11. The apparatus of claim 1 , wherein the planar liquid-crystal structure operates as an absorptive diffraction grating.

12. The apparatus of claim 1 , wherein the planar liquid-crystal structure operates as a transmissive diffraction grating.

13. The apparatus of claim 1 , wherein the at least one projector:

emits the monochromatic light of the first color of light during a first time period when the first plurality of voltages are applied to at least some of the plurality of electrodes; and

emits the monochromatic light of the second color of light toward the planar liquid-crystal structure during a second time period when the second plurality of voltages are applied to at least some of the plurality of electrodes.

14. A method comprising:

applying, to at least some of a plurality of electrodes coupled to a planar liquid-crystal structure comprising a plurality of liquid crystals within a waveguide display assembly of a wearable device, a first plurality of voltages such that the plurality of liquid crystals are oriented to cause the planar liquid-crystal structure to operate as a diffraction grating having a first pitch that diffracts a first color of light at a first angle;

switching a projector from emitting monochromatic light of a first color to emitting monochromatic light of a second color; and

when the projector switches to emitting monochromatic light of the second color, applying, to at least some of the plurality of electrodes, a second plurality of voltages such that the plurality of liquid crystals are oriented to cause the planar liquid-crystal structure to operate as a diffraction grating having a second pitch different from the first pitch that diffracts a second color of light at substantially the first angle, wherein the second color of light is different than the first color of light such that, when the waveguide display assembly directs light of the first and second colors toward an eye of a user of the wearable device, the monochromatic light of the first and second colors is perceived as a single polychromatic image.

15. The method of claim 14 , further comprising:

applying, to at least some of the plurality of electrodes, a third plurality of voltages such that the plurality of liquid crystals are oriented to cause the planar liquid-crystal structure to operate as a diffraction grating having a third pitch different from the first pitch and the second pitch.

16. The method of claim 15 , wherein:

the first pitch and the first color of light correspond to a wavelength of a red light;

the second pitch and the second color of light correspond to a wavelength of a green light; and

the third pitch and a third color of light correspond to a wavelength of a blue light.

17. The method of claim 16 , wherein:

the plurality of electrodes are spaced evenly along a surface of the planar liquid-crystal structure;

the first plurality of voltages comprise alternating positive and negative voltages that are applied to every seventh electrode of the plurality of electrodes;

the second plurality of voltages comprise alternating positive and negative voltages that are applied to every sixth electrode of the plurality of electrodes; and

the third plurality of voltages comprise alternating positive and negative voltages that are applied to every fifth electrode of the plurality of electrodes.

18. The method of claim 14 , wherein:

the first plurality of voltages comprise alternating positive and negative voltages such that a first distance along the planar liquid-crystal structure between consecutive ones of the positive and negative voltages is equal to the first pitch; and

the second plurality of voltages comprise alternating positive and negative voltages such that a second distance along the planar liquid-crystal structure between consecutive ones of the positive and negative voltages is equal to the second pitch.

19. The method of claim 18 , wherein the first plurality of voltages further comprise a ground voltage applied between consecutive ones of the positive and negative voltages.

20. A system comprising:

a projector that:

emits, during a first time period, monochromatic light of a first color of light; and

emits, during a second time period, monochromatic light of a second color of light;

a planar liquid-crystal structure comprising a plurality of liquid crystals;

a plurality of electrodes coupled to the planar liquid-crystal structure; and

a controller that:

applies a first plurality of voltages to at least some of the plurality of electrodes during the first time period to orient the plurality of liquid crystals such that the planar liquid-crystal structure operates as a diffraction grating having a first pitch that diffracts the first color of light at a first angle; and

applies a second plurality of voltages to at least some of the plurality of electrodes during the second time period to orient the plurality of liquid crystals such that:

the planar liquid-crystal structure operates as a diffraction grating having a second pitch that diffracts the second color of light at substantially the first angle; and

when the diffraction grating directs light of the first and second colors toward an eye of a user of a wearable device, the monochromatic light of the first and second colors is perceived as a single polychromatic image.