Fabrication of tilted gratings

Abstract

The present disclosure relates to optical components for display systems, such as augmented and virtual reality display systems. The method includes patterning a plurality of first trenches in a surface of a substrate and etching the plurality of first trenches with an etchant having an etch rate for a first crystal plane of the substrate that is greater than an etch rate for a second crystal plane of the substrate. The etching forms a tilted grating in the substrate. In some embodiments, sidewalls of the tilted grating are defined by the second crystal plane.

Description

[Technical Field]

[0001] Field of Disclosure The present disclosure relates to optical components for display systems, such as augmented and virtual reality display systems. [Background technology]

[0002] background Modern computing and display technologies have facilitated the development of systems for so-called "virtual reality" or "augmented reality" experiences, in which digitally rendered images or portions thereof are presented to the user in such a way that they appear 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. 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, typically involving virtual objects that are integrated into and responsive to the natural world. For example, in MR scenarios, AR image content can be blocked by, or otherwise perceived as, interacting with real-world objects.

[0003] Referring to FIG. 1 , an augmented reality scene 10 is shown in which a user of the AR technology sees a real-world, park-like setting 20 featuring people, trees, buildings, and a concrete platform 30 in the background. In addition to these items, the user of the AR technology also perceives "seeing" "virtual content," such as a robotic figure 40 standing on the real-world platform 30 and a flying, cartoon-like avatar character 50 resembling an anthropomorphic bumblebee, although these elements 40, 50 do not even exist in the real world. Due to the complexity of the human visual perception system, it can be difficult to create AR technology that facilitates a pleasant, natural-feeling, rich presentation of virtual image elements among other virtual or real-world image elements.

[0004] The systems and methods disclosed herein address various challenges associated with AR and VR technologies. Summary of the Invention [Means for solving the problem]

[0005] overview Some embodiments of the present disclosure describe a method that includes patterning a plurality of first trenches in a surface of a substrate and etching the plurality of first trenches with an etchant having an etch rate for a first crystal face of the substrate that is greater than an etch rate for a second crystal face of the substrate. The etching forms a tilted lattice in the substrate.

[0006] This method and the other described methods can have at least one or more of the following features.

[0007] In some embodiments, the sidewalls of the tilted lattice are defined by the second crystal plane.

[0008] In some embodiments, the substrate has a diamond cubic crystal structure and the second crystallographic plane is a {1 1 1} plane of the diamond cubic crystal structure.

[0009] In some embodiments, the substrate comprises a silicon substrate or a germanium substrate.

[0010] In some embodiments, the etchant comprises potassium hydroxide (KOH) or tetramethylammonium hydroxide (TMAH).

[0011] In some embodiments, the tilted lattice is formed by a plurality of second trenches, each having a depth extending into the surface of the substrate, a width extending between two sidewalls defined by {1 1 1} planes, and a length greater than the width, the length extending parallel to the <1 1 0> direction of the diamond cubic crystal structure.

[0012] In some embodiments, the width extends parallel to the <2 −1 −1> direction of the diamond cubic crystal structure.

[0013] In some embodiments, the substrate comprises a (1 1 1) oriented substrate, and the sidewalls of the tilted grating have a tilt angle of about 19.5° degrees.

[0014] In some embodiments, the normal to the surface of the substrate has a first angle of 19.5°-θ° with respect to the {1 1 1} plane of the diamond cubic crystal structure, and the sidewalls of the tilted lattice have a tilt angle equal to the first angle, where 0°<θ°<19.5°.

[0015] In some embodiments, the normal to the surface of the substrate has a first angle of 19.5°+θ° with respect to the {1 1 1} planes of the diamond cubic crystal structure, and the sidewalls of the tilted lattice have a tilt angle equal to the first angle, where θ°>0°.

[0016] In some embodiments, the surface of the substrate is tilted in the <2 −1 −1> direction of the diamond cubic crystal structure relative to the (1 1 1) plane of the diamond cubic crystal structure.

[0017] In some embodiments, patterning the plurality of first trenches in the surface of the substrate includes forming a mask over the surface of the substrate and anisotropically etching the substrate through openings in the mask to form the plurality of first trenches.

[0018] In some embodiments, each trench of the plurality of first trenches has vertical sidewalls.

[0019] In some embodiments, anisotropically etching the substrate comprises plasma etching the substrate.

[0020] In some embodiments, the method includes removing the mask from the surface of the substrate after etching the plurality of first trenches.

[0021] In some embodiments, the method includes removing a portion of the mask adjacent to at least one first trench of the plurality of first trenches after patterning the plurality of first trenches and before etching the plurality of first trenches.

[0022] In some embodiments, the base of the tilted lattice is defined by the second crystallographic plane.

[0023] In some embodiments, the tilted lattice is formed by a plurality of second trenches, each having a width extending between two sidewalls defined by the second crystal plane, the width being between 50 nm and 1 μm.

[0024] In some embodiments, the tilted grating has a pitch between 20 μm and 200 μm.

[0025] In some embodiments, the tilted grating is formed by a plurality of second trenches, and the depth of the second trenches is between 50 nm and 1 μm.

[0026] In some embodiments, the method includes imprinting a replication material using the tilted grating as a mold to form a corresponding tilted grating in the replication material.

[0027] In some embodiments, the method includes determining a target width for the second trenches of the sloped grating, determining a first width based on the target width and a predetermined change in width caused by the etchant, and patterning the plurality of first trenches to have the first width.

[0028] Some aspects of the present disclosure describe another method that includes providing a master template substrate, forming a tilted grating pattern in a surface of the master template substrate, and using the master template substrate with the tilted grating pattern to imprint the tilted grating pattern onto a device substrate.

[0029] This method and the other described methods can have at least one or more of the following features.

[0030] In some embodiments, the master template substrate has a diamond cubic crystal structure, and the tilted grating pattern is defined by a first {1 1 1} plane of the diamond cubic crystal structure.

[0031] In some embodiments, the method includes forming a second tilted grating pattern in a surface of the master template substrate, the second tilted grating pattern being defined by second {1 1 1} planes of the diamond cubic crystal structure, the second {1 1 1} planes being different from the first {1 1 1} planes.

[0032] In some embodiments, the sidewalls of the tilted grating pattern are defined by crystal planes of the master template substrate.

[0033] In some embodiments, the tilted grating pattern is a first tilted grating pattern, and the method includes forming a second tilted grating pattern in a surface of a master template substrate, the second tilted grating pattern having a different alignment direction than the first tilted grating pattern and the second tilted grating pattern, and imprinting the second tilted grating pattern on a device substrate using the master template substrate.

[0034] Some aspects of the present disclosure describe another method, which includes determining a target tilt angle of a tilted lattice, determining a substrate orientation corresponding to the target tilt angle based on a crystal structure of a material, providing a substrate having the determined substrate orientation, the substrate being composed of the material, and forming a tilted lattice in a surface of the substrate.

[0035] In some embodiments, providing a substrate having the determined substrate orientation includes determining a cutting angle based on the substrate orientation, and slicing an ingot of material at the cutting angle to obtain a substrate sliced ​​from the ingot having the determined substrate orientation.

[0036] Some embodiments of the present disclosure describe another method. The method includes providing a substrate including a first set of parallel trenches and a second set of parallel trenches, and etching the first set of parallel trenches to form a first tilted lattice and the second set of trenches to form a second tilted lattice. The first tilted lattice includes first trenches, each having a first width defined by two first crystal planes and a first length greater than the first width. The second tilted lattice includes second trenches, each having a second width defined by two second crystal planes and a second length greater than the second width. The first and second lengths extend in different directions.

[0037] This method and the other described methods can have at least one or more of the following features.

[0038] In some embodiments, the etching of the first set of parallel trenches and the etching of the second set of trenches are performed in a common simultaneous etching process.

[0039] In some embodiments, the substrate has a diamond cubic crystal structure, the first crystallographic face is a first {1 1 1} plane, and the second crystallographic face is a second {1 1 1} plane that is different from the first {1 1 1} plane.

[0040] Some aspects of the present disclosure describe an optical device that includes a waveguide and a tilted grating positioned to guide light into the waveguide, the tilted grating having a tilt angle of 19.5°.

[0041] Some aspects of the present disclosure describe an optical device that includes a waveguide and a tilted grating defined in a surface of a substrate, the tilted grating being positioned to guide light into the waveguide, with sidewalls of the tilted grating defined by crystal planes of the substrate.

[0042] In some embodiments, the substrate has a diamond cubic crystal structure and the sidewalls are defined by the {1 1 1} planes of the diamond cubic crystal structure.

[0043] In some embodiments, the substrate comprises a waveguide.

[0044] Some aspects of the present disclosure describe a display system including a waveguide and an optical coupling element including a tilted grating, the tilted grating being fabricated in a process including etching the substrate with an etchant having an etching rate for a first crystal face of the substrate that is greater than the etching rate for a second crystal face of the substrate.

[0045] This and other described display systems can have at least one or more of the following features.

[0046] In some embodiments, the display system includes a virtual reality (VR) or augmented reality (AR) display system.

[0047] In some embodiments, the substrate comprises a waveguide.

[0048] In some embodiments, the process forms a master template tilted grating in a substrate, and the tilted grating of the opto-coupling elements is formed in the replication material by imprinting the master template tilted grating in the replication material.

[0049] The tilted grating of the optical coupling element can be any tilted grating shown and / or described throughout this disclosure (e.g., tilted gratings 1122, 1522, or 1822) and / or a tilted grating formed by imprinting a tilted grating into a device substrate using one of the tilted gratings as a master template. The process for forming the tilted grating can include any of the processes shown and / or described throughout this disclosure, such as the processes shown in Figures 11A-11E, 15A-15B, 17A-17D, 18A-18C, 19A-19B, 20, or 21A-21B.

[0050] The details of one or more embodiments are set forth in the accompanying drawings and the description below. Other aspects, features, and advantages will become apparent from the description and drawings, and from the claims. [Brief explanation of the drawings]

[0051] BRIEF DESCRIPTION OF THE DRAWINGS [Figure 1] FIG. 1 shows a user's view of an augmented reality (AR) device.

[0052] [Figure 2] FIG. 2 shows a conventional display system for simulating a three-dimensional image for a user.

[0053] [Figure 3] 3A-3C show the relationship between the radius of curvature and the radius of focus.

[0054] [Figure 4A] Figure 4A shows a representation of the accommodation-vergence-divergence motor response of the human visual system.

[0055] [Figure 4B] FIG. 4B shows examples of different accommodation and vergence / divergence states of a user's eye pair.

[0056] [Figure 4C] FIG. 4C shows an example of a representation of a top-down view of a user viewing content through a display system.

[0057] [Figure 4D] FIG. 4D shows another example of a representation of a top view of a user viewing content through a display system.

[0058] [Figure 5] FIG. 5 illustrates an embodiment of a technique for simulating a three-dimensional image by correcting for wavefront divergence.

[0059] [Figure 6] FIG. 6 shows an example of a waveguide stack for outputting image information to a user.

[0060] [Figure 7] FIG. 7 shows an example of an emitted beam output by a waveguide.

[0061] [Figure 8] FIG. 8 shows an example of a stacked waveguide assembly in which each depth plane contains an image formed using multiple different component colors.

[0062] [Figure 9A] FIG. 9A shows a cross-sectional side view of an example set of stacked waveguides, each containing an incoupling optical element.

[0063] [Figure 9B] FIG. 9B shows a perspective view of an example of multiple stacked waveguides of FIG. 9A.

[0064] [Figure 9C] FIG. 9C shows a top view of an example of multiple stacked waveguides of FIGS. 9A and 9B.

[0065] [Figure 9D] FIG. 9D shows an example of a wearable display system.

[0066] [Figure 10A] FIG. 10A shows an example of a tilted grating.

[0067] [Figure 10B] FIG. 10B shows an example of a display device including a tilted grating.

[0068] [Figure 11-1] 11A-11E show an example of a process for fabricating a tilted grating. [Figure 11-2] 11A-11E show an example of a process for fabricating a tilted grating. [Figure 11-3] 11A-11E show an example of a process for fabricating a tilted grating.

[0069] [Figure 12] 12A and 12B show an example of a substrate having an orientation suitable for producing a tilted grating.

[0070] [Figure 13] FIG. 13 is a scanning electron microscope image of the tilted grating.

[0071] [Figure 14] 14A and 14B show an example of the substrate orientation based on the cutting angle.

[0072] [Figure 15] 15A-15B show an example of a process for fabricating a tilted grating.

[0073] [Figure 16]16A and 16B show an example of the substrate orientation based on the cutting angle.

[0074] [Figure 17-1] 17A-17D show an example of a process for fabricating a tilted grating. [Figure 17-2] 17A-17D show an example of a process for fabricating a tilted grating.

[0075] [Figure 18-1] 18A-18C show an example of a process for fabricating a tilted grating. [Figure 18-2] 18A-18C show an example of a process for fabricating a tilted grating.

[0076] [Figure 19] 19A-19B show an example of an imprint process.

[0077] [Figure 20] FIG. 20 shows an example of a process for making a tilted grating.

[0078] [Figure 21] 21A-21B show an example of a process for fabricating a tilted grating. DETAILED DESCRIPTION OF THE INVENTION

[0079] Detailed Description The AR system may display virtual content to a user or viewer while allowing the user to see the surrounding world. Preferably, this content is displayed on a head-mounted display, e.g., 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 to enable a view of the surrounding environment. As used herein, a "head-mounted" or "head-mountable" display is understood to be a display that can be worn on the viewer's or user's head.

[0080] Various AR systems disclosed herein include virtual / augmented / mixed displays, which may include one or more optical elements formed on or as part of a waveguide. The optical elements may include, for example, incoupling optics that can be employed to couple light into the waveguide and / or outcoupling optics that can be employed to couple light out of the waveguide to a user's eye. To achieve high efficiency in incoupling light into the waveguide and / or outcoupling light from the waveguide, the optical elements may include diffraction gratings. In some display systems, the relatively high diffraction efficiency of the optical elements may be achieved in part by including a tilted grating, which is one type of diffraction grating that can provide high diffraction efficiency for incoupled / outcoupled light. The tilted grating can be fabricated by imprinting a tilted grating pattern on a device substrate, such as a waveguide, using a device master template.

[0081] 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 representations which are not necessarily drawn to scale.

[0082] FIG. 2 illustrates a conventional display system for simulating a three-dimensional image for a user. It will be appreciated 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 separate images 190, 200, one to each eye, with slightly different views of the same virtual object, corresponding to the views of the virtual object that would be seen by each eye 210, 220 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.

[0083] Continuing with reference to FIG. 2 , images 190 and 200 are spaced a distance 230 along the z-axis from eyes 210 and 220. The z-axis is parallel to the viewer's optical axis, with the viewer's eyes fixating on an object at optical infinity directly in front of the viewer. Images 190 and 200 are flat and are at a fixed distance from eyes 210 and 220. Based on slightly different views of the virtual object in the images presented to each eye 210 and 220, the eyes naturally rotate, causing the image of the object to fall on corresponding points on each eye's retina to maintain single binocular vision. This rotation can cause the gaze of each eye 210 and 220 to converge on a point in space where the virtual object is perceived to reside. As a result, providing a three-dimensional image traditionally involves manipulating the convergence and divergence of the user's eyes 210 and 220 and providing binocular cues that the human visual system interprets to provide the perception of depth.

[0084] However, creating a realistic and comfortable depth perception is challenging. It is understood that light from objects at different distances from the eye has wavefronts with different amounts of divergence. Figures 3A-3C illustrate the relationship between distance and divergence of light rays. The distances between the object and the eye 210 are represented by R1, R2, and R3, in order of decreasing distance. As shown in Figures 3A-3C, light rays become more divergent as the distance to the object decreases. Conversely, as the distance increases, light rays become more collimated. In other words, the light field produced by a point (an object or portion of an object) may be said to have a spherical wavefront curvature that is a function of how far the point is from the user's eye. The curvature increases as the distance between the object and the eye 210 decreases. While only a single eye 210 is shown in Figures 3A-3C and other figures herein for clarity, discussions regarding the eye 210 may also apply to both eyes 210 and 220 of the viewer.

[0085] Continuing with reference to FIGS. 3A-3C , light from an object at which a viewer's eye is fixating may have different degrees of wavefront divergence. Due to the different amounts of wavefront divergence, the light may be focused differently by the eye's lens, which may then need to assume different shapes to 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 trigger the ciliary muscles surrounding the eye's lens to relax or contract, thereby adjusting the force applied to the suspensory ligaments that hold the lens in place, thus changing the shape of the eye's lens until retinal blur of the fixated object is eliminated or minimized, thereby forming a focused image of the fixated object on the eye's retina (e.g., the fovea). The process by which the eye's lens changes shape may be called accommodation, and the shape of the eye's lens required to form a focused image of a gazed-at object on the eye's retina (e.g., the fovea) may be called the state of accommodation.

[0086] Referring now to Figure 4A, a representation of the accommodation-vergence response of the human visual system is shown. Eye movements to fixate on an object cause 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 may provide a cue for accommodation, and the relative location of the image on the retina may provide a cue for vergence. Accommodative cues cause accommodation, resulting in each eye's lens adopting a specific accommodation state that forms a focused image of the object on the eye's retina (e.g., the fovea). Conversely, vergence cues cause vergence movements (eye rotations) so that the images formed on each retina of each eye are at corresponding retinal points, maintaining single binocular vision. In these positions, the eyes may be said to adopt a specific vergence state. Continuing with reference to FIG. 4A , accommodation may be understood as the process by which the eyes achieve a particular accommodation state, and convergence may be understood as the process by which the eyes achieve a particular convergence state. As shown in FIG. 4A , the accommodation state and convergence state of the eyes may change when the user gazes at a different object. For example, the accommodation state may change when the user gazes at a new object at a different depth on the z-axis.

[0087] Without being limited by theory, it is believed that a viewer of an object may perceive the object as "three-dimensional" through a combination of convergence-divergence and accommodation. As noted above, the vergence-divergence movement of the two eyes relative to one another (e.g., the rotation of the eyes toward or away from one another to converge the pupils to fixate on an object) is closely linked to the accommodation of the eye's lenses. Under normal conditions, changing the shape of the eye's lenses to change focus from one object to another at a different distance automatically produces a corresponding change in vergence-divergence for the same distance, under a relationship known as the "accommodation-vergence-divergence reflex." Similarly, changes in vergence-divergence cause a corresponding change in lens shape under normal conditions.

[0088] 4B, examples of different accommodation and convergence states of the eyes are shown. Eye pair 222a is fixating on an object at optical infinity, while eye pair 222b is fixating on object 221 at less than optical infinity. Notably, the convergence states of each eye pair are different, with eye pair 222a looking straight ahead and eye pair 222 converging on object 221. The accommodation states of the eyes forming each eye pair 222a and 222b are also different, as represented by the different shapes of lenses 210a, 220a.

[0089] Unfortunately, many users of conventional "3D" display systems find them uncomfortable or experience no depth perception at all due to the mismatch between accommodation and convergence states in these displays. As noted above, many stereoscopic or "3D" display systems display a scene by providing slightly different images to each eye. Such systems are uncomfortable for many viewers because, among other things, they only provide different presentations of the scene, causing changes in the eyes' convergence states without a corresponding change in the eyes' accommodation states. Rather, images are presented by displays at a fixed distance from the eyes, causing the eyes to view all image information in a single accommodation state. This arrangement adversely affects the "accommodation-vergence-divergence reflex" by causing changes in the convergence states without a corresponding change in the accommodation state. This mismatch is thought to cause discomfort to viewers. Display systems that provide better matching between accommodation and convergence may produce more realistic and comfortable simulations of three-dimensional images.

[0090] 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 may provide both vergence-divergence cues and accommodation-matching cues, thereby providing physiologically correct accommodation-vergence-divergence matching.

[0091] 4B, two depth planes 240 are shown 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 viewpoint 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 produced by points at that depth plane 240.

[0092] In the illustrated embodiment, the distance along the z-axis of depth plane 240 containing point 221 is 1 meter. As used herein, distance or depth along the z-axis may be measured at a zero point located at the exit pupil of a user's eye. Thus, depth plane 240 located at a depth of 1 meter corresponds to a distance of 1 meter away from the exit pupil of a user's eye on the optical axis of those eyes when the eyes are pointed at optical infinity. As an approximation, 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) plus the value of the distance between the device and the exit pupil of the user's eye. That value may be referred to as eye relief 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 eye relief value may be a normalized value commonly used for all viewers. For example, the eye relief may be assumed to be 20 mm, and a depth plane at a depth of 1 meter may be at a distance of 980 mm in front of the display.

[0093] 4C and 4D, examples of matched and mismatched accommodation-vergence-divergence distances are shown, respectively. As shown 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 at 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, both 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.

[0094] It will be appreciated that each of the accommodation states and convergence-divergence states of the eyes 210, 220 is 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-divergence distance V associated with the eye in a particular convergence-divergence state may be called d , or positions relative to each other. When the accommodation distance and the convergence distance are consistent, the relationship between accommodation and convergence can be said to be physiologically correct. This is considered to be the most comfortable scenario for the viewer.

[0095] However, in a stereoscopic display, the accommodation distance and the vergence distance may not necessarily match. For example, as shown in FIG. 4D , images displayed to the eyes 210, 220 may be displayed with a wavefront divergence corresponding to a depth plane 240, and the eyes 210, 220 may be in a particular accommodation state focused on points 15a, 15b on that depth plane. 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, in some embodiments, the accommodation distance 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, an accommodation-vergence mismatch exists. Such discrepancies are considered undesirable and may cause discomfort to the user. d -A d ) and can be characterized in terms of diopters.

[0096] It will be appreciated 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 discrepancy, so long as that 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 ocular lens (e.g., a waveguide in a display device) to the depth plane, etc.

[0097] Without being limited by theory, it is believed that a user may still perceive an accommodation-vergence-divergence mismatch of up to about 0.25 diopters, up to about 0.33 diopters, and up to about 0.5 diopters as physiologically correct, and the mismatch itself does not cause significant discomfort. In some embodiments, a display system disclosed herein (e.g., display system 250 of FIG. 6 ) presents 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.

[0098] 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 prescribed amount of wavefront divergence corresponding to the wavefront divergence of the light field produced 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. Additionally, it is shown that the user's other eye may be provided with image information from a similar waveguide.

[0099] In some embodiments, a single waveguide may be configured to output light with a set amount of 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 wavelength range. As a result, in some embodiments, multiples or stacks of waveguides may be utilized to provide different amounts of wavefront divergence for different depth planes and / or to output light in different wavelength ranges. As used herein, it will be understood that a depth plane may be planar or may follow the contours of a curved surface.

[0100] 6 shows 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 three-dimensional perception to the eye / brain using multiple waveguides 270, 280, 290, 300, 310. It will be appreciated that in some embodiments, display system 250 may be considered a light field display. Additionally, waveguide assembly 260 may also be referred to as an eyepiece.

[0101] In some embodiments, display system 250 may be configured to provide a substantially continuous convergence cue and multiple distinct accommodation cues. Convergence cues may be provided by displaying different images to each of the user's eyes, and accommodation cues may be provided by outputting light forming images with selectable distinct amounts of wavefront divergence. Stated another way, display system 250 may be configured to output light having variable levels of wavefront divergence. In some embodiments, each distinct level of wavefront divergence corresponds to a particular depth plane and may be provided by a particular one of waveguides 270, 280, 290, 300, 310.

[0102] 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 deliver image information to the eye at 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 act as light sources for the waveguides and may be utilized to inject image information into the waveguides 270, 280, 290, 300, 310, each of which may be configured to distribute incident light across each respective waveguide for output toward the eye 210, as described herein. Light exits output faces 410, 420, 430, 440, 450 of the image injection devices 360, 370, 380, 390, 400 and is injected into corresponding input faces 460, 470, 480, 490, 500 of the waveguides 270, 280, 290, 300, 310. In some embodiments, each of the input faces 460, 470, 480, 490, 500 may be an edge of the corresponding waveguide or may be 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 light beam (e.g., a collimated beam) may be injected into each waveguide to output a full field of cloned collimated beams, which are directed toward the eye 210 at a particular angle (and amount of divergence) corresponding to the depth plane associated with the particular waveguide. In some embodiments, a single one of the image injection devices 360, 370, 380, 390, 400 may be associated with and inject light into multiple (e.g., three) waveguides 270, 280, 290, 300, 310.

[0103] In some embodiments, image injection devices 360, 370, 380, 390, 400 are individual displays that each produce image information for injection into corresponding waveguides 270, 280, 290, 300, 310. In some other embodiments, image injection devices 360, 370, 380, 390, 400 are the output 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 injection devices 360, 370, 380, 390, 400. It will be understood that the image information provided by image injection devices 360, 370, 380, 390, 400 may include light of different wavelengths or colors (e.g., different component colors, as discussed herein).

[0104] In some embodiments, light injected into the waveguides 270, 280, 290, 300, 310 is provided by a light projector system 520 that includes a light module 530, which may include light emitters such as light emitting diodes (LEDs). Light from the light module 530 may be directed through a beam splitter 550 to and modified by a light modulator 540, such as a spatial light modulator. The light modulator 540 may be configured to change the perceived intensity of the light injected into the waveguides 270, 280, 290, 300, 310 to encode the light with image information. Examples of spatial light modulators include liquid crystal displays (LCDs), including liquid crystal on silicon (LCOS) displays. It will be understood that image injection devices 360, 370, 380, 390, 400 are shown schematically, and in some embodiments, these image injection devices may represent different light paths and locations within a common projection system configured to output light to associated ones of waveguides 270, 280, 290, 300, 310. In some embodiments, the waveguides of waveguide assembly 260 may act as ideal lenses, relaying light injected into the waveguides to the user's eye. In this concept, the object may be spatial light modulator 540, and the image may be an image on a depth plane.

[0105] In some embodiments, the display system 250 may be a scanning fiber display including 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 generally represent a single scanning fiber or a bundle of scanning fibers configured to inject light into one or more of the waveguides 270, 280, 290, 300, 310. In some embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may generally 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 will be appreciated 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 will be appreciated 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.

[0106] Controller 560 controls the operation of one or more of stacked waveguide assembly 260, including the operation of image injection 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 includes 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, by any of the various manners disclosed herein. In some embodiments, the controller may be a single integrated device or a distributed system connected by wired or wireless communication channels. Controller 560 may, in some embodiments, be part of processing module 140 or 150 (FIG. 9D).

[0107] Continuing with reference to FIG. 6 , the waveguides 270, 280, 290, 300, and 310 may be configured to propagate light within each respective waveguide by total internal reflection (TIR). The waveguides 270, 280, 290, 300, and 310 may each be planar or have another shape (e.g., curved) and have top and bottom major surfaces and edges extending between their top and bottom major surfaces. In the illustrated configuration, the waveguides 270, 280, 290, 300, and 310 may each include outcoupling optics 570, 580, 590, 600, and 610 configured to extract light from the waveguide by redirecting light propagating within each respective waveguide from the waveguide to output image information to the eye 210. The extracted light may be referred to as outcoupling light, and the outcoupling optics may be referred to as light extraction optics. The extracted light beam may be output by the waveguide where light propagating within the waveguide impinges on a light extraction optical element. The outcoupling optical elements 570, 580, 590, 600, 610 may be, for example, a grating including diffractive optical features (e.g., any of the tilted gratings described herein and / or tilted gratings formed using any of the processes described herein, including imprinting using a master template tilted grating fabricated as described herein), as further described herein. For ease of illustration and clarity of the drawings, the outcoupling optical elements 570, 580, 590, 600, 610 are shown mounted on the bottom major surfaces of the waveguides 270, 280, 290, 300, 310, but in some embodiments, they may be mounted on the top and / or bottom major surfaces and / or directly within the volume of the waveguides 270, 280, 290, 300, 310, as further discussed herein. In some embodiments, the outcoupling optical elements 570 , 580 , 590 , 600 , 610 may be formed in a layer of material attached to a transparent substrate to form 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 the piece of material.

[0108] Continuing with reference to FIG. 6 , as discussed herein, each waveguide 270, 280, 290, 300, 310 is configured to output light to 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-up 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 a first lens 350 may be configured to create a slightly convex wavefront curvature so that the eye / brain interprets light coming from the neighboring waveguide 280 as coming 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 incremental amount of wavefront curvature, causing the eye / brain to interpret the light coming from the third waveguide 290 as coming from a second focal plane that is further inward from optical infinity towards the person than the light from the next upper waveguide 280.

[0109] 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 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 coming from the world 510 on the other side of the stacked waveguide assembly 260, a compensatory lens layer 620 may be installed on top of the stack to compensate for the collective power of the lens stacks 320, 330, 340, 350 below. Such a configuration provides as many perceived focal planes as there are available waveguide / lens pairings. Both the waveguide outcoupling optics and the lens focal aspects may be static (i.e., not dynamic or electrically active). In some alternative embodiments, either or both may be dynamic using electro-active features.

[0110] 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, one set for each depth plane. This may provide advantages for forming tiled images to provide an extended field of view at those depth planes.

[0111] Continuing with reference to FIG. 6 , outcoupling optics 570, 580, 590, 600, 610 may be configured to redirect light from their respective waveguides and output this light with the 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 optics 570, 580, 590, 600, 610 that output light with different amounts of divergence depending on the associated depth plane. In some embodiments, light extraction optics 570, 580, 590, 600, 610 may be volume or surface features that may be configured to output light at a specific angle. For example, light extraction optics 570, 580, 590, 600, 610 may be volume holograms, surface holograms, and / or diffraction gratings. In some embodiments, 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).

[0112] 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. Thus, the light carrying the image information is split into several related exit beams that exit the waveguide at multiple locations, resulting in a fairly uniform pattern of exit radiation toward the eye 210 for this particular collimated beam bouncing within the waveguide.

[0113] 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 include a layer of polymer-dispersed liquid crystal in which microdroplets contain a diffractive pattern in 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 appreciably diffract incident light), or the microdroplets may be switched to a refractive index that does not match the refractive index of the host medium (in which case the pattern actively diffracts incident light).

[0114] In some embodiments, a camera assembly 630 (e.g., a digital camera including a visible light and infrared light camera) 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 condition 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 for projecting 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 for each eye to monitor each eye separately.

[0115] 7, an example of an exit beam output by a waveguide is shown. While one waveguide is shown, it will be understood that if the waveguide assembly 260 includes multiple waveguides, other waveguides within the waveguide assembly 260 (FIG. 6) may function similarly. Light 640 is injected into the waveguide 270 at the input face 460 of the waveguide 270 and propagates within the waveguide 270 by TIR. At the point where the light 640 impinges on the DOE 570, a portion of the light exits the waveguide as exit beam 650. Although exit beam 650 is shown as substantially parallel, it may be redirected to propagate to the eye 210 at an angle (e.g., forming a diverging exit beam) depending on the depth plane associated with the waveguide 270, as discussed herein. It will be understood that a substantially parallel exit beam may refer to a waveguide having outcoupling optics that outcouples light to form an image that appears to be set on a depth plane at a large distance (e.g., optical infinity) from the eye 210. Other waveguides or other sets of outcoupling optics may output an exit beam pattern that is more divergent, which requires the eye 210 to accommodate to a closer distance to focus on the retina, and is interpreted by the brain as light from a distance closer to the eye 210 than optical infinity.

[0116] In some embodiments, a full-color image may be formed in each depth plane by overlapping images of each of the component colors, for example, three or more component colors. FIG. 8 shows an example of a stacked waveguide assembly in which each depth plane includes an image formed using multiple different component colors. The illustrated embodiment shows depth planes 240a-240f, although more or fewer depths are contemplated. Each depth plane may have three or more component color images associated with it, including a first image of a first color, G, a second image of a second color, R, and a third image of a third color, B. Different depth planes are indicated in the diagram by different numbers of diopters (dpt) following the letters G, R, and B. By way of example, the number following each of these letters indicates the diopter (1 / m) or inverse distance of the depth plane from the viewer, and each box in the diagram represents an individual component color image. In some embodiments, the exact positioning of the different component color depth planes may vary to account for differences in the eye's focusing of different wavelengths of light. For example, different component color images for a given depth plane may be positioned on the depth plane corresponding to different distances from the user. Such an arrangement may improve visual acuity and user comfort and / or reduce chromatic aberration.

[0117] In some embodiments, light for each component 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, in which case three component color images are provided per depth plane. While the waveguides associated with each depth plane are shown adjacent to each other in this diagram for ease of illustration, it will 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 component colors may be output by the same waveguide, such that, for example, only a single waveguide may be provided per depth plane.

[0118] 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 may replace one or more of red, green, or blue.

[0119] It will be understood that references throughout this disclosure to a given color of light are understood to encompass light of one or more wavelengths within the wavelength range of light 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.

[0120] In some embodiments, the light source 530 (FIG. 6) may be configured to emit light at one or more wavelengths outside the viewer's visual range, such as infrared and / or ultraviolet wavelengths. Additionally, the waveguide incoupling, outcoupling, and other light redirecting structures of the display 250 may be configured to direct and emit this light from the display toward the user's eye 210, for example, for imaging and / or user stimulation applications.

[0121] Referring now to FIG. 9A , in some embodiments, light impinging on a waveguide may need to be redirected to incouple the light into the waveguide. Incoupling optics may be used to redirect and incouple the light into its corresponding waveguide. FIG. 9A shows a cross-sectional side view of an example of a plurality or set 660 of stacked waveguides, each including an incoupling optic. The waveguides may each be configured to output light of one or more different wavelengths or one or more different wavelength ranges. It will be understood that stack 660 may correspond to stacked waveguide assembly 260 ( FIG. 6 ), and the illustrated waveguides of stack 660 may correspond to portions of the plurality of 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.

[0122] The illustrated stacked waveguide set 660 includes waveguides 670, 680, and 690. Each waveguide includes an associated incoupling optical element (which may also be referred to as a light input region on the waveguide), having, for example, an incoupling optical element 700 located on a major surface (e.g., the top major surface) of waveguide 670, an incoupling optical element 710 located on a major surface (e.g., the top major surface) of waveguide 680, and an incoupling optical element 720 located on a major surface (e.g., the top major surface) of waveguide 690. In some embodiments, one or more of the incoupling optical elements 700, 710, 720 may be located on the bottom major surface of the respective waveguide 670, 680, 690 (particularly when one or more of the incoupling optical elements is a reflective, deflecting optical element). As shown, the incoupling optical elements 700, 710, 720 may be located on the upper major surfaces of their respective waveguides 670, 680, 690 (or on top of the next lower waveguide), particularly if the incoupling optical elements are transmissive deflecting optical elements. In some embodiments, the incoupling optical elements 700, 710, 720 may be located within the body of the respective waveguides 670, 680, 690. In some embodiments, as discussed herein, the incoupling optical elements 700, 710, 720 are wavelength-selective, such that they selectively redirect one or more wavelengths of light while transmitting other wavelengths of light. While shown on one side or corner of their respective waveguides 670, 680, 690, it will be understood that in some embodiments, the incoupling optical elements 700, 710, 720 may be located within other regions of their respective waveguides 670, 680, 690.

[0123] As shown, the incoupling optical elements 700, 710, 720 may be laterally offset from one another. In some embodiments, each incoupling optical element may be offset to receive light without the light passing through another incoupling optical element. For example, each incoupling optical element 700, 710, 720 may be configured to receive light from a different image injection device 360, 370, 380, 390, and 400, as shown in FIG. 6 , and may be separated (e.g., laterally spaced) from the other incoupling optical elements 700, 710, 720 so as to substantially not receive light from another one of the incoupling optical elements 700, 710, 720.

[0124] Each waveguide also includes an associated light distribution element, having, for example, a light distribution element 730 disposed on a major surface (e.g., the top major surface) of waveguide 670, a light distribution element 740 disposed on a major surface (e.g., the top major surface) of waveguide 680, and a light distribution element 750 disposed on a major surface (e.g., the top major surface) of waveguide 690. In some other embodiments, light distribution elements 730, 740, 750 may be disposed on the bottom major surface of the associated waveguide 670, 680, 690, respectively. In some other embodiments, light distribution elements 730, 740, 750 may be disposed on both the top and bottom major surfaces of the associated waveguide 670, 680, 690, respectively, or light distribution elements 730, 740, 750 may be disposed on different ones of the top and bottom major surfaces of different associated waveguides 670, 680, 690, respectively.

[0125]

[0084] The waveguides 670, 680, 690 may be spaced apart and separated by, for example, gas, liquid, and / or solid material layers. 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 the waveguides 670, 680, 690). Preferably, the refractive index of the material forming layers 760a, 760b is 0.05 or greater, or 0.10 or less than the refractive index of the material forming waveguides 670, 680, 690. Advantageously, the low refractive index layers 760a, 760b may function as cladding layers to facilitate 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 will be understood that the top and bottom of the illustrated set of waveguides 660 may include immediately adjacent cladding layers.

[0126] 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 differ between one or more waveguides, and / or the materials forming layers 760a, 760b may differ while still maintaining the various refractive index relationships noted above.

[0127] 9A, light rays 770, 780, 790 are incident on the set of waveguides 660. It will be appreciated 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).

[0128] In some embodiments, the light rays 770, 780, 790 have different properties, for example, different wavelengths or different wavelength ranges that may correspond to different colors. Each of the incoupling optics 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 optics 700, 710, 720 selectively deflects one or more particular wavelengths of light while transmitting other wavelengths to the underlying waveguide and associated incoupling optic.

[0129] For example, incoupling optical element 700 may be configured to deflect light beam 770 having a first wavelength or wavelength range while transmitting light beams 780 and 790 having different second and third wavelengths or wavelength ranges, respectively. Transmitted light beam 780 impinges on and is deflected by incoupling optical element 710 configured to deflect light of the second wavelength or wavelength range. Light beam 790 is deflected by incoupling optical element 720 configured to selectively deflect light of the third wavelength or wavelength range.

[0130] 9A , the deflected light rays 770, 780, 790 are deflected such that they propagate through their corresponding waveguides 670, 680, 690. That is, the incoupling optical element 700, 710, 720 of each waveguide deflects the light into its corresponding waveguide 670, 680, 690, incoupling the light into its corresponding waveguide. The light rays 770, 780, 790 are deflected at an angle that causes the light to propagate through their respective waveguides 670, 680, 690 by TIR. The light rays 770, 780, 790 propagate through their respective waveguides 670, 680, 690 by TIR until they impinge on the waveguide's corresponding light distribution element 730, 740, 750.

[0131] Figure 9B shows a perspective view of an example of the multiple stacked waveguides of Figure 9A. As noted above, incoupled light rays 770, 780, and 790 are deflected by incoupling optical elements 700, 710, and 720, respectively, and then propagate by TIR within waveguides 670, 680, and 690, respectively. Light rays 770, 780, and 790 then impinge on light distribution elements 730, 740, and 750, respectively. Light distribution elements 730, 740, and 750 deflect light rays 770, 780, and 790 to propagate toward outcoupling optical elements 800, 810, and 820, respectively.

[0132] In some embodiments, the light distribution elements 730, 740, 750 are orthogonal pupil expanders (OPEs). In some embodiments, the OPEs deflect or distribute light to the outcoupling optics 800, 810, 820, and in some embodiments, may increase the beam or spot size of the light as it propagates to the outcoupling optics. In some embodiments, the light distribution elements 730, 740, 750 may be omitted, and the incoupling optics 700, 710, 720 may be configured to deflect light directly to the outcoupling optics 800, 810, 820. For example, with reference to FIG. 9A , the light distribution elements 730, 740, 750 may be replaced by the outcoupling optics 800, 810, 820, respectively. In some embodiments, the outcoupling optics 800, 810, 820 are exit pupils (EPs) or exit pupil expanders (EPEs) that direct light to the viewer's eye 210 ( FIG. 7 ). It will be appreciated that an OPE may be configured to increase the dimension of the eyebox in at least one axis, and an EPE may increase the eyebox in an axis that intersects the axis of the OPE, e.g., orthogonal to the axis of the OPE. For example, each OPE may be configured to redirect a portion of the light striking the OPE to the EPE of the same waveguide while allowing the remaining portion of the light to continue propagating through the waveguide. Upon striking the OPE again, another portion of the remaining light is redirected to the EPE, which continues to propagate further through the waveguide, and so on. Similarly, upon striking the EPE, a portion of the striking light is redirected from the waveguide to the user, and that remaining portion of the light continues to propagate through the waveguide until it again strikes the EPE, at which point another portion of the striking light is redirected from the waveguide, and so on. As a result, a single incoupled light beam may be "replicated" each time a portion of that light is redirected by the OPE or EPE, thereby forming a field of cloned light beams, as shown in FIG. 6. In some embodiments, the OPE and / or EPE may be configured to modify the size of the light beam.

[0133] 9A and 9B, in some embodiments, a waveguide set 660 includes waveguides 670, 680, 690, incoupling optical elements 700, 710, 720, light distribution elements (e.g., OPEs) 730, 740, 750, and outcoupling optical elements (e.g., EPs) 800, 810, 820 for each component color. The waveguides 670, 680, 690 may be stacked with an air gap / cladding layer between each one. The incoupling optical elements 700, 710, 720 redirect or deflect incident light into their respective waveguides (with different incoupling optical elements receiving light of different wavelengths). The light then propagates at an angle that results in TIR within each waveguide 670, 680, 690. In the illustrated example, light ray 770 (e.g., blue light) is deflected by the first incoupling optical element 700 and then continues bouncing down the waveguide, interacting with the light distribution element (e.g., OPE) 730 and then the outcoupling optical element (e.g., EP) 800 in the manner previously described. Light rays 780 and 790 (e.g., green and red light, respectively) pass through the waveguide 670, whereupon light ray 780 strikes and is deflected by the incoupling optical element 710. Light ray 780 then bounces down the waveguide 680 via TIR to its light distribution element (e.g., OPE) 740 and then to the outcoupling optical element (e.g., EP) 810. Finally, light ray 790 (e.g., red light) passes through the waveguide 690 and strikes the incoupling optical element 720 of the waveguide 690. The incoupling optic 720 deflects the light ray 790 so that it propagates by TIR to the light distribution element (e.g., OPE) 750 and then by TIR to the outcoupling optic (e.g., EP) 820. The outcoupling optic 820 then finally outcouples the light ray 790 to the viewer, who also receives outcoupled light from the other waveguides 670, 680.

[0134] FIG. 9C shows a top-down view of an example of the multiple stacked waveguides of FIGS. 9A and 9B. As shown, the waveguides 670, 680, 690, along with each waveguide's associated light distribution elements 730, 740, 750 and associated outcoupling optics 800, 810, 820, may be vertically aligned. However, as discussed herein, the incoupling optics 700, 710, 720 are not vertically aligned. Rather, the incoupling optics preferably do not overlap (e.g., are laterally spaced apart as seen in the top-down view). As discussed further herein, this non-overlapping spatial arrangement facilitates one-to-one injection of light from different sources into different waveguides, thereby enabling unique coupling of specific light sources to specific waveguides. In some embodiments, arrangements including non-overlapping, spatially separated incoupling optics may be referred to as shifted pupil systems, and the incoupling optics in these arrangements may correspond to sub-pupils.

[0135] 9D shows an example of a wearable display system 60 into which the various waveguides and associated systems disclosed herein may be incorporated. In some embodiments, the display system 60 is the system 250 of FIG. 6, which schematically illustrates some portions of the system 60 in more detail. For example, the waveguide assembly 260 of FIG. 6 may be part of the display 70.

[0136] 9D , display system 60 includes a display 70 and various mechanical and electronic modules and systems to support the functionality of the display 70. Display 70 is coupled to a frame 80 that is wearable by a user 90 or viewer of the display system and configured to position display 70 in front of the user's 90 eyes. In some embodiments, display 70 may be considered eyewear. In some embodiments, a speaker 100 is coupled to frame 80 and configured to be positioned adjacent to the user's 90 ear canal (in some embodiments, a separate speaker, not shown, may be positioned adjacent the user's other ear canal, if desired, to provide stereo / shapeable sound control). Display system 60 may also include one or more microphones 110 or other devices for detecting sound. In some embodiments, the microphones are configured to allow a user to provide input or commands to system 60 (e.g., selecting voice menu commands, natural language questions, etc.) and / or enable voice communication with others (e.g., with other users of similar display systems). The microphone may further be configured as an ambient sensor for collecting audio data (e.g., sounds from the user and / or the environment). In some embodiments, the display system may also include ambient sensors 120a that are separate from the frame 80 and may be attached to the body of the user 90 (e.g., on the head, torso, limbs, etc. of the user 90). The ambient sensors 120a, in some embodiments, may be configured to obtain data characterizing a physiological state of the user 90. For example, the sensors 120a may be electrodes.

[0137] 9D , the display 70 is operably coupled to a local data processing module 140 by a communication link 130, such as a wired lead or a wireless connection, which may be mounted in a variety of configurations, such as fixedly attached to the frame 80, fixedly attached to a helmet or hat worn by the user, embedded in headphones, or otherwise removably attached to the user 90 (e.g., a backpack-type configuration, a belt-type configuration). Similarly, the sensor 120 a may be operably coupled to the local processor and data module 140 by a communication link 120 b, such as a wired lead or a wireless connection. The local processing and data module 140 may include 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 assist in processing, caching, and storing data. If desired, the 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 (e.g., cameras), microphones, inertial measurement units, accelerometers, compasses, GPS units, wireless devices, gyros, 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) for passing to display 70 after such processing or retrieval, if possible.The local processing and data module 140 may be operably coupled by communication links 170, 180 to a remote processing module 150 and a remote data repository 160, e.g., via wired or wireless communication links, such that the remote modules 150, 160 are operably coupled to each other and available as resources to the local processing and data module 140. In some embodiments, the 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 gyro. In some other embodiments, one or more of these sensors may be mounted to the frame 80 or may be a standalone structure that communicates with the local processing and data module 140 by a wired or wireless communication path.

[0138] 9D , in some embodiments, remote processing module 150 may include 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 include a digital data storage facility that may be available via 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 to local processing and data module 140 and / or remote processing module 150, e.g., information for generating augmented reality content. In some embodiments, all data is stored and all computations are performed within 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 and receive information to and from modules 140, 150, 160, e.g., via a wireless or wired connection.

[0139] Waveguides integrated with optical elements containing tilted gratings Providing an immersive experience to a user of a waveguide-based display system, such as the various display systems configured for virtual / augmented / mixed reality display applications described above, e.g., various translucent or transparent display systems, relies on, among other things, various properties of the light coupling into and out of the waveguides of the display system. For example, a virtual / augmented / mixed reality display with high light incoupling and outcoupling efficiency for one or more polarizations of light can enhance the visual experience by providing relatively high brightness and / or clarity.

[0140] As described above, for example, with reference to FIGS. 6 and 7 , display systems according to various embodiments described herein may include optical elements, such as incoupling optics, outcoupling optics, and light distribution elements, which may include a diffraction grating or a diffractive optical element (DOE). An incoupling optic, such as an incoupling grating (ICG) (which may be a tilted grating as described herein), may be employed to couple light into the waveguide, and an outcoupling optic, such as an exit pupil expander (EPE), may be employed to couple light out of the waveguide and into the user's eye. For example, as described above with reference to FIGS. 6 and 7 , light 640 injected into the waveguide 270 at the input face 460 of the waveguide 270 propagates within the waveguide 270 by total internal reflection (TIR). At the point where the light 640 impinges on the outcoupling optic 570, a portion of the light exits the waveguide as beamlet 650. In some embodiments, any of the optical elements 570, 580, 590, 600, 610 may include or be configured as a diffraction grating or DOE.

[0141] 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 or DOEs can be formed of suitable materials and have suitable structures to control various optical properties, including diffractive properties. Desirable diffractive properties include spectral selectivity, angular selectivity, polarization selectivity, high spectral bandwidth, wide field of view, and high diffraction efficiency, among other properties.

[0142] To achieve one or more of these and other advantages, including relatively high diffraction efficiency of the optical elements, various exemplary optical elements described herein include tilted gratings (sometimes referred to as "tilted diffraction gratings"). A tilted grating refers to a grating having an array of surface-relief trenches, the sidewalls of the trenches in the tiling direction of the array having a substantially uniform non-normal tilt angle with respect to the surface on which the trenches are formed, such as the substrate surface. The tilt angle partially determines the intensity of light diffracted by the tilted grating. A tilted grating can be distinguished from a blazed grating (in which the sidewalls of the surface-relief features in the tiling direction of the feature array are non-parallel to each other) and a binary grating (in which the sidewalls of the surface-relief features in the tiling direction of the feature array are perpendicular to the surface on which the features are formed). Compared to a binary grating, a tilted grating can provide higher diffraction efficiency (e.g., for a particular order, such as the first diffraction order) to, for example, more efficiently guide output light in a desired direction and / or more efficiently guide input light into a waveguide.

[0143] Tilted gratings are often (but not always) used in transmission mode. For example, a tipped grating can be placed above a waveguide. Light incident on the tipped grating passes through the grating and is diffracted into the waveguide. Compared to blazed gratings, tipped gratings can diffract light with less dependence on the polarization of the light.

[0144] FIG. 10A is a cross-sectional view of an example of a tilted grating 1000 formed in a substrate 1002. The tilted grating 1000 can be included as part of an optical element, such as an incoupling optical element and / or an outcoupling optical element, and / or the tilted grating 1000 can be used as a master template for fabricating other tilted gratings. The tilted grating 1000 includes trenches 1004 (e.g., periodically repeated trenches) tiled in an array direction 1006. Each trench 1004 (sometimes referred to herein as a "second trench" formed by etching a "first trench") is partially defined by sidewalls (e.g., sidewalls 1008 a, 1008 b) in the array direction 1006 that are substantially parallel to each other. The sidewalls 1008 a, 1008 b have a tilt angle 1010 with respect to a normal to a surface 1012 of the substrate 1002. The base 1014 of each trench 1004 has a slope angle 1016 relative to the surface 1012. The slope angle 1016 can be 0° (e.g., a flat-bottom trench) or non-zero in various embodiments.

[0145] In addition to the tilt angle 1010 and slope angle 1016, the tilted grating 1000 can be defined by a width 1018 of each trench 1004, a pitch 1020 that defines the spacing between the trenches, and a height (depth) 1022 of each trench 1004. The height 1022, as defined herein, refers to the distance between the deepest point of each trench 1004 and the surface 1012 on which the trench 1004 is defined.

[0146] In some embodiments, the width 1018 and pitch 1020 are uniform throughout the tilted grating 1000, such that the tilted grating 1000 includes a periodic array of identical trenches 1004 with identical pitch 1020. However, in some embodiments, one or both of these parameters vary between the trenches 1004. For example, by way of non-limiting example, the trenches 1004 can alternate between wider and thinner trenches (larger and smaller widths 1018) and / or can alternately be closer and farther apart (larger and smaller pitch 1020). As a further example, one or both of the width 1018 or pitch 1020 can gradually increase or decrease in the direction 1006 of the array of trenches 1004. The width 1018 and pitch 1020 of the master template can be determined by the geometry of the lithography mask features formed during fabrication of the tilted grating 1000.

[0147] In some embodiments, the width 1018 is between 50 nm and 1 μm, e.g., between 100 nm and 500 nm. In some embodiments, the pitch 1020 is between 50 nm and 2 μm. In some embodiments, the height 1022 is between 50 nm and 1 μm, e.g., between 50 nm and 400 nm. The above dimensions can be based, for example, on the wavelength(s) of light that the tilted grating is configured to diffract.

[0148] A width 1018 extends between two sidewalls 1008 (e.g., parallel sidewalls 1008 defined by crystal planes) of each trench 1004. The trenches 1004 have a length that is longer than the width 1018, e.g., a length that extends longitudinally orthogonal to the alignment direction 1006, e.g., in / out of the plane of the cross-section of FIG. 10A . For example, the length can be at least 10 times, at least 100 times, or at least 1000 times the width 1018.

[0149] The tilted grating can be fabricated by using a master template (itself a tilted grating) as an imprint mold to imprint a tilted grating pattern into a replication material on a device substrate, such as a device substrate that is or includes a waveguide. For example, the master template can be a tilted grating pattern of a "hard" material such as a semiconductor, oxide, or nitride, while the replication material can be a "soft" material such as a polymer, e.g., a thermoplastic polymer. Therefore, the quality of the tilted grating on the device substrate (determined by the topological features of the tilted grating) depends on the quality of the corresponding tilted grating in the master template.

[0150] A master template for a tilted grating can be fabricated using ion milling to form the trenches of the grating. For example, a mask layer with periodically repeating openings can be formed on a semiconductor substrate, and the substrate can be etched through the openings using an ion beam (e.g., a fluoride-based ion beam) incident on the substrate at a non-perpendicular angle. However, the trenches formed by this process often have tapered (non-parallel) and / or otherwise uneven or poorly defined sidewalls, including, for example, bumps / depressions in the sidewalls, high sidewall roughness, etc. This can result in tilted gratings with poor optical performance, such as lower diffraction efficiency and / or more scattered light, compared to tilted gratings with more uniform profiles.

[0151] Embodiments according to the present disclosure include methods for forming tilted gratings using etching processes with crystal plane selectivity. The trenches of tilted gratings formed by these methods are defined by crystal planes and are therefore highly smooth and uniform within and between trenches. The resulting tilted gratings can provide improved optical performance (e.g., higher diffraction efficiency, more efficient light incoupling, and / or more efficient light outcoupling) over more non-uniform tilted gratings formed by alternative methods. Moreover, in some embodiments, these methods replace time-consuming and expensive ion milling processes with relatively fast and lower-cost wet chemical etching, improving overall process efficiency.

[0152] FIG. 10B shows a cross-sectional view of a portion of a display device 1050 including a waveguide 1054 and a tilted grating 1000 formed on the waveguide 1054, according to some embodiments. The tilted grating 1000 is configured to diffract light having wavelengths in the visible spectrum such that the light is guided within the waveguide 1054 by TIR. The waveguide 1054 may correspond, for example, to one of the waveguides 670, 680, 690 described above with respect to FIGS. 9A-9C. As mentioned above, the tilted grating 1000 may correspond, for example, to an incoupling optical element (700, 710, 720; FIGS. 9A-9C), also referred to herein as an incoupling grating (ICG). The display device 1050 may further include various other optical elements as part of the display device described above, including outcoupling optical elements. For example, in the illustrated embodiment, display device 1050 further includes light distribution elements 730, 740, 750 similar to those described above with respect to Figures 9A-9C. Display device 1050 can include other elements including, for example, outcoupling optical elements (800, 810, 820, Figures 9A-9C).

[0153] In operation, when an incident light beam 1066, e.g., visible light, is incident on the tilted grating 1000 at an incident angle α measured with respect to a plane normal 1052 that is normal or orthogonal to the surface extending in the yx-plane (e.g., the plane of the surface 1012), the tilted grating 1000 at least partially diffracts the incident light beam 1066 as a diffracted light beam 1074 at a diffraction angle θ measured with respect to the plane normal 1052, while at least partially transmitting the incident light as a transmitted light beam 1070. When the diffracted light beam 1024 is diffracted at a diffraction angle θ that exceeds the critical angle θ_TIR at which total internal reflection occurs in the waveguide 1054, the diffracted light beam 1074 is guided within the waveguide 1054 along the x-axis via total internal reflection (TIR) ​​until the diffracted light beam 1074 reaches, for example, one of the light distribution elements 730, 740, 750 or, for example, one of the outcoupling optical elements (800, 810, 820, Figures 9A-9C).

[0154] Fabrication of tilted gratings 11A-11E illustrate an example process for fabricating a graded lattice. As shown in FIGS. 11A-11C, an array of first trenches 1106 (e.g., periodically repeating trenches) is patterned into a surface 1102 of a substrate 1104. The substrate 1104 is a crystalline substrate having a defined, regular crystal structure. For example, in some embodiments, the substrate 1104 is a silicon substrate, a germanium substrate, a crystalline aluminum oxide substrate, or another substrate having a defined, regular crystal structure that can be etched with crystallographic plane selectivity. The crystalline structure, in combination with crystallographically selective etching, facilitates the fabrication of a graded lattice, as described below.

[0155] In some embodiments (e.g., in the embodiments of FIGS. 11A-11E), the first trenches 1106 are patterned using a mask-based lithography process. As shown in FIG. 11A, a mask layer 1108 is formed / provided on a substrate 1104. The mask layer 1108 is composed of one or more materials that are selectively resistant to etching, relative to the substrate 1104, by (i) a first etching process to form the array of first trenches 1106 and (ii) a second etching process to etch the surfaces of the first trenches 1106 to form the sloped grating. For example, in some embodiments, the mask layer 1108 is an oxide (e.g., silicon oxide (e.g., silicon dioxide)), a nitride (e.g., silicon nitride), a metal, a semiconductor, or an organic material (e.g., a photoresist or a polymer). The mask layer 1108 can be formed by one or more fabrication processes such as thermal evaporation, electron beam evaporation, sputtering, chemical vapor deposition (CVD), atomic layer deposition (ALD), spin deposition, and / or film growth (e.g., oxidation of the silicon substrate 1104 to obtain a silicon dioxide mask layer 1108), any of which can be combined with thermal anneal(s) and / or other processes to form the mask layer 1108.

[0156] 11B, an opening 1110 is formed in the mask layer 1108 to expose the underlying surface 1102. For example, the opening 1110 can be formed by photolithography and / or electron beam lithography processes. In some embodiments, the mask layer 1108 is composed of a hard mask material (e.g., oxide or nitride), and the opening 1110 is formed by depositing a photoresist or electron beam resist layer over the mask layer 1108, lithographically patterning a first opening in the resist layer, and etching the mask layer 1108 through the first opening to form the opening 1110.

[0157] 11C , in some embodiments, the substrate 1104 is etched in a first etch through the openings 1110 to form first trenches 1106 tiled (e.g., periodically repeating) in the array direction 1124. The first etch is selective to the substrate 1104 compared to the mask layer 1108. In some embodiments, the substrate 1104 is a silicon substrate, and the first etch comprises a dry etch, such as a plasma etch, e.g., a chlorine-based plasma etch, a bromine-based plasma etch, and / or a fluorine-based plasma etch. If the mask layer 1108 is silicon dioxide or silicon nitride, these and / or other plasma etches may be highly selective to the silicon substrate 1104 compared to the mask layer 1108. In some embodiments, the first etch comprises another type of etch, such as a chemical etch using an etchant. In some embodiments, the first etch is a vertical anisotropic etch, such that the first trench 1106 has substantially vertical sidewalls 1112 aligned with the edges of the mask layer 1108 .

[0158] 11A-11C. For example, in some embodiments, the first trench 1106 is patterned by direct ion milling of the substrate 1104 (e.g., without using a mask layer 1108) or by a maskless stop layer method.

[0159] In some embodiments, patterning the first trenches 1106, on which the tilted grating is fabricated as described below, allows for the dimensions of the tilted grating to be set based on precise and reliable lithography methods. For example, the center-to-center distance(s) of the first trenches 1106 are equal to the pitch(es) 1020 of the tilted grating. The depth(s) of the first trenches 1106 can be approximately equal to the height(s) 1022 of the trenches of the tilted grating. Whether the height 1022 differs from the depth of the first trenches 1106 depends at least on the crystal orientation of the substrate 1104. For example, when the base of the first trench 1106 is defined by a slow etch of a crystallographic plane (e.g., when the base is defined by a (1 1 1) plane of a diamond cubic crystal structure, e.g., when the base is parallel to the surface 1102 of the (1 1 1)-oriented substrate 1104), the base is etched slowly or not at all by a subsequent crystallographically selective etch, and the height 1022 is equal to the depth of the first trench 1106. When the base is not defined by a slow plane, the height 1022 can be modified by etching. The width 1018 of the tilted lattice increases compared to the width of the first trench 1106. For example, for a (1 1 1) oriented substrate 1104, the width 1018 is increased compared to the width of the first trench 1106 by an amount (height 1022) tan(19.5°), and in some embodiments, the width 1018 is increased by about (height 1022) tan(θ), where θ is the tilt angle of the tilted grating being fabricated. Thus, the width of the first trench 1106 can be determined based on the known increase to obtain the target width 1018 of the tilted grating.

[0160] The dimensions of the first trenches 1106 can be provided by precision lithography to define openings 1110 in the mask layer 1108, followed by precision etching (e.g., using plasma etching at a well-controlled etch rate) to form the first trenches 1106 within the openings 1110. This precise control over the dimensions of the first trenches 1106 then translates to the dimensions of the trenches of the graded grating, such that the dimensions of the graded grating are precisely controllable. Thus, the graded grating can be provided with dimensions that facilitate desired optical properties.

[0161] As shown in FIG. 11D , in a second etching process, the surfaces of the first trenches 1106 are etched using an etchant with crystal face selectivity to pattern second trenches 1114 that together form a tilted lattice 1122. The etchant has crystal face selectivity in that the etchant etches a first crystal face of the substrate 1104 faster than a second crystal face of the substrate 1104. The second trenches 1114 are tiled (e.g., periodically repeated) in an array direction 1124. The second etch etches toward some crystal face(s) of the substrate 1104 (“fast” faces) faster than other crystal face(s) (“slow” faces). Appropriate selection of (i) substrate 1104, (ii) the orientation of substrate 1104 (e.g., the crystal planes represented by surface 1102), and (iii) the second etch can together result in second trench 1114 having sidewalls that are inclined relative to surface 1102. Specifically, if the slow planes of the crystal structure of substrate 1104 are at an inclination angle relative to surface 1102, the second etch can substantially terminate at those slow planes, such that the sidewalls 1116 of second trench 1114 (formed by the second etch of the surface of first trench 1106) are The tilt angle 1120 of the tilted lattice 1122 corresponds to the angle of the low-velocity plane relative to the crystal plane of the surface 1102. Because the low-velocity planes of the crystal structure are parallel to each other, the sidewalls 1116 of the second trenches 1114 are also formed parallel to each other. Furthermore, in some embodiments, the sidewalls 1116 are smooth based on the smoothness of the crystal planes (e.g., sub-nm smoothness). Moreover, the precise and reliable placement of the planes within the crystal structure allows the tilt angle 1120 to be precisely determined and configured based on knowledge of the crystal structure and the corresponding selection of the substrate 1104.

[0162] Some embodiments according to the present disclosure are based on materials with a diamond cubic crystal structure, such as silicon, germanium, silicon-germanium alloys, and diamond. When the substrate is composed of a single crystal or nearly single crystal of such a material, slow etching of the {1 1 1} plane of the substrate allows the {1 1 1} plane to define the sidewalls of the second trench, forming a tilted lattice. Slow etching of the {1 1 1} plane of diamond cubic crystal material can be provided by various chemical etchants. For example, potassium hydroxide (KOH) solutions (e.g., 10% to 50% KOH) etch the {1 1 1} plane of silicon 10x to 100x more slowly than other planes, such as the {1 1 0} and {1 0 0} planes. The {1 1 1} plane is the slow plane, while the {1 1 0} and {1 0 0} planes are the fast planes. Tetramethylammonium hydroxide (TMAH) is another example of an etchant with crystal plane selectivity to silicon that can be used to form tilted-lattice trenches with sidewalls defined by {1 1 1} planes. In one example of chemical etching, the structure shown in FIG. 11C (e.g., using a silicon substrate 1104) is immersed for 10-30 seconds, e.g., 20 seconds, in a 10%-20% solution of KOH maintained at 65°C-75°C. The etch rate of silicon under these conditions can be approximately 1 μm / min for some planes and slower for other planes, such as the {1 1 1} plane. Etching with crystal plane selectivity is not limited to wet chemical etching. In some embodiments, plasma etching with crystal plane selectivity is used. For example, for silicon, plasma etching in SF6, C4F8, and O2 gases exhibits selective slow etching of the {1 1 1} plane. In some embodiments, the germanium substrate is etched using a hydrogen peroxide (H2O2) based solution, where the {1 1 1} planes are the slow planes.

[0163] For example, the substrate can have a surface defined by the {1 1 1} plane of the diamond cubic crystal structure. As shown in Figure 12A, a (1 1 1) substrate 1200 (often supplied in wafer form as a (1 1 1) wafer) has its surface 1202 perpendicular to the [1 1 1 1] direction of the diamond cubic crystal structure, or equivalently, the surface 1202 is defined by the (1 1 1) plane of the diamond cubic crystal structure. The {1 1 1} plane family includes the (-1 1 1), (1 -1 1), and (1 1 -1) planes in addition to the (1 1 1) plane. If the substrate 1200 is a (1 1 1) substrate or a substrate having another suitable orientation (e.g., as described with reference to Figures 12A-12B, 14A-14B, and 16A-16B), one or more of the (-1 1 1), (1 -1 1), or (1 1 -1) planes can be used in conjunction with an etch in which the {1 1 1} plane is the slow plane to define the sloped sidewalls of the sloped grating. Equivalently, the substrate 1200 can be referred to, for example, as a (-1 1 1) substrate, in which case the (1 1 1), (1 -1 1), and / or (1 1 -1) planes can define the sidewalls of the sloped grating. This disclosure uses the convention of a (1 1 1) substrate and references specific examples of relevant crystal planes (e.g., (1 -1 1) planes) as defining sidewalls, with the understanding that crystal symmetry allows the same fabrication process to be described for other but equivalent crystal planes / orientations.

[0164] 12A , a (1 1 1) substrate 1200 can be used to form a tilted grating having an alignment direction (e.g., directions 1006, 1124) in the <2 −1 −1> direction in the (1 1 1) plane, e.g., the [2 −1 −1] direction, the [−1 −1 2] direction, and / or the [−1 2 −1] direction. The alignment direction is the direction in which the sidewalls are tilted. The trenches of the tilted grating extend longitudinally along the perpendicular <1 1 0> direction in the (1 1 1) plane, e.g., in the [0 1 −1] direction, the [1 −1 0] direction, and / or the [−1 0 1] direction, respectively. These three pairs of directions correspond to three other planes (other than (1 1 1)) within the {1 1 1} family of planes, e.g., the (-1 1 1) plane, the (1 1 -1) plane, and / or the (1 -1 1) plane, respectively, which define the sidewalls of the resulting tilted lattice.

[0165] For example, Figure 12B shows a cross section cut in the [-1 2 -1] direction, which is perpendicular to the [-1 0 -1] direction. A tilted grating 1204 can be formed with an alignment direction in the [-1 2 -1] direction. In the cross section, the (1 -1 1) plane has an angle of approximately 19.5° with the normal direction 1206 to the (1 1 1) plane. Because the (1 -1 1) plane is a low-velocity plane that can substantially define the sidewalls of the resulting trenches, the trenches of the tilted grating 1204 have a corresponding tilt angle of 19.5°.

[0166] Referring to FIG. 11D , when the tilted grating 1122 is a tilted grating 1204, the alignment direction 1124 is the [−1 2 −1] direction (more generally, the <2 −1 −1> direction), the surface 1102 is a (1 1 1) plane (more generally, a {1 1 1} plane), the sidewall 1116 is a (1 −1 1) plane (more generally, a {1 1 1} plane), the tilt angle 1120 is 19.5°, and the base 1126 is a (1 1 1) plane (more generally, a {1 1 1} plane) parallel to the surface 1102. In this example, for example, because the base of first trench 1106 is also defined by the (1 1 1) plane, base 1126 is parallel to surface 1102, and as a result, the base of first trench 1106 is uniformly etched to maintain a constant (parallel) orientation relative to surface 1102. However, in some embodiments, the base of the trenches of the tilted lattice are non-parallel to the surface in which the trenches are formed, as in the examples of Figures 15B and 18C.

[0167] 11E, after forming the second trenches 1114 of the tilted grating 1122, the mask layer 1108 (if present) can be removed to leave the tilted grating 1122 exposed as a surface relief structure in the substrate 1104. In some embodiments, the mask layer 1108 is removed using a wet chemical etch. For example, a silicon dioxide mask layer 1108 can be removed using a hydrofluoric acid (HF) etch.

[0168] Figure 13 is a scanning electron microscope (SEM) image of a tilted grating formed by periodically repeating trenches in a silicon wafer according to the process shown in Figures 11A-11E. The tilted grating was formed using a (1 1 1) silicon wafer, a silicon dioxide mask layer 1108, and a KOH etch with crystal plane selectivity. As is evident in the SEM image, the trench sidewalls are highly uniform and smooth, parallel to each other, and tilted (in this example, with the base of the trench parallel to the (1 1 1) surface of the wafer in which the trenches were formed).

[0169] Because the trench sidewalls are defined by specific slow planes in the substrate's crystal structure, and for a given substrate, the slow planes have a set, predetermined relationship to the substrate's surface, the tilt angle of the trench (defined with respect to the normal to the substrate surface) may be an unmodifiable parameter for a given substrate. For example, for a (1 1 1) substrate in which the {1 1 1} planes are the slow planes, the tilt angle is approximately 19.5°. However, by appropriate selection of the substrate, any tilt angle can be obtained.

[0170] In embodiments where a tilted lattice is formed using the {1 1 1} slow planes in the diamond cubic crystal structure, tilt angles other than 19.5° can be obtained by using a substrate with a surface tilted directly in the <2-1-1> direction relative to the {1 1 1} plane. For example, the substrate can be obtained by slicing a {1 1 1} oriented ingot at a cutting angle inclined toward the {2-1-1} direction (or can be crystallographically equivalent to the substrate obtained thereby). As shown in FIG. 14A, a (1 1 1) oriented ingot 1400 has a (1 1 1) surface 1402. To form a (1 1 1) wafer, the ingot 1400 is cut parallel to the surface 1402. To obtain a substrate 1404 (shown in FIG. 14B ) configured to produce a tilted lattice with a tilt angle of less than 19.5°, the ingot 1400 is sliced ​​in the {2 −1 −1} direction (in this example, the [−1 2 −1] direction) at a cutting angle θ relative to the (1 1 1) plane. That is, the slice plane 1406 along which the ingot 1400 is sliced ​​is the (1 1 1) plane that slopes downward in the [−1 2 −1] direction. The cutting angle θ is in the range of 0<θ<19.5°.

[0171] Due to this slicing, the substrate 1404 has a surface 1408 that is inclined with respect to the (1 1 1) plane by a cutting angle θ. Furthermore, the normal direction 1410 to the surface 1408 forms an angle of 19.5°-θ with the (1 -1 1) plane, rather than forming an angle of 19.5° with the (1 -1 1) plane.

[0172] As shown in Figure 15A, a first trench 1506 can be patterned in substrate 1404 using a mask layer 1508, for example, as described with reference to Figures 11A-11C. The first trench 1506 is formed in a surface 1408 of substrate 1404 (surface 1408 having an angle θ with respect to the (1 1 1) plane). Elements in Figures 15A-15B can have the characteristics as described for the corresponding elements in Figures 11A-11E, unless otherwise specified.

[0173] As shown in FIG. 15B , the substrate 1404 is etched with an etching process in which the (1-1-1) plane is a slow plane (e.g., the etching process described with reference to FIG. 11D ) so that second trenches 1514 are formed with sidewalls 1516 defined by the (1-1-1) plane. The second trenches 1514 form tilted gratings 1522. The second trenches 1514 have a tilt angle 1518 (defined as the angle of the sidewalls relative to the normal to the surface 1408) equal to 19.5°-θ. Thus, by appropriately selecting a substrate 1404 having a surface at an angle θ relative to the (1-1-1) plane, a tilted grating 1522 having a desired tilt angle less than 19.5° can be fabricated in a substrate having a diamond cubic crystal structure, e.g., to configure the diffraction intensity of the tilted grating 1522 using a target tilt angle less than 19.5°.

[0174] A base 1526 of the second trench 1514 is defined by a (1 1 1) plane. The base 1526 is angled upwardly with respect to the surface 1408 in which the second trench 1514 is formed, where angle 1520 is equal to the cutting angle θ.

[0175] After fabrication of the tilted grating 1522, in some embodiments, the mask layer 1508 is removed, for example, as described with reference to Figure 11E.

[0176] A similar method can be used to fabricate a tilted lattice with a tilt angle greater than 19.5° in a substrate having a diamond cubic crystal structure. As shown in FIGS. 16A-16B, an ingot 1600 having a (1 1 1) surface 1602 can be cut at a cutting angle θ outward from the <2 −1 −1> direction, e.g., outward from the [−1 2 −1] direction, opposite to the tilt direction in FIGS. 14A-14B. The slice plane 1606 used to slice the ingot 1600 is the (1 1 1) plane tilted downward in the [−1 2 −1] direction. The cutting angle θ is θ>0. Thus, a substrate 1604 is obtained having a surface 1608 aligned with the slice plane 1606, with the surface 1608 forming a cutting angle θ with respect to the (1 1 1) plane. A normal direction 1610 to the surface 1608 forms an angle of 19.5°+θ with the (1 −1 1) plane.

[0177] As shown in Figure 17A, a first trench 1706 can be patterned in substrate 1604 using a mask layer 1708, for example, as described with reference to Figures 11A-11C. The first trench 1706 is formed in surface 1608 of substrate 1604 (surface 1608 having an angle θ with respect to the (1 1 1) plane). Elements in Figures 17A-17D can have the characteristics as described for the corresponding elements in Figures 11A-11E, unless otherwise specified.

[0178] As shown in FIG. 17B , the substrate 1604 is etched with an etching process in which the (1 -1 1) plane is a slow plane (e.g., the etching process described with reference to FIG. 11D ) so that a second trench 1714 is formed having sidewalls 1716 defined by the (1 -1 1) plane. The second trench 1714 has a slope angle 1718 (defined as the angle of the sidewall with respect to the normal to the surface 1608) equal to 19.5° + θ. A base 1726 of the second trench 1714 is defined by the (1 1 1) plane. The base 1726 is angled downwardly with respect to the surface 1608 in which the second trench 1714 is formed, with angle 1720 equal to the cut angle θ.

[0179] However, unlike the case of FIGS. 15A-15B for obtaining a tilt angle of less than 19.5°, in the example of FIGS. 17A-17B, the cantilever 1730 is formed under the mask layer 1708, and the bottom surface 1732 of the cantilever 1730 is defined by the (1 1 1) plane. As shown in FIG. 17C, when the mask layer 1708 is removed, the cantilever 1730 remains above each second trench 1714. If not removed, the cantilever 1730 may interfere with the desired optical operation of the tilted grating, for example, causing optical diffraction in undesired direction(s). The cantilever 1730 may also interfere with a subsequent imprinting process in which the structure of FIG. 17C is used as a master template for imprinting the tilted grating into a device substrate, such as a device substrate that is or includes a waveguide. For example, the cantilever 1730 may make it difficult to separate the master template from the waveguide.

[0180] As shown in FIG. 17D , in some embodiments, the structure of FIG. 17C is further etched to remove the cantilevers 1730. For example, plasma etching can be used to uniformly “trim” the substrate 1604, e.g., to remove the top portion of the substrate both inside and outside the second trenches 1714, including the portion 1734 containing the cantilevers 1730, while substantially maintaining the angular orientation of the sidewalls of the second trenches 1714. Thus, a tilted grating 1736 with a tilt angle of 19.5°+θ and no cantilevers can be created. However, further etching to remove the cantilevers may distort the dimensions of the second trenches 1714, e.g., making the second trenches 1714 deeper or shallower. Further etching may alternatively or additionally roughen or otherwise degrade the surface of the second trenches 1714, e.g., causing the sidewalls and / or base of the second trenches 1714 to have increased roughness.

[0181] 18A-18C show another example of a process for fabricating tilted gratings with tilt angles greater than 19.5° and without cantilevers in diamond cube material. In some embodiments, this process does not include the uniform etching shown by FIG. 17D and may therefore result in tilted gratings with improved morphology and / or more precisely controlled dimensions.

[0182] 18A shows the same structure as shown in FIG. 17A, including a first trench 1706 formed in a substrate 1604 having a surface 1608 oriented at an angle θ away from the [−1 2 −1] direction relative to the (1 1 1) plane. The first trench 1706 is formed through a hole in a mask layer 1708.

[0183] As shown in FIG. 18B , portions of mask layer 1708 adjacent at least one first trench 1706 are removed. For example, portions 1804 of mask layer 1708 between first trenches 1706 can be trimmed by width 1802 (e.g., in some embodiments, at least 10 nm). Width 1802 can be uniform for all first trenches 1706 or can vary between first trenches 1706. In some embodiments, portions of mask layer 1708 are removed with a lithography process that includes, for example, depositing a resist layer, patterning the resist layer, and etching away portions of mask layer 1708 using one or more suitable etching processes. In some embodiments, portions of mask layer 1708 are removed with an isotropic etching process, such as an isotropic wet chemical etching process, which, in some embodiments, can be performed without additional lithography / patterning steps. For example, the structure of FIG. 18A can be briefly immersed in an etchant that selectively etches mask layer 1708 relative to substrate 1604 (e.g., an HF dip (e.g., in a buffered oxide etch (BOE)) if mask layer 1708 is a SiO layer and substrate 1604 is a silicon substrate). The resulting isotropic etch not only removes side portions 1804 of mask layer 1708, but also etches the top of mask layer 1708, although in some embodiments, the removed width 1802 is much less than the thickness of mask layer 1708, such that the isotropic etch can remove width 1802 while a substantial thickness of mask layer 1708 remains.

[0184] Removing the portion of mask layer 1708 adjacent to first trench 1706 exposes the fast surfaces of substrate 1604 that would otherwise be masked by mask layer 1708. Thus, as shown in FIG. 18C , when substrate 1604 is etched with an etchant whose slow surfaces are {1 1 1} planes (e.g., as described with reference to FIGS. 11D and 15B ), second trenches 1814 are formed without cantilevers, and second trenches 1814 form tilted gratings 1822. Second trenches 1814 have sidewalls 1816 defined by (1 -1 1) planes and bases 1826 defined by (1 1 1) planes. The tilt angle 1818 of second trenches 1814 is 19.5°+θ, with bases 1826 angled downward relative to surface 1608 of substrate 1604. The width 1830 and pitch 1832 of the second trenches 1814 are determined by at least the dimensions of the portion of the mask layer 1708 that remains after removing the portion of the mask layer 1708 adjacent to the first trenches 1706 .

[0185] In some embodiments, the mask layer 1708 may then be removed from the tilted grating 1822, for example as described with reference to Figure 11E.

[0186] Therefore, by appropriately selecting a substrate 1604 having a surface at an angle θ relative to the (1 1 1) plane, a tilted lattice 1822 with a desired tilt angle greater than 19.5° can be fabricated in a substrate having a diamond cubic crystal structure. For example, in some embodiments, the tilt angle is between 19.5° and 80°.

[0187] Once fabricated as described herein, the tilted grating in a rigid substrate (such as a silicon substrate) can be used as a master template to fabricate corresponding tilted gratings in other material(s), for example, by nanoimprint lithography (NIL). As shown in Figures 19A-19B, a replication material 1902 (such as a polymer) disposed on a substrate 1904 is imprinted with the tilted grating 1822. The substrate 1604 is the master template substrate in this example. The replication material 1902 and the substrate 1904 can be collectively referred to as a device substrate. In some embodiments, the substrate 1904 is not included below the replication material 1902. In some embodiments, the device substrate includes one or more waveguides, and the imprinted tilted grating can be positioned to incouple and / or outcouple light to / from the one or more waveguides.

[0188] Heat and / or pressure are applied to remove the tilted grating 1822, forming a surface relief structure 1906 that is itself a tilted grating, i.e., a negative of the tilted grating 1822. In some embodiments, the replication material is cured (e.g., cross-linked), for example, by heat treatment and / or UV light. Based on appropriate selection of the dimensions and tilt angle of the tilted grating 1822, a corresponding tilted grating 1906 can be formed in the replication material 1902. The high uniformity and surface smoothness provided by the tilted gratings defined by the crystal planes described herein are directly transferred to the imprint structure, resulting in the imprint structure also providing the optical advantages described for tilted gratings fabricated as described herein.

[0189] Other imprint processes are also within the scope of this disclosure. For example, in some embodiments, the replication material to be imprinted is deposited on a master template (e.g., including on the tilted grating pattern to be transferred), and the master template with the deposited replication material is brought into contact with a substrate to transfer the replication material to the substrate with the transferred tilted grating pattern.

[0190] 20 illustrates an example of a process 2000 that can be implemented according to some embodiments of the present disclosure. In the process 2000, a target tilt angle for a tilted lattice is determined (2002). A substrate orientation corresponding to the target tilt angle is determined (2004). For example, if the target tilt angle is 19.5°, the determined substrate orientation can be the (1 1 1) orientation of a substrate having a diamond cubic crystal structure. If the target tilt angle is less than or greater than 19.5°, the determined substrate orientation may deviate from the (1 1 1) plane at the appropriate tilt angle and direction, as described herein.

[0191] A substrate having the determined orientation is provided 2006. For example, the substrate may be provided by slicing a (1 1 1) ingot at an appropriate angle, e.g., as described with reference to Figures 14A-14B and 16A-16B.

[0192] As described throughout this disclosure, a tilted lattice is fabricated in a substrate 2008. For example, periodic trenches can be patterned in the surface of the substrate, and the sidewalls of the periodic trenches can be etched with an etch that has crystal plane selectivity.

[0193] In some embodiments, crystal symmetry facilitates the creation of multiple tilted lattices oriented in different directions within the same substrate. The substrate can have multiple low-velocity planes that are equivalent to each other in the same crystal plane family, and the multiple low-velocity planes can define sidewalls of different respective tilted lattices. As shown in FIG. 21A, a (1 1 1) silicon wafer 2100 is patterned with six mask layer patterns 2102a-2102f. Each mask layer pattern 2102 includes a set of elongated mask layer strips with gaps therebetween, and the set of elongated strips has an alignment direction and a vertical longitudinal direction. For example, a cross section through the set of strips and wafer 2100 can have a cross section as shown in FIG. 11B.

[0194] The mask layer patterns 2102 are arranged with alignment directions aligned with the three-fold symmetry crystal directions. Mask layer patterns 2102a and 2102d have alignment directions [-1 -1 2], mask layer patterns 2102b and 2102e have alignment directions [2 -1 -1], and mask layer patterns 2102c and 2102f have alignment directions [-1 2 -1]. Correspondingly, the extended strips of the mask layers have lengths extending in the perpendicular [1 -1 0], [0 1 -1], and [-1 0 1] directions, respectively.

[0195] The wafer 2100 is etched to form first trenches (e.g., as described with reference to FIG. 11C), the first trenches are etched using an etchant that etches certain crystal plane(s) faster than other crystal plane(s) to form tilted gratings (e.g., as described with reference to FIG. 11D), and the hard mask layer is removed (e.g., as described with reference to FIG. 11E). These etching processes can be performed in a common simultaneous etching process for all mask layer patterns / first trenches, increasing fabrication efficiency. As a result, six tilted gratings 2104a-2104f are fabricated, as shown in FIG. 21B. Adjacent tilted grating patterns (included for illustrative purposes only) indicate the respective tilt directions of the tilted gratings 2104. The tilted gratings 2104 are oriented in different directions (both the tilt direction / alignment direction (the direction of the width of the second trench forming the tilted grating 2104) and the extension direction of the length of the second trench), and the different directions correspond to both the three-fold symmetric [2-1-1] crystal direction and the patterning direction of the mask layer pattern 2102, which is arranged to align with the [2-1-1] direction. Specifically, tilted gratings 2104a and 2104d have the alignment direction [-1-1-2], tilted gratings 2104b and 2104e have the alignment direction [2-1-1], and tilted gratings 2104c and 2104d have the alignment direction [-1-2-1]. Because wafer 2100 is a (1-1-1) wafer, tilted gratings 2104 have a tilt angle of 19.5° with the sidewall defined by the slow {1-1-1} plane. Therefore, a master template 2108 having tilted gratings of different orientations is obtained. The master template 2108 can be used to imprint corresponding tilted gratings of different orientations into a device substrate, for example, as described with reference to Figures 19A-19B.

[0196] In some cases, manufacturing throughput may be limited by the number of tilted grating patterns that a device master template can simultaneously imprint on a device substrate. Advantageously, according to some embodiments of the fabrication processes described herein, the device master template can be configured to simultaneously imprint a relatively large number of tilted diffraction grating patterns on a device substrate, thereby enabling a relatively high fabrication throughput of tilted diffraction gratings. For example, in some embodiments, the device master template includes tilted diffraction patterns that extend in multiple directions, e.g., at least partially radially. For example, master template substrate 2108 includes six tilted gratings 2104, each with a radial alignment direction. Tilted gratings 2104a, 2104c, and 2104e have an outward radial alignment direction (sloped sidewalls that slope radially outward), while tilted gratings 2104b, 2104d, and 2104f have an inward radial alignment direction (sloped sidewalls that slope radially inward). A similar process (e.g., based on appropriate provision of a mask layer pattern) can facilitate the fabrication of other / additional tilted gratings on the master template substrate 2108. This allows efficient use of the area of ​​the device master template for high-throughput parallel imprinting of tilted diffraction patterns on device substrates such as waveguides.

[0197] Several embodiments have been described. Nevertheless, it will be understood that various modifications may be made. Elements of one or more embodiments may be combined, deleted, modified, or supplemented to form further embodiments. In yet another example, the logic flow depicted in the figures does not require the particular order shown, or sequential order, to achieve desirable results. Additionally, other steps may be provided or steps may be eliminated from the described flow, and other components may be added to or removed from the described systems. Accordingly, other embodiments are within the scope of the following claims.

Claims

1. 1. A method comprising: patterning a plurality of first trenches in a surface of a substrate; etching the plurality of first trenches with an etchant having an etch rate for a first crystallographic surface of the substrate that is greater than an etch rate for a second crystallographic surface of the substrate; Including, The method wherein the etching forms a tilted grating in the substrate.

2. The method of claim 1 , wherein a sidewall of the tilted lattice is defined by the second crystal plane.

3. The method of claim 1 or 2, wherein the base of the tilted lattice is defined by the second crystal plane.

4. the substrate has a diamond cubic crystal structure; The method of claim 2 , wherein the second crystallographic plane is a {1 1 1} plane of the diamond cubic crystal structure.

5. The method of claim 4 , wherein the substrate comprises a silicon substrate or a germanium substrate.

6. The method of claim 4 or 5, wherein the etchant comprises potassium hydroxide (KOH) or tetramethylammonium hydroxide (TMAH).

7. the tilted grating is formed by a plurality of second trenches; the second trench has a depth extending into the surface of the substrate, a width extending between two sidewalls defined by the {1 1 1} planes, and a length greater than the width; A method according to any one of claims 4 to 6, wherein said length extends parallel to the <1 1 0> direction of the diamond cubic crystal structure.

8. 8. The method of claim 7, wherein the width extends parallel to the <2-1-1> direction of the diamond cubic crystal structure.

9. the substrate comprises a (1 1 1) oriented substrate; The method of any one of claims 4 to 8, wherein the sidewalls of the tilted grating have a tilt angle of about 19.5° degrees.

10. a normal to the surface of the substrate has a first angle of 19.5°-θ° with respect to the {1 1 1} plane of the diamond cubic crystal structure; the sidewalls of the tilted grating have a tilt angle equal to the first angle; 9. The method according to claim 4, wherein 0°<θ°<19.5°.

11. a normal to the surface of the substrate has a first angle of 19.5°+θ° with respect to the {1 1 1} plane of the diamond cubic crystal structure; the sidewalls of the tilted grating have a tilt angle equal to the first angle; The method according to any one of claims 4 to 8, wherein θ°>0°.

12. The method according to any one of claims 4 to 8 or 10 to 11, wherein the surface of the substrate is tilted in the <2-1-1> direction of the diamond cubic crystal structure with respect to the (111) plane of the diamond cubic crystal structure.

13. patterning the plurality of first trenches in the surface of the substrate includes: forming a mask on the surface of the substrate; anisotropically etching the substrate through the openings in the mask to form the plurality of first trenches; The method according to any one of claims 1 to 12, comprising:

14. 14. The method of claim 13, wherein each trench of the plurality of first trenches has vertical sidewalls.

15. 15. The method of claim 13 or 14, wherein anisotropically etching the substrate comprises plasma etching the substrate.

16. The method of any one of claims 13 to 15, comprising removing the mask from the surface of the substrate after etching the plurality of first trenches.

17. 17. The method of claim 13, further comprising removing a portion of the mask adjacent to at least one of the plurality of first trenches after patterning the plurality of first trenches and before etching the plurality of first trenches.

18. the tilted grating is formed by a plurality of second trenches; the second trench has a width extending between two sidewalls defined by the second crystal plane; The method according to any one of claims 1 to 17, wherein the width is between 50 nm and 1 μm.

19. The method according to any one of the preceding claims, wherein the tilted grating has a pitch between 20 μm and 200 μm.

20. the tilted grating is formed by a plurality of second trenches; The method according to any one of claims 1 to 19, wherein the depth of the second trench is between 50 nm and 1 μm.

21. A method according to any preceding claim, comprising imprinting a replication material using the tilted grating as a mold to form a corresponding tilted grating in the replication material.

22. determining a target width of the second trench of the tilted grating; determining a first width based on the target width and a predetermined change in width caused by the etching; patterning the plurality of first trenches to have the first width; The method of any one of claims 1 to 21, comprising:

23. 1. A method comprising: providing a master template substrate; forming a tilted grating pattern in a surface of the master template substrate; using the master template substrate having the tilted grating pattern to imprint the tilted grating pattern onto a device substrate; A method comprising:

24. 24. The method of claim 23, wherein the master template substrate has a diamond cubic crystal structure, and the tilted grating pattern is defined by a first {1 1 1} plane of the diamond cubic crystal structure.

25. 25. The method of claim 24, comprising forming a second tilted grating pattern in the surface of the master template substrate, the second tilted grating pattern being defined by a second {1 1 1} plane of the diamond cubic crystal structure, the second {1 1 1} plane being different from the first {1 1 1} plane.

26. The method of any one of claims 23 to 25, wherein the sidewalls of the tilted grating pattern are defined by crystal planes of the master template substrate.

27. the tilted diffraction grating pattern is a first tilted diffraction grating pattern, and the method includes: forming a second tilted grating pattern in the surface of the master template substrate, the first tilted grating pattern and the second tilted grating pattern having different alignment directions; imprinting the second tilted grating pattern onto the device substrate using the master template substrate; The method according to any one of claims 23 to 25, comprising:

28. 1. A method comprising: determining a target tilt angle of the tilted grating; determining a substrate orientation corresponding to the target tilt angle based on a crystalline structure of the material; providing a substrate having the determined substrate orientation, the substrate being composed of the material; and forming the tilted grating within the surface of the substrate; A method comprising:

29. Providing the substrate having the determined substrate orientation comprises: determining a cutting angle based on the substrate orientation; slicing the ingot of material at the cutting angle to obtain the substrate sliced ​​from the ingot and having the determined substrate orientation; 29. The method of claim 28, comprising:

30. 1. A method comprising: providing a substrate including a first set of parallel trenches and a second set of parallel trenches; etching a first set of parallel trenches to form a first tilted grating and etching a second set of parallel trenches to form a second tilted grating; Including, the first tilted lattice includes first trenches, each first trench having a first width defined by two first crystal planes and a first length greater than the first width; the second tilted lattice includes second trenches, each second trench having a second width defined by two second crystal planes and a second length greater than the second width; The method, wherein the first length and the second length extend in different directions.

31. 31. The method of claim 30, wherein etching the first set of parallel trenches and etching the second set of trenches are performed in a common simultaneous etching process.

32. the substrate has a diamond cubic crystal structure; the first crystal face is a first {1 1 1} face, 32. The method of claim 30 or 31, wherein the second crystallographic plane is a second {1 1 1} plane that is different from the first {1 1 1} plane.

33. 1. An optical device comprising: A waveguide; a tilted grating positioned to guide light into the waveguide, the tilted grating having a tilt angle of 19.5°; An optical device comprising:

34. 1. An optical device, comprising: A waveguide; a tilted grating defined within the surface of the substrate; Equipped with The optical device, wherein the tilted grating is positioned to guide light into the waveguide, and sidewalls of the tilted grating are defined by crystal planes of the substrate.

35. 35. The optical device of claim 34, wherein the substrate has a diamond cubic crystal structure and the sidewalls are defined by {1 1 1} planes of the diamond cubic crystal structure.

36. 36. The optical device of claim 34 or 35, wherein the substrate comprises the waveguide.

37. 1. A display system comprising: A waveguide; an optical coupling element having a tilted grating; Equipped with A display system wherein the tilted grating is fabricated in a process that includes etching the substrate with an etchant that has an etch rate of a first crystalline face of the substrate that is greater than an etch rate of a second crystalline face of the substrate.

38. 38. The display system of claim 37, wherein the display system comprises a virtual reality (VR) or augmented reality (AR) display system.

39. 39. A display system according to claim 37 or 38, wherein the substrate comprises the waveguide.

40. the process forms a master template tilted grating in the substrate; 39. The display system of claim 37 or 38, wherein the tilted grating of the optical coupling element is formed in the replication material by imprinting the master template tilted grating into the replication material.

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