Slanted surface relief grating for rainbow reduction in waveguide display

1. A waveguide display comprising:

a substrate comprising two opposite surfaces; and

a slanted grating at a first surface of the two opposite surfaces of the substrate, wherein:

the slanted grating comprises a plurality of ridges and is characterized by a grating period in one direction;

the plurality of ridges is tilted at a slant angle with respect to a surface normal of the first surface and is characterized by a height; and

the height of the plurality of ridges, the grating period, and the slant angle are configured to cause destructive interference between ambient light diffracted in both +1st order and −1st order by the slanted grating.

2. The waveguide display of claim 1 , wherein:

a difference between the height of the plurality of ridges and an integer multiple of the grating period divided by the tangent of the slant angle is less than a threshold value.

3. The waveguide display of claim 2 , wherein:

the threshold value is equal to or less than 10% of the height of the plurality of ridges.

4. The waveguide display of claim 1 , further comprising:

an anti-reflective coating on a second surface of the two opposite surfaces of the substrate.

5. The waveguide display of claim 1 , further comprising:

an anti-reflective coating on a surface of the slanted grating opposite to the first surface of the two opposite surfaces of the substrate.

6. The waveguide display of claim 1 , further comprising:

an over-coat layer on a surface of the slanted grating opposite to the first surface of the two opposite surfaces of the substrate.

7. The waveguide display of claim 1 , wherein:

a difference between the height of the plurality of ridges and the grating period divided by the tangent of the slant angle is less than a threshold value.

8. The waveguide display of claim 1 , wherein:

the slanted grating comprises a surface-relief grating.

9. The waveguide display of claim 1 , wherein:

the slant angle is greater than 50 degrees.

10. The waveguide display of claim 1 , wherein:

the slanted grating comprises a two-dimensional grating.

11. The waveguide display of claim 1 , wherein:

the substrate is configured to reflect display light at the two opposite surfaces by total internal reflection; and

the slanted grating is arranged with respect to the substrate to reflectively diffract the display light and transmissively diffract the ambient light from an environment in front of the waveguide display.

12. The waveguide display of claim 1 , wherein:

the substrate is configured to reflect display light at the two opposite surfaces by total internal reflection; and

the slanted grating is arranged with respect to the substrate to transmissively diffract the display light and the ambient light from an environment in front of the waveguide display.

13. A grating coupler comprising:

a slanted grating characterized by a grating period, the slanted grating comprising a plurality of slanted ridges, wherein:

the plurality of slanted ridges is characterized by a height and a slant angle with respect to a surface normal of the slanted grating; and

a difference between the height of the plurality of slanted ridges and an integer multiple of the grating period divided by the tangent of the slant angle is less than a threshold value such that ambient light diffracted in ±1st diffraction orders by an upper portion of the slanted grating at least partially destructively interferes with ambient light diffracted in ±1st diffraction orders by a lower portion of the slanted grating.

14. The grating coupler of claim 13 , wherein:

the height of the plurality of slanted ridges is equal to the grating period divided by the tangent of the slant angle.

15. The grating coupler of claim 13 , further comprising:

an over-coat layer on the slanted grating, wherein:

the over-coat layer fills gaps between the plurality of slanted ridges; and

a refractive index of the over-coat layer is different from a refractive index of the plurality of slanted ridges.

16. An optical element comprising:

a slanted grating configured to:

destructively interfere at least a portion of ambient light diffracted in both +1st order and −1st order by the slanted grating; and

transmit the ambient light in 0th diffraction order.

17. A near-eye display comprising:

an image source;

a waveguide;

an input coupler configured to couple display light from the image source into the waveguide; and

an output coupler coupled to the waveguide and configured to:

transmit ambient light from an environment in front of the near-eye display; and

couple the display light out of the waveguide,

wherein:

the output coupler comprises a slanted grating characterized by a grating period, the slanted grating comprising a plurality of slanted ridges;

the plurality of slanted ridges is characterized by a height and a slant angle with respect to a surface normal of the slanted grating; and

a difference between the height of the plurality of slanted ridges and an integer multiple of the grating period divided by the tangent of the slant angle is less than a threshold value such that ambient light diffracted in ±1st diffraction orders by an upper portion of the slanted grating at least partially destructively interferes with ambient light diffracted in ±1st diffraction orders by a lower portion of the slanted grating.

18. The near-eye display of claim 17 , further comprising:

an anti-reflective coating on a surface of the waveguide opposite to the output coupler.

19. The near-eye display of claim 17 , further comprising:

an anti-reflective coating on a surface of the output coupler opposite to the waveguide.

20. The near-eye display of claim 17 , wherein the output coupler further comprises:

an over-coat layer on the slanted grating, wherein:

the over-coat layer fills gaps between the plurality of slanted ridges; and

a refractive index of the over-coat layer is different from a refractive index of the plurality of slanted ridges.