Birefringent polymer based surface relief grating

1. A waveguide display comprising:

a substrate transparent to at least one of visible or near infrared light; and

a surface relief grating on the substrate, wherein:

the surface relief grating includes ridges formed using a birefringent material and is configured to:

diffract incident light in a first polarization state from a light source into the substrate, or diffract the incident light in the first polarization state and propagating within the substrate out of the substrate towards an eye of a user; and

transmit incident light in a second polarization state orthogonal to the first polarization state without changing a propagation direction of the incident light in the second polarization state; and

the birefringent material in the ridges is characterized by an optic axis in a constant direction parallel to a plane that includes a grating vector of the surface relief grating.

2. The waveguide display of claim 1 , wherein the birefringent material is characterized by a birefringence greater than 0.05.

3. The waveguide display of claim 2 , wherein the birefringent material is characterized by the birefringence greater than 0.1.

4. The waveguide display of claim 1 , wherein the birefringent material includes at least one of a birefringent polymer, a birefringent ceramic, an aligned liquid crystal polymer, or aligned single crystal organic molecules.

5. The waveguide display of claim 4 , wherein the birefringent material includes polyethylene naphthalate (PEN) or polyethylene terephthalate.

6. The waveguide display of claim 1 , wherein the birefringent material includes a uniaxial birefringent material or a biaxial birefringent material.

7. The waveguide display of claim 1 , wherein the plane includes the grating vector of the surface relief grating and a lateral extension direction of the ridges.

8. The waveguide display of claim 1 , further comprising an overcoat layer characterized by a refractive index matching a refractive index of the birefringent material.

9. The waveguide display of claim 1 , wherein the surface relief grating includes a transmissive grating or a reflective grating.

10. The waveguide display of claim 1 , wherein the surface relief grating is configured to diffract the incident light in the first polarization state from the light source into the substrate at a first angle such that the incident light coupled into the substrate propagates within the substrate through total internal reflection.

11. The waveguide display of claim 10 , further comprising a second grating configured to selectively couple the incident light in the first polarization state and propagating within the substrate out of the substrate.

12. The waveguide display of claim 1 , further comprising a light source or a polarizer configured to generate the incident light in the first polarization state.

13. The waveguide display of claim 1 , wherein the birefringent material in the ridges is characterized by a higher index axis parallel to the plane that includes the grating vector of the surface relief grating.

14. The waveguide display of claim 1 , wherein the surface relief grating includes a one-dimensional grating or a two-dimensional grating.

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

a polarization selective reflective layer on the substrate and configured to reflect light in the second polarization state, wherein the polarization selective reflective layer and the surface relief grating are on opposite sides of the substrate; or

a second grating on the substrate and configured to reflectively diffract light in the second polarization state, wherein the second grating and the surface relief grating are on opposite sides of the substrate.

16. A surface relief grating comprising:

a substrate; and

a plurality of ridges formed using a birefringent material,

wherein the birefringent material in the plurality of ridges is characterized by an optic axis in a constant direction parallel to a plane that includes a grating vector of the surface relief grating such that the surface relief grating is configured to:

diffract incident light in a first polarization state from a light source into the substrate, or diffract the incident light in the first polarization state and propagating within the substrate out of the substrate towards an eye of a user; and;

transmit incident light in a second polarization state orthogonal to the first polarization state without changing a propagation direction of the incident light in the second polarization state.

17. The surface relief grating of claim 16 , wherein the substrate includes a reflective surface.

18. The surface relief grating of claim 16 , wherein the birefringent material includes a uniaxial or biaxial birefringent material that includes at least one of a birefringent polymer, a birefringent ceramic, an aligned liquid crystal polymer, or aligned single crystal organic molecules and is characterized by a birefringence greater than 0.1.

19. The surface relief grating of claim 16 , wherein the plurality of ridges includes a two-dimensional array of three-dimensional microstructures.

20. The surface relief grating of claim 19 , wherein the two-dimensional array of three-dimensional microstructures includes at least one of cylindrical pillars, cuboidal pillars, cavities, or pyramids.

21. The surface relief grating of claim 16 , wherein:

the birefringent material includes a uniaxial birefringent material; and

the optic axis is parallel to a polarization direction of the incident light in the first polarization state.

22. The surface relief grating of claim 16 , wherein the plurality of ridges is characterized by a pitch greater than a wavelength of the incident light in the surface relief grating.

23. The surface relief grating of claim 16 , further comprising an overcoat layer on the plurality of ridges, the overcoat layer characterized by a refractive index matching a refractive index of the birefringent material.