Display device having a diffraction grating with reduced polarization sensitivity

Abstract

A display device having a diffraction grating with reduced polarization sensitivity is provided. Blazed diffraction gratings provide optical elements within head-mounted display systems, for example, to in-couple light into or out-couple light from a waveguide. These blazed diffraction gratings may be configured to have reduced polarization sensitivity. Such gratings may, for example, in-couple or out-couple light of different polarizations with similar levels of efficiency. The blazed diffraction gratings and waveguides may be formed within a high-index substrate, such as lithium niobate. In some implementations, the blazed diffraction gratings may include diffractive features having feature heights of 40 nm to 120 nm, e.g., 80 nm. The diffractive features may be etched into the high-index substrate, e.g., lithium niobate.

Description

[Technical Field]

[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of priority to U.S. Provisional Application No. 62 / 876,205, filed July 19, 2019, and entitled "DISPLAY DEVICE HAVING DIFFRACTION GRATINGS WITH REDUCED POLARIZATION SENSITIVITY," and U.S. Provisional Application No. 62 / 902,328, filed September 18, 2019, and entitled "DISPLAY DEVICE HAVING DIFFRACTION GRATINGS WITH REDUCED POLARIZATION SENSITIVITY," the contents of which are incorporated herein by reference in their entireties. (Incorporated by reference)

[0002] This application is incorporated by reference into the following patent applications: U.S. Patent Application No. 14 / 555,585, filed November 27, 2014, published on July 23, 2015 as U.S. Patent Publication No. 2015 / 0205126; U.S. Patent Application No. 14 / 555,585, filed April 18, 2015, published on October 22, 2015 as U.S. Patent Publication No. 2015 / 0302652; No. 690,401, U.S. Patent Application No. 14 / 212,961, filed March 14, 2014, issued August 16, 2016, now U.S. Patent No. 9,417,452, and U.S. Patent Application No. 14 / 331,218, filed July 14, 2014, published October 29, 2015 as U.S. Patent Publication No. 2015 / 0309263, each of which is incorporated in its entirety.

[0003] The present disclosure relates to display systems, and more particularly to augmented and virtual reality display systems. [Background technology]

[0004] Description of Related Art Modern computing and display technologies have facilitated the development of systems for so-called "virtual reality" or "augmented reality" experiences, in which digitally reproduced images or portions thereof are presented to a user in a manner that appears or can be perceived as real. Virtual reality, or "VR," scenarios typically involve the presentation of digital or virtual image information without transparency to other actual real-world visual input, while augmented reality, or "AR," scenarios typically involve the presentation of digital or virtual image information as an augmentation to the user's visualization of the real world around them. Mixed reality, or "MR," scenarios are a type of AR scenario that typically involve virtual objects integrated into and responsive to the natural world. For example, in an MR scenario, AR image content may be perceived as occluded by or otherwise interacting with objects in the real world.

[0005] Referring to Figure 1, an augmented reality scene 10 is depicted in which a user of the AR technology sees a real-world park-like setting 20 featuring people, trees, a building in the background, and a concrete platform 30. In addition to these items, the user of the AR technology also perceives that they "see" "virtual content," such as a robotic figure 40 standing on the real-world platform 30 and a flying, cartoon-like avatar character 50 that appears to be an anthropomorphic bumblebee, although these elements 40, 50 do not exist in the real world. The human visual perception system is complex, making it difficult to produce AR technology that facilitates a pleasant, natural-feeling, and rich presentation of virtual image elements among other virtual or real-world image elements.

[0006] The systems and methods disclosed herein address various challenges associated with AR and VR technologies. Summary of the Invention [Means for solving the problem]

[0007] In one aspect, a head-mounted display system includes a head-mountable frame, an optical projection system configured to output light and provide image content, and a waveguide supported by the frame. The waveguide includes a substrate including a material having a refractive index of at least 1.9. The substrate is configured to guide at least a portion of the light from the optical projection system to be coupled into the waveguide. The head-mounted display system additionally includes a blazed diffraction grating formed in the substrate or in a layer disposed over the substrate. The blazed diffraction grating has a first diffraction efficiency for a first polarization over a range of angles of light incident thereon and a second diffraction efficiency for a second polarization over a range of angles of light incident thereon. The first diffraction efficiency is one to two times the second diffraction efficiency.

[0008] In another aspect, an optical waveguide includes a substrate including a material having a refractive index of at least 1.9. The substrate is configured to guide light coupled into the waveguide within the waveguide via total internal reflection. The optical waveguide additionally includes a blazed diffraction grating formed in the substrate or in a layer disposed over the substrate. The blazed diffraction grating has a first diffraction efficiency for a first polarization over a range of angles for light incident thereon and a second diffraction efficiency for a second polarization over a range of angles for light incident thereon. The first diffraction efficiency is one to two times the second diffraction efficiency. The present invention provides, for example, the following. (Item 1) 1. A head-mounted display system, comprising: A head mountable frame; a light projection system configured to output light and provide image content; a waveguide supported by the frame, the waveguide comprising a substrate comprising a material having a refractive index of at least 1.9, the substrate configured to guide at least a portion of light from the optical projection system such that the light is coupled into the waveguide; and a blazed diffraction grating formed in the substrate or in a layer disposed across the substrate; Equipped with 1. A head-mounted display system, wherein the blazed diffraction grating has a first diffraction efficiency for a first polarization over a range of angles of light incident thereon and a second diffraction efficiency for a second polarization over a range of angles of light incident thereon, the first diffraction efficiency being between 1 and 2 times the second diffraction efficiency. (Item 2) Item 1. A head-mounted display system as described in item 1, wherein the blazed diffraction grating is formed within the substrate and arranged to be in optical communication with the substrate. (Item 3) Item 1. A head-mounted display system as described in item 1, wherein the blazed diffraction grating is in a layer disposed across the substrate and arranged to be in optical communication with the substrate. (Item 4) Item 4. The head-mounted display system of item 3, wherein the layer is in physical contact with the substrate. (Item 5) Item 10. The head-mounted display system of item 1, wherein the material having a refractive index of at least 1.9 comprises a lithium-based oxide, silicon carbide, zirconium dioxide, or titanium dioxide. (Item 6) Item 1. A head-mounted display system as described in item 1, wherein the blazed diffraction grating is formed in a layer disposed across the substrate, the layer comprising silicon nitride, zirconium dioxide, titanium dioxide, or silicon carbide. (Item 7) Item 1. A head-mounted display system as described in item 1, wherein the blazed diffraction grating is formed in a layer disposed over the substrate, the layer having a lower refractive index than the substrate. (Item 8) Item 2. The head-mounted display system according to item 1, wherein the material has a refractive index of at least 2.0 to 2.7. (Item 9) Item 10. The head-mounted display system of item 1, wherein the blazed diffraction grating comprises diffractive features with points spaced apart by grooves therebetween. (Item 10) Item 1. A head-mounted display system as described in item 1, wherein the blazed diffraction grating has diffractive features comprising a plurality of straight lines. (Item 11) Item 11. The head-mounted display system of item 10, wherein the plurality of straight lines comprises discontinuous straight lines. (Item 12) Item 1. A head-mounted display system as described in item 1, wherein the blazed diffraction grating comprises diffractive features comprising a plurality of pillars protruding from the surface of the substrate. (Item 13) Item 1. The head-mounted display system of item 1, wherein the blazed diffraction grating comprises diffractive features having a peak height or groove depth of 10 to 150 nm. (Item 14) Item 10. The head-mounted display system of item 1, wherein the diffractive features are asymmetric. (Item 15) Item 2. The head-mounted display system according to item 1, wherein the blazed diffraction grating has a pitch of 250 to 350 nm. (Item 16) Item 1. A head-mounted display system according to item 1, wherein the blazed diffraction grating has a pitch of 300 to 450 nm. (Item 17) Item 1. A head-mounted display system according to item 1, wherein the substrate is planar and the blazed diffraction grating has a blaze angle of 10 to 30 degrees relative to the plane of the substrate. (Item 18) 2. The head mounted display system according to item 1, wherein the first diffraction efficiency is 1 to 1.5 times the second diffraction efficiency. (Item 19) Item 2. The head-mounted display system of item 1, wherein the range of angles is at least 6 degrees. (Item 20) Item 2. A head-mounted display system as described in item 1, wherein the angle range is between ±3 degrees relative to the plane of the substrate. (Item 21) Item 1. A head-mounted display system as described in item 1, wherein the first and second polarizations comprise first and second linear polarizations having different polarization angles. (Item 22) Item 1. A head-mounted display system as described in item 1, wherein the first and second polarizations comprise first and second linear polarizations oriented in orthogonal directions. (Item 23) Item 1. A head-mounted display system as described in item 1, wherein the first polarization comprises one of transverse magnetic and transverse electric polarization, and the second polarization comprises the other of transverse magnetic and transverse electric polarization. (Item 24) Item 1. A head-mounted display system as described in item 1, wherein the first diffraction efficiency comprises a diffraction efficiency for one of transverse magnetic polarization and transverse electric polarization averaged across the visible light spectrum, and the second diffraction efficiency comprises a diffraction efficiency for the other of transverse magnetic polarization and transverse electric polarization averaged across the visible light spectrum. (Item 25) Item 1. The head-mounted display system of item 1, wherein the blazed diffraction grating has a diffraction efficiency for red wavelengths of light having the first polarization that is 1 to 2 times the diffraction efficiency for red wavelengths of the second polarization. (Item 26) Item 1. The head-mounted display system of item 1, wherein the blazed diffraction grating has a diffraction efficiency for green wavelengths of light having the first polarization that is 1 to 1.5 times the diffraction efficiency for green wavelengths of the second polarization. (Item 27) Item 1. The head-mounted display system according to item 1, wherein the blazed diffraction grating has a diffraction efficiency for blue wavelengths of light having the first polarization that is 0.7 to 1 times the diffraction efficiency for blue wavelengths of light having the second polarization. (Item 28) Item 1. A head-mounted display system as described in item 1, wherein the waveguide is contained within an eyepiece configured to direct light to the eye of a user wearing the head-mounted display. (Item 29) Item 29. A head-mounted display system as described in Item 28, wherein the eyepiece is positioned on the frame and configured to direct light from the optical projection system into the user's eye and display augmented reality image content in the user's field of view, at least a portion of the eyepiece is transparent and is positioned in front of the user's eye when the user wears the head-mounted display system, and the transparent portion allows light from a portion of the physical environment in front of the user to pass through to the user's eye and provide a view of a portion of the physical environment in front of the user. (Item 30) 29. The head-mounted display system of item 28, wherein the eyepiece lens comprises the at least one waveguide, and the at least one waveguide is transparent to visible light so that the user can see through the waveguide. (Item 31) Item 1, a head-mounted display system, wherein the waveguide comprises an internal coupling optical element for coupling light from the optical projection system into the waveguide so that the light is guided therein. (Item 32) Item 1, a head-mounted display system, wherein the waveguide comprises an external coupling optical element for coupling light from the optical projection system out of the waveguide, directing the light to the user's eye, and presenting the image content to the viewer. (Item 33) Item 1. The head-mounted display system of item 1, wherein the blazed diffraction grating comprises an internal coupling grating (ICG) configured to internally couple light from the optical projection system into the waveguide. (Item 34) Item 1, a head-mounted display system, wherein the blazed diffraction grating comprises an external coupling grating (EPE) configured to externally couple light from the optical projection system guided within the waveguide out of the waveguide. (Item 35) Item 1, a head-mounted display system, wherein the blazed diffraction grating comprises diffractive features formed in a one-dimensional (1D) array. (Item 36) Item 1, a head-mounted display system, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array. (Item 37) Item 37. The head-mounted display system of item 36, wherein the two-dimensional (2D) array comprises a square array. (Item 38) Item 1. The head-mounted display system of item 1, wherein the blazed diffraction grating comprises a 1D grating. (Item 39) Item 1. The head-mounted display system of item 1, wherein the blazed diffraction grating comprises a 2D grating. (Item 40) Item 1. The head-mounted display system of item 1, wherein the blazed diffraction grating comprises a 2D grating comprising a square array. (Item 41) Item 10. The head-mounted display system of item 1, wherein the blazed diffraction grating is configured to preferentially direct light in two or more directions. (Item 42) Item 1, a head-mounted display system, wherein the blazed diffraction grating comprises an internal coupling optical element arranged to receive light from an image source and couple the light into the substrate so that it is guided therein. (Item 43) Item 1, a head-mounted display system, wherein the blazed diffraction grating comprises a light-dispersing optical element arranged to receive light from an image source guided within the substrate and direct the light to an external coupling optical element to be coupled out of the substrate. (Item 44) Item 1, a head-mounted display system, wherein the blazed diffraction grating comprises a light-dispersing optical element arranged to receive light from an image source guided within the substrate and spread the light within the waveguide to increase the beam size or eyebox size. (Item 45) Item 1, a head-mounted display system, wherein the blazed diffraction grating comprises an external coupling optical element positioned to receive light from an image source guided within the substrate and couple the light out of the substrate. (Item 46) Item 1. A head-mounted display system as described in item 1, wherein the blazed diffraction grating comprises a combined light dispersing / outcoupling optical element arranged to receive light from an image source guided within the substrate, diffuse the light in at least two directions, and couple the light out from the substrate. (Item 47) Item 1. A head-mounted display system as described in item 1, wherein the blazed diffraction grating comprises an associated pupil expander-extractor arranged to receive light from an image source guided within the substrate, diffuse the light, and couple the light out of the substrate. (Item 48) An optical waveguide, a substrate comprising a material having a refractive index of at least 1.9, the substrate being configured to guide light coupled into the waveguide within the waveguide via total internal reflection; a blazed diffraction grating formed in the substrate or in a layer disposed across the substrate; Equipped with an optical waveguide, wherein the blazed diffraction grating has a first diffraction efficiency for a first polarization over a range of angles for light incident thereon, and a second diffraction efficiency for a second polarization over a range of angles for light incident thereon, the first diffraction efficiency being between 1 and 2 times the second diffraction efficiency. (Item 49) Item 49. The optical waveguide of item 48, wherein the blazed grating is formed in the substrate and arranged in optical communication with the substrate. (Item 50) Item 49. The optical waveguide of item 48, wherein the blazed grating is in a layer disposed over the substrate and arranged to be in optical communication with the substrate. (Item 51) Item 51. The optical waveguide of item 50, wherein the layer is in physical contact with the substrate. (Item 52) Item 49. The optical waveguide of item 48, wherein the material having a refractive index greater than 1.9 comprises a lithium-based oxide, silicon carbide, zirconium dioxide, or titanium dioxide. (Item 53) Item 49. The optical waveguide of item 48, wherein the blazed grating is formed in a layer disposed over the substrate, the layer comprising silicon nitride, zirconium dioxide, titanium dioxide, or silicon carbide. (Item 54) Item 49. The optical waveguide of item 48, wherein the blazed grating is formed in a layer disposed over the substrate, the layer having a lower refractive index than the substrate. (Item 55) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises diffractive features having a tip height or groove depth of 10 to 150 nm. (Item 56) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises diffractive features comprising a plurality of straight lines. (Item 57) Item 57. The optical waveguide of item 56, wherein the plurality of straight lines comprises discontinuous straight lines. (Item 58) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises diffractive features comprising a plurality of posts protruding from a surface of the substrate. (Item 59) Item 49. The optical waveguide of item 48, wherein the diffractive features are asymmetric. (Item 60) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises diffractive features formed in a one-dimensional (1D) array. (Item 61) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array. (Item 62) Item 62. The optical waveguide of item 61, wherein the two-dimensional (2D) array comprises a square array. (Item 63) Item 49. The optical waveguide of item 48, wherein the blazed grating comprises a 1D grating. (Item 64) Item 49. The optical waveguide of item 48, wherein the blazed grating comprises a 2D grating. (Item 65) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises a 2D grating comprising a square array. (Item 66) Item 49. The optical waveguide of item 48, wherein the blazed grating is configured to direct light preferentially in two or more directions. (Item 67) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises an internal coupling optical element positioned to receive light from an image source and couple the light into the substrate so that it is guided therein. (Item 68) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises a light dispersing optical element positioned to receive light from an image source guided within the substrate and direct the light to an outcoupling optical element to be coupled out of the substrate. (Item 69) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises a light-dispersing optical element positioned to receive light from an image source guided within the substrate and spread the light within the waveguide to increase beam size or eyebox size. (Item 70) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises an outcoupling optical element positioned to receive light from an image source guided within the substrate and couple the light out of the substrate. (Item 71) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises a combined light dispersing / outcoupling optical element arranged to receive light from an image source guided within the substrate, diffuse the light in at least two directions, and couple the light out from the substrate. (Item 72) Item 49. The optical waveguide of item 48, wherein the blazed diffraction grating comprises an associated pupil expander-extractor positioned to receive light from an image source guided within the substrate, diffuse the light, and couple the light out of the substrate. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 illustrates a user's view of an augmented reality (AR) device.

[0010] [Figure 2] FIG. 2 illustrates a conventional display system for simulating a three-dimensional image for a user.

[0011] [Figure 3] 3A-3C illustrate the relationship between the radius of curvature and the radius of focus.

[0012] [Figure 4A] Figure 4A illustrates the representation of the accommodation-vergence-divergence motor response of the human visual system.

[0013] [Figure 4B] FIG. 4B illustrates examples of different accommodation and convergence states of a pair of eyes of a user.

[0014] [Figure 4C] FIG. 4C illustrates an example of a top-down view representation of a user viewing content through a display system.

[0015] [Figure 4D] FIG. 4D illustrates another example of a top-down view representation of a user viewing content through a display system.

[0016] [Figure 5] FIG. 5 illustrates aspects of an approach for simulating three-dimensional images by correcting for wavefront divergence.

[0017] [Figure 6] FIG. 6 illustrates an embodiment of a waveguide stack for outputting image information to a user.

[0018] [Figure 7] FIG. 7 illustrates an example of an output beam output by a waveguide.

[0019] [Figure 8] FIG. 8 illustrates an example of a stacked waveguide assembly in which each depth plane contains an image formed using multiple different primary colors.

[0020] [Figure 9A] FIG. 9A illustrates a cross-sectional side view of an example of a set of stacked waveguides, each including an internal coupling optical element.

[0021] [Figure 9B] FIG. 9B illustrates a perspective view of the multiple stacked waveguide embodiment of FIG. 9A.

[0022] [Figure 9C] FIG. 9C illustrates a top-down plan view of the multiple stacked waveguide embodiment of FIGS. 9A and 9B.

[0023] [Figure 9D] FIG. 9D illustrates an example of a wearable display system.

[0024] [Figure 10A] FIG. 10A schematically illustrates a cross-sectional view of a portion of a waveguide having a diffraction grating disposed thereon, for example, to incouple light into the waveguide.

[0025] [Figure 10B] FIG. 10B illustrates a cross-sectional view of a waveguide having a blazed grating disposed thereon, showing the field of view (FOV) Δα of the waveguide.

[0026] [Figure 11A] FIG. 11A illustrates an etching process for forming a waveguide having a single-stage blazed grating disposed thereon.

[0027] [Figure 11B] FIG. 11B is a scanning electron micrograph of a single-stage blazed photoresist grating.

[0028] [Figure 11C] FIG. 11C illustrates an etching process for forming a waveguide having a multi-stage blazed grating disposed thereon.

[0029] [Figure 11D] FIG. 11D is a scanning electron micrograph of a multi-stage blazed photoresist grating.

[0030] [Figure 11E] FIG. 11E illustrates a cross-sectional side view of two different blazed geometries for a diffraction grating.

[0031] [Figure 12A] 12A-12F show scanning electron micrographs of various substrates with blazed diffraction gratings formed thereon, with different blazed geometries. [Figure 12B] 12A-12F show scanning electron micrographs of various substrates with blazed diffraction gratings formed thereon, with different blazed geometries. [Figure 12C] 12A-12F show scanning electron micrographs of various substrates with blazed diffraction gratings formed thereon, with different blazed geometries. [Figure 12D] 12A-12F show scanning electron micrographs of various substrates with blazed diffraction gratings formed thereon, with different blazed geometries. [Figure 12E] 12A-12F show scanning electron micrographs of various substrates with blazed diffraction gratings formed thereon, with different blazed geometries. [Figure 12F] 12A-12F show scanning electron micrographs of various substrates with blazed diffraction gratings formed thereon, with different blazed geometries.

[0032] [Figure 13] FIG. 13 is a plot of the ratio of the diffraction efficiency of transverse magnetic (TM) polarized light to the diffraction efficiency of transverse electric (TE) polarized light as a function of the angle of incidence for various diffraction gratings having different blazed geometries.

[0033] [Figure 14] FIG. 14 is a plot of the ratio of the diffraction efficiency of transverse magnetic (TM) polarization to the diffraction efficiency of transverse electric (TE) polarization as a function of incident angle for a diffraction grating having diffractive features with 80 nm tip height or groove depth for green, blue, and red wavelengths.

[0034] [Figure 15] FIG. 15 is a plot of diffraction efficiency for a grating having an 80 nm tip height or groove depth for green, blue, and red wavelengths.

[0035] [Figure 16] FIG. 16 illustrates the coherence uniformity of a blazed photoresist grating for unpolarized and linearly polarized inputs.

[0036] [Figure 17] FIG. 17 illustrates the coherence uniformity of a blazed grating etched into a lithium niobate substrate for unpolarized and linearly polarized inputs.

[0037] [Figure 18] FIG. 18 is a perspective view of a two-dimensional (2D) diffraction grating comprising a two-dimensional array of blazed diffractive features.

[0038] [Figure 18A] 18A and 18B are cross-sectional and plan views, respectively, of a 2D diffraction grating having a two-dimensional array of blazed diffractive features. [Figure 18B] 18A and 18B are cross-sectional and plan views, respectively, of a 2D diffraction grating having a two-dimensional array of blazed diffractive features.

[0039] [Figure 19A] FIG. 19A is a perspective view of a 2D diffraction grating having a two-dimensional array of diffractive features that are blazed in two directions.

[0040] [Figure 19B] FIG. 19B illustrates how a 2D diffraction grating, which has a two-dimensional array of diffractive features that are blazed in two directions, can direct light preferentially in different directions.

[0041] [Figure 20A] 20A and 20B are schematic diagrams of a method for fabricating a blazed grating using a master template. [Figure 20B] 20A and 20B are schematic diagrams of a method for fabricating a blazed grating using a master template.

[0042] [Figure 21] FIG. 21 is a schematic diagram of a method for fabricating a blazed grating using different master templates.

[0043] Throughout the drawings, reference numbers may be reused to indicate correspondence between referenced elements. The drawings are provided to illustrate example embodiments described herein and are not intended to limit the scope of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0044] Detailed Description The AR system may display virtual content to a user or viewer while still allowing the user to see the world around them. Preferably, this content is displayed on a head-mounted display, for example, as part of eyewear that projects image information to the user's eyes. In addition, the display may also transmit light from the surrounding environment to the user's eyes, allowing a view of the surrounding environment. As used herein, it should be understood that a "head-mounted" or "head-mountable" display is a display that can be mounted on the viewer's or user's head.

[0045] In some AR systems, virtual / augmented / composite displays with a relatively wide field of view (FOV) can enhance the viewing experience. The FOV of a display depends on the angle of light output by the eyepiece waveguide through which the viewer sees the projected image into their eye. A waveguide with a relatively high refractive index, e.g., 2.0 or greater, can provide a relatively high FOV. However, to efficiently couple light into a high-index waveguide, the diffractive optical coupling element should also have a correspondingly high refractive index. To achieve this goal, among other advantages, some displays for AR systems according to embodiments described herein include a waveguide including a relatively high refractive index (e.g., greater than or equal to 2.0) material, such as a Li-based oxide, with a correspondingly high refractive index, having a separate diffraction grating formed thereon. For example, the diffraction grating may be formed on a Li-based oxide waveguide by directly patterning a surface portion of the waveguide formed from the Li-based oxide.

[0046] Some high-index diffractive optical coupling elements, such as internal or external coupling optical elements, have strong polarization dependence. For example, an internal coupling grating (ICG) for internally coupling light into a waveguide, where the diffractive optical coupling element comprises a high-index material, may accept significantly more light of a given polarization than light of another polarization. Such an element may, for example, internally couple light with TM polarization into a waveguide at approximately three times the rate of light with TE polarization. Diffractive optical coupling elements with this type of polarization dependence may have reduced efficiency (due to poor efficiency and general blocking of certain polarizations) and may also create coherence artifacts, reducing the uniformity of the far-field image formed by the light coupled out of the waveguide. To obtain a diffractive optical coupling element that is polarization-insensitive or at least has reduced polarization sensitivity (e.g., couples light with relatively polarization-independent efficiency), some displays for AR systems according to various implementations described herein include a waveguide with a diffraction grating formed with a blazed geometry. Diffraction gratings may also be formed directly within a waveguide, which may include a high refractive index material (e.g., having a refractive index of at least 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, or up to 2.7, or any range between any of these values). Diffraction gratings may be formed within high refractive index materials, such as Li-based oxides like lithium niobate (LiNbO) or lithium tantalate (LiTaO), or zirconium oxide (ZrO), titanium dioxide (TiO), or silicon carbide (SiC), for example, by patterning the high refractive index material with a blazed geometry.

[0047] Reference will now be made to the drawings in which like reference numerals refer to like parts throughout. Unless otherwise indicated, the drawings are schematic and are not necessarily drawn to scale.

[0048] FIG. 2 illustrates a conventional display system for simulating a three-dimensional image for a user. It should be understood that when a user's eyes are spaced apart and viewing a real object in space, each eye may have a slightly different view of the object, forming an image of the object at a different location on each eye's retina. This may be referred to as binocular disparity and may be utilized by the human visual system to provide the perception of depth. Conventional display systems simulate binocular disparity by presenting two distinct images 190, 200, one for each eye 210, 220, with slightly different views of the same virtual object, corresponding to the view of the virtual object as it would appear by each eye as if the virtual object were a real object at a desired depth. These images provide binocular cues that the user's visual system may interpret to derive the perception of depth.

[0049] Continuing with reference to FIG. 2 , the images 190, 200 are spaced apart from the eyes 210, 220 by a distance 230 on the z-axis. The z-axis is parallel to the optical axis of the viewer when the eyes are fixating on an object at optical infinity directly in front of the viewer. The images 190, 200 are flat and at a fixed distance from the eyes 210, 220. Based on slightly different views of the virtual object in the images presented to each eye 210, 220, the eyes may necessarily rotate so that the image of the object falls on a corresponding point on each eye's retina, maintaining single binocular vision. This rotation may cause the gaze of each eye 210, 220 to converge on a point in space where the virtual object is perceived to reside. As a result, providing three-dimensional images traditionally involves manipulating the convergence and divergence of the user's eyes 210, 220 and providing binocular cues that the human visual system interprets to provide the perception of depth.

[0050] However, creating a realistic and comfortable perception of depth is difficult. It should be understood that light from an object at different distances from the eye has a wavefront with different amounts of divergence. Figures 3A-3C illustrate the relationship between distance and light ray divergence. The distance between the object and the eye 210 is represented in order of decreasing distances R1, R2, and R3. As shown in Figures 3A-3C, light rays become more divergent as the distance to the object decreases. Conversely, as the distance increases, the light rays become more collimated. In other words, the light field generated by a point (an object or part of an object) can be said to have a spherical wavefront curvature that is a function of the distance the point is from the user's eye. The curvature increases with decreasing distance between the object and the eye 210. While only a single eye 210 is illustrated in Figures 3A-3C and other figures herein for clarity of illustration, the discussion regarding the eye 210 can apply to both eyes 210 and 220 of the viewer.

[0051] Continuing with reference to Figures 3A-3C, light from an object that a viewer's eye is fixating may have different wavefront divergences. Due to the different wavefront divergences, the light may be focused differently by the eye's lens, which in turn may require the lens to assume a different shape and form a focused image on the eye's retina. If a focused image is not formed on the retina, the resulting retinal blur acts as an accommodative cue, causing the shape of the eye's lens to change until a focused image is formed on the retina. For example, the accommodative cue may induce relaxation or contraction of the ciliary muscles surrounding the eye's lens, thereby modulating the force applied to the suspensory ligaments that hold the lens in place, thus changing the shape of the eye's lens and forming a focused image of the fixated object on the eye's retina (e.g., the fovea) until retinal blur of the fixated object is eliminated or minimized. The process by which the eye's lens changes shape can be referred to as accommodation, and the shape of the eye's lens required to form a focused image of a fixated object on the eye's retina (e.g., the fovea) can be referred to as the state of accommodation.

[0052] Referring now to Figure 4A, a representation of the accommodation-vergence response of the human visual system is illustrated. Eye movement to fixate an object causes the eye to receive light from the object, which forms an image on each of the eye's retinas. The presence of retinal blur in the image formed on the retina can provide a cue for accommodation, and the relative location of the image on the retina can provide a cue for vergence. The accommodation cue causes accommodation, leading the eye's lens to adopt a specific accommodation state that forms a focused image of the object on the eye's retina (e.g., the fovea). Conversely, the vergence cue causes vergence movement (eye rotation) so that the image formed on each retina of each eye is at the corresponding retinal point, maintaining single binocular vision. In these positions, the eyes can be said to be in a specific vergence state. Continuing with reference to FIG. 4A , accommodation can be understood as the process by which the eyes achieve a particular accommodation state, and convergence can be understood as the process by which the eyes achieve a particular convergence state. As shown in FIG. 4A , the accommodation and convergence states of the eyes can change when the user fixates on a different object. For example, the accommodated state can change when the user fixates on a new object at a different depth on the z-axis.

[0053] Without being limited by theory, it is believed that a viewer of an object may perceive the object as "three-dimensional" due to a combination of convergence-divergence and accommodation. As noted above, the convergence-divergence of the two eyes relative to one another (e.g., eye rotation such that the pupils move toward or away from one another, converging the eyes' lines of sight and fixating on an object) is closely coupled to accommodation of the eye's lenses. Under normal conditions, a change in the shape of the eye's lenses to change focus from one object to another at a different distance will automatically produce a corresponding change in convergence-divergence to the same distance, a relationship known as the "accommodation-divergence reflex." Similarly, a change in convergence-divergence will, under normal conditions, induce a corresponding change in lens shape.

[0054] 4B, an example of different accommodation and convergence states of the eyes is illustrated. Pair of eyes 222a fixates an object at optical infinity, while pair of eyes 222b fixates an object 221 at less than optical infinity. Notably, the convergence states of each pair of eyes are different: pair of eyes 222a points straight ahead, while pair of eyes 222 converge on object 221. The accommodation states of the eyes forming each pair of eyes 222a and 222b are also different, as represented by the different shapes of lenses 210a, 220a.

[0055] Unfortunately, many users of conventional "3-D" display systems may find such systems uncomfortable or may not perceive any depth perception due to a mismatch between accommodation and convergence states in these displays. As noted above, many stereoscopic or "3-D" display systems display a scene by providing a slightly different image to each eye. Such systems are uncomfortable for many viewers because, among other things, they simply provide different presentations of a scene, causing changes in the eyes' convergence states without a corresponding change in the eyes' accommodation states. Rather, images are presented by the display at a fixed distance from the eyes so that the eyes view all image information in a single accommodation state. Such an arrangement defies the "accommodation-vergence-divergence reflex" by causing changes in the convergence states without a corresponding change in the accommodation state. This mismatch is believed to cause viewer discomfort. Display systems that provide a better match between accommodation and convergence-divergence movements may produce a more realistic and comfortable simulation of three-dimensional images.

[0056] Without being limited by theory, it is believed that the human eye can typically interpret a finite number of depth planes to provide depth perception. As a result, a highly realistic simulation of perceived depth can be achieved by providing the eye with different presentations of images corresponding to each of these limited number of depth planes. In some embodiments, the different presentations can provide both vergence cues and matching cues for accommodation, thereby providing physiologically correct accommodation-vergence divergence matching.

[0057] 4B , two depth planes 240 are illustrated, corresponding to different distances in space from the eyes 210, 220. For a given depth plane 240, vergence-divergence cues may be provided by displaying appropriately different perspective images for each eye 210, 220. Additionally, for a given depth plane 240, the light forming the image provided to each eye 210, 220 may have a wavefront divergence corresponding to the light field generated by a point at the distance of that depth plane 240.

[0058] In the illustrated embodiment, the distance along the z-axis of depth plane 240 containing point 221 is 1 m. As used herein, distance or depth along the z-axis may be measured with a zero point located at the exit pupil of the user's eye. Thus, depth plane 240 located at a depth of 1 m corresponds to a distance of 1 m away from the exit pupil of the user's eye on the optical axis of the eye with the eye pointed toward optical infinity. As an approximation, the depth or distance along the z-axis may be measured from the display in front of the user's eye (e.g., from the surface of the waveguide) and a value for the distance between the device and the exit pupil of the user's eye may be added. That value may be referred to as pupil distance and corresponds to the distance between the exit pupil of the user's eye and the display worn by the user in front of the eye. In practice, the value for pupil distance may be a normalized value generally used for all viewers. For example, pupil distance may be assumed to be 20 mm, and the depth plane at a depth of 1 m may be at a distance of 980 mm in front of the display.

[0059] 4C and 4D, examples of matched accommodation-vergence-divergence distances and mismatched accommodation-vergence-divergence distances are illustrated, respectively. As illustrated in FIG. 4C, the display system may provide an image of a virtual object to each eye 210, 220. The image may cause the eyes 210, 220 to assume a convergence-divergence state in which the eyes converge on point 15 on the depth plane 240. In addition, the image may be formed by light having a wavefront curvature corresponding to the real object on that depth plane 240. As a result, the eyes 210, 220 assume an accommodation state in which the image is focused on the retinas of those eyes. Therefore, the user may perceive the virtual object as being at point 15 on the depth plane 240.

[0060] It should be understood that the accommodation and convergence states of the eyes 210, 220 are each associated with a particular distance on the z-axis. For example, an object at a particular distance from the eyes 210, 220 will cause those eyes to assume a particular accommodation state based on the distance of the object. The distance associated with a particular accommodation state is referred to as the accommodation distance A. d Similarly, a particular convergence distance V associated with the eyes in a particular convergence state or position relative to one another may be referred to as d When the accommodation distance and the convergence distance match, the relationship between accommodation and convergence is said to be physiologically correct. This is considered the most comfortable scenario for the viewer.

[0061] However, in a stereoscopic display, the accommodation distance and the vergence distance may not always coincide. For example, as illustrated in FIG. 4D , the images displayed to the eyes 210, 220 may be displayed with a wavefront divergence corresponding to the depth plane 240, and the eyes 210, 220 may be in a particular accommodation state in which points 15a, 15b on that depth plane are in focus. However, the images displayed to the eyes 210, 220 may provide a convergence cue that causes the eyes 210, 220 to converge on a point 15 that is not located on the depth plane 240. As a result, the accommodation distance, in some embodiments, corresponds to the distance from the exit pupils of the eyes 210, 220 to the depth plane 240, while the vergence distance corresponds to the greater distance from the exit pupils of the eyes 210, 220 to point 15. The accommodation distance is different from the vergence distance. As a result, there is an accommodation-vergence-divergence mismatch. Such a mismatch may be considered undesirable and may cause discomfort to the user. The mismatch may be related to distance (e.g., V d -A d ) and can be characterized in terms of diopters.

[0062] It should be understood that in some embodiments, a reference point other than the exit pupil of the eye 210, 220 may be used to determine the distance for determining accommodation-vergence mismatch, so long as the same reference point is used for accommodation distance and vergence distance. For example, the distance may be measured from the cornea to the depth plane, from the retina to the depth plane, from the eyepiece (e.g., a waveguide in a display device) to the depth plane, etc.

[0063] Without being limited by theory, it is believed that a user may still perceive accommodation-vergence-divergence mismatches of up to about 0.25 diopters, up to about 0.33 diopters, and up to about 0.5 diopters as physiologically correct without the mismatch itself causing significant discomfort. In some embodiments, a display system disclosed herein (e.g., display system 250, FIG. 6 ) presents images to a viewer with an accommodation-vergence-divergence mismatch of about 0.5 diopters or less. In some other embodiments, the accommodation-vergence-divergence mismatch of images provided by the display system is about 0.33 diopters or less. In still other embodiments, the accommodation-vergence-divergence mismatch of images provided by the display system is about 0.25 diopters or less, including about 0.1 diopters or less.

[0064] FIG. 5 illustrates aspects of an approach for simulating a three-dimensional image by modifying wavefront divergence. The display system includes a waveguide 270 configured to receive light 770 encoded with image information and output the light to a user's eye 210. The waveguide 270 may output light 650 with a defined amount of wavefront divergence that corresponds to the wavefront divergence of a light field generated by a point on a desired depth plane 240. In some embodiments, the same amount of wavefront divergence is provided for all objects presented on that depth plane. In addition, it will be illustrated that the user's other eye may be provided with image information from a similar waveguide.

[0065] In some embodiments, a single waveguide may be configured to output light with a set wavefront divergence corresponding to a single or limited number of depth planes, and / or the waveguide may be configured to output light in a limited range of wavelengths. Consequently, in some embodiments, multiple or stacked waveguides may be utilized to provide different wavefront divergences for different depth planes and / or to output light in different ranges of wavelengths. As used herein, it should be understood that a depth plane may follow the contour of a flat or curved surface.

[0066] 6 illustrates an example of a waveguide stack for outputting image information to a user. Display system 250 includes a stack of waveguides or stacked waveguide assembly 260 that can be utilized to provide a three-dimensional perception to the eye / brain using multiple waveguides 270, 280, 290, 300, 310. It should be understood that display system 250 can be considered a light field display in some embodiments. Additionally, waveguide assembly 260 can also be referred to as an eyepiece.

[0067] In some embodiments, display system 250 may be configured to provide a substantially continuous cue for convergence and multiple discrete cues for accommodation. The cues for convergence may be provided by displaying different images to each of the user's eyes, and the cues for accommodation may be provided by outputting light forming images with selectable discrete amounts of wavefront divergence. In other words, display system 250 may be configured to output light with variable levels of wavefront divergence. In some embodiments, each discrete level of wavefront divergence corresponds to a particular depth plane and may be provided by a particular one of waveguides 270, 280, 290, 300, and 310.

[0068] Continuing with reference to FIG. 6 , the waveguide assembly 260 may also include multiple features 320, 330, 340, 350 between the waveguides. In some embodiments, the features 320, 330, 340, 350 may be one or more lenses. The waveguides 270, 280, 290, 300, 310 and / or multiple lenses 320, 330, 340, 350 may be configured to transmit image information to the eye using various levels of wavefront curvature or ray divergence. Each waveguide level may be associated with a particular depth plane and configured to output image information corresponding to that depth plane. The image injection devices 360, 370, 380, 390, 400 may function as light sources for the waveguides and may each be utilized to inject image information into the waveguides 270, 280, 290, 300, 310, which may be configured to disperse incident light across each individual waveguide for output toward the eye 210, as described herein. Light exits output surfaces 410, 420, 430, 440, 450 of the image injection devices 360, 370, 380, 390, 400 and is injected into corresponding input surfaces 460, 470, 480, 490, 500 of the waveguides 270, 280, 290, 300, 310. In some embodiments, each input surface 460, 470, 480, 490, 500 may be an edge of the corresponding waveguide or a portion of a major surface of the corresponding waveguide (i.e., one of the waveguide surfaces that directly faces the world 510 or the viewer's eye 210). In some embodiments, a single beam of light (e.g., a collimated beam) may be launched into each waveguide, outputting an entire field of cloned collimated beams directed toward the eye 210 at a particular angle (and divergence) corresponding to the depth plane associated with the particular waveguide. In some embodiments, a single one of the image launch devices 360, 370, 380, 390, 400 may be associated with and launch light into multiple (e.g., three) waveguides 270, 280, 290, 300, 310.

[0069] In some embodiments, image input devices 360, 370, 380, 390, 400 are discrete displays that each generate image information for input into a corresponding waveguide 270, 280, 290, 300, 310. In some other embodiments, image input devices 360, 370, 380, 390, 400 are outputs of a single multiplexed display that may, for example, send image information via one or more optical conduits (such as fiber optic cables) to each of image input devices 360, 370, 380, 390, 400. It should be understood that the image information provided by image input devices 360, 370, 380, 390, 400 may include light of different wavelengths or colors (e.g., different primary colors, as discussed herein).

[0070] In some embodiments, light injected into the waveguides 270, 280, 290, 300, 310 is provided by a light projector system 520 comprising a light module 530, which may include light emitters such as light emitting diodes (LEDs). Light from the light module 530 may be directed via a beam splitter 550 to and modified by a light modulator 540, e.g., a spatial light modulator. The light modulator 540 may be configured to vary the perceived intensity of the light injected into the waveguides 270, 280, 290, 300, 310 and encode the light with image information. Examples of spatial light modulators include liquid crystal displays (LCDs), including liquid crystal on silicon (LCOS) displays. It should be understood that image injection devices 360, 370, 380, 390, 400 are illustrated diagrammatically, and in some embodiments, these image injection devices may represent different light paths and locations within a common projection system configured to output light into associated ones of waveguides 270, 280, 290, 300, 310. In some embodiments, the waveguides of waveguide assembly 260 may function as ideal lenses, relaying light injected into the waveguides to the user's eye. In this concept, the object may be a spatial light modulator 540, and the image may be an image on a depth plane.

[0071] In some embodiments, the display system 250 may be a scanning fiber display comprising one or more scanning fibers configured to project light in various patterns (e.g., raster scan, spiral scan, Lissajous pattern, etc.) into one or more waveguides 270, 280, 290, 300, 310 and ultimately to the viewer's eye 210. In some embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may diagrammatically represent a single scanning fiber or a bundle of scanning fibers configured to inject light into one or more waveguides 270, 280, 290, 300, 310. In some other embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may diagrammatically represent multiple scanning fibers or multiple bundles of scanning fibers, each configured to inject light into an associated one of the waveguides 270, 280, 290, 300, 310. It should be understood that one or more optical fibers may be configured to transmit light from the optical module 530 to one or more waveguides 270, 280, 290, 300, 310. It should be understood that one or more intervening optical structures may be provided between the scanning fiber or fibers and one or more waveguides 270, 280, 290, 300, 310, for example, to redirect light exiting the scanning fiber into one or more waveguides 270, 280, 290, 300, 310.

[0072] Controller 560 controls the operation of one or more of stacked waveguide assemblies 260, including the operation of image input devices 360, 370, 380, 390, 400, light source 530, and light modulator 540. In some embodiments, controller 560 is part of local data processing module 140. Controller 560 contains programming (e.g., instructions in a non-transitory medium) that coordinates the timing and provision of image information to waveguides 270, 280, 290, 300, 310, for example, according to any of the various schemes disclosed herein. In some embodiments, the controller may be a single integrated device or a distributed system connected by a wired or wireless communication channel. Controller 560 may, in some embodiments, be part of processing module 140 or 150 (FIG. 9D).

[0073] Continuing with reference to FIG. 6 , the waveguides 270, 280, 290, 300, and 310 may be configured to propagate light within each individual waveguide by total internal reflection (TIR). Each of the waveguides 270, 280, 290, 300, and 310 may be planar or have another shape (e.g., curved) with major top and bottom surfaces and edges extending between the major top and bottom surfaces. In the illustrated configuration, the waveguides 270, 280, 290, 300, and 310 may each include outcoupling optical elements 570, 580, 590, 600, and 610 configured to extract light from the waveguide by redirecting light propagating within each individual waveguide out of the waveguide and outputting image information to the eye 210. The extracted light may also be referred to as outcoupling light, and the outcoupling optical elements may also be referred to as light extraction optical elements. The extracted beam of light may be output by the waveguide at a location where light propagating within the waveguide strikes the light extraction optical element. The outcoupling optical element 570, 580, 590, 600, 610 may be, for example, a grating including diffractive optical features as discussed further herein. While shown disposed on the bottom major surface of the waveguides 270, 280, 290, 300, 310 for ease of explanation and clarity of drawing, in some embodiments, the outcoupling optical element 570, 580, 590, 600, 610 may be disposed on the top and / or bottom major surfaces and / or directly within the volume of the waveguides 270, 280, 290, 300, 310, as discussed further herein. In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 may be formed within a layer of material that is attached to a transparent substrate and forms the waveguides 270, 280, 290, 300, 310. In some other embodiments, the waveguides 270, 280, 290, 300, 310 may be a monolithic piece of material, and the outcoupling optical elements 570, 580, 590, 600, 610 may be formed on and / or within that piece of material.

[0074] Continuing with reference to FIG. 6 , as discussed herein, each waveguide 270, 280, 290, 300, 310 is configured to output light and form an image corresponding to a particular depth plane. For example, the waveguide 270 closest to the eye may be configured to deliver collimated light (injected into such waveguide 270) to the eye 210. The collimated light may represent an optical infinity focal plane. The next upper waveguide 280 may be configured to send collimated light that passes through a first lens 350 (e.g., a negative lens) before reaching the eye 210. Such first lens 350 may be configured to generate a slight convex wavefront curvature so that the eye / brain interprets light emerging from the next upper waveguide 280 as emerging from a first focal plane closer inward from optical infinity toward the eye 210. Similarly, the third upper waveguide 290 passes its output light through both the first lens 350 and the second lens 340 before reaching the eye 210. The combined refractive power of the first lens 350 and the second lens 340 may be configured to produce another, increasing amount of wavefront curvature such that the eye / brain interprets the light emerging from the third upper waveguide 290 as originating from a second focal plane that is closer inward from optical infinity towards the person than was the light from the next upper waveguide 280.

[0075] The other waveguide layers 300, 310 and lenses 330, 320 are similarly configured, with the highest waveguide 310 in the stack sending its output through all of the lenses between it and the eye for a collective focal power representing the focal plane closest to the person. To compensate for the stack of lenses 320, 330, 340, 350 when viewing / interpreting light originating from the world 510 on the other side of the stacked waveguide assembly 260, a compensating lens layer 620 may be placed on top of the stack to compensate for the collective power of the lower lens stacks 320, 330, 340, 350. Such a configuration provides as many perceived focal planes as there are available waveguide / lens pairs. Both the waveguide outcoupling optical elements and the focusing sides of the lenses may be static (i.e., not dynamic or electro-active). In some alternative embodiments, one or both may be dynamic using electro-active features.

[0076] In some embodiments, two or more of the waveguides 270, 280, 290, 300, 310 may have the same associated depth plane. For example, multiple waveguides 270, 280, 290, 300, 310 may be configured to output images set at the same depth plane, or multiple subsets of waveguides 270, 280, 290, 300, 310 may be configured to output images set at the same multiple depth planes, with one set per depth plane. This may provide advantages for forming tiled images to provide an extended field of view at those depth planes.

[0077] Continuing with reference to FIG. 6 , the outcoupling optical elements 570, 580, 590, 600, 610 may be configured to redirect light out of their respective waveguides and output the light with an appropriate amount of divergence or collimation for the particular depth plane associated with the waveguide. As a result, waveguides with different associated depth planes may have different configurations of outcoupling optical elements 570, 580, 590, 600, 610 that output light with different amounts of divergence depending on the associated depth plane. In some embodiments, the light-extracting optical elements 570, 580, 590, 600, 610 may be solid or surface features that may be configured to output light at specific angles. For example, the light-extracting optical elements 570, 580, 590, 600, 610 may be solid holograms, surface holograms, and / or diffraction gratings. In some embodiments, the features 320, 330, 340, 350 may not be lenses. Rather, they may simply be spacers (eg, cladding layers and / or structures to form an air gap).

[0078] In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 are diffractive features or "diffractive optical elements" (also referred to herein as "DOEs") that form a diffraction pattern. Preferably, the DOEs have a sufficiently low diffraction efficiency so that only a portion of the light in the beam is deflected toward the eye 210 at each intersection of the DOE, while the remainder continues traveling through the waveguide via TIR. The light carrying the image information is thus split into several related output beams that exit the waveguide at multiple locations, resulting in a very uniform pattern of output emission toward the eye 210 for this particular collimated beam bouncing within the waveguide.

[0079] In some embodiments, one or more DOEs may be switchable between an "on" state in which they actively diffract and an "off" state in which they do not significantly diffract. For example, a switchable DOE may comprise a layer of polymer-dispersed liquid crystal in which microdroplets comprise a diffractive pattern within a host medium, and the refractive index of the microdroplets may be switched to substantially match the refractive index of the host material (in which case the pattern does not significantly diffract incident light), or the microdroplets may be switched to a refractive index that does not match that of the host medium (in which case the pattern actively diffracts incident light).

[0080] In some embodiments, a camera assembly 630 (e.g., a digital camera, including visible and infrared light cameras) may be provided to capture images of the eye 210 and / or tissue surrounding the eye 210, for example, to detect user input and / or monitor the physiological state of the user. As used herein, a camera may be any image capture device. In some embodiments, the camera assembly 630 may include an image capture device and a light source that projects light (e.g., infrared light) onto the eye, which may then be reflected by the eye and detected by the image capture device. In some embodiments, the camera assembly 630 may be mounted on the frame 80 (FIG. 9D) and may be in electrical communication with processing modules 140 and / or 150, which may process image information from the camera assembly 630. In some embodiments, one camera assembly 630 may be utilized per eye, monitoring each eye separately.

[0081] 7, an example of an output beam output by a waveguide is shown. While one waveguide is illustrated, it should be understood that other waveguides in waveguide assembly 260 (FIG. 6) may function similarly, and that waveguide assembly 260 includes multiple waveguides. Light 640 is launched into waveguide 270 at input surface 460 of waveguide 270 and propagates within waveguide 270 by TIR. At the point where light 640 impinges on DOE 570, a portion of the light exits the waveguide as output beam 650. Although output beams 650 are illustrated as being approximately parallel, as discussed herein, they may also be redirected to propagate to eye 210 at an angle (e.g., forming a diverging output beam) depending on the depth plane associated with waveguide 270. It should be understood that a substantially collimated exit beam may refer to a waveguide with outcoupling optics that outcouples light to form an image that appears to be set on a depth plane at a long distance (e.g., optical infinity) from the eye 210. Other waveguides or other sets of outcoupling optics may output a more divergent exit beam pattern, which would require the eye 210 to accommodate to a closer distance and focus on the retina, and would be interpreted by the brain as light from a distance closer to the eye 210 than optical infinity.

[0082] In some embodiments, a full-color image may be formed at each depth plane by overlaying an image in each of the primary colors, for example, three or more primary colors. FIG. 8 illustrates an example of a stacked waveguide assembly in which each depth plane includes an image formed using multiple different primary colors. The illustrated embodiment shows depth planes 240a-240f, but more or fewer depths are also contemplated. Each depth plane may have three or more primary color images associated with it, including a first image in a first color G, a second image in a second color R, and a third image in a third color B. Different depth planes are indicated in the diagram by different numbers in diopters (dpt) following the letters G, R, and B. By way of example only, the number following each of these letters indicates the diopter (1 / m), i.e., the inverse distance of the depth plane from the viewer, and each box in the diagram represents an individual primary color image. In some embodiments, the exact placement of the depth planes for the different primary colors may be varied to account for differences in the eye's focusing of light of different wavelengths. For example, different primary color images for a given depth plane may be placed on depth planes corresponding to different distances from the user. Such an arrangement may increase visual acuity and user comfort and / or reduce chromatic aberration.

[0083] In some embodiments, light for each primary color may be output by a single dedicated waveguide, such that each depth plane may have multiple waveguides associated with it. In such embodiments, each box in the diagram containing the letter G, R, or B may be understood to represent an individual waveguide, and three waveguides may be provided per depth plane, with three primary color images provided per depth plane. While the waveguides associated with each depth plane are shown adjacent to each other in this drawing for ease of illustration, it should be understood that in a physical device, the waveguides may all be arranged in a stack with one waveguide per level. In some other embodiments, multiple primary colors may be output by the same waveguide, such that, for example, only a single waveguide may be provided per depth plane.

[0084] 8, in some embodiments, G is green, R is red, and B is blue. In some other embodiments, other colors associated with other wavelengths of light, including magenta and cyan, may be used in addition to or replace one or more of red, green, or blue.

[0085] It should be understood that references throughout this disclosure to a given color of light will be understood to encompass light of one or more wavelengths within the range of wavelengths of light that are perceived by a viewer as being of that given color. For example, red light may include one or more wavelengths of light in the range of about 620-780 nm, green light may include one or more wavelengths of light in the range of about 492-577 nm, and blue light may include one or more wavelengths of light in the range of about 435-493 nm.

[0086] In some embodiments, light source 530 (FIG. 6) may be configured to emit light at one or more wavelengths outside the range of a viewer's visual perception, e.g., infrared and / or ultraviolet wavelengths. Additionally, the waveguide incoupling, outcoupling, and other light redirecting structures of display 250 may be configured to direct and emit this light from the display toward the user's eye 210, e.g., for imaging and / or user stimulation applications.

[0087] Referring now to FIG. 9A , in some embodiments, light impinging on a waveguide may need to be redirected to incoupling the light into the waveguide. An incoupling optical element may be used to redirect and incoupling the light into its corresponding waveguide. FIG. 9A illustrates a cross-sectional side view of an example of a plurality or set 660 of stacked waveguides, each including an incoupling optical element. The waveguides may each be configured to output light of one or more different wavelengths or one or more different wavelength ranges. It should be understood that stack 660 may correspond to stack 260 ( FIG. 6 ), and that the illustrated waveguide of stack 660 may correspond to a portion of multiple waveguides 270, 280, 290, 300, 310, except that light from one or more of image injection devices 360, 370, 380, 390, 400 is injected into the waveguide from a location requiring the light to be redirected for incoupling.

[0088] The illustrated set 660 of stacked waveguides includes waveguides 670, 680, and 690. Each waveguide includes an associated internal coupling optical element (which may also be referred to as the light input area on the waveguide), for example, internal coupling optical element 700 is disposed on a major surface (e.g., the top major surface) of waveguide 670, internal coupling optical element 710 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and internal coupling optical element 720 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some embodiments, one or more of internal coupling optical elements 700, 710, 720 may be disposed on the bottom major surface of an individual waveguide 670, 680, 690 (particularly if one or more of the internal coupling optical elements is a reflective polarizing optical element). As shown, the internal coupling optical elements 700, 710, 720 may be disposed on the upper major surfaces of the respective waveguides 670, 680, 690 (or on top of the next lower waveguide), particularly if the internal coupling optical elements are transmissive deflecting optical elements. In some embodiments, the internal coupling optical elements 700, 710, 720 may be disposed within the body of the respective waveguides 670, 680, 690. In some embodiments, as discussed herein, the internal coupling optical elements 700, 710, 720 are wavelength selective so as to selectively redirect one or more wavelengths of light while transmitting other wavelengths of light. While illustrated on one side or corner of the respective waveguides 670, 680, 690, it should be understood that the internal coupling optical elements 700, 710, 720 may be disposed within other areas of the respective waveguides 670, 680, 690 in some embodiments.

[0089] As shown, the in-coupling optical elements 700, 710, 720 may be laterally offset from one another. In some embodiments, each in-coupling optical element may be offset to receive light without that light passing through another in-coupling optical element. For example, each in-coupling optical element 700, 710, 720 may be configured to receive light from a different image input device 360, 370, 380, 390, and 400, as shown in FIG. 6 , and may be separated (e.g., laterally spaced) from the other in-coupling optical elements 700, 710, 720 so as to substantially not receive light from others of the in-coupling optical elements 700, 710, 720.

[0090] Each waveguide also includes an associated optically dispersive element, for example, optically dispersive element 730 is disposed on a major surface (e.g., the top major surface) of waveguide 670, optically dispersive element 740 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and optically dispersive element 750 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some other embodiments, optically dispersive elements 730, 740, 750 may be disposed on the bottom major surfaces of associated waveguides 670, 680, 690, respectively. In some other embodiments, optically dispersive elements 730, 740, 750 may be disposed on both the top and bottom major surfaces of associated waveguides 670, 680, 690, respectively, or optically dispersive elements 730, 740, 750 may be disposed on different ones of the top and bottom major surfaces in different associated waveguides 670, 680, 690, respectively.

[0091] Waveguides 670, 680, 690 may be spaced apart and separated, for example, by gas, liquid, and / or solid layers of material. For example, as shown, layer 760a may separate waveguides 670 and 680, and layer 760b may separate waveguides 680 and 690. In some embodiments, layers 760a and 760b are formed from a low refractive index material (i.e., a material having a lower refractive index than the material forming the immediately adjacent ones of waveguides 670, 680, 690). Preferably, the refractive index of the material forming layers 760a, 760b is 0.05 or more, or 0.10 or less, than the refractive index of the material forming waveguides 670, 680, 690. Advantageously, the lower refractive index layers 760a, 760b may function as cladding layers that promote total internal reflection (TIR) ​​of light through the waveguides 670, 680, 690 (e.g., TIR between the top and bottom major surfaces of each waveguide). In some embodiments, the layers 760a, 760b are formed from air. Although not shown, it should be understood that the top and bottom of the illustrated set of waveguides 660 may include immediate cladding layers.

[0092] Preferably, for ease of manufacturing and other considerations, the materials forming waveguides 670, 680, 690 are similar or the same, and the materials forming layers 760a, 760b are similar or the same. In some embodiments, the materials forming waveguides 670, 680, 690 may vary between one or more waveguides, and / or the materials forming layers 760a, 760b may vary while still maintaining the various refractive index relationships described above.

[0093] 9A, light rays 770, 780, 790 enter the set of waveguides 660. It should be understood that light rays 770, 780, 790 may be injected into the waveguides 670, 680, 690 by one or more image injection devices 360, 370, 380, 390, 400 (FIG. 6).

[0094] In some embodiments, light rays 770, 780, 790 have different properties, such as different wavelengths or different wavelength ranges, which may correspond to different colors. Each of the incoupling optical elements 700, 710, 720 deflects incident light such that the light propagates through a respective one of the waveguides 670, 680, 690 by TIR. In some embodiments, each of the incoupling optical elements 700, 710, 720 selectively deflects one or more particular wavelengths of light while transmitting other wavelengths to the underlying waveguide and associated incoupling optical element.

[0095] For example, in-coupling optical element 700 may be configured to selectively deflect light ray 770 having a first wavelength or wavelength range while transmitting light rays 780 and 790 having different second and third wavelengths or wavelength ranges, respectively. Transmitted light ray 780 impinges on and is deflected by in-coupling optical element 710, which is configured to deflect light of the second wavelength or wavelength range. Light ray 790 is deflected by in-coupling optical element 720, which is configured to selectively deflect light of the third wavelength or wavelength range.

[0096] 9A , the deflected light rays 770, 780, 790 are deflected to propagate through the corresponding waveguides 670, 680, 690. That is, the in-coupling optical element 700, 710, 720 of each waveguide deflects the light into its corresponding waveguide 670, 680, 690, in-coupling the light into the corresponding waveguide. The light rays 770, 780, 790 are deflected at an angle that causes the light to propagate through the respective waveguides 670, 680, 690 by TIR. The light rays 770, 780, 790 propagate through the respective waveguides 670, 680, 690 by TIR until they impinge on the waveguide's corresponding optical dispersive element 730, 740, 750.

[0097] 9B, a perspective view of the multiple stacked waveguide embodiment of FIG. 9A is illustrated. As described above, in-coupled light rays 770, 780, 790 are deflected by in-coupling optical elements 700, 710, 720, respectively, and then propagate by TIR within waveguides 670, 680, 690, respectively. Light rays 770, 780, 790 then impinge on optically dispersive elements 730, 740, 750, respectively. Optically dispersive elements 730, 740, 750 deflect light rays 770, 780, 790 to propagate toward out-coupling optical elements 800, 810, 820, respectively.

[0098] In some embodiments, the optically dispersive elements 730, 740, 750 are orthogonal pupil expanders (OPEs). In some embodiments, the OPEs deflect or disperse light into the out-coupling optical elements 800, 810, 820, and in some embodiments, may also increase the beam or spot size of this light as it propagates into the out-coupling optical elements. In some embodiments, the optically dispersive elements 730, 740, 750 may be omitted, and the in-coupling optical elements 700, 710, 720 may be configured to deflect light directly into the out-coupling optical elements 800, 810, 820. For example, with reference to FIG. 9A , the optically dispersive elements 730, 740, 750 may be replaced with the out-coupling optical elements 800, 810, 820, respectively. In some embodiments, the outcoupling optical elements 800, 810, 820 are exit pupils (EPs) or exit pupil expanders (EPEs) that direct light into the viewer's eye 210 ( FIG. 7 ). It should be understood that an OPE can be configured to increase the size of the eyebox in at least one axis, and that the EPE can increase the eyebox in an axis that intersects the axis of the OPE, e.g., orthogonal to it. For example, each OPE may be configured to redirect a portion of the light striking the OPE to an EPE in the same waveguide, while allowing the remaining portion of the light to continue propagating down the waveguide. Again, in response to striking the OPE, another portion of the remaining light is redirected to the EPE, which continues to propagate further down the waveguide, and so on. Similarly, in response to striking the EPE, a portion of the impinging light is directed out of the waveguide toward the user, and that remaining portion of the light continues to propagate through the waveguide until it again strikes an EP, at which point another portion of the impinging light is directed out of the waveguide, and so on. As a result, a single beam of internally coupled light may be "replicated" each time a portion of that light is redirected by an OPE or EPE, thereby forming a cloned beam field of light, as shown in Figure 6. In some embodiments, the OPE and / or EPE may be configured to modify the size of the beam of light.

[0099] 9A and 9B, in some embodiments, a waveguide set 660 includes, for each primary color, waveguides 670, 680, 690, in-coupling optical elements 700, 710, 720, optically dispersive elements (e.g., OPEs) 730, 740, 750, and out-coupling optical elements (e.g., EPs) 800, 810, 820. The waveguides 670, 680, 690 may be stacked with an air gap / cladding layer between each one. The in-coupling optical elements 700, 710, 720 redirect or deflect incident light into that waveguide (with different in-coupling optical elements receiving different wavelengths of light). The light then propagates at an angle that will result in TIR within the individual waveguides 670, 680, 690. In the example shown, light ray 770 (e.g., blue light) is deflected by the first in-coupling optical element 700 in the manner previously described, then continues bouncing down the waveguide, interacting with the optically dispersive element (e.g., OPE) 730 and then the out-coupling optical element (e.g., EP) 800. Light rays 780 and 790 (e.g., green and red light, respectively) pass through the waveguide 670, with light ray 780 impinging on and being deflected by the in-coupling optical element 710. Light ray 780 then bounces down the waveguide 680, via TIR, to its optically dispersive element (e.g., OPE) 740 and then the out-coupling optical element (e.g., EP) 810. Finally, light ray 790 (e.g., red light) passes through the waveguide 690 and impinges on the optically in-coupling optical element 720 of the waveguide 690. The light in-coupling optical element 720 deflects the light ray 790 so that it propagates by TIR to the light dispersive element (e.g., OPE) 750 and then by TIR to the out-coupling optical element (e.g., EP) 820. The out-coupling optical element 820 then finally out-couples the light ray 790 to a viewer, who also receives light out-coupled from the other waveguides 670, 680.

[0100] FIG. 9C illustrates a top-down plan view of an example of the multiple stacked waveguides of FIGS. 9A and 9B. As shown, waveguides 670, 680, 690 may be vertically aligned, along with each waveguide's associated optically dispersive element 730, 740, 750 and associated out-coupling optical elements 800, 810, 820. However, as discussed herein, the in-coupling optical elements 700, 710, 720 are not vertically aligned. Rather, the in-coupling optical elements are preferably non-overlapping (e.g., laterally spaced apart, as seen in the top-down view). As discussed further herein, this non-overlapping spatial arrangement facilitates the injection of light from different sources into different waveguides on a one-to-one basis, thereby allowing a specific light source to be uniquely coupled to a specific waveguide. In some embodiments, arrays including non-overlapping, spatially separated in-coupling optical elements may be referred to as shifted-pupil systems, and the in-coupling optical elements in these arrays may correspond to sub-pupils.

[0101] 9D illustrates an example of a wearable display system 60 into which the various waveguide and associated systems disclosed herein may be integrated. In some embodiments, the display system 60 is the system 250 of FIG. 6, which diagrammatically illustrates some portions of the system 60 in greater detail. For example, the waveguide assembly 260 of FIG. 6 may be part of the display 70.

[0102] Continuing with reference to FIG. 9D , display system 60 includes display 70 and various mechanical and electronic modules and systems to support the functionality of display 70. Display 70 may be coupled to a frame 80 that is wearable by a display system user or viewer 90 and configured to position display 70 in front of the user's 90's eye. Display 70, in some embodiments, may be considered an eyepiece. In some embodiments, a speaker 100 is coupled to frame 80 and configured to be positioned adjacent to the user's 90's ear canal (in some embodiments, another speaker, not shown, may optionally be positioned adjacent the user's other ear canal to provide stereo / shapeable sound control). Display system 60 may also include one or more microphones 110 or other devices to detect sound. In some embodiments, the microphones may be configured to allow a user to provide input or commands (e.g., voice menu command selections, natural language questions, etc.) to system 60 and / or enable audio communication with other persons (e.g., other users of similar display systems). The microphone may further be configured as an ambient sensor to collect audio data (e.g., sounds from the user and / or the environment). In some embodiments, the display system may also include ambient sensor 120a, which may be separate from frame 80 and attached to the body of user 90 (e.g., on the head, torso, limbs, etc. of user 90). Ambient sensor 120a, in some embodiments, may be configured to obtain data characterizing a physiological state of user 90. For example, sensor 120a may be an electrode.

[0103] 9D , display 70 is operably coupled to local data processing module 140 by a communication link 130, such as wired or wireless connectivity, which may be mounted in a variety of configurations, such as fixedly attached to frame 80, fixedly attached to a helmet or hat worn by the user, integrated into headphones, or otherwise removably attached to user 90 (e.g., in a backpack-style configuration, in a belt-linked configuration). Similarly, sensor 120a may be operably coupled to local processor and data module 140 by a communication link 120b, such as wired or wireless connectivity. Local processing and data module 140 may comprise a hardware processor and digital memory, such as non-volatile memory (e.g., flash memory or a hard disk drive), both of which may be utilized to aid in processing, caching, and storing data. Optionally, local processor and data module 140 may include one or more central processing units (CPUs), graphics processing units (GPUs), dedicated processing hardware, etc. The data may include (a) data captured from sensors (e.g., which may be operatively coupled to frame 80 or otherwise attached to user 90), such as image capture devices (such as cameras), microphones, inertial measurement units, accelerometers, compasses, GPS units, wireless devices, gyroscopes, and / or other sensors disclosed herein, and / or (b) data obtained and / or processed using remote processing module 150 and / or remote data repository 160 (including data related to virtual content), possibly for processing or retrieval and then passing to display 70. Local processing and data module 140 may be operatively coupled to remote processing module 150 and remote data repository 160 by communication links 170, 180, such as via wired or wireless communication links, such that these remote modules 150, 160 are operatively coupled to each other and available as resources to local processing and data module 140.In some embodiments, local processing and data module 140 may include one or more of an image capture device, a microphone, an inertial measurement unit, an accelerometer, a compass, a GPS unit, a wireless device, and / or a gyroscope. In some other embodiments, one or more of these sensors may be mounted to frame 80 or may be a stand-alone structure that communicates with local processing and data module 140 by a wired or wireless communication path.

[0104] 9D , in some embodiments, remote processing module 150 may comprise one or more processors configured to analyze and process data and / or image information, including, for example, one or more central processing units (CPUs), graphics processing units (GPUs), dedicated processing hardware, etc. In some embodiments, remote data repository 160 may comprise a digital data storage facility, which may be available through the Internet or other networking configuration in a “cloud” resource configuration. In some embodiments, remote data repository 160 may include one or more remote servers that provide information, for example, information for generating augmented reality content, to local processing and data module 140 and / or remote processing module 150. In some embodiments, all data is stored and all calculations are performed in the local processing and data module, allowing for fully autonomous use from the remote module. Optionally, an external system (e.g., one or more processors, one or more computer systems), including a CPU, GPU, etc., may perform at least a portion of the processing (e.g., generating image information, processing data) and provide information to and receive information from modules 140, 150, 160, e.g., via a wireless or wired connection. (Diffraction grating with reduced polarization sensitivity)

[0105] Providing a high-quality immersive experience to users of waveguide-based display systems, such as the various display systems configured for virtual / augmented / composite display applications described above, relies, among other things, on various characteristics of light coupling into and / or out of the waveguide within the eyepiece of the display system. For example, a virtual / augmented / composite display with high light in-coupling and out-coupling efficiency can improve the viewing experience by increasing the brightness of the light directed toward the user's eye. As discussed above, an in-coupling optical element, such as an in-coupling grating, may be employed to couple light into the waveguide as guided therein by total internal reflection. Similarly, an out-coupling optical element, such as an out-coupling grating, may be employed to couple light guided within the waveguide out of the waveguide by total internal reflection.

[0106] 6 and 7, a display system according to various implementations described herein may include a combined pupil expander-extractor (CPE), which may include optical elements, such as an in-coupling optical element, an out-coupling optical element, a light-dispersing element, and / or a diffraction grating. As disclosed herein, a CPE may operate both as a light-dispersing element, which spreads or disperses light within the waveguide, potentially increasing the beam size and / or the eyebox, and as an out-coupling optical element, which couples light out of the waveguide.

[0107] 7, light 640 launched into waveguide 270 at input surface 460 of waveguide 270 propagates and is guided within waveguide 270 by total internal reflection (TIR). In various implementations, at the point where light 640 impinges on outcoupling optical element 570, a portion of the light guided within the waveguide may exit the waveguide as beamlet 650. In some implementations, any of optical elements 570, 580, 590, 600, 610, which may include one or more of an incoupling optical element, an outcoupling optical element, a light distribution element, or a CPE, may be configured as a diffraction grating.

[0108] To achieve desired properties for incoupling light into (or outcoupling light from) the waveguides 270, 280, 290, 300, 310, the optical elements 570, 580, 590, 600, 610 configured as diffraction gratings can be formed from suitable materials and have suitable structures to control various optical properties, including diffractive properties such as diffraction efficiency as a function of polarization. Possibly desirable diffractive properties may include any one or more of the following: spectral selectivity, angular selectivity, polarization selectivity (or non-selectivity), high spectral bandwidth, high diffraction efficiency, or wide field of view (FOV), among other properties.

[0109] Some diffraction gratings have strong polarization dependence and therefore may have relatively reduced overall efficiency (due to the blocking of certain polarizations). Such diffraction gratings may also create coherence artifacts and reduce the uniformity of far-field images. To provide a diffraction grating with reduced polarization sensitivity (e.g., coupling light with relatively polarization-independent efficiency), some displays for AR systems according to implementations described herein include a waveguide with a blazed diffraction grating formed therein. The blazed grating may comprise diffractive features having, for example, a "sawtooth" shape. In some implementations, the blazed grating may achieve improved grating diffraction efficiency for a given diffraction order, while the diffraction efficiency of other orders is reduced or minimized. As a result, more light may be directed into a particular given diffraction order as opposed to any of the other orders in some implementations.

[0110] FIG. 10A illustrates a cross-sectional view of a portion of a display device 1000, such as an eyepiece, comprising a waveguide 1004 and a blazed diffraction grating 1008 formed on a substrate that is the waveguide 1004, according to some designs described herein. In the implementation shown, the blazed diffraction grating 1008 is formed in the substrate / waveguide 1004 (which, in this example, is planar). The surface of the substrate or waveguide 1004 has a surface topography with diffractive features that together form the diffraction grating 1008. The blazed diffraction grating 1008 is configured to diffract light having wavelengths within the visible spectrum such that light incident thereon is guided within the waveguide 1004 by TIR. The waveguide 1004 may be transparent and may form part of the eyepiece through which a user's eye can see. Such a waveguide 1004 and eyepiece may be included in a head-mounted display, such as an augmented reality display. Waveguide 1004 may correspond, for example, to one of waveguides 670, 680, 690 described above with respect to Figures 9A-9C. Blazed grating 1008 may correspond, for example, to one of internal coupling optical elements 700, 710, 720 described above with respect to Figures 9A-9C. Blazed grating 1008 configured to internally couple light into waveguide 1004 may be referred to herein as an internal coupling grating (ICG). Display device 1000 may additionally include optical element 1012, which may correspond, for example, to a light dispersive element (e.g., one of light dispersive elements 730, 740, 750 shown in Figures 9A-9C) or an external coupling optical element (e.g., one of external coupling optical elements 800, 810, 820 shown in Figures 9A-9C).

[0111] In operation, when an incident light beam 1016, e.g., visible light such as from an optical projection system providing image content, is incident on the blazed grating 1008 at an angle of incidence α measured with respect to a surface normal 1002 that is normal to or orthogonal to the blazed grating or the extended surface or plane of the substrate / waveguide and / or the surface 1004S of the waveguide 1004, e.g., the major surface of the waveguide on which the grating is formed (shown in FIG. 10A as extending parallel to the yx-plane), the blazed grating at least partially diffracts the incident light beam 1016 as a diffracted light beam 1024 at a diffraction angle θ measured with respect to the surface normal 1002. The diffracted light beam 1024 is incident at a critical angle θ due to the occurrence of total internal reflection within the waveguide 1004. TIR Upon diffracting at a diffraction angle θ greater than θ, the diffracted light beam 1024 propagates and is guided within the waveguide 1004 via total internal reflection (TIR) ​​generally along a direction parallel to the x-axis and along the length of the waveguide. A portion of this light guided within the waveguide 1004 may reach one of the optically dispersive elements 730, 740, 750 or one of the outcoupling optical elements (800, 810, 820, FIGS. 9A-9C) and may, for example, be diffracted again.

[0112] As described herein, in the illustrated implementation, a light beam incident at an angle in a clockwise direction relative to the surface normal 1002 (i.e., to the right of the surface normal 1002) is said to have a negative α (α<0), while a light beam incident at an angle in a counterclockwise direction relative to the surface normal 1002 (i.e., to the left of the surface normal) is said to have a positive α (α>0).

[0113] As further described elsewhere herein, a suitable combination of high-index materials and / or structures of the diffraction grating 1008 can result in a particular range (Δα) of incident angles α, referred to herein as the range of acceptance angles or field of view (FOV). A range Δα can be described by a range of angles spanning negative and / or positive values ​​of α, outside which the diffraction efficiency drops by more than 10%, more than 25%, more than 50%, or more than 75%, more than 80%, more than 90%, more than 95%, or any value within a range defined by any of these values, relative to the diffraction efficiency at α=0 or some other direction. In some implementations, it may be desirable to have Δα within a range where the diffraction efficiency is relatively high and constant, for example, if a uniform intensity of the diffracted light is desired within Δα. Thus, in some implementations, Δα is related to the angular bandwidth of the diffraction grating 1008 such that an incident light beam 1016 in Δα is efficiently diffracted by the diffraction grating 1008 at a diffraction angle θ relative to the surface normal 1002 (e.g., a direction parallel to the yz plane), and θ is related to the angular bandwidth of the diffraction grating 1008 such that the diffracted light is guided within the waveguide 1004 under total internal reflection (TIR). TIR exceeding . In some implementations, this angle Δα range can affect the field of view seen by a user. It should be understood that in various implementations, light can be directed onto the internal coupling grating (ICG) from both sides. For example, light can be directed through a substrate or waveguide 1004 and incident on a reflective internal coupling grating (ICG) 1008, such as that shown in FIG. 10A. The light can be coupled into the substrate or waveguide 1004 by the internal coupling grating 1008, experiencing the same effect, e.g., so that the light is guided within the substrate or waveguide by total internal reflection. The range of incident angles α (Δα), referred to herein as the range of acceptance angles or field of view (FOV), can be affected by the refractive index of the substrate or waveguide material. In FIG. 10A, for example, the reduced angle range (Δα') illustrates the effect of refraction of the high refractive index material on the light incident on the internal coupling grating (ICG). However, the range of angles (Δα) or FOV is larger.

[0114] FIG. 10B illustrates a cross-sectional view of an exemplary blazed transmission grating 1008. The grating 1008 includes grating features having peaks 1003 and grooves 1005. The blazed transmission grating 1008 includes a surface corresponding to the surface of a substrate or waveguide 1004S, with a "sawtooth" shaped pattern as viewed from the cross-section shown. The patterned "sawtooth" is formed by first sloped portions 1007 of the surface 1004S. In the example shown in FIG. 10B, the grating 1008 also includes second (steeper) sloped portions 1009. In the example shown, the first sloped portions 1007 have a shallower slope than the second sloped portions 1009, which have a steeper slope. The first sloped portions 1007 are also wider than the second sloped portions 1009 in this example.

[0115] The point 1003 has a height H, which corresponds to the distance from the bottom of the groove 1005 to the top of the point 1003. Therefore, this value may be referred to herein as the point height and / or groove depth, the grating height or grating depth, or the height of the diffractive feature of the diffraction grating. In the example shown in FIG. 10B , the bottom of the groove 1005 is formed by the intersection of the first and second sloped portions 1007, 1009 of two adjacent point 1003. The first sloped portion 1007 is on one of the adjacent point 1003, and the second sloped portion 1009 is on the other adjacent point. Similarly, the top of the point 1003 is formed by the intersection of the first and second sloped portions 1007, 1009 at the top of the point 1003. However, other configurations are also possible. For example, the first and second sloped portions do not necessarily intersect if, for example, the bottom of the groove 1005 has a flat base or the top of the point 1003 includes a flat platform, as discussed below. The blazed diffraction grating 1008 has a line spacing or pitch d, which, in some implementations, may be constant. The line spacing or pitch d may be a measure of the separation of the apexes of the point 1003 in a grating 1008, for example, having a shape similar to that shown in FIG. 10B. Similarly, the line spacing or pitch d may be a measure of the separation of the deepest locations of adjacent grooves 1005. The line spacing or pitch d may also be measured from other locations on the grating feature.

[0116] The tilt may be angled at an angle δ relative to a plane parallel to the grating 1008 or the surface of the waveguide (e.g., the surface 1004S of the waveguide, which may extend beyond the grating or surface 1004S' of the waveguide, as opposed to the grating of FIG. 10A). This angle δ of the first (shallower) tilted portion 1007 may be referred to herein as the blaze angle.

[0117] As shown in Figure 10B, the blazed grating 1008 can include grating lines or features with asymmetric shapes, e.g., with asymmetrically shaped tip 1003 and / or groove 1005. For example, in the grating shown in Figure 10B, the diffractive features include tip 1003 and / or groove 1005 with an asymmetric triangular cross-sectional shape. As discussed above, this asymmetric shape results in different slopes and / or widths of the first and second sloped portions 1007, 1009. However, other shapes are also possible.

[0118] In designs where the diffractive features are asymmetric, e.g., where a first sloped portion has a shallower slope while a second sloped portion has a steeper slope, the diffractive features may be considered to be formed from repeated slopes and steps. Such structures may be referred to herein as sloped step structures. In some implementations, the second portion may be so steep that there is no slope, e.g., the second portion may be parallel to the normal 1002.

[0119] However, in other implementations of the "sawtooth" pattern, the point 1003 and / or groove 1005 may be symmetrical. For example, the first and second sloped portions 1007, 1009 may have the same slope and be the same width.

[0120] The cross-sectional pattern shown in Figure 10B may be referred to herein as a single-step geometry, in comparison to the multi-step structure discussed below, shown, for example, in Figure 11D.

[0121] Whether the diffractive features are asymmetric or symmetric, in some implementations a flat base or portion may be located on top of the headland 1003, as discussed below. A diffraction grating 1008 comprising diffractive features having a flat base or portion on top of the headland 1003 is shown, for example, in Figures 11B and 11D.

[0122] Figure 10B shows an incident light beam 1016 incident on the grating 1008 at an angle α with respect to the normal direction 1002. (As discussed above with respect to Figure 10A, in other embodiments, the light can pass through the substrate or waveguide 1004 and be incident on the diffraction grating 1008 from the other side.) As discussed above, the normal 1002 is normal to or orthogonal to the extended surface of the blazed diffraction grating 1008 or the plane of the grating or waveguide and / or the surface 1004S of the waveguide 1004, e.g., the major or opposing planar surface 1004S' of the waveguide on which the grating is formed. In Figure 10B, the light 1016 incident on the diffraction grating 1008 is shown to be diffracted at an angle β with respect to the normal direction 1002.

[0123] According to various embodiments, when configured as an in-coupling optical element or an in-coupling grating, the grating 1008 can diffractively couple light incident into the substrate 1004, which may be a waveguide as described above. The grating 1008 may also be configured as an out-coupling optical element, if desired, and in such embodiments, can diffractively couple light out of the substrate 1004, which may also be a waveguide as described above.

[0124] 10A and 10B , in some implementations, the substrate 1004 comprises a high-refractive-index material having a refractive index of at least 1.9. The refractive index can be, for example, at least 2.0, at least 2.1, at least 2.2, or at least 2.3, and may be 2.4 or less, 2.5 or less, 2.6 or less, 2.7 or less, 2.8 or less, or within any range formed by any of these values, or outside these ranges. In some implementations, for example, the substrate comprises a Li-based oxide. In various examples disclosed herein, diffractive features of the diffraction grating 1008 may be formed on a surface of the substrate 1004. The diffractive features may be formed either within the substrate 1004, e.g., a waveguide, or within a separate layer formed across the substrate 1004, e.g., a waveguide, and in optical communication with the substrate 1004, e.g., configured to couple light into or out of the substrate 1004. In the illustrated embodiment, the diffractive features of the diffraction grating 1008, such as lines, are formed in the substrate 1004, such as in the surface of the substrate. The diffractive features may be etched into the substrate 1004, which includes a high refractive index material, such as a Li-based oxide. The substrate may include, for example, lithium niobate, and the diffraction grating may be formed in the lithium niobate substrate by etching or patterning the surface of the substrate. Other materials with high refractive indexes may also be used. For example, other lithium-containing materials, such as lithium oxides, e.g., lithium tantalate (LiTaO), may be employed as the substrate. Silicon carbide (SiC) is another option for the substrate material. The embodiment is not so limited. In other embodiments, the diffractive features of the diffraction grating 1008 may be formed in a separate layer disposed over, e.g., physically contacting, the substrate 1004. For example, a thin film coating of zinc oxide (ZnO), silicon nitride (Si3N4), zirconium dioxide (ZrO2), titanium dioxide (TiO2), silicon carbide (SiC), etc., less than 200 nm thick, may be disposed over an existing high refractive index substrate. The thin film coating may be patterned to form diffractive features. However, in some implementations, the diffractive features, such as the lines of the diffraction grating 1008, may be formed from a different material than that of the substrate.The substrate may include a high refractive index material such as, for example, a Li-based oxide (e.g., lithium niobate (LiNbO) or lithium tantalate (LiTaO)); however, the diffractive features may be formed from a different material, such as a coating of zinc oxide (ZnO), zirconium dioxide (ZrO), titanium dioxide (TiO), silicon carbide (SiC), or another material described herein. In some implementations, this other material formed on the substrate may have a lower refractive index. In some cases, the substrate 1004 may include a material (including an amorphous high refractive index glass substrate), such as, for example, silica glass (e.g., doped silica glass), silicon oxynitride, transition metal oxide (e.g., hafnium oxide, tantalum oxide, zirconium oxide, niobium oxide, aluminum oxide (e.g., sapphire)), plastic, polymer, or other-based material that is substantially optically transparent to visible light, having a suitable refractive index, e.g., as described above, different from the material of the Li-based oxide features 1008.

[0125] However, as explained above, in various implementations described herein, the grating 1008 and the substrate 1004 or waveguide both comprise the same material, e.g., a Li-based oxide. In some implementations, the grating 1008 is patterned directly into the substrate 1004 such that the grating 1008 and the substrate 1004 form a single piece or monolithic structure. For example, the substrate 1004 comprises a waveguide, with the grating 1008 formed directly within the surface of the waveguide or substrate. In these implementations, a bulk Li-based oxide material may be patterned on the surface 1004S to form the grating 1008, while the Li-based oxide material below the grating 1008 may form the waveguide. In yet some other implementations, the bulk or substrate 1004 and the surface 1004S patterned to form the grating 1008 comprise different Li-based oxides. For example, the bulk Li-based oxide material patterned on the surface region and forming the grating 1008 may be formed from a first Li-based oxide material, while the Li-based oxide material below the grating 1008, forming the substrate 1004 or substrate region, may be formed from a second Li-based oxide material different from the first Li-based oxide material. As discussed above, in some other implementations, the grating 1008 is made of a different high refractive index material, such as zirconium dioxide (ZrO), titanium dioxide (TiO), silicon carbide (SiC), etc., and the material below the grating 1008, forming the substrate 1004 or substrate region, may be formed from a second material different from the first material coated as a thin film, such as LiTaO, LiNbO, etc.

[0126] In the example illustrated in Figures 10A and 10B, the diffraction grating 1008 may include a plurality of blazed grating lines elongated in a first horizontal direction, or y-direction, and periodically repeated in a second horizontal direction, or x-direction. The grating lines may be, for example, straight, continuous lines extending in the y-direction. However, the embodiment is not so limited. In some implementations, the grating lines may be, for example, discontinuous lines in the y-direction. In some other implementations, the discontinuous lines may form a plurality of pillars protruding from the surface of the grating substrate. In some implementations, at least some of the grating lines may have different widths in the x-direction.

[0127] In the illustrated example, the grating lines of the grating 1008 have a profile, e.g., a sawtooth profile, with asymmetric opposing side surfaces that form different angles with respect to the plane of the substrate. However, embodiments are not so limited, and in other implementations, the grating lines can have symmetric opposing side surfaces that form similar angles with respect to the plane of the substrate.

[0128] 10A and 10B, according to various embodiments, the diffraction grating 1008 may have various dimensions. For example, the diffractive features of the diffraction grating 1008 may have a height (H) that is 10 nm, or 40 nm to 150 nm, or 200 nm, 50 nm to 110 nm, 60 nm to 100 nm, 70 nm to 90 nm, or approximately 80 nm, or a height within a range defined by any of these values, according to embodiments. This height may correspond to the height of the tip 1003 and / or the depth of the groove 1005. Such heights, along with blazed geometries in high-index materials, may provide a diffraction grating with reduced polarization sensitivity. However, other heights are also possible.

[0129] The diffraction grating 1008 may have a pitch of 250 nm to 350 nm, 300 nm to 400 nm, 250 nm to 450 nm, or any range defined by any of these values, according to various embodiments. Other pitches are also possible.

[0130] The diffraction grating 1008 may have a blaze angle (shallow side) of approximately 10-70 degrees and a reverse blaze angle (steep side) of 140-70 degrees, or any value within the range defined by these values. Values ​​outside these ranges are also possible.

[0131] Blazed diffraction gratings of either single-stage or multi-stage geometries may be formed, as shown in Figures 11A-11D. In the example shown in Figures 11A-11D, the gratings are formed by depositing blazed photoresist, then etching and patterning the photoresist.

[0132] FIG. 11A illustrates the formation of a single - stage blazed grating 1106 in a substrate 1104, which can be a waveguide 1004 (FIG. 10A). A patternable material such as a photoresist 1102 may be deposited on the substrate 1104, which may include a waveguide 1004. The patternable material / photoresist 1102 is patterned to have the shape of a blazed grating. The step of forming a blazed geometry in the photoresist 1102 may, in some implementations, involve imprinting a pattern such as a single - stage "sawtooth" pattern into the photoresist 1102 (e.g., depositing the photoresist on the substrate 1104 and then imprinting the blazed geometry). The photoresist 1102 may include a mask such as a hard mask. The patterned photoresist 1102 and the substrate 1104 are then etched to form a blazed pattern in the substrate 1106. The step of etching the photoresist 1102 and the substrate 1104 may involve, for example, dry plasma or chemical etching and / or wet chemical etching. In some implementations, the etching illustrated in FIG. 11A etches away the material at a relatively constant rate such that the portion where the patterned photoresist was thickest results in a relatively small removal of material from the substrate, e.g., negligible or no removal, while the portion where the patterned photoresist was thinnest (or did not exist) results in a relatively large removal of material from the substrate or the deepest etching into the substrate.

[0133] FIG. 11B is a scanning electron micrograph of a blazed photoresist grating 1112, where the blazed grating pattern is formed in the photoresist 1104, for example, by imprinting the photoresist using a patterned master. The shown diffraction grating 1112 has a single - stage blazed geometry.

[0134] FIG. 11C illustrates the formation of a multi-stage blazed grating 1156 in a substrate 1154, which may be a waveguide 1004 (FIG. 10A). A patternable material, such as photoresist 1152, may be deposited on the substrate 1154. The patternable material / photoresist 1152 is patterned to have the shape of the blazed grating. Forming the blazed photoresist 1152 may, in some implementations, involve imprinting a pattern, such as a multi-stage “sawtooth” pattern, into the photoresist 1152 (e.g., depositing photoresist on the substrate 1154 and then imprinting a blazed geometric shape). The patterned photoresist 1152 and substrate 1154 may then be etched to form the multi-stage blazed substrate 1156. The photoresist 1152 may comprise a mask, such as a hard mask. The patterned photoresist 1152 and substrate 1154 may then be etched to form a blazed pattern in the substrate 1156. Etching the photoresist 1152 and substrate 1154 may involve, for example, dry plasma or chemical etching and / or wet chemical etching. In some implementations, the etching illustrated in FIG. 11C may etch away material at a relatively constant rate, such that areas where the patterned photoresist was thickest result in a relatively small amount of material being removed from the substrate, e.g., negligible or no removal, while areas where the blazed photoresist was thinnest (or absent) result in a relatively large amount of material being removed from the substrate or the deepest etching into the substrate.

[0135] 11D is a scanning electron micrograph of a blazed photoresist grating 1162, where the blazed grating pattern is formed on photoresist 1164, for example, by imprinting the photoresist with a patterned master. The diffraction grating 1162 may have a multi-step blazed geometry. The width of the tip 1003 is shown to be about 200 nm.

[0136] As shown in FIG. 11E, the blazed geometry of a diffraction grating formed in a high-index substrate, such as grating 1008 of FIGS. 10A and 10B, can be varied to have different heights and / or blaze angles. In particular, FIG. 11E illustrates a first diffraction grating 1170 (e.g., Geometry 1) having a first shape and a first height (which may be approximately 80 nm in some implementations). FIG. 11E also illustrates a second diffraction grating 1180 (e.g., Geometry 2) having a second shape and a second height (which may be lower than the first height and, for some designs, may be approximately 35 nm). As will be discussed in connection with at least FIG. 13, varying the geometry of a blazed diffraction grating can vary the performance characteristics of the grating. For example, Geometry 1 with a height (or depth) of 80 nm may provide lower polarization sensitivity than Geometry 2 with a height (or depth) of 35 nm.

[0137] 12A-12F show scanning electron micrographs (SEMs) of various blazed gratings formed in a substrate. The substrates and gratings of Figures 12A-12F are merely illustrative examples; in general, feature size, pitch, angle, and other properties may be varied to achieve desired performance characteristics.

[0138] 12A-12C show a lithium niobate (LiNbO) substrate having an upper surface with a blazed diffraction grating shape (e.g., a blazed geometry). FIG. 12A shows an SEM image 1200 of a blazed diffraction grating formed in the lithium niobate (LiNbO) substrate, where the step height or peak height of the blazed grating is measured to be approximately 31.90 nm. The angle δ of the first (shallower) sloped surface relative to the plane of the substrate is approximately 12.1 degrees. (This angle δ may be referred to herein as the blaze angle.) FIG. 12B shows an SEM image 1202 of the blazed grating from a different perspective. FIG. 12B shows the pitch (e.g., the distance between the peaks, steps, or grooves) measured to be approximately 331.8 nm. In the SEM image 1204 shown in Figure 12C, the blazed grating formed in a lithium niobate (LiNbO) substrate is shown to have a point or step height measured to be about 46.26 nm. The angle δ of the first (shallower) inclined surface relative to the plane of the substrate is about 19.5 degrees. (This angle δ may be referred to herein as the blaze angle.)

[0139] Figure 12D shows an SEM image 1206 of a silicon substrate being etched to form a blazed diffraction grating therein. The height of the blazed diffraction features in the example of Figure 12D, e.g., the height of the points or the depth of the grooves, is measured to be approximately 63.80 nm. The width of the points is measured to be approximately 167.5 nm. The "steep" angle of the points, e.g., the angle of the second, steeper sloped portion, is measured to be approximately 53.0 degrees (relative to the extended plane of the substrate). The "shallow" angle of the points, e.g., the angle δ of the first, shallower sloped portion (which may be referred to as the blaze angle), is measured to be approximately 27.9 degrees (relative to the extended plane of the substrate).

[0140] Figure 12E shows an SEM image 1208 of a silicon substrate being etched to form a multi-step blazed diffraction grating therein. The height of the multi-step blazed feature in the example of Figure 12D, e.g., the height of the tip or the depth of the groove, is measured to be approximately 66.85 nm. The width of the multi-step blazed feature or tip (e.g., the width not including any spacing between adjacent multi-step features) is measured to be approximately 206.9 nm. The overall "shallow" angle of the tip, determined based on the height of the tip relative to the distance from the base of the tip to the top of the tip, is measured to be approximately 22.5 degrees (relative to the extended plane of the substrate). The "steep" angle, e.g., the angle of the second, steeper slope of the tip, is measured to be approximately 68.8 degrees (relative to the extended plane of the substrate).

[0141] 12F shows an SEM image 1210 of a substrate formed from glass having a refractive index (RI) of 1.8. The imaged substrate has a blazed diffraction grating formed therein, with steps or feature heights of approximately 87.09 nm.

[0142] In general, varying the geometry of a blazed diffraction grating, such as grating 1008 in Figures 10A and 10B, can modify the performance characteristics of the grating. In at least some implementations, for example, a diffraction grating that is less sensitive to the polarization of light (e.g., a diffractive optical coupling element that incouples or outcouples light relatively independently of the polarization of the light) can be obtained by suitably adjusting parameters of the grating, such as the thickness of the grating or the height of the diffractive features. A diffraction grating with reduced polarization sensitivity can have a higher overall efficiency (e.g., can couple more light than a more polarization-sensitive grating) and can provide a more uniform image for the viewer, since polarization-sensitive gratings can introduce undesirable coherent artifacts, reducing the uniformity of far-field images produced, for example, by the eyepieces of a head-mounted display.

[0143] FIG. 13, for example, illustrates the polarization sensitivity of various blazed diffraction gratings. In particular, FIG. 13 illustrates the TM / TE incoupling grating diffraction efficiency (DE) ratio as a function of incident angle. The TM / TE ICG DE ratio may correspond, for example, to the incoupling efficiency for transverse magnetic (TM) polarization divided by the incoupling efficiency for transverse electric (TE) polarization. The incident angle may be, for example, incident angle α, as referenced in FIGS. 10A and 10B.

[0144] Plot 1300 illustrates the TM / TE ratio as a function of incidence angle α for a blazed diffraction grating formed in photoresist disposed on a lithium niobate substrate. As shown in plot 1300, a diffraction grating formed from blazed photoresist on a lithium niobate substrate can be relatively polarization sensitive, e.g., have an efficiency for TM polarization that is 3 to 4 times greater than the efficiency of the grating for TE polarization within a range of incidence angles.

[0145] Plot 1302 illustrates the TM / TE ratio as a function of incidence angle α for a blazed diffraction grating (such as grating 1180 having geometry 2 shown in FIG. 11E) with diffractive features formed in a lithium niobate substrate having a feature or tip height (or groove depth) H of 35 nm. As shown in plot 1302, the diffraction grating with an etched feature height of 35 nm is not as polarization sensitive as a blazed grating formed in a photoresist layer deposited on the lithium niobate substrate. Over most of the range of measured incidence angles, the diffraction grating with an etched feature height of 35 nm only slightly favors TM polarization over TE polarization, by a ratio of about 1.5 to 2.0 or 2.2 (e.g., the grating therefore has a slightly reduced polarization sensitivity).

[0146] Plot 1304 illustrates the TM / TE ratio as a function of incidence angle α for a blazed diffraction grating (such as grating 1170 having geometry 1 shown in FIG. 11E) with diffractive features formed in a lithium niobate substrate having a feature or tip height (or groove depth) H of 80 nm. As shown in plot 1304, the diffraction grating with an etched diffractive feature height of 80 nm has a TM / TE diffraction efficiency ratio of about 1 over a wide range of incidence angles (e.g., the grating has reduced polarization sensitivity, e.g., is substantially insensitive to polarization).

[0147] 14 illustrates the TM / TE diffraction efficiency of a blazed grating formed in a lithium niobate substrate with a feature height of 80 nm for different colored light (e.g., for green, blue, and red light). As shown in FIG. 14, the TM / TE diffraction efficiency ratio (of the grating 1170) is about 1 over a wide range of incident angles for both green and blue light. In addition, for red light, the TM / TE diffraction efficiency ratio is generally about 1.5, increasing to more than 2 (but less than 2.5) for some incident angles.

[0148] 15 illustrates the average diffraction efficiency of a blazed grating formed in lithium niobate with a feature height of 80 nm for green, blue, and red light as a function of incident angle. The average diffraction efficiency may indicate, for example, the efficiency of the grating for in-coupling (or out-coupling) unpolarized light.

[0149] In addition to the general reduction in efficiency and brightness, some highly polarization-sensitive diffraction gratings can also create coherent artifacts and reduce the uniformity of the far-field image produced by the eyepiece in a head-mounted display, which directs the image content to the user's eyes.

[0150] FIG. 16 shows the distribution of light output from an eyepiece with an internal coupling grating, which includes a blazed diffraction grating formed in photoresist deposited on a lithium niobate substrate to internally couple light into a waveguide-based eyepiece and a light redirecting element (orthogonal pupil expander) and an external coupling optical element (exit pupil expander). As shown in FIG. 16, an eyepiece with an internal coupling optical element including a blazed diffraction grating in photoresist deposited on a lithium niobate substrate can produce a coherence uniformity of approximately 9.45% for unpolarized light input and approximately 11.3% for linearly polarized light input. The graph and image in FIG. 16 were taken from a 500-micron-thick Z-cut lithium niobate substrate having a layer of photoresist thereon patterned by imprinting to form an internal coupling grating. FIG. 16 shows non-uniformity in a far-field image 1600. In this example, the plotted uniformity score is a mathematical value derived from analyzing pixel values ​​of a captured image over an area, giving an indication of non-uniformity in the values ​​captured at different sampling spatial frequencies across the image, with lower values ​​indicating a more uniform color distribution across the field of view of the captured or desired image.

[0151] FIG. 17 shows the distribution of light output from an eyepiece with a blazed grating formed in a lithium niobate substrate to incoupling light into a waveguide-based eyepiece and light redirecting element (orthogonal pupil expander) and an outcoupling optical element (exit pupil expander). As shown in FIG. 17, an incoupling optical element with a blazed grating having an 80 nm feature height (tip height or groove depth) formed by etching into the lithium niobate substrate can have improved coherent uniformity, such as a coherent uniformity of approximately 8.1% for unpolarized input and approximately 8.35% for linearly polarized input. The graph and image in FIG. 17 were taken from a 500-micron-thick Z-cut lithium niobate substrate with a blazed grating etched into the substrate. An EPE and OPE are also etched into the substrate. FIG. 17 shows a reduction in nonuniformity in far-field image 1700 relative to far-field image 1600.

[0152] Thus, a blazed grating formed in a high refractive index substrate, such as lithium niobate, having certain dimensions, such as a thickness, of about 40 to 120, or 60 to 100, or 70 to 90, or 80 nanometers, or any value within a range between any of these values, can provide reduced polarization sensitivity.

[0153] The structure and its fabrication method may differ from those examples specifically described above. For example, a blazed grating may be used as an outcoupling optical element (e.g., EPE) and / or a light redirecting optical element (e.g., OPE). In addition, instead of a diffraction grating, other types of diffractive optical elements may be formed, for example, in a high-index substrate. For example, a different high-index material, such as lithium tantalate (e.g., LiTaO), may be used for the waveguide and the diffractive features formed therein. As discussed above, in some other implementations, the waveguide and the diffractive features formed therein may include other high-index materials, such as silicon carbide or high-index amorphous glass. Additionally, in some implementations, the diffraction grating 1008 may include a different high refractive index material or coating, such as zinc oxide (ZnO), silicon nitride (Si3N4), zirconium dioxide (ZrO2), titanium dioxide (TiO2), silicon carbide (SiC), etc., and the material below the substrate 1004 or forming the substrate region may include a second high refractive index material, such as LiTaO3, LiNbO3, etc. (Diffraction grating with a two-dimensional (2D) array of diffractive features)

[0154] Various implementations of diffraction gratings with reduced polarization sensitivity can be implemented as one-dimensional (1D) arrays of diffractive features, e.g., lines, as described above. For example, FIG. 10A shows a cross-sectional side view of an exemplary device 1000 having a series of diffractive features 1012 that may have a "sawtooth" shape with sloped sidewalls and are laterally arranged in one direction (e.g., the first horizontal or x-direction in FIG. 10A). The diffractive features 1012 are undulating in one direction (e.g., the first horizontal or x-direction in FIG. 10A) or elongated in one direction (e.g., the second horizontal or y-direction in FIG. 10A), and are therefore referred to as 1D. As a further example of 1D diffractive features, FIG. 11B shows a perspective view of a blazed photoresist grating configured as a 1D array. The diffractive features 1012 (FIG. 10A) can form a series of elongated longitudinal features, such as lines, that extend in one direction (e.g., the second horizontal or y-direction in FIG. 10A) that are aligned along and repeated in one direction (e.g., the first horizontal or x-direction in FIG. 10A).

[0155] In some embodiments, the array of structures can also be arranged in two directions to form a two-dimensional (2D) array of diffractive features. The 2D array of diffractive features can include undulations in two directions. In some instances, the undulations can be periodic, while in other instances, the pitch of the undulations can vary in at least one direction. According to various examples described herein, the diffractive features have opposing sidewalls that are asymmetrically angled or sloped. According to various examples described herein, the diffractive features may be tapered. In some implementations, the diffractive features can have opposing sidewalls that are substantially angled or sloped. In some implementations, the opposing sidewalls can be sloped in the same direction, while in other implementations, the opposing sidewalls can be sloped in opposite directions. In some other implementations, the diffractive features can have one of the opposing sidewalls that is substantially sloped, while the other sidewall is sloped approximately perpendicular or orthogonal to the horizontal axis, or at least by less than the other sidewall. In various embodiments of the 2D diffractive features described herein, the 2D diffractive features can be formed in or on an underlying substrate, which may be a waveguide, as described above with respect to various embodiments of the 1D diffractive features. For example, the 2D diffractive features can be formed by patterning a separate layer that is etched into or formed on the underlying substrate. Thus, the 2D diffractive features can be formed from the same or different material as the substrate, similar to those described above with respect to the various 2D diffractive features. Other variations and configurations are also possible.

[0156] FIG. 18 shows an example device 3600 having a 2D array of diffractive features 3603 (e.g., diffractive features 3603 arranged laterally in two dimensions or directions). In this example, the array resembles a checkerboard pattern. The diffractive features 3603 may be referred to as protrusions. The diffractive features have sloped sidewalls that are sloped in opposite directions. One of the sidewall slopes may have a slope that is less than the other of the sidewall slopes. The result of this configuration is that the diffractive features are blazed.

[0157] The diffractive features in the illustrated embodiment of FIG. 18 are asymmetric in at least one lateral direction. FIGS. 18A and 18B show cross-sectional side and top views, respectively, of an exemplary array of asymmetric diffractive features. The present 2D diffractive grating comprises a blazed diffractive grating. The diffractive features may be tapered, for example, in thickness, with height. In the embodiment shown in FIG. 18, the diffractive features have two opposingly sloped sidewalls or facets, one slope greater than the other and sloped in opposite directions, while in the embodiment shown in FIGS. 18A and 18B, one sidewall is sloped while the other opposing sidewall has a slope on the second sidewall that is approximately vertical, or has no slope, or is negligible. In both cases, the slope of one of the opposing sidewalls exceeds that of the other opposing sidewall (if applicable), such that the diffractive feature is asymmetric and blazed. As a result, the diffractive feature diffracts light preferentially in one direction over the other. Such a diffraction grating may be useful, for example, as an in-coupling optical element configured to diffract light received from a projector toward a light distributing element, an out-coupling optical element, or a combination of a light distributing element and an out-coupling optical element, such as a combined pupil expander-extractor (CPE). Such a diffraction grating may be useful for out-coupling light into the eye, as opposed to facing the environment or world in front of the user and head-mounted display. In some implementations, the sidewall tilt angle is less than 30 degrees relative to the horizontal axis on one side and greater than 80 degrees (e.g., 80-90 degrees) on the other side. However, other tilts and tilt angles are also possible. In some instances, the diffractive features may form a 2D array of sawtooth structures, such as sawtooth nanostructures.

[0158] Thus, in various implementations, a 2D array of symmetric or asymmetric diffractive features can act as a blazed diffraction grating. As discussed above, the shape of the diffraction grating (e.g., the slope angle of the sidewalls) can determine the direction in which the grating directs or preferentially directs light toward. For example, a grating may direct more light toward other gratings (e.g., EPE, OPE, or CPE) and / or toward the viewer. In some instances, the diffractive features can be faceted to bias light propagation in more than one direction (e.g., blazed in multiple directions). For example, FIG. 19A shows an example device 3700 having a 2D array of diffractive features 3703 formed in or on a substrate 3701. The diffractive feature 3703 has a first sidewall or facet 3703b-1 and a second sidewall or facet 3703b-2 that is sloped. Thus, the diffractive feature tapers, for example, in thickness, with height. The diffractive feature 3703 can be configured to preferentially direct light in a direction based on the slope angle of the first and second sidewalls or facets 3703b-1, 3703b-2. Figure 19B shows an example diffractive feature that directs more light in two specific directions (as illustrated by the two thick solid arrows pointing up and to the right and down and to the left). Other implementations are also possible.

[0159] Thus, any of the structures or devices described herein, such as grating structures, may comprise 1D gratings. Similarly, any of the structures or devices described herein, such as grating structures, may comprise 2D gratings. Such 2D gratings may diffuse light. These gratings may also comprise blazed gratings. Such blazed gratings may preferentially direct light in one direction. In some implementations, a 2D grating (e.g., having one tilted facet on the diffractive features) preferentially directs light in one direction, while in other implementations, a 2D grating (e.g., having two different tilted facets on the diffractive features) preferentially directs light in multiple directions. Similarly, any of the methods or processes described herein can be used for 1D gratings. Similarly, any of the methods or processes described herein can be used for 2D gratings. These 1D or 2D gratings may be included in or on substrates and / or waveguides, included in eyepieces, and possibly integrated into head-mounted displays, as disclosed herein. These gratings may be employed as input gratings (e.g., ICG), output gratings (EPE), light distribution gratings (OPE), or combined light distribution / output gratings (e.g., CPE).

[0160] FIG. 20A shows an example method 3800 for forming a blazed grating. The method 3800 includes providing a template or master 3810. If the diffractive features are to be angled, tilted, or slanted, the template 3810 can be patterned to form the angled structures. Various processes, e.g., etching processes, may be directed and angled to form such angled structures. Some examples of angled processes, such as angled etching processes, include ion beam milling, angled dry etching, ion etching, GLAD etching, angled etching, Faraday cage etching, etc. In some implementations, the selection of material employed for the template 3810 may aid in producing angled structures with angled sidewalls within the template. In this example, the angled structures comprise angled elongated protrusions (e.g., for a 1D grating) or angled posts (e.g., for a 2D grating). These angled elongated protrusions or angled posts may have sidewalls that are tilted in the same direction and, in some cases, may be substantially parallel. Once the template 3810 is fabricated, a layer of patternable material (e.g., polymer, resist, photoresist, etc.) can be deposited on the substrate 3801 and this layer can be imprinted using the imprint template 3810. The template 3810 can be imprinted into a patternable material (e.g., a resist material) 3805 on the substrate 3801 to form a mask 3805 for the substrate. In other implementations, the patternable material can be deposited on the template and the substrate, with the patternable material thereon, can be contacted with the template. The template can be removed and the resist material 3805 and underlying substrate 3801 can be dry etched to form the diffractive features 3803 in the substrate 3801. In various implementations, dry etching is employed as shown. The etching can be directional. In the example shown, the etching process is not angled.The resulting diffractive features 3803 formed in substrate 3801 (or in a layer of material disposed on substrate 3801) may have a shape, for example, may be blazed as a result of angled features in mask 3805. In the example shown, the cross section of the diffractive features has a trapezoidal or generally triangular shape with two slanted sides. The sides are slanted in opposite directions. In the example shown, one side is more slanted than the other, creating a blazed structure. This process may be used to form 1D or 2D arrays of diffractive features.

[0161] FIG. 20B illustrates another exemplary method 3850 for forming blazed diffractive features. The mask 3855 and underlying substrate 3851 can be etched (e.g., dry etched) at an angle to form diffractive features 3853 in the substrate 3851 (or in a layer of material disposed on the substrate 3851). In an angled etching process, the direction of the etchant forms an angle that is tilted relative to the surface normal of the substrate 3851, which can be due to either a tilt in the etchant's entry angle or a tilt in the surface of the substrate 3851. Some examples of angled directional etching processes (e.g., angled etching) include ion beam milling, angled dry etching, ion etching, GLAD etching, angled etching, Faraday cage etching, etc. The template can include elongated protrusions (e.g., for 1D gratings) or tapered posts (e.g., for 2D gratings) with trapezoidal or approximately triangular cross-sections. These elongated protrusions or tapered posts can have sidewalls that are sloped in opposite directions. One sidewall may be more sloped than the other. Applying an angled etching process to these elongated protrusions or tapered posts can produce a blazed grating in a material, such as a substrate underlying the elongated protrusions or tapered posts or a layer of material disposed on a substrate. Blazed diffractive features may be produced with sides that are sloped in the same direction. In various implementations, one of the sides is sloped more than the other. This process may be used to form 1D or 2D arrays of diffractive features.

[0162] In various implementations, the resulting diffractive features may be blazed in more than one direction (e.g., as shown in FIG. 19A ) as a result of angled features in a mask (e.g., as shown in FIG. 20A ) and / or as a result of using an angling process (e.g., as shown in FIG. 20B ). Diffractive features or gratings blazed in more than one direction may be produced by etching twice. In some implementations, for example, diffractive features or gratings blazed in more than one direction may be produced by etching with a first mask and then etching again with a second, different mask. In some instances, as shown in FIG. 21 , mask 3905 and substrate 3901 may be etched to form a first sidewall of diffractive feature 3903 in substrate 3901. Additionally, patterning may be provided to form a second sidewall. In various implementations, a second mask having a different orientation and / or shape may be used to form the second sidewall. A second mask (e.g., at an angle and / or a different orientation relative to the first sidewall) may be etched, for example, to form the second sidewall. In some implementations, after the first sidewall of the diffractive feature 3903 is formed, a planarizing layer 3907 may be added to the intermediate diffractive feature 3903 and the substrate 3901. The planarizing layer 3907, the intermediate diffractive feature 3903, and / or the substrate 3901 may be patterned and etched (e.g., at an angle relative to the first sidewall) to form the second sidewall. Although the above examples are discussed in the context of patterning a substrate, in some implementations, the processes described above may be employed to pattern a layer formed on the substrate rather than the substrate. Alternatively, in some implementations, the processes described above may be employed to pattern the substrate and a layer formed on the substrate.

[0163] Additionally, while exemplary methods 3800, 3850, 3900 are illustrated as forming a 2D array of asymmetric diffractive features, the methods can also be used to form a 2D array of symmetric diffractive features (with or without angled sidewalls). The methods can also be used to form a 1D array of diffractive features. In some instances, the diffractive features within the 1D array can be symmetric, with or without angled sidewalls. In some instances, the diffractive features within the 1D array can be asymmetric, for example, with angled sidewalls. Thus, in some cases, blazed diffractive features may be formed. Additional Examples - Part I: Example 1 1. A head-mounted display system, comprising: A head mountable frame; a light projection system configured to output light and provide image content; a waveguide supported by a frame, the waveguide comprising: a substrate comprising a material having a refractive index of at least 1.9; and a blazed diffraction grating formed in the substrate, the substrate configured to guide at least a portion of light from the optical projection system to be coupled into the waveguide; a blazed diffraction grating having a first diffraction efficiency for a first polarization over a range of angles of light incident thereon and a second diffraction efficiency for a second polarization over a range of angles of light incident thereon, the first diffraction efficiency being between 1 and 2 times the second diffraction efficiency. Example 2 2. The head-mounted display system of example 1, wherein the material comprises a lithium-based oxide having a refractive index of at least 1.9. Example 3 3. The head-mounted display system of any one of claims 1 to 2, wherein the material having a refractive index of at least 1.9 comprises lithium niobate. Example 4 3. The head-mounted display system of any one of claims 1 to 2, wherein the material has a refractive index of at least 1.9 and comprises lithium tantalate. Example 5 2. The head-mounted display system of example 1, wherein the material comprises silicon carbide, the material having a refractive index of at least 1.9. Example 6 2. The head-mounted display system of example 1, wherein the material having a refractive index of at least 1.9 comprises zirconium dioxide. Example 7 2. The head-mounted display system of example 1, wherein the material having a refractive index of at least 1.9 comprises titanium dioxide. Example 8 A head mounted display system according to any of the previous examples, wherein the material has a refractive index of at least 2.0 to 2.7. Example 9 A head mounted display system according to any of the previous examples, wherein the material has a refractive index of at least 2.1 to 2.7. Example 10 A head mounted display system according to any of the previous examples, wherein the material has a refractive index of at least 2.2 to 2.7. Example 11 A head mounted display system according to any of the previous examples, wherein the material has a refractive index of at least 2.3 to 2.7. Example 12 A head mounted display system according to any of the previous examples, wherein the material has a refractive index of at least 2.4 to 2.7. Example 13 A head mounted display system according to any of the previous examples, wherein the material has a refractive index of at least 2.5 to 2.7. Example 14 A head mounted display system according to any of the previous examples, wherein the material has a refractive index of at least 2.6 to 2.7. Example 15 10. A head mounted display system according to any of the preceding examples, wherein the blazed grating comprises diffractive features having points spaced apart by grooves therebetween. Example 16 10. A head mounted display system according to any of the preceding examples, wherein the blazed diffraction grating comprises diffractive features comprising a plurality of straight lines. Example 17 A head mounted display system according to any of the previous embodiments, wherein the blazed diffraction grating comprises diffractive features having a tip height or groove depth of 40 to 120 nm. Example 18 A head mounted display system according to any of the previous embodiments, wherein the blazed diffraction grating comprises diffractive features having a tip height or groove depth of 60-100 nm. Example 19 A head mounted display system according to any of the previous embodiments, wherein the blazed diffraction grating comprises diffractive features having a peak height or groove depth of 70-90 nm. Example 20 10. A head mounted display system according to any of the preceding examples, wherein the blazed grating comprises diffractive features having a peak height or groove depth of about 80 nm. Example 21 10. A head mounted display system according to any of the preceding embodiments, wherein the diffractive features are asymmetric. Example 22 A head mounted display system according to any of the preceding embodiments, wherein the blazed diffraction grating has a pitch of 250 to 350 nm. Example 23 A head mounted display system according to any one of the preceding embodiments, wherein the blazed diffraction grating has a pitch of 300 to 450 nm. Example 24 A head mounted display system according to any of the previous embodiments, wherein the substrate is planar and the blazed diffraction grating has a blaze angle of 10 to 30 degrees relative to the plane of the substrate. Example 25 A head mounted display system according to any of the previous embodiments, wherein the substrate is planar and the blazed diffraction grating has a blaze angle of 15 to 25 degrees relative to the plane of the substrate. Example 26 10. A head mounted display system according to any of the preceding embodiments, wherein the substrate is planar and the blazed grating has a blaze angle of about 19.5 degrees relative to the plane of the substrate. Example 27 A head mounted display system according to any of the preceding embodiments, wherein the first diffraction efficiency is 1 to 1.5 times the second diffraction efficiency. Example 28 A head mounted display system according to any of the preceding embodiments, wherein the first diffraction efficiency is 1 to 1.4 times the second diffraction efficiency. Example 29 A head mounted display system according to any of the preceding embodiments, wherein the first diffraction efficiency is 1 to 1.3 times the second diffraction efficiency. Example 30 A head mounted display system according to any of the preceding embodiments, wherein the first diffraction efficiency is 1 to 1.2 times the second diffraction efficiency. Example 31 A head mounted display system according to any of the preceding embodiments, wherein the first diffraction efficiency is 1 to 1.1 times the second diffraction efficiency. Example 32 10. A head mounted display system according to any of the previous embodiments, wherein the range of angles is at least 6 degrees. Example 33 10. A head mounted display system according to any of the previous embodiments, wherein the range of angles is at least 12 degrees. Example 34 10. A head mounted display system according to any of the previous embodiments, wherein the range of angles is at least 18 degrees. Example 35 10. A head mounted display system according to any of the previous embodiments, wherein the range of angles is at least 22 degrees. Example 36 A head mounted display system according to any of the previous examples, wherein the range of angles is between ±3 degrees relative to the plane of the substrate. Example 37 A head mounted display system according to any of the previous examples, wherein the range of angles is between ±6 degrees relative to the plane of the substrate. Example 38 A head mounted display system according to any of the previous examples, wherein the range of angles is between ±9 degrees relative to the plane of the substrate. Example 39 A head mounted display system according to any of the previous examples, wherein the range of angles is between ±11 degrees relative to the plane of the substrate. Example 40 10. The head mounted display system of any of the preceding examples, wherein the first and second polarizations comprise first and second linear polarizations having different polarization angles. Example 41 10. The head mounted display system of any of the preceding examples, wherein the first and second polarizations comprise first and second linear polarizations oriented in orthogonal directions. Example 42 10. A head-mounted display system according to any of the preceding examples, wherein the first and second polarizations comprise transverse magnetic and transverse electric polarizations, respectively. Example 43 10. A head-mounted display system according to any of the preceding examples, wherein the first and second polarizations comprise transverse electric and transverse magnetic polarizations, respectively. Example 44 A head-mounted display system as described in any of the above examples, wherein the first diffraction efficiency comprises a diffraction efficiency for transverse magnetic polarization averaged across the visible light spectrum, and the second diffraction efficiency comprises a diffraction efficiency for transverse electric polarization averaged across the visible light spectrum. Example 45 A head-mounted display system as described in any of the above examples, wherein the first diffraction efficiency comprises a diffraction efficiency for transverse electric polarization averaged across the visible light spectrum, and the second diffraction efficiency comprises a diffraction efficiency for transverse magnetic polarization averaged across the visible light spectrum. Example 46 10. The head-mounted display system of any of the preceding embodiments, wherein the blazed diffraction grating has a diffraction efficiency for red wavelengths of light having the first polarization that is 1 to 2 times the diffraction efficiency for red wavelengths of light having the second polarization. Example 47 10. The head-mounted display system of any of the preceding embodiments, wherein the blazed diffraction grating has a diffraction efficiency for green wavelengths of light having the first polarization that is 1 to 1.5 times the diffraction efficiency for green wavelengths of light having the second polarization. Example 48 10. The head mounted display system of any of the preceding examples, wherein the blazed diffraction grating has a diffraction efficiency for blue wavelengths of light, having the first polarization, that is 0.7 to 1 times its diffraction efficiency for blue wavelengths of light, having the second polarization. Example 49 A head-mounted display system as described in any of the above examples, wherein the waveguide is included in an eyepiece configured to direct light to the eye of a user wearing the head-mounted display. Example 50 A head-mounted display system as described in Example 49, wherein the eyepiece is positioned on the frame and configured to direct light from the light projection system into the user's eye and display augmented reality image content in the user's field of view, at least a portion of the eyepiece is transparent and is positioned in front of the user's eye when the user wears the head-mounted display system, and the transparent portion allows light from a portion of the physical environment in front of the user to pass through to the user's eye and provide a view of a portion of the physical environment in front of the user. Example 51 A head-mounted display system as described in Example 49 or 50, wherein the eyepiece lens comprises at least one waveguide, and the at least one waveguide is transparent to visible light so that a user can see through the waveguide. Example 52 A head-mounted display system as described in any of the above examples, wherein the waveguide comprises an internal coupling optical element for coupling light from the optical projection system into the waveguide so that it is guided therein. Example 53 A head-mounted display system as described in any of the above examples, wherein the waveguide comprises an external coupling optical element for coupling light from the optical projection system out of the waveguide, directing the light to a user's eye, and presenting the image content to a viewer. Example 54 A head-mounted display system as described in any of the above examples, wherein the blazed diffraction grating comprises an internal coupling grating (ICG) configured to internally couple light from the optical projection system into the waveguide. Example 55 A head-mounted display system as described in any of the above examples, wherein the blazed diffraction grating comprises an external coupling grating (EPE) configured to externally couple light from the optical projection system guided within the waveguide out of the waveguide. Example 56 An optical waveguide, a substrate comprising a material having a refractive index of at least 1.9, the substrate being configured to guide light coupled into the waveguide within the waveguide via total internal reflection; a blazed diffraction grating formed in the substrate; an optical waveguide, comprising: a blazed diffraction grating having a first diffraction efficiency for a first polarization over a range of angles for light incident thereon; and a second diffraction efficiency for a second polarization over a range of angles for light incident thereon; and the first diffraction efficiency is one to two times the second diffraction efficiency. Example 57 57. The optical waveguide of example embodiment 56, wherein the material having a refractive index greater than 1.9 comprises a lithium-based oxide. Example 58 58. The optical waveguide of any one of Examples 56 to 57, wherein the material having a refractive index greater than 1.9 comprises lithium niobate. Example 59 58. The optical waveguide of any one of Examples 56 to 57, wherein the material has a refractive index greater than 1.9 and comprises lithium tantalate. Example 60 57. The optical waveguide of example embodiment 56, wherein the material having a refractive index greater than 1.9 comprises silicon carbide. Example 61 57. The optical waveguide of example embodiment 56, wherein the material having a refractive index greater than 1.9 comprises zirconium dioxide. Example 62 57. The optical waveguide of example embodiment 56, wherein the material having a refractive index greater than 1.9 comprises titanium dioxide. Example 63 The optical waveguide of any of Examples 56-62, wherein the blazed grating comprises diffractive features having a tip height or groove depth of 40 to 120 nm. Example 64 The optical waveguide of any of Examples 56-63, wherein the blazed grating comprises diffractive features having a tip height or groove depth of 60-100 nm. Example 65 The optical waveguide of any of Examples 56-64, wherein the blazed grating comprises diffractive features having a tip height or groove depth of 70-90 nm. Example 66 The optical waveguide of any of Examples 56-65, wherein the blazed grating comprises diffractive features having a peak height or groove depth of about 80 nm. Example 67 The optical waveguide of any of Examples 56-66, wherein the diffractive characteristics are asymmetric. Example 68 A head-mounted display system as described in any of Examples 1-55 or an optical waveguide as described in any of Examples 56-67, wherein the blazed diffraction grating comprises diffractive features formed in a one-dimensional (1D) array. Example 69 A head-mounted display system as described in any of Examples 1-55 or an optical waveguide as described in any of Examples 56-67, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array. Example 70 A head-mounted display system described in any of Examples 1-55 or an optical waveguide described in any of Examples 56-67, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array comprising a square array. Example 71 A head-mounted display system described in any of Examples 1-55 or an optical waveguide described in any of Examples 56-67, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array, and the blazed diffraction grating comprises a 1D grating. Example 72 A head-mounted display system described in any of Examples 1-55 or an optical waveguide described in any of Examples 56-67, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array, and the blazed diffraction grating comprises a 2D grating. Example 73 A head-mounted display system as described in any of Examples 1-55 or an optical waveguide as described in any of Examples 56-67, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array, and the blazed diffraction grating comprises a 2D grating having a square array. Example 74 A head-mounted display system described in any of Examples 1-55 or an optical waveguide described in any of Examples 56-67, wherein the blazed diffraction grating is configured to preferentially direct light in at least two directions. Example 75 A head-mounted display system according to any one of Examples 1-55 or an optical waveguide according to any one of Examples 56-67, wherein the blazed diffraction grating is blazed in two directions. Example 76 A head-mounted display system described in any of Examples 1-55 or an optical waveguide described in any of Examples 56-67, wherein the blazed diffraction grating comprises an internal coupling optical element arranged to receive light from an image source and couple the light into the substrate so that it is guided therein. Example 77 A head-mounted display system described in any of Examples 1-55 or an optical waveguide described in any of Examples 56-67, wherein the blazed diffraction grating comprises a light-dispersing optical element arranged to receive light from an image source guided within the substrate and direct the light to an external coupling optical element so that it is coupled out of the substrate. Example 78 A head-mounted display system described in any of Examples 1-55 or an optical waveguide described in any of Examples 56-67, wherein the blazed diffraction grating comprises a light-dispersing optical element arranged to receive light from an image source guided within the substrate and diffuse the light within the waveguide to increase the beam size or eyebox size. Example 79 A head-mounted display system described in any of Examples 1-55 or an optical waveguide described in any of Examples 56-67, wherein the blazed diffraction grating comprises an external coupling optical element arranged to receive light from an image source guided within the substrate and couple the light out of the substrate. Example 80 A head-mounted display system described in any of Examples 1-55 or an optical waveguide described in any of Examples 56-67, wherein the blazed diffraction grating comprises a combined light dispersion / external coupling optical element arranged to receive light from an image source guided within the substrate, diffuse the light in at least two directions, and couple the light out from the substrate. Example 81 A head-mounted display system described in any of Examples 1-55 or an optical waveguide described in any of Examples 56-67, wherein the blazed diffraction grating has an associated pupil expander-extractor arranged to receive light from an image source guided within the substrate, diffuse the light, and couple the light out of the substrate. Additional Examples - Part II: Example 1 1. A head-mounted display system, comprising: A head mountable frame; a light projection system configured to output light and provide image content; a waveguide supported by a frame, the waveguide comprising a substrate comprising a material having a refractive index of at least 1.9, the substrate configured to guide at least a portion of light from the optical projection system to be coupled into the waveguide; a layer disposed over the substrate; and a blazed diffraction grating formed within the layer; a blazed diffraction grating having a first diffraction efficiency for a first polarization over a range of angles of light incident thereon and a second diffraction efficiency for a second polarization over a range of angles of light incident thereon, the first diffraction efficiency being between 1 and 2 times the second diffraction efficiency. Example 2 2. The head-mounted display system of example 1, wherein the substrate material comprises a lithium-based oxide having a refractive index of at least 1.9. Example 3 3. The head-mounted display system of any one of claims 1 to 2, wherein the material having a refractive index of at least 1.9 comprises lithium niobate. Example 4 3. The head-mounted display system of any one of claims 1 to 2, wherein the material has a refractive index of at least 1.9 and comprises lithium tantalate. Example 5 2. The head-mounted display system of example 1, wherein the material having a refractive index greater than 1.9 comprises silicon carbide. Example 6 2. The head-mounted display system of example 1, wherein the material having a refractive index greater than 1.9 comprises titanium dioxide. Example 7 2. The head-mounted display system of example 1, wherein the material having a refractive index greater than 1.9 comprises zirconium dioxide. Example 8 10. The head mounted display system of any of the previous examples, wherein the layer comprises zinc oxide. Example 9 10. The head mounted display system of any of the previous examples, wherein the layer comprises silicon nitride. Example 10 10. The head mounted display system of any of the previous examples, wherein the layer comprises zirconium dioxide. Example 11 10. The head mounted display system of any of the previous examples, wherein the layer comprises titanium dioxide. Example 12 10. The head mounted display system of any of the previous examples, wherein the layer comprises silicon carbide. Example 13 10. A head mounted display system according to any of the previous examples, wherein the layer has a lower refractive index than the substrate. Example 14 A head mounted display system according to any of the previous embodiments, wherein the substrate material has a refractive index of at least 2.0 to 2.7. Example 15 A head mounted display system according to any of the previous embodiments, wherein the substrate material has a refractive index of at least 2.1 to 2.7. Example 16 A head mounted display system according to any of the previous embodiments, wherein the substrate material has a refractive index of at least 2.2 to 2.7. Example 17 A head mounted display system according to any of the previous embodiments, wherein the substrate material has a refractive index of at least 2.3 to 2.7. Example 18 A head mounted display system according to any of the previous embodiments, wherein the substrate material has a refractive index of at least 2.3 to 2.4. Example 19 A head mounted display system according to any of the previous embodiments, wherein the substrate material has a refractive index of at least 2.3 to 2.5. Example 20 A head mounted display system according to any of the previous embodiments, wherein the substrate material has a refractive index of at least 2.6 to 2.7. Example 21 10. A head mounted display system according to any of the preceding examples, wherein the blazed grating comprises diffractive features having points spaced apart by grooves therebetween. Example 22 10. A head mounted display system according to any of the preceding examples, wherein the blazed diffraction grating comprises diffractive features comprising a plurality of straight lines. Example 23 A head mounted display system according to any of the previous embodiments, wherein the blazed diffraction grating comprises diffractive features having a tip height or groove depth of 40 to 120 nm. Example 24 A head mounted display system according to any of the previous embodiments, wherein the blazed diffraction grating comprises diffractive features having a tip height or groove depth of 60-100 nm. Example 25 A head mounted display system according to any of the previous embodiments, wherein the blazed diffraction grating comprises diffractive features having a peak height or groove depth of 70-90 nm. Example 26 10. A head mounted display system according to any of the preceding examples, wherein the blazed grating comprises diffractive features having a peak height or groove depth of about 80 nm. Example 27 10. The waveguide of any of the preceding embodiments, wherein the diffractive features are asymmetric. Example 28 A head mounted display system according to any of the preceding embodiments, wherein the blazed diffraction grating has a pitch of 250 to 350 nm. Example 29 A head mounted display system according to any one of the preceding embodiments, wherein the blazed diffraction grating has a pitch of 300 to 450 nm. Example 30 A head mounted display system according to any of the previous embodiments, wherein the substrate is planar and the blazed diffraction grating has a blaze angle of 10 to 30 degrees relative to the plane of the substrate. Example 31 A head mounted display system according to any of the previous embodiments, wherein the substrate is planar and the blazed diffraction grating has a blaze angle of 15 to 25 degrees relative to the plane of the substrate. Example 32 10. A head mounted display system according to any of the preceding embodiments, wherein the substrate is planar and the blazed grating has a blaze angle of about 19.5 degrees relative to the plane of the substrate. Example 33 A head mounted display system according to any of the preceding embodiments, wherein the first diffraction efficiency is 1 to 1.5 times the second diffraction efficiency. Example 34 A head mounted display system according to any of the preceding embodiments, wherein the first diffraction efficiency is 1 to 1.4 times the second diffraction efficiency. Example 35 A head mounted display system according to any of the preceding embodiments, wherein the first diffraction efficiency is 1 to 1.3 times the second diffraction efficiency. Example 36 A head mounted display system according to any of the preceding embodiments, wherein the first diffraction efficiency is 1 to 1.2 times the second diffraction efficiency. Example 37 A head mounted display system according to any of the preceding embodiments, wherein the first diffraction efficiency is 1 to 1.1 times the second diffraction efficiency. Example 38 10. A head mounted display system according to any of the previous embodiments, wherein the range of angles is at least 6 degrees. Example 39 10. A head mounted display system according to any of the previous embodiments, wherein the range of angles is at least 12 degrees. Example 40 10. A head mounted display system according to any of the previous embodiments, wherein the range of angles is at least 18 degrees. Example 41 10. A head mounted display system according to any of the previous embodiments, wherein the range of angles is at least 22 degrees. Example 42 A head mounted display system according to any of the previous examples, wherein the range of angles is between ±3 degrees relative to the plane of the substrate. Example 43 A head mounted display system according to any of the previous examples, wherein the range of angles is between ±6 degrees relative to the plane of the substrate. Example 44 A head mounted display system according to any of the previous examples, wherein the range of angles is between ±9 degrees relative to the plane of the substrate. Example 45 A head mounted display system according to any of the previous examples, wherein the range of angles is between ±11 degrees relative to the plane of the substrate. Example 46 10. The head mounted display system of any of the preceding examples, wherein the first and second polarizations comprise first and second linear polarizations having different polarization angles. Example 47 10. The head mounted display system of any of the preceding examples, wherein the first and second polarizations comprise first and second linear polarizations oriented in orthogonal directions. Example 48 10. A head-mounted display system according to any of the preceding examples, wherein the first and second polarization directions comprise transverse magnetic and transverse electric polarizations, respectively. Example 49 10. A head mounted display system according to any of the preceding examples, wherein the first and second polarization directions comprise transverse electric and transverse magnetic polarizations, respectively. Example 50 A head-mounted display system as described in any of the above examples, wherein the first diffraction efficiency comprises a diffraction efficiency for transverse magnetic polarization averaged across the visible light spectrum, and the second diffraction efficiency comprises a diffraction efficiency for transverse electric polarization averaged across the visible light spectrum. Example 51 A head-mounted display system as described in any of the above examples, wherein the first diffraction efficiency comprises a diffraction efficiency for transverse electric polarization averaged across the visible light spectrum, and the second diffraction efficiency comprises a diffraction efficiency for transverse magnetic polarization averaged across the visible light spectrum. Example 52 A head-mounted display system as described in any of the above examples, wherein the waveguide is included in an eyepiece configured to direct light to the eye of a user wearing the head-mounted display. Example 53 A head-mounted display system as described in Example 52, wherein the eyepiece is positioned on the frame and configured to direct light from the light projection system into the user's eye and display augmented reality image content in the user's field of view, at least a portion of the eyepiece is transparent and is positioned in front of the user's eye when the user wears the head-mounted display system, and the transparent portion allows light from a portion of the physical environment in front of the user to pass through to the user's eye and provide a view of a portion of the physical environment in front of the user. Example 54 A head-mounted display system as described in Example 52 or 53, wherein the eyepiece lens comprises at least one waveguide, and the at least one waveguide is transparent to visible light so that a user can see through the waveguide. Example 55 A head-mounted display system as described in any of the above examples, wherein the waveguide comprises an internal coupling optical element for coupling light from the optical projection system into the waveguide so that it is guided therein. Example 56 A head-mounted display system as described in any of the above examples, wherein the waveguide comprises an external coupling optical element for coupling light from the optical projection system out of the waveguide, directing the light to a user's eye, and presenting the image content to a viewer. Example 57 A head-mounted display system as described in any of the above examples, wherein the blazed diffraction grating comprises an internal coupling grating (ICG) configured to internally couple light from the optical projection system into the waveguide. Example 58 A head-mounted display system as described in any of the above examples, wherein the blazed diffraction grating comprises an external coupling grating (EPE) configured to externally couple light from the optical projection system guided within the waveguide out of the waveguide. Example 59 An optical waveguide, a substrate comprising a material having a refractive index of at least 1.9, the substrate being configured to guide light coupled into the waveguide within the waveguide via total internal reflection; a layer disposed over the substrate; and a blazed diffraction grating formed within the layer; an optical waveguide, comprising: a blazed diffraction grating having a first diffraction efficiency for a first polarization over a range of angles for light incident thereon; and a second diffraction efficiency for a second polarization over a range of angles for light incident thereon; and the first diffraction efficiency is one to two times the second diffraction efficiency. Example 60 60. The optical waveguide of example embodiment 59, wherein the material having a refractive index greater than 1.9 comprises a lithium-based oxide. Example 61 61. The optical waveguide of any one of Examples 59 to 60, wherein the material having a refractive index greater than 1.9 comprises lithium niobate. Example 62 61. The optical waveguide of any one of Examples 59 to 60, wherein the material has a refractive index greater than 1.9 and comprises lithium tantalate. Example 63 60. The optical waveguide of embodiment 59, wherein the material having a refractive index greater than 1.9 comprises silicon carbide. Example 64 60. The optical waveguide of example embodiment 59, wherein the material having a refractive index greater than 1.9 comprises titanium dioxide. Example 65 60. The optical waveguide of example embodiment 59, wherein the material having a refractive index greater than 1.9 comprises zirconium dioxide. Example 66 The optical waveguide of any of Examples 59-65, wherein the layer comprises zinc oxide. Example 67 The optical waveguide of any of Examples 59-66, wherein the layer comprises silicon nitride. Example 68 The optical waveguide of any of Examples 59-67, wherein the layer comprises zirconium dioxide. Example 69 The optical waveguide of any of Examples 59-68, wherein the layer comprises titanium dioxide. Example 70 70. The optical waveguide of any of Examples 59-69, wherein the layer comprises silicon carbide. Example 71 The optical waveguide of any of Examples 59-70, wherein the layer has a lower refractive index than the substrate. Example 72 The optical waveguide of any of Examples 59-71, wherein the blazed grating comprises diffractive features having a tip height or groove depth of 40 to 120 nm. Example 73 The optical waveguide of any of Examples 59-72, wherein the blazed grating comprises diffractive features having a tip height or groove depth of 60-100 nm. Example 74 The optical waveguide of any of Examples 59-73, wherein the blazed grating comprises diffractive features having a tip height or groove depth of 70-90 nm. Example 75 The optical waveguide of any of Examples 59-74, wherein the blazed grating comprises diffractive features having a peak height or groove depth of about 80 nm. Example 76 The optical waveguide of any of Examples 59-75, wherein the diffractive characteristics are asymmetric. Example 77 A head-mounted display system as described in any of Examples 1-58 or an optical waveguide as described in any of Examples 59-76, wherein the blazed diffraction grating comprises diffractive features formed in a one-dimensional (1D) array. Example 78 A head-mounted display system as described in any of Examples 1-58 or an optical waveguide as described in any of Examples 59-76, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array. Example 79 A head-mounted display system described in any of Examples 1-58 or an optical waveguide described in any of Examples 59-76, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array comprising a square array. Example 80 A head-mounted display system described in any of Examples 1-58 or an optical waveguide described in any of Examples 59-76, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array, and the blazed diffraction grating comprises a 1D grating. Example 81 A head-mounted display system described in any of Examples 1-58 or an optical waveguide described in any of Examples 59-76, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array, and the blazed diffraction grating comprises a 2D grating. Example 82 A head-mounted display system as described in any of Examples 1-58 or an optical waveguide as described in any of Examples 59-76, wherein the blazed diffraction grating comprises diffractive features formed in a two-dimensional (2D) array, and the blazed diffraction grating comprises a 2D grating having a square array. Example 83 A head-mounted display system described in any of Examples 1-58 or an optical waveguide described in any of Examples 59-76, wherein the blazed diffraction grating is configured to preferentially direct light in at least two directions. Example 84 A head-mounted display system according to any one of Examples 1-58 or an optical waveguide according to any one of Examples 59-76, wherein the blazed diffraction grating is blazed in two directions. Example 85 A head-mounted display system described in any of Examples 1-58 or an optical waveguide described in any of Examples 59-76, wherein the blazed diffraction grating comprises an internal coupling optical element arranged to receive light from an image source and couple the light into the substrate so that it is guided therein. Example 86 A head-mounted display system described in any of Examples 1-58 or an optical waveguide described in any of Examples 59-76, wherein the blazed diffraction grating comprises a light-dispersing optical element arranged to receive light from an image source guided within the substrate and direct the light to an external coupling optical element so that it is coupled out of the substrate. Example 87 A head-mounted display system described in any of Examples 1-58 or an optical waveguide described in any of Examples 59-76, wherein the blazed diffraction grating comprises a light-dispersing optical element arranged to receive light from an image source guided within the substrate and diffuse the light within the waveguide to increase the beam size or eyebox size. Example 88 A head-mounted display system described in any of Examples 1-58 or an optical waveguide described in any of Examples 59-76, wherein the blazed diffraction grating comprises an external coupling optical element arranged to receive light from an image source guided within the substrate and couple the light out from the substrate. Example 89 A head-mounted display system described in any of Examples 1-58 or an optical waveguide described in any of Examples 59-76, wherein the blazed diffraction grating comprises a combined light dispersion / external coupling optical element arranged to receive light from an image source guided within the substrate, diffuse the light in at least two directions, and couple the light out from the substrate. Example 90 A head-mounted display system described in any of Examples 1-58 or an optical waveguide described in any of Examples 59-76, wherein the blazed diffraction grating has an associated pupil expander-extractor arranged to receive light from an image source guided within the substrate, diffuse the light, and couple the light out of the substrate. (Additional Considerations)

[0164] In the foregoing specification, the invention has been described with reference to specific embodiments thereof. It will, however, be apparent that various modifications and changes can be made therein without departing from the broader spirit and scope of the invention. The specification and drawings are, therefore, to be regarded in an illustrative rather than a restrictive sense.

[0165] Indeed, it should be understood that the systems and methods of the present disclosure each have several innovative aspects, no single one of which is solely responsible for or required for the desirable attributes disclosed herein. The various features and processes described above may be used independently of one another or may be combined in various ways. All possible combinations and subcombinations are intended to fall within the scope of the present disclosure.

[0166] Certain features described herein in the context of separate embodiments may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented in multiple embodiments separately or in any suitable subcombination. Furthermore, while features may be described above as operative in a combination and may even be initially claimed as such, one or more features from the claimed combination may, in some cases, be deleted from the combination, and the claimed combination may be directed to a subcombination or variation of the subcombination. No single feature or group of features is required or essential to every embodiment.

[0167] In particular, conditional statements used herein, such as "can," "could," "might," "may," "eg," and the like, should be understood to generally convey that certain embodiments include certain features, elements, and / or steps, while other embodiments do not, unless specifically stated otherwise or understood otherwise within the context as used. Thus, such conditional statements are generally not intended to imply that features, elements, and / or steps are in any way required for one or more embodiments, or that one or more embodiments necessarily include logic for determining whether those features, elements, and / or steps are to be included or performed in any particular embodiment, with or without authorial input or prompting. The terms "comprising," "including," "having," and the like, are synonymous and used inclusively in a non-limiting manner and do not exclude additional elements, features, acts, operations, etc. Also, the term "or," for example, when used to connect a list of elements, is used in its inclusive sense (and not its exclusive sense), so as to mean one, some, or all of the elements in the list. Additionally, the articles "a," "an," and "the," as used in this application and the appended claims, should be interpreted to mean "one or more" or "at least one," unless otherwise specified. Similarly, while operations may be depicted in the figures in a particular order, it should be recognized that such operations need not be performed in the particular order shown, or in sequential order, or that all of the illustrated operations need not be performed, to achieve desirable results. Furthermore, the figures may diagrammatically depict one or more exemplary processes in the form of a flowchart. However, other operations not depicted may also be incorporated within the diagrammatically illustrated exemplary methods and processes. For example, one or more additional operations may be performed before, after, concurrently with, or during any of the illustrated operations.Additionally, operations may be rearranged or reordered in other embodiments. In some situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system components in the above-described embodiments should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems may generally be integrated together in a single software product or packaged into multiple software products. Additionally, other implementations are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results.

[0168] Thus, the claims are not intended to be limited to the embodiments shown herein but are to be accorded the widest scope consistent with the present disclosure, the principles, and novel features disclosed herein.

Claims

1. An optical waveguide, wherein the optical waveguide is A substrate configured to guide light coupled into the optical waveguide through total internal reflection within the optical waveguide, A diffraction grating formed on the surface of the substrate Equipped with, The diffraction grating comprises a plurality of protrusions, each of which includes a first side wall and a second side wall opposite to the first side wall, the first side wall forming a first inclination angle with respect to the surface of the substrate, and the second side wall forming a second inclination angle with respect to the surface of the substrate, the first inclination angle being greater than the second inclination angle. The diffraction grating has a first diffraction efficiency for light having a first state over an angular range with respect to light incident on the diffraction grating, and the diffraction grating has a second diffraction efficiency for light having a second state over the angular range with respect to light incident on the diffraction grating. The first state is a transversely electrically polarized state, and the second state is a transversely magnetically polarized state. Both the first diffraction efficiency and the second diffraction efficiency are for blue light, An optical waveguide in which the first diffraction efficiency is 1 to 2 times that of the second diffraction efficiency.

2. The optical waveguide according to claim 1, wherein the substrate has a refractive index of at least about 1.9, at least about 2.0, at least about 2.1, at least about 2.2, at least about 2.3, at least about 2.4, at least about 2.5, at least about 2.6, or up to 2.7, or any range between any of these values.

3. The optical waveguide according to claim 1, wherein the substrate comprises one or more of lithium-based oxides, silicon carbide, zirconium dioxide, or titanium dioxide.

4. The optical waveguide according to claim 1, wherein the diffraction grating has diffraction features having a tip height or groove depth of 10 nm to 150 nm.

5. The optical waveguide according to claim 1, wherein the diffraction grating comprises a plurality of protrusions arranged in a two-dimensional (2D) array.

6. The optical waveguide according to claim 5, wherein the diffraction grating comprises the plurality of protrusions arranged in a square array.

7. The optical waveguide according to claim 5, wherein the diffraction grating comprises a plurality of protrusions arranged in a grating pattern.

8. The optical waveguide according to claim 5, wherein the diffraction grating is configured to direct light in two or more directions.

9. The diffraction grating is An internal coupling optical element is arranged to receive light from an image source and couple the light into the substrate so that the light is guided within the substrate, An external coupling optical element is provided to receive light from an image source induced within the substrate and to couple the light out of the substrate. Optical dispersion elements and Having one or more of the following, The aforementioned light-dispersing optical element receives light from an image source induced within the substrate, The light is directed towards an external coupling optical element so that it is coupled to the outside of the substrate, By diffusing the aforementioned light within the optical waveguide, the beam size or eyebox size can be increased. An optical waveguide according to claim 1, arranged to perform one or more of the following:

10. The optical waveguide according to claim 1, wherein the plurality of protrusions are tapered in thickness with increasing height.

11. The optical waveguide according to claim 1, wherein the plurality of protrusions are arranged to preferentially direct light based on the first tilt angle and the second tilt angle.

12. A head-mounted display system, wherein the head-mounted display system is A frame that can be mounted on the head, A light projection system configured to provide image content by outputting light, An eyepiece comprising an optical waveguide as described in any one of claims 1 to 11 Equipped with, A head-mounted display system wherein the optical waveguide is arranged to guide at least a portion of the light output by the light projection system.

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