Wide-view polarization switch using liquid crystal optical elements with pretilt angles

Abstract

To provide a wide field-of-view polarization switch using a liquid crystal optical element with a suitable pretilt angle.SOLUTION: A switchable optical assembly comprises a switchable wave plate configured to be electrically activated and deactivated to selectively alter a polarization state of light incident on the wave plate. The switchable wave plate comprises first and second surfaces and a liquid crystal layer disposed between the first surface and the second surface. The first liquid crystal layer includes a plurality of liquid crystal molecules. The first and second surfaces may be curved. The plurality of liquid crystal molecules may vary a tilt angle with respect to the first and second surfaces with outward radial distance from an axis through the first and second surfaces and the liquid crystal layer in a plurality of radial directions. The switchable wave plate additionally comprises a first plurality of electrodes to apply an electrical signal across the first liquid crystal layer.SELECTED DRAWING: Figure 19

Description

[Technical Field]

[0001] (Priority Claim) This application claims the benefit of priority under 35 U.S.C. § 119(e) to U.S. Provisional Application No. 62 / 685,857, filed June 15, 2018. The entire disclosure of this priority document is incorporated herein by reference. (Incorporated by reference)

[0002] This application is incorporated by reference into the following patent applications: U.S. Patent Application No. 14 / 555,585, filed November 27, 2014, and published on July 23, 2015, as U.S. Patent Publication No. 2015 / 0205126; U.S. Patent Application No. 14 / 655,585, filed April 18, 2015, and published on October 22, 2015, as U.S. Patent Publication No. 2015 / 0302652; No. 90,401, filed March 14, 2014 and issued August 16, 2016, now U.S. Patent No. 9,417,452, and U.S. Patent Application No. 14 / 331,218, filed July 14, 2014, and published October 29, 2015, as U.S. Patent Publication No. 2015 / 0309263. (Technical field)

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

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

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

[0006] The systems and methods disclosed herein address various challenges associated with AR or VR technology. [Means for solving the problem]

[0007] The AR system may display virtual content to a user or viewer while still allowing the user to see the world around them. Preferably, this content is displayed on a head-mounted display, for example, as part of eyewear, that projects image information into the user's eyes. In addition, the display may also transmit light from the surrounding environment to the user's eyes, allowing a view of that surrounding environment. As used herein, it should be understood that a "head-mounted" or "head-mountable" display is a display that can be mounted on the viewer's or user's head.

[0008] In some AR systems, the multiple waveguides may be configured to form virtual images at multiple virtual depth planes (also simply referred to herein as "depth planes"). Different waveguides of the multiple waveguides may have different refractive powers and may be formed at different distances from the user's eyes. The display system may also include multiple lenses that provide, or additionally provide, refractive power. The refractive power of the waveguides and / or lenses may provide images at different virtual depth planes. Undesirably, the waveguides and lenses may each increase the overall thickness, weight, and cost of the display.

[0009] Advantageously, in various embodiments described herein, an adaptive lens assembly may be utilized to provide variable optical power, e.g., to modify the wavefront divergence of light propagating through the lens assembly and provide a virtual depth plane at different perceived distances from the user. The adaptive lens assembly may include a pair of waveplate lenses with a switchable waveplate disposed therebetween. The first and second waveplate lenses may each be configured to alter the polarization state of light passing therethrough, and the switchable waveplate may be switchable between multiple states, e.g., a first state that allows light to pass without changing the polarization of the light, and a second state that alters the polarization of the light (e.g., by changing the handedness of the polarization). In some embodiments, one or both of the waveplate lenses may be switchable between these first and second states, and the intervening switchable waveplate may be omitted.

[0010] It should be understood that an adaptive lens assembly may comprise a stack of multiple waveplate lenses and multiple switchable waveplates. For example, an adaptive lens assembly may comprise multiple subassemblies comprising pairs of waveplate lenses with intervening switchable waveplates. In some embodiments, an adaptive lens assembly may include alternating waveplate lenses and switchable waveplates. Advantageously, such an alternating arrangement allows for thickness and weight reduction by having adjacent switchable waveplates share a common waveplate lens. In some embodiments, more than two discrete levels of optical power may be provided by switching the states of various combinations of switchable plates in the stack.

[0011] In some embodiments, the adaptive lens assembly, together with the waveguide assembly, forms a display device and forms images at different virtual depth planes. In various embodiments, the display device includes a pair of adaptive lens assemblies interposed by a waveguide assembly. The waveguide assembly includes a waveguide configured to propagate light (e.g., visible light) therein (e.g., via total internal reflection) and to outcouple the light. For example, the light may be outcoupled along an optical axis direction normal to a major surface of the waveguide. One of the pair of adaptive lens assemblies may be formed on a first side of the waveguide assembly and may be configured to provide variable refractive power, modify the wavefront of the light passing through the adaptive lens assembly, and form images at each of a plurality of virtual depth planes. For example, the adaptive lens assembly may converge or diverge the outcoupled light received from the waveguide assembly. To compensate for modifications of the real-world view due to convergence or divergence of ambient light propagating through the adaptive lens assembly and / or the waveguide assembly, the other of the pair of adaptive lens assemblies is additionally provided on a second side of the waveguide assembly opposite the first side. When the switchable waveplates of each adaptive lens assembly assume corresponding states, the adaptive lens assemblies may have optical powers with opposite signs such that the other of the adaptive lens assemblies corrects distortions caused by the adaptive lens assembly on the first side of the waveguide assembly.

[0012] Advantageously, utilizing a switchable waveplate switchable between two states for a continuously variable adaptive lens having a continuously variable optical element simplifies driving the adaptive lens assembly and reduces the computational power required to determine how to properly activate the adaptive lens assembly for a desired optical power. Additionally, by allowing the adaptive lens assembly to modify the wavefront divergence of light output by the waveguides, the number of waveguides required to provide multiple depth planes is reduced relative to an arrangement in which each waveguide provides a specific amount of wavefront divergence. The present specification also provides, for example, the following items: (Item 1) 1. A switchable optical assembly comprising: 1. A switchable waveplate configured to be electrically activated and deactivated to selectively alter the polarization state of light incident thereon, said switchable waveplate comprising: first and second curved surfaces; a liquid crystal layer disposed between the first curved surface and the second curved surface such that the liquid crystal layer is curved; a plurality of electrodes for applying electrical signals across the curved liquid crystal layer; A switchable waveplate comprising: 1. A switchable optical assembly comprising: (Item 2) Item 1. The switchable optical assembly of item 1, wherein the first and second curved surfaces on the switchable waveplate comprise curved surfaces on a curved substrate. (Item 3) 10. The switchable optical assembly of claim 1, wherein the first and second curved surfaces have the same curvature. (Item 4) the switchable optical assembly further comprises a first waveplate lens comprising a liquid crystal layer, the first waveplate lens having different refractive powers for different polarizations of light incident thereon; The switchable optical assembly comprises: a first lens state configured to have a first refractive power; a second lens state configured to have a second refractive power different from the first refractive power; 10. The switchable optical assembly of claim 1, configured to be selectively switched between at least two lens states, including: (Item 5) Item 5. The switchable optical assembly of item 4, wherein the second optical power is zero optical power. (Item 6) 1. A switchable optical assembly comprising: 1. A switchable waveplate configured to be electrically activated and deactivated to selectively alter the polarization state of light incident thereon, said switchable waveplate comprising: first and second surfaces; a liquid crystal layer disposed between the first and second surfaces, the liquid crystal layer comprising a plurality of liquid crystal molecules that vary in tilt angle relative to the first and second surfaces with outward radial distance from an axis passing through the first and second surfaces and the liquid crystal layer in a plurality of radial directions; a plurality of electrodes for applying electrical signals across the liquid crystal layer; A switchable waveplate comprising: 1. A switchable optical assembly comprising: (Item 7) Item 7. The switchable optical assembly of item 6, wherein the first and second surfaces comprise planar surfaces. (Item 8) 8. A switchable optical assembly according to any of items 6-7, wherein the first and second surfaces comprise planar surfaces on a planar substrate. (Item 9) 9. A switchable optical assembly according to any one of items 6-8, wherein the axis is normal to the first and second surfaces. (Item 10) 10. A switchable optical assembly according to any of items 6-9, wherein the liquid crystal molecules have tilt angles relative to the first and second surfaces that increase with outward radial distance from the axis in the radial directions. (Item 11) 11. A switchable optical assembly according to any one of items 6-10, configured to transmit light to an eye of a viewer located at a distance from the switchable optical assembly, wherein the plurality of liquid crystal molecules each have a tilt angle that matches the angle of incidence of the light propagating along a path from a location within the field of view of the viewer's eye to the viewer's eye. (Item 12) 12. A switchable optical assembly according to any one of items 6-11, wherein the liquid crystal molecules have an orientation such that the liquid crystal molecules are arranged in a symmetrical array that is rotatable about the axis. (Item 13) 12. A switchable optical assembly according to any of items 6-11, wherein the liquid crystal molecules have an orientation such that the liquid crystal molecules have at least four-fold rotational symmetry about the axis. (Item 14) the switchable optical assembly further comprises a first waveplate lens comprising a liquid crystal layer, the first waveplate lens having different refractive powers for different polarizations of light incident thereon; The switchable optical assembly comprises: a first lens state configured to have a first refractive power; a second lens state configured to have a second refractive power different from the first refractive power; 14. The switchable optical assembly of any of items 6-13, configured to be selectively switched between at least two lens states including: (Item 15) Item 15. The switchable optical assembly of item 14, wherein the second optical power is zero optical power. (Item 16) The plurality of liquid crystal molecules, which vary in tilt angle relative to the first and second surfaces with outward radial distance from the axis in a plurality of radial directions, are spaced apart at least 1 cm across the first layer. 2 16. The switchable optical assembly according to items 6-15, comprising at least 50% of the molecules extending over a range of (Item 17) The plurality of liquid crystal molecules, which vary in tilt angle relative to the first and second surfaces with outward radial distance from the axis in a plurality of radial directions, are spaced apart at least 2 cm across the first layer. 2 16. The switchable optical assembly according to items 6-15, comprising at least 50% of the molecules extending over a range of (Item 18) The plurality of liquid crystal molecules, which vary in tilt angle relative to the first and second surfaces with outward radial distance from the axis in a plurality of radial directions, are spaced apart at least 1 cm across the first layer. 2 16. The switchable optical assembly according to items 6-15, comprising at least 80% of the molecules extending over a range of (Item 19) The plurality of liquid crystal molecules, which vary in tilt angle relative to the first and second surfaces with outward radial distance from the axis in a plurality of radial directions, are spaced apart at least 2 cm across the first layer. 2 16. The switchable optical assembly according to items 6-15, comprising at least 80% of the molecules extending over a range of (Item 20) Item 6-19, a switchable optical assembly, wherein the axis includes a central axis passing through the first and second surfaces and the liquid crystal layer. [Brief explanation of the drawings]

[0013] [Figure 1] FIG. 1 illustrates a user's view of an augmented reality (AR) device.

[0014] [Figure 2] FIG. 2 illustrates a conventional display system for simulating a three-dimensional image for a user.

[0015] [Figure 3] 3A-3C illustrate the relationship between the radius of curvature and the radius of focus.

[0016] [Figure 4A] Figure 4A illustrates a representation of the accommodation-vergence response of the human visual system.

[0017] [Figure 4B] FIG. 4B illustrates an example of different accommodation and convergence states of a pair of a user's eyes.

[0018] [Figure 4C] FIG. 4C illustrates an example of a top-down view representation of a user viewing content through a display system.

[0019] [Figure 4D] FIG. 4D illustrates another example of a top-down view representation of a user viewing content through a display system.

[0020] [Figure 5] FIG. 5 illustrates aspects of an approach for simulating three-dimensional images by correcting for wavefront divergence.

[0021] [Figure 6] FIG. 6 illustrates an embodiment of a waveguide stack for outputting image information to a user.

[0022] [Figure 7] FIG. 7 illustrates an example of an output beam output by a waveguide.

[0023] [Figure 8] FIG. 8 illustrates an example of a stacked waveguide assembly where each depth plane contains an image formed using multiple different primary colors.

[0024] [Figure 9A] FIG. 9A illustrates a cross-sectional side view of an example of a set of stacked waveguides, each including an internal coupling optical element.

[0025] [Figure 9B] FIG. 9B illustrates a perspective view of the multiple stacked waveguide embodiment of FIG. 9A.

[0026] [Figure 9C] FIG. 9C illustrates a top-down plan view of the multiple stacked waveguide embodiment of FIGS. 9A and 9B.

[0027] [Figure 9D] FIG. 9D illustrates an example of a wearable display system.

[0028] [Figure 10] FIG. 10 illustrates an example of a display system comprising a pair of adaptive lens assemblies.

[0029] [Figure 11] Figure 11A illustrates an example of the display system of Figure 10 displaying virtual content to a user in a virtual depth plane, and Figure 11B illustrates an example of the display system of Figure 10 providing a user with a view of real-world content.

[0030] [Figure 12A] FIG. 12A illustrates an example of a waveplate lens assembly comprising a liquid crystal.

[0031] [Figure 12B] FIG. 12B illustrates an example of a switchable waveplate lens comprising a liquid crystal.

[0032] [Figure 13A] FIG. 13A illustrates a cross-sectional view of an example of a switchable waveplate layer comprising a layer of twisted nematic liquid crystal.

[0033] [Figure 13B] FIG. 13B illustrates an example of a switchable waveplate assembly comprising the switchable waveplate of FIG. 13A interposed between a pair of quarter-waveplates, in operation, the switchable waveplate being activated or deactivated.

[0034] [Figure 13C] FIG. 13C illustrates an example of a quarter wave plate comprising multiple layers of twisted nematic liquid crystal layers.

[0035] [Figure 13D] FIG. 13D illustrates an example of a switchable waveplate assembly comprising the switchable waveplate of FIG. 13A sandwiched between a pair of quarter-waveplates that are integrated into a single stack using an adhesive layer.

[0036] [Figure 13E] FIG. 13E illustrates an example of a switchable waveplate assembly comprising a layer of twisted nematic liquid crystal sandwiched between a pair of quarter-waveplates integrated as a single stack.

[0037] [Figure 13F] FIG. 13F illustrates an example of a switchable waveplate assembly comprising a layer of twisted nematic liquid crystal sandwiched between a pair of quarter-waveplates of FIG. 13C integrated into a single stack.

[0038] [Figure 14] Figure 14A illustrates a perspective view of one embodiment of a pair of transparent electrodes for switching layers of liquid crystals, Figure 14B illustrates a perspective view of another embodiment of a pair of transparent electrodes for switching layers of liquid crystals, and Figure 14C illustrates a perspective view of an embodiment of a pair of vertically separated transparent electrodes for switching layers of liquid crystals.

[0039] [Figure 15A] FIG. 15A illustrates a plan view of an embodiment of a pair of horizontally interlaced transparent electrodes for switching layers of liquid crystal.

[0040] [Figure 15B] FIG. 15B illustrates a cross-sectional view of an embodiment of a switchable waveplate assembly including the pair of horizontally interlaced transparent electrodes of FIG. 15A.

[0041] [Figure 16-1] 16A and 16B illustrate plan views of an embodiment of a waveplate lens comprising a liquid crystal.

[0042] [Figure 16-2] Figure 16C illustrates an example of a waveplate lens that provides different refractive powers depending on the polarization of the light and the side the light is incident on, causing light passing through it to diverge or converge. Figure 16D illustrates an example of a waveplate lens that provides different refractive powers depending on the polarization of the light and the side the light is incident on, causing light passing through it to diverge or converge.

[0043] [Figure 17] 17 illustrates an example of an adaptive lens assembly comprising a waveplate lens and a switchable waveplate that receives light from a wide field of view. Light from objects on the periphery of the field of view is incident on the switchable waveplate at an angle that reduces the efficiency with which the polarization is converted / rotated.

[0044] [Figure 18] 18 is a plot illustrating the efficiency with which a switchable waveplate converts / rotates the polarization of light incident thereon at different angles. Bright areas (e.g., at the edges) indicate reduced efficiency.

[0045] [Figure 19] 19 illustrates an example design for a switchable waveplate configured to increase the efficiency of polarization conversion / rotation for light from objects on the periphery of the field of view. The switchable waveplate is curved so that light is incident on the switchable waveplate near the normal with respect to the off-axis object.

[0046] [Figure 20] 20 illustrates another exemplary design for a switchable waveplate configured to increase the efficiency of polarization conversion / rotation for light from objects on the periphery of the field of view. The switchable waveplate includes a liquid crystal layer with molecules that are tilted with increasing outward radial distance from a central axis so that light is incident on the molecules closer to the normal with respect to the off-axis object.

[0047] Throughout the drawings, reference numbers may be reused to indicate correspondence between referenced elements. The drawings are provided to illustrate example embodiments described herein and are not intended to limit the scope of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0048] Reference will now be made to the drawings, in which like reference numerals refer to like parts throughout. Unless otherwise indicated, the drawings are schematic and are not necessarily drawn to scale. Exemplary Display Systems

[0049] FIG. 2 illustrates a conventional display system for simulating a three-dimensional image for a user. It should be understood that when a user's eyes are spaced apart and viewing a real object in space, each eye may have a slightly different view of the object, forming an image of the object at a different location on each eye's retina. This may be referred to as binocular disparity and may be utilized by the human visual system to provide the perception of depth. Conventional display systems simulate binocular disparity by presenting two distinct images 190, 200, one for each eye 210, 220, with slightly different views of the same virtual object, corresponding to the view of the virtual object as it would appear by each eye as if it 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.

[0050] Continuing with reference to FIG. 2 , images 190 and 200 are spaced apart from eyes 210 and 220 by a distance 230 on the z-axis. The z-axis is parallel to the optical axis of the viewer when the eye is fixating on an object at optical infinity directly in front of the viewer. Images 190 and 200 are flat and at a fixed distance from eyes 210 and 220. Based on slightly different views of the virtual object in the images presented to eyes 210 and 220, respectively, the eyes may necessarily rotate so that the image of the object falls on a corresponding point on each eye's retina, maintaining single binocular vision. This rotation may cause the gaze of each eye 210 and 220 to converge on a point in space where the virtual object is perceived to reside. As a result, providing three-dimensional images traditionally involves manipulating the convergence and divergence of the user's eyes 210 and 220 and providing binocular cues that the human visual system interprets to provide the perception of depth.

[0051] However, creating a realistic and comfortable perception of depth is challenging. It should be understood that light from an object at different distances from the eye has a wavefront with different amounts of divergence. Figures 3A-3C illustrate the relationship between distance and light ray divergence. The distance between the object and the eye 210 is represented in order of decreasing distances R1, R2, and R3. As shown in Figures 3A-3C, light rays become more divergent as the distance to the object decreases. Conversely, as the distance increases, the light rays become more collimated. In other words, the light field generated by a point (an object or portion of an object) can be said to have a spherical wavefront curvature that is a function of the distance the point is from the user's eye. As the curvature increases, the distance between the object and the eye 210 decreases. While only a single eye 210 is illustrated in Figures 3A-3C and various other figures herein for clarity of illustration, the discussion regarding the eye 210 may apply to both eyes 210 and 220 of the viewer.

[0052] Continuing with reference to Figures 3A-3C, light from an object that a viewer's eye is fixating may have different wavefront divergences. Due to the different wavefront divergences, the light may be focused differently by the eye's lens, which in turn may require the lens to assume a different shape 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 induce relaxation or contraction of the ciliary muscles surrounding the eye's lens, thereby modulating the force applied to the suspensory ligaments that hold the lens, thus changing the shape of the eye's lens and thereby forming a focused image of the fixated object on the eye's retina (e.g., the fovea) until retinal blur of the fixated object is eliminated or minimized. The process by which the eye's lens changes shape can be referred to as accommodation, and the shape of the eye's lens required to form a focused image of a fixated object on the eye's retina (e.g., the fovea) can be referred to as the state of accommodation.

[0053] Referring now to Figure 4A, a representation of the accommodation-vergence response of the human visual system is illustrated. Eye movement to fixate an object causes the eye to receive light from the object, which forms an image on each of the eye's retinas. The presence of retinal blur in the image formed on the retina can provide a cue for accommodation, and the relative location of the image on the retina can provide a cue for vergence. Accommodation cues cause accommodation, resulting in the eye's lens adopting a specific accommodation state in which a focused image of the object is formed 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 can be said to adopt a specific vergence state. Continuing with reference to FIG. 4A , accommodation can be understood as the process by which the eyes achieve a particular accommodation state, and convergence can be understood as the process by which the eyes achieve a particular convergence state. As shown in FIG. 4A , the accommodation and convergence states of the eyes can change when the user fixates on a different object. For example, the accommodated state can change when the user fixates on a new object at a different depth on the z-axis.

[0054] Without being limited by theory, it is believed that a viewer of an object may perceive the object as "three-dimensional" due to a combination of convergence-divergence and accommodation. As previously mentioned, vergence-divergence movements of the two eyes relative to one another (e.g., eye rotation such that the pupils move toward or away from one another, converging the eyes' lines of sight and fixating on an object) are closely linked to accommodation of the eye's lenses. Under normal conditions, changing the shape of the eye's lenses and shifting focus from one object to another at a different distance will automatically produce a corresponding change in vergence-divergence to the same distance, a relationship known as the "accommodation-divergence reflex." Similarly, a change in vergence-divergence will induce a corresponding change in lens shape under normal conditions.

[0055] 4B, an example of different accommodation and convergence states of the eyes is illustrated. Paired eye 222a fixates an object at optical infinity, while paired eye 222b fixates an object 221 at less than optical infinity. Notably, the convergence states of each pair of eyes are different: paired eye 222a points straight ahead, while paired eye 222 converges on object 221. The accommodation states of the eyes forming each pair of eyes 222a and 222b are also different, as represented by the different shapes of lenses 210a, 220a.

[0056] Unfortunately, many users of conventional "3-D" display systems may find such systems uncomfortable or may not perceive any depth perception due to a mismatch between accommodation and convergence states in these displays. As previously mentioned, many stereoscopic or "3-D" display systems display a scene by providing a slightly different image to each eye. Such systems are uncomfortable for many viewers because, among other things, they simply provide different presentations of a scene, causing changes in the eyes' convergence states without corresponding changes in the eyes' accommodation states. Rather, images are presented by the display at a fixed distance from the eyes so that the eyes view all image information in a single accommodation state. Such an arrangement counters the "accommodation-vergence-divergence reflex" by causing changes in the convergence states without a corresponding change in the accommodation state. This mismatch is believed to cause viewer discomfort. Display systems that provide better alignment between accommodation and convergence-divergence movements may create a more realistic and comfortable simulation of three-dimensional images.

[0057] Without being limited by theory, it is believed that the human eye is typically capable of interpreting a finite number of depth planes to provide depth perception. As a result, a highly realistic simulation of perceived depth may 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 cues and matching cues for accommodation, thereby providing physiologically correct accommodation-vergence divergence matching.

[0058] 4B , two depth planes 240 are illustrated, corresponding to different distances in space from the eyes 210, 220. For a given depth plane 240, vergence-divergence cues may be provided by displaying appropriately different perspective images for each eye 210, 220. Additionally, for a given depth plane 240, the light forming the image provided to each eye 210, 220 may have a wavefront divergence corresponding to the light field generated by a point at the distance of that depth plane 240.

[0059] 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 with a zero point located at the exit pupil of the 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 the user's eye on the optical axis of the eye with the eye pointed toward optical infinity. As an approximation, the depth or distance along the z-axis may be measured from a display (e.g., the surface of a waveguide) in front of the user's eye, and a value for the distance between the device and the exit pupil of the user's eye may be added. That value may be referred to as pupil distance and may correspond to the distance between the exit pupil of the user's eye and a display worn by the user in front of the eye. In practice, the value for pupil distance may be a normalized value generally used for all viewers. For example, pupil distance may be assumed to be 20 mm, and the depth plane at a depth of 1 meter may be at a distance of 980 mm in front of the display.

[0060] 4C and 4D, examples of matched accommodation-vergence-divergence distances and mismatched accommodation-vergence-divergence distances are illustrated, respectively. As illustrated in FIG. 4C, the display system may provide an image of a virtual object to each eye 210, 220. The image may cause the eyes 210, 220 to assume a convergence-divergence state in which the eyes converge on point 15 on the depth plane 240. In addition, the image may be formed by light having a wavefront curvature corresponding to the real object on that depth plane 240. As a result, the eyes 210, 220 assume an accommodation state in which the image is focused on the retinas of those eyes. Thus, the user may perceive the virtual object as being at point 15 on the depth plane 240.

[0061] It should be understood that the accommodation and convergence states of the eyes 210, 220 are each associated with a particular distance on the z-axis. For example, an object at a particular distance from the eyes 210, 220 will cause those eyes to assume a particular accommodation state based on the distance of the object. The distance associated with a particular accommodation state is referred to as the accommodation distance A. d Similarly, a particular convergence-divergence distance V associated with the eyes in a particular convergence-divergence state can be d Or, there exists a position relative to each other. When the accommodation distance and the convergence distance are matched, the relationship between accommodation and convergence is said to be physiologically correct. This is considered to be the most comfortable scenario for the viewer.

[0062] However, in a stereoscopic display, the accommodation distance and the convergence distance may not always be aligned. For example, as illustrated in FIG. 4D , images displayed to the eyes 210, 220 may be displayed with a wavefront divergence corresponding to the depth plane 240, and the eyes 210, 220 may be in a particular accommodation state in which points 15a, 15b on that depth plane are in focus. However, the images displayed to the eyes 210, 220 may provide convergence cues that cause 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 convergence 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 convergence distance. As a result, there is an accommodation-vergence-divergence mismatch. Such a mismatch is considered undesirable and can cause discomfort to the user. The mismatch can be caused by distance (e.g., V d -A d ) and can be characterized in terms of diopters.

[0063] It should be understood that in some embodiments, a reference point other than the exit pupil of the eye 210, 220 may be used to determine the distance for determining accommodation-vergence mismatch, so long as the same reference point is used for accommodation distance and vergence distance. For example, the distance may be measured from the cornea to the depth plane, from the retina to the depth plane, from the eyepiece (e.g., a waveguide in a display device) to the depth plane, etc.

[0064] 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 without the mismatch itself causing significant discomfort. In some embodiments, a display system disclosed herein (e.g., display system 250, FIG. 6 ) presents images to a viewer with an accommodation-vergence-divergence mismatch of about 0.5 diopters or less. In some other embodiments, the accommodation-vergence-divergence mismatch of images provided by the display system is about 0.33 diopters or less. In still other embodiments, the accommodation-vergence-divergence mismatch of images provided by the display system is about 0.25 diopters or less, including about 0.1 diopters or less.

[0065] FIG. 5 illustrates aspects of an approach for simulating a three-dimensional image by modifying wavefront divergence. The display system includes a waveguide 270 configured to receive light 770 encoded with image information and output the light to a user's eye 210. The waveguide 270 may output light 650 with a defined amount of wavefront divergence corresponding to the wavefront divergence of a light field generated by a point on a desired depth plane 240. In some embodiments, the same amount of wavefront divergence is provided for all objects presented on that depth plane. In addition, the user's other eye will be illustrated as being provided with image information from a similar waveguide.

[0066] In some embodiments, a single waveguide may be configured to output light with a set wavefront divergence corresponding to a single or limited number of depth planes, and / or the waveguide may be configured to output light of a limited range of wavelengths. As a result, in some embodiments, multiple or stacked waveguides may be utilized to provide different wavefront divergences for different depth planes and / or to output light of different ranges of wavelengths. It should be understood that, as used herein, a depth plane may be a plane or may follow the contour of a curved surface.

[0067] 6 illustrates an example of a waveguide stack for outputting image information to a user. Display system 250 includes a stack of waveguides or stacked waveguide assembly 260 that can be utilized to provide a three-dimensional perception to the eye / brain using multiple waveguides 270, 280, 290, 300, 310. It should be understood that display system 250 may be considered a light field display in some embodiments. Additionally, waveguide assembly 260 may also be referred to as an eyepiece.

[0068] In some embodiments, display system 250 may be configured to provide a substantially continuous cue for convergence and multiple discrete cues for accommodation. The cues for convergence may be provided by displaying different images to each of the user's eyes, and the cues for accommodation may be provided by outputting light that forms images with selectable discrete amounts of wavefront divergence. In other words, display system 250 may be configured to output light with variable levels of wavefront divergence. In some embodiments, each discrete level of wavefront divergence corresponds to a particular depth plane and may be provided by a particular one of waveguides 270, 280, 290, 300, and 310.

[0069] Continuing with reference to FIG. 6 , the waveguide assembly 260 may also include multiple features 320, 330, 340, 350 between the waveguides. In some embodiments, the features 320, 330, 340, 350 may be one or more lenses. The waveguides 270, 280, 290, 300, 310 and / or multiple lenses 320, 330, 340, 350 may be configured to transmit image information to the eye using various levels of wavefront curvature or ray divergence. Each waveguide level may be associated with a particular depth plane and configured to output image information corresponding to that depth plane. The image injection devices 360, 370, 380, 390, 400 may act as light sources for the waveguides and may be utilized to inject image information into the waveguides 270, 280, 290, 300, 310, each configured to disperse incident light across each individual waveguide for output toward the eye 210, as described herein. Light exits output surfaces 410, 420, 430, 440, 450 of the image injection devices 360, 370, 380, 390, 400 and is injected into corresponding input surfaces 460, 470, 480, 490, 500 of the waveguides 270, 280, 290, 300, 310. In some embodiments, each input surface 460, 470, 480, 490, 500 may be an edge of the corresponding waveguide or 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 beam of light (e.g., a collimated beam) may be launched into each waveguide, outputting a total field of cloned collimated beams that are directed toward the eye 210 at a particular angle (and divergence) corresponding to the depth plane associated with the particular waveguide. In some embodiments, a single one of the image launch devices 360, 370, 380, 390, 400 may be associated with and launch light into multiple (e.g., three) waveguides 270, 280, 290, 300, 310.

[0070] In some embodiments, each of the image input devices 360, 370, 380, 390, 400 is a discrete display that generates image information for input into a corresponding waveguide 270, 280, 290, 300, 310. In some other embodiments, the image input 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 the image input devices 360, 370, 380, 390, 400. It should be understood that the image information provided by the image input devices 360, 370, 380, 390, 400 may include light of different wavelengths or colors (e.g., different primary colors, as discussed herein).

[0071] In some embodiments, light injected into the waveguides 270, 280, 290, 300, 310 is provided by a light projector system 520, which includes a light module 530, which may include a light emitter such as a light emitting diode (LED). Light from the light module 530 may be directed and modified by a light modulator 540, e.g., a spatial light modulator, via a beam splitter 550. The light modulator 540 may be configured to vary the perceived intensity of the light injected into the waveguides 270, 280, 290, 300, 310 and encode the light with image information. Examples of spatial light modulators include liquid crystal displays (LCDs), including liquid crystal on silicon (LCOS) displays. It should be understood that image injection devices 360, 370, 380, 390, 400 are illustrated diagrammatically, and in some embodiments, these image injection devices may represent different light paths and locations within a common projection system configured to output light into associated ones of waveguides 270, 280, 290, 300, 310. In some embodiments, the waveguides of waveguide assembly 260 may function as ideal lenses, relaying light injected into the waveguides to the user's eye. In this concept, the object may be a spatial light modulator 540, and the image may be an image on a depth plane.

[0072] In some embodiments, the display system 250 may be a scanning fiber display comprising one or more scanning fibers configured to project light in various patterns (e.g., raster scan, spiral scan, Lissajous pattern, etc.) into one or more waveguides 270, 280, 290, 300, 310 and ultimately to the viewer's eye 210. In some embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may diagrammatically represent a single scanning fiber or a bundle of scanning fibers configured to inject light into one or more waveguides 270, 280, 290, 300, 310. In some other embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may diagrammatically represent multiple scanning fibers or multiple bundles of scanning fibers, each configured to inject light into an associated one of the waveguides 270, 280, 290, 300, 310. It should be understood that one or more optical fibers may be configured to transmit light from the optical module 530 to one or more waveguides 270, 280, 290, 300, 310. It should be understood that one or more intervening optical structures may be provided between the scanning fiber or fibers and one or more waveguides 270, 280, 290, 300, 310, for example, to redirect light exiting the scanning fiber into one or more waveguides 270, 280, 290, 300, 310.

[0073] Controller 560 controls the operation of one or more of stacked waveguide assemblies 260, including the operation of image input devices 360, 370, 380, 390, 400, light source 530, and light modulator 540. In some embodiments, controller 560 is part of local data processing module 140. Controller 560 contains programming (e.g., instructions in a non-transitory medium) that coordinates the timing and provisioning of image information to waveguides 270, 280, 290, 300, 310, for example, according to any of the various schemes disclosed herein. In some embodiments, the controller may be a single integrated device or a distributed system connected by wired or wireless communication channels. Controller 560 may, in some embodiments, be part of processing module 140 or 150 (FIG. 2).

[0074] Continuing with reference to FIG. 6 , the waveguides 270, 280, 290, 300, and 310 may be configured to propagate light within each individual waveguide by total internal reflection (TIR). Each of the waveguides 270, 280, 290, 300, and 310 may be planar or have another shape (e.g., curved) with major top and bottom surfaces and edges extending between the major top and bottom surfaces. In the illustrated configuration, the waveguides 270, 280, 290, 300, and 310 may each include outcoupling optical elements 570, 580, 590, 600, and 610 configured to extract light from the waveguide by redirecting the light, causing it to propagate within each individual waveguide, and outputting image information from the waveguide to the eye 210. The extracted light may also be referred to as outcoupling light, and the outcoupling optical element light may also be referred to as a light extraction optical element. The extracted beam of light may be output by the waveguide at a location where light propagating within the waveguide strikes the light-extraction optical element. The outcoupling optical element 570, 580, 590, 600, 610 may be a grating, for example, including diffractive optical features as discussed further herein. While shown disposed on the bottom major surface of the waveguides 270, 280, 290, 300, 310 for ease of explanation and clarity of the drawings, in some embodiments, the outcoupling optical element 570, 580, 590, 600, 610 may be disposed on the top and / or bottom major surfaces and / or directly within the volume of the waveguides 270, 280, 290, 300, 310, as discussed further herein. In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 may be formed within a layer of material attached to a transparent substrate and forming the waveguides 270, 280, 290, 300, 310. In some other embodiments, the waveguides 270, 280, 290, 300, 310 may be monolithic material components, and the outcoupling optical elements 570, 580, 590, 600, 610 may be formed on and / or within the material surfaces of the components.

[0075] Continuing with reference to FIG. 6 , as discussed herein, each waveguide 270, 280, 290, 300, 310 is configured to output light and form an image corresponding to a particular depth plane. For example, the waveguide 270 closest to the eye may be configured to deliver collimated light (injected into such waveguide 270) to the eye 210. The collimated light may represent an optical infinity focal plane. The next upper waveguide 280 may be configured to send collimated light that passes through a first lens 350 (e.g., a negative lens) before reaching the eye 210. Such first lens 350 may be configured to generate a slight convex wavefront curvature so that the eye / brain interprets light emerging from the next upper waveguide 280 as emerging from a first focal plane closer inward from optical infinity toward the eye 210. Similarly, the third upper waveguide 290 passes its output light through both the first lens 350 and the second lens 340 before reaching the eye 210. The combined refractive power of the first lens 350 and the second lens 340 may be configured to produce another, increasing amount of wavefront curvature so that the eye / brain interprets the light emerging from the third waveguide 290 as originating from a second focal plane closer inward toward the person from optical infinity, which was the light from the next upper waveguide 280.

[0076] The other waveguide layers 300, 310 and lenses 330, 320 are similarly configured, with the highest waveguide 310 in the stack sending its output through all of the lenses between it and the eye for a collective focal power representing the focal plane closest to the person. To compensate for the stack of lenses 320, 330, 340, 350 when viewing / interpreting light originating from the world 510 on the other side of the stacked waveguide assembly 260, a compensating lens layer 620 may be placed on top of the stack to compensate for the collective power of the lower lens stacks 320, 330, 340, 350. Such a configuration provides as many perceived focal planes as there are available waveguide / lens pairs. Both the waveguide outcoupling optical elements and the focusing sides of the lenses may be static (i.e., not dynamic or electro-active). In some alternative embodiments, one or both may be dynamic using electro-active features.

[0077] 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 depth planes, with one set per depth plane. This may provide the advantage of forming tiled images to provide an extended field of view at those depth planes.

[0078] Continuing with reference to FIG. 6 , the outcoupling optical elements 570, 580, 590, 600, 610 may be configured to redirect light from its respective waveguide and output the light with an appropriate amount of divergence or collimation for a particular depth plane associated with that waveguide. As a result, waveguides with different associated depth planes may have different configurations of outcoupling optical elements 570, 580, 590, 600, 610, which output light with different amounts of divergence depending on the associated depth plane. In some embodiments, the light-extracting optical elements 570, 580, 590, 600, 610 may be volume or surface features that may be configured to output light at specific angles. For example, the light-extracting optical elements 570, 580, 590, 600, 610 may be volume holograms, surface holograms, and / or diffraction gratings. In some embodiments, the features 320, 330, 340, 350 may not be lenses. Rather, they may simply be spacers (eg, cladding layers and / or structures for forming air gaps).

[0079] In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 are diffractive features or "diffractive optical elements" (also referred to herein as "DOEs") that form a diffraction pattern. Preferably, the DOEs have a sufficiently low diffraction efficiency so that only a portion of the light in the beam is deflected toward the eye 210 at each intersection of the DOE, while the remainder continues traveling through the waveguide via TIR. The light carrying the image information is thus split into several related output beams that exit the waveguide at various locations, resulting in a very uniform pattern of output emission toward the eye 210 for this particular collimated beam bouncing within the waveguide.

[0080] In some embodiments, one or more DOEs may be switchable between an "on" state in which they actively diffract and an "off" state in which they do not significantly diffract. For example, a switchable DOE may comprise a layer of polymer-dispersed liquid crystal in which microdroplets comprise a diffractive pattern 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 significantly diffract incident light), or the microdroplets may be switched to a refractive index that does not match that of the host medium (in which case the pattern actively diffracts incident light).

[0081] In some embodiments, a camera assembly 630 (e.g., a digital camera, including visible and infrared light cameras) may be provided to capture images of the eye 210 and / or tissue surrounding the eye 210, for example, to detect user input and / or monitor the physiological state of the user. As used herein, a camera may be any image capture device. In some embodiments, the camera assembly 630 may include an image capture device and a light source that projects light (e.g., infrared light) onto the eye, which may then be reflected by the eye and detected by the image capture device. In some embodiments, the camera assembly 630 may be mounted on the frame 80 (FIG. 9D) and may be in electrical communication with processing modules 140 and / or 150, which may process image information from the camera assembly 630. In some embodiments, one camera assembly 630 may be utilized per eye, monitoring each eye separately.

[0082] 7, an example of an output beam output by a waveguide is shown. While one waveguide is illustrated, it should be understood that other waveguides in waveguide assembly 260 (FIG. 6) may function similarly, and that waveguide assembly 260 includes multiple waveguides. Light 640 is launched into waveguide 270 at input surface 460 of waveguide 270 and propagates within waveguide 270 by TIR. At the point where light 640 impinges on DOE 570, a portion of the light exits the waveguide as output beam 650. Output beam 650 is illustrated as being approximately parallel, but may be redirected to propagate to eye 210 at an angle (e.g., forming a diverging output beam), as discussed herein and depending on the depth plane associated with waveguide 270. It should be understood that a nearly collimated exit beam may refer to a waveguide with outcoupling optics that outcouples light to form an image that appears to be set at 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 a more divergent exit beam pattern, which would require the eye 210 to accommodate to a closer distance and focus on the retina, and would be interpreted by the brain as light from a distance closer to the eye 210 than optical infinity.

[0083] In some embodiments, a full-color image may be formed at each depth plane by overlaying an image in each of the primary colors, for example, three or more primary colors. FIG. 8 illustrates an example of a stacked waveguide assembly, with each depth plane including an image formed using multiple different primary colors. The illustrated embodiment shows depth planes 240a-240f, but more or fewer depths are also contemplated. Each depth plane may have three or more primary color images associated with it, including a first image in a first color G, a second image in a second color R, and a third image in a third color B. Different depth planes are indicated in the diagram by different numbers for diopters (dpt) following the letters G, R, and B. By way of example only, the number following each of these letters indicates the diopter (1 / m), i.e., the inverse distance of the depth plane from the viewer, and each box in the diagram represents an individual primary color image. In some embodiments, the exact locations of the depth planes for different primary colors may be varied to account for differences in the eye's focusing of light of different wavelengths. For example, different primary color images for a given depth plane may be placed on depth planes corresponding to different distances from the user. Such an arrangement may increase visual acuity and user comfort and / or reduce chromatic aberrations.

[0084] In some embodiments, light for each primary color may be output by a single dedicated waveguide, such that each depth plane may have multiple waveguides associated with it. In such embodiments, each box in the diagram containing the letter G, R, or B may be understood to represent an individual waveguide, and three waveguides may be provided per depth plane, resulting in three primary color images per depth plane. While the waveguides associated with each depth plane are shown adjacent to each other in this drawing for ease of illustration, it should be understood that in a physical device, the waveguides may all be arranged in a stack with one waveguide per level. In some other embodiments, multiple primary colors may be output by the same waveguide, such that, for example, only a single waveguide may be provided per depth plane.

[0085] 8, in some embodiments, G is green, R is red, and B is blue. In some other embodiments, other colors associated with other wavelengths of light, including magenta and cyan, may be used in addition to or replace one or more of red, green, or blue.

[0086] It should be understood that references to a given color of light throughout this disclosure will be understood to encompass light of one or more wavelengths within the range of wavelengths of light that are perceived by a viewer to be of that given color. For example, red light may include one or more wavelengths of light within a range of about 620-780 nm, green light may include one or more wavelengths of light within a range of about 492-577 nm, and blue light may include one or more wavelengths of light within a range of about 435-493 nm.

[0087] In some embodiments, light source 530 (FIG. 6) may be configured to emit light at one or more wavelengths outside the range of a viewer's visual perception, e.g., infrared and / or ultraviolet wavelengths. Additionally, the waveguide incoupling, outcoupling, and other light redirecting structures of display 250 may be configured to direct and emit this light from the display toward the user's eye 210, e.g., for imaging and / or user stimulation applications.

[0088] Referring now to FIG. 9A , in some embodiments, light impinging on a waveguide may need to be redirected to incoupling the light into the waveguide. An incoupling optical element may be used to redirect and incoupling the light into its corresponding waveguide. FIG. 9A illustrates a cross-sectional side view of an example of a plurality or set 660 of stacked waveguides, each including an incoupling optical element. The waveguides may each be configured to output light of one or more different wavelengths or one or more different wavelength ranges. Stack 660 may correspond to stack 260 ( FIG. 6 ), and the illustrated waveguides of stack 660 may correspond to a portion of multiple waveguides 270, 280, 290, 300, 310, although it should be understood 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.

[0089] The illustrated set 660 of stacked waveguides includes waveguides 670, 680, and 690. Each waveguide includes an associated internal coupling optical element (which may also be referred to as the light input area on the waveguide), for example, internal coupling optical element 700 is disposed on a major surface (e.g., the top major surface) of waveguide 670, internal coupling optical element 710 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and internal coupling optical element 720 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some embodiments, one or more of internal coupling optical elements 700, 710, 720 may be disposed on the bottom major surface of an individual waveguide 670, 680, 690 (particularly, one or more internal coupling optical elements are reflective polarizing optical elements). As shown, the internal coupling optical elements 700, 710, 720 may be disposed on the upper major surface of the respective waveguide 670, 680, 690 (or on top of the next lower waveguide), and in particular, the internal coupling optical elements are transmissive turning optical elements. In some embodiments, the internal coupling optical elements 700, 710, 720 may be disposed within the body of the respective waveguide 670, 680, 690. In some embodiments, as discussed herein, the internal coupling 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 illustrated on one side or corner of the respective waveguide 670, 680, 690, it should be understood that the internal coupling optical elements 700, 710, 720 may be disposed within other areas of the respective waveguide 670, 680, 690 in some embodiments.

[0090] As shown, the in-coupling optical elements 700, 710, 720 may be laterally offset from one another. In some embodiments, each in-coupling optical element may be offset to receive light without that light passing through another in-coupling optical element. For example, each in-coupling optical element 700, 710, 720 may be configured to receive light from a different image input device 360, 370, 380, 390, and 400, as shown in FIG. 6 , and may be separated (e.g., laterally spaced) from the other in-coupling optical elements 700, 710, 720 so as to substantially not receive light from others of the in-coupling optical elements 700, 710, 720.

[0091] Each waveguide also includes an associated optically dispersive element, for example, optically dispersive element 730 is disposed on a major surface (e.g., the top major surface) of waveguide 670, optically dispersive element 740 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and optically dispersive element 750 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some other embodiments, optically dispersive elements 730, 740, 750 may be disposed on the bottom major surfaces of associated waveguides 670, 680, 690, respectively. In some other embodiments, optically dispersive elements 730, 740, 750 may be disposed on both the top and bottom major surfaces of associated waveguides 670, 680, 690, respectively, or optically dispersive elements 730, 740, 750 may be disposed on different ones of the top and bottom major surfaces in different associated waveguides 670, 680, 690, respectively.

[0092] Waveguides 670, 680, 690 may be spaced apart and separated, for example, by gas, liquid, and / or solid layers of material. For example, as shown, layer 760a may separate waveguides 670 and 680, and layer 760b may separate waveguides 680 and 690. In some embodiments, layers 760a and 760b are formed from a low refractive index material (i.e., a material having a lower refractive index than the material forming the immediately adjacent waveguides 670, 680, 690). Preferably, the refractive index of the material forming layers 760a, 760b is 0.05 or more, or 0.10 or less, relative to the refractive index of the material forming waveguides 670, 680, 690. Advantageously, the lower refractive index layers 760a, 760b may function as cladding layers that promote total internal reflection (TIR) of light through the waveguides 670, 680, 690 (e.g., TIR between the top and bottom major surfaces of each waveguide). In some embodiments, the layers 760a, 760b are formed from air. Although not shown, it should be understood that the top and bottom of the illustrated set of waveguides 660 may include immediate cladding layers.

[0093] 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 discussed above.

[0094] 9A, light rays 770, 780, 790 enter the set of waveguides 660. It should be understood that light rays 770, 780, 790 may be injected into the waveguides 670, 680, 690 by one or more image injection devices 360, 370, 380, 390, 400 (FIG. 6).

[0095] In some embodiments, light rays 770, 780, 790 have different properties, e.g., different wavelengths or different wavelength ranges, which may correspond to different colors. Each of the incoupling optical elements 700, 710, 720 deflects incident light such that the light propagates through a respective one of the waveguides 670, 680, 690 by TIR. In some embodiments, each of the incoupling optical elements 700, 710, 720 selectively deflects one or more particular wavelengths of light while transmitting other wavelengths to the underlying waveguide and associated incoupling optical element.

[0096] For example, in-coupling optical element 700 may be configured to deflect light ray 770 having a first wavelength or wavelength range while transmitting light rays 780 and 790 having different second and third wavelengths or wavelength ranges, respectively. Transmitted light ray 780 impinges on and is deflected by in-coupling optical element 710, which is configured to deflect light of the second wavelength or wavelength range. Light ray 790 is deflected by in-coupling optical element 720, which is configured to selectively deflect light of the third wavelength or wavelength range.

[0097] 9A , the deflected light rays 770, 780, 790 are deflected to propagate through the corresponding waveguides 670, 680, 690. That is, the in-coupling optical element 700, 710, 720 of each waveguide deflects the light into its corresponding waveguide 670, 680, 690, in-coupling the light into the corresponding waveguide. The light rays 770, 780, 790 are deflected at an angle that causes the light to propagate through the respective waveguides 670, 680, 690 by TIR. The light rays 770, 780, 790 propagate through the respective waveguides 670, 680, 690 by TIR until they impinge on the waveguide's corresponding optical dispersive element 730, 740, 750.

[0098] 9B, a perspective view of the multiple stacked waveguide embodiment of FIG. 9A is illustrated. As previously described, in-coupled light rays 770, 780, 790 are deflected by in-coupling optical elements 700, 710, 720, respectively, and then propagate by TIR within waveguides 670, 680, 690, respectively. Light rays 770, 780, 790 then impinge on optically dispersive elements 730, 740, 750, respectively. Optically dispersive elements 730, 740, 750 deflect light rays 770, 780, 790 to propagate toward out-coupling optical elements 800, 810, 820, respectively.

[0099] In some embodiments, the optically dispersive elements 730, 740, 750 are orthogonal pupil expanders (OPEs). In some embodiments, the OPEs deflect or disperse light into the out-coupling optical elements 800, 810, 820, and in some embodiments, may also increase the beam or spot size of this light as it propagates into the out-coupling optical elements. In some embodiments, the optically dispersive elements 730, 740, 750 may be omitted, and the in-coupling optical elements 700, 710, 720 may be configured to deflect light directly into the out-coupling optical elements 800, 810, 820. For example, with reference to FIG. 9A , the optically dispersive elements 730, 740, 750 may be replaced with the out-coupling optical elements 800, 810, 820, respectively. In some embodiments, the outcoupling optical elements 800, 810, 820 are exit pupils (EPs) or exit pupil expanders (EPEs) that direct light toward the viewer's eye 210 ( FIG. 7 ). It should be understood that an OPE may be configured to increase the size of the eyebox in at least one axis, and that the 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 an EPE of the same waveguide, while allowing the remaining portion of the light to continue propagating down the waveguide. Upon striking the OPE, again, another portion of the remaining light is redirected to the EPE, and the remainder of that portion continues to propagate further down the waveguide, etc. Similarly, upon striking the EPE, a portion of the impinging light is directed out of the waveguide toward the user, and the remaining portion of that light continues to propagate through the waveguide until it again strikes an EP, at which point another portion of the impinging light is directed out of the waveguide, etc. As a result, a single beam of internally coupled light may be "replicated" each time a portion of that light is redirected by an OPE or EPE, thereby forming a cloned beam field of light, as shown in Figure 6. In some embodiments, the OPE and / or EPE may be configured to modify the size of the beam of light.

[0100] 9A and 9B, in some embodiments, a waveguide set 660 includes, for each primary color, waveguides 670, 680, 690, in-coupling optical elements 700, 710, 720, optically dispersive elements (e.g., OPEs) 730, 740, 750, and out-coupling optical elements (e.g., EPs) 800, 810, 820. The waveguides 670, 680, 690 may be stacked with an air gap / cladding layer between each one. The in-coupling optical elements 700, 710, 720 redirect or deflect incident light into that waveguide (with different in-coupling optical elements receiving different wavelengths of light). The light then propagates at an angle that will result in TIR within the individual waveguides 670, 680, 690. In the example shown, light ray 770 (e.g., blue light) is deflected by the first in-coupling optical element 700 in the manner described above, then continues bouncing down the waveguide, interacting with the optically dispersive element (e.g., OPE) 730 and then the out-coupling optical element (e.g., EP) 800. Light rays 780 and 790 (e.g., green and red light, respectively) pass through the waveguide 670, with light ray 780 impinging on and being deflected by the in-coupling optical element 710. Light ray 780 will then, via TIR, bounce down the waveguide 680, to its optically dispersive element (e.g., OPE) 740 and then the out-coupling optical element (e.g., EP) 810. Finally, light ray 790 (e.g., red light) passes through the waveguide 690 and impinges on the optically in-coupling optical element 720 of the waveguide 690. The light in-coupling optical element 720 deflects the light ray 790 so that it propagates by TIR to the light dispersive element (e.g., OPE) 750 and then by TIR to the out-coupling optical element (e.g., EP) 820. The out-coupling optical element 820 then finally out-couples the light ray 790 to a viewer, who also receives the out-coupled light from the other waveguides 670, 680.

[0101] FIG. 9C illustrates a top-down plan view of an example of the multiple stacked waveguides of FIGS. 9A and 9B. As shown, waveguides 670, 680, 690 may be vertically aligned, along with each waveguide's associated optically dispersive elements 730, 740, 750 and associated out-coupling optical elements 800, 810, 820. However, as discussed herein, the in-coupling optical elements 700, 710, 720 are not vertically aligned. Rather, the in-coupling optical elements are preferably non-overlapping (e.g., laterally spaced apart, as seen in the top-down view). As discussed further herein, this non-overlapping spatial arrangement facilitates the injection of light from different sources into different waveguides on a one-to-one basis, thereby allowing a specific light source to be uniquely coupled to a specific waveguide. In some embodiments, arrays including non-overlapping, spatially separated in-coupling optical elements may be referred to as shifted-pupil systems, and the in-coupling optical elements in these arrays may correspond to sub-pupils.

[0102] 9D illustrates an example of a wearable display system 60 into which the various waveguide and associated systems disclosed herein may be integrated. In some embodiments, the display system 60 is the system 250 of FIG. 6, which diagrammatically illustrates some portions of the system 60 in greater detail. For example, the waveguide assembly 260 of FIG. 6 may be part of the display 70.

[0103] Continuing with reference to FIG. 9D , display system 60 includes a display 70 and various mechanical and electronic modules and systems to support the functionality of the display 70. The display 70 may be coupled to a frame 80, which is wearable by a display system user or viewer 90 and configured to position the display 70 directly in front of the user's 90's eye. The display 70, in some embodiments, may be considered an eyepiece. In some embodiments, a speaker 100 is coupled to frame 80 and configured to be positioned adjacent to the user's 90 ear canal (in some embodiments, another speaker, not shown, may optionally be positioned adjacent the user's other ear canal to provide stereo / shapeable sound control). Display system 60 may also include one or more microphones 110 or other devices to detect sound. In some embodiments, the microphones are configured to allow a user to provide input or commands to system 60 (e.g., voice menu command selections, natural language queries, etc.) and / or enable audio communication with other persons (e.g., other users of similar display systems). The microphone may further be configured as an ambient sensor to collect audio data (e.g., sounds from the user and / or the environment). In some embodiments, the display system may also include an ambient sensor 120a, which may be separate from the frame 80 and mounted on the body of the user 90 (e.g., the head, torso, limbs, etc. of the user 90). The ambient sensor 120a, in some embodiments, may be configured to obtain data characterizing a physiological state of the user 90. For example, the sensor 120a may be an electrode.

[0104] 9D , display 70 is operably coupled to local data processing module 140 by a communication link 130, such as wired or wireless connectivity, which may be mounted in a variety of configurations, such as fixedly attached to frame 80, fixedly attached to a helmet or hat worn by the user, embedded within headphones, or otherwise removably attached to user 90 (e.g., in a backpack-style configuration, in a belt-linked configuration). Similarly, sensor 120a may be operably coupled to local processor and data module 140 by a communication link 120b, such as wired or wireless connectivity. Local processing and data module 140 may comprise a hardware processor and digital memory, such as non-volatile memory (e.g., flash memory or a hard disk drive), both of which may be utilized to aid in processing, caching, and storing data. Optionally, local processing 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 (such as image capture devices (cameras, etc.), microphones, inertial measurement units, accelerometers, compasses, GPS units, wireless devices, gyroscopes, and / or other sensors disclosed herein (e.g., which may be operatively coupled to frame 80 or otherwise attached to user 90)) and / or b) data obtained and / or processed using remote processing module 150 and / or remote data repository 160 (including data related to virtual content), possibly for passage to display 70 after processing or retrieval. Local processing and data module 140 may be operatively coupled to remote processing module 150 and remote data repository 160 by communication links 170, 180, such as via wired or wireless communication links, such that these remote modules 150, 160 are operatively coupled to each other and available as resources to local processing and data module 140.In some embodiments, local processing and data module 140 may include one or more of an image capture device, a microphone, an inertial measurement unit, an accelerometer, a compass, a GPS unit, a wireless device, and / or a gyroscope. In some other embodiments, one or more of these sensors may be mounted on frame 80 or may be a freestanding structure that communicates with local processing and data module 140 by a wired or wireless communication path.

[0105] 9D , in some embodiments, remote processing module 150 may comprise one or more processors configured to analyze and process data and / or image information, and may include, for example, one or more central processing units (CPUs), graphics processing units (GPUs), dedicated processing hardware, etc. In some embodiments, remote data repository 160 may comprise digital data storage facilities that may be available through the Internet or other networking configurations in a “cloud” resource configuration. In some embodiments, remote data repository 160 may include one or more remote servers, which provide information, for example, information for generating augmented reality content, to local processing and data module 140 and / or remote processing module 150. In some embodiments, all data is stored and all 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 information to and receive information from modules 140, 150, 160, e.g., via a wireless or wired connection. Liquid Crystal Materials for Broadband Adaptive Waveplate Lens Assemblies

[0106] Generally, liquid crystals possess physical properties that may be intermediate between traditional fluids and solids. Liquid crystals are fluid-like in some aspects, but unlike most fluids, the arrangement of molecules within liquid crystals exhibits a structural order. Different types of liquid crystals include thermotropic, lyotropic, and polymeric liquid crystals. The thermotropic liquid crystals disclosed herein can be implemented in a variety of physical states, e.g., phases, including nematic, smectic, chiral nematic, or chiral smectic states / phases.

[0107] As described herein, liquid crystals in a nematic state or phase can have calamitic (rod-shaped) or discotic (disk-shaped) organic molecules that have relatively little positional order but long-range directional order, with their long axes generally parallel. Thus, the organic molecules can flow freely, their center-of-mass positions randomly dispersed as in a liquid, while still maintaining their long-range directional order. In some implementations, liquid crystals in the nematic phase can be uniaxial, i.e., the liquid crystals have one axis that is longer and preferred, and the other two are approximately equal. In some implementations, the liquid crystal molecules align along their long axes. In other implementations, the liquid crystals can be biaxial, i.e., in addition to aligning their long axes, the liquid crystals can also align along their secondary axes.

[0108] As described herein, liquid crystals in a smectic state or phase can have organic molecules that form relatively well-defined layers that can slide over one another. In some implementations, liquid crystals in a smectic phase can be positionally ordered along one direction. In some implementations, the long axes of the molecules can be oriented approximately normal to the plane of the liquid crystal layer, while in other implementations, the long axes of the molecules can be tilted relative to the normal to the plane of the layer.

[0109] Here, and throughout this disclosure, nematic liquid crystals consist of rod-shaped molecules with the long axes of neighboring molecules approximately aligned with one another. To describe this anisotropic structure, a dimensionless unit vector n, called the director, can be used to describe the direction of preferred orientation of the liquid crystal molecules.

[0110] Here, and throughout this disclosure, the azimuthal angle or rotation angle φ is used to describe the angle of rotation of liquid crystal molecules about an axis normal to the layer or major surfaces of the liquid crystal layer, measured in a plane parallel to the major surfaces of the liquid crystal layer or substrate, e.g., the xy plane, and measured between the alignment direction, e.g., the stretch direction or director direction, and a direction parallel to the major surfaces, e.g., the y-direction.

[0111] Here, and throughout this disclosure, when angles such as rotation angle φ are referred to as being substantially the same or different between different regions, it should be understood that the average alignment angle may be, for example, within about 1%, about 5%, or about 10% of each other, although the average alignment may be greater in some cases.

[0112] As described herein, some liquid crystals in the nematic or smectic state can also exhibit a twist in the layer normal direction. Such liquid crystals are referred to as twisted nematic (TN) or twisted smectic (SN) liquid crystals. TN or SN liquid crystals can exhibit molecular twist about an axis perpendicular to the director, with the molecular axis parallel to the director. When the degree of twist is relatively large, the twisted liquid crystal can be referred to as a chiral or cholesteric phase.

[0113] As described herein, TN or SN liquid crystals may be described as having a twist angle or net twist angle (φ), which may refer, for example, to the relative azimuthal rotation between the top and bottom liquid crystal molecules across a defined length, e.g., the thickness of the liquid crystal layer.

[0114] As described herein, "polymerizable liquid crystal" may refer to a liquid crystal material that can be polymerized, for example, photopolymerized in situ, and may also be described herein as a reactive mesogen (RM).

[0115] Liquid crystal molecules, in some embodiments, may be polymerizable and, once polymerized, may form large-scale networks with other liquid crystal molecules. For example, liquid crystal molecules may be linked by chemical bonds or by linking chemical species to other liquid crystal molecules. Once joined together, the liquid crystal molecules may form liquid crystal domains that have substantially the same orientation and location as before they were linked together. The term "liquid crystal molecules," as used herein, may refer to both the liquid crystal molecules before polymerization and the liquid crystal domains formed by these molecules after polymerization. Once polymerized, the polymerized network may be referred to as a liquid crystal polymer (LCP).

[0116] In some embodiments, prior to polymerization, unpolymerized or polymerizable liquid crystal molecules may have at least limited rotational freedom. These unpolymerized liquid crystal molecules may rotate or tilt, for example, under electrical stimulation, resulting in altered optical properties. For example, by applying an electric field, some liquid crystal layers containing unpolymerized liquid crystal molecules may be switched between one or more states with different diffraction or polarization-altering properties.

[0117] The inventors recognize that the above-described properties of liquid crystals or reactive mesogens (RMs) can be advantageously applied to various components of the broadband switchable waveplates and waveplate lenses disclosed herein. For example, in some unpolymerized RMs, the orientation of the LC molecules can be altered after deposition, for example, by application of an external stimulus, such as an electric field. Based on this recognition, the inventors disclose herein waveplates and waveplate lenses that can be switched between multiple states by application of an external stimulus.

[0118] Additionally, the inventors recognize that, when not polymerized, the orientation of LC molecules at the surface or interface of some LCs or RMs can be matched by controlling the surface or interface on which the LC molecules are formed. For example, a stack of multiple LC layers can be formed, and by controlling the orientation of the LC molecules closest to the surface of an LC layer, the orientation of the immediately adjacent LC in the next LC layer can be controlled to have, for example, the same orientation as the LC molecules closest to the surface in the previous LC layer or the same orientation as the elongated microstructures in the adjacent layer. Additionally, the LC molecules between LC molecules at a surface or interface can be controlled to have a predetermined amount of twist. Based on the recognition of these and other attributes, including birefringence, chirality, and ease of multiple coatings, the inventors disclose herein waveplates and waveplate lenses with tailored optical properties, such as broadband capability with diffraction efficiency, optical power, and polarization, to name a few. Display device having a switchable broadband adaptive waveplate lens assembly

[0119] 6, some display systems, according to embodiments, include a waveguide assembly 260 configured to form images at multiple virtual depth planes. The waveguide assembly 260 includes waveguides 270, 280, 290, 300, 310, each configured to propagate light by total internal reflection (TIR), and includes outcoupling optical elements 570, 580, 590, 600, 610, each configured to redirect light and thereby extract light out of a respective one of the waveguides 270, 280, 290, 300, 310. Each of the waveguides 270, 280, 290, 300, 310 is configured to output light and form an image corresponding to a particular depth plane. The waveguide assembly 260 may also optionally include multiple lenses 320, 330, 340, 350 between the waveguides to provide different refractive powers for forming images at different virtual depth planes.

[0120] In the illustrated embodiment of waveguide assembly 260 in FIG. 6 , the number of depth planes may be directly proportional to the number of waveguides and lenses. However, the inventors recognize various challenges associated with implementing a waveguide assembly configured to display images at multiple depth planes by having a proportional number of waveguides and lenses. For example, a large number of waveguides 270, 280, 290, 300, 310 and a large number of corresponding lenses 320, 330, 340, 350 can undesirably increase the overall thickness, weight, cost, and manufacturing challenges for waveguide assembly 260. For example, when formed from conventional lens materials, such as glass, lenses 320, 330, 340, 350 can each add several millimeters or tens of millimeters of thickness and corresponding weight to the display. Additionally, a large number of waveguides and lenses can produce optical effects that are undesirable to the user, such as relatively high absorption losses. Thus, in one aspect, the inventors recognize potential advantages for display systems that, in some cases, may generate images at multiple depth planes using fewer waveguides, fewer lenses, thinner and lighter waveguides and lenses, and / or fewer lenses per waveguide.

[0121] Still referring to FIG. 6 , it should be understood that lenses 320, 330, 340, and 350 can be configured to form images at different depth planes by imparting individual optical powers to light from waveguides 310, 300, 290, and 280. In various embodiments, light coupled out from the waveguides can have a polarization, e.g., circular polarization. However, when polarized light coupled out from the waveguides passes through a waveplate lens or waveplate formed from liquid crystals, less than 100% of the coupled light transmitted therethrough can be optically affected, e.g., diffracted, diverged, focused, or otherwise altered in polarization, resulting in some of the coupled light passing through optically unaffected. Light passing through a lens in this manner optically unaffected is sometimes referred to as leaked light. The leaked light can be undesirably focused, defocused, or have its polarization altered, or it can be unaffected at all, in the downstream optical path. When a significant portion of light passing through a waveplate or waveplate lens constitutes leakage light, a user may experience undesirable effects such as a "lasting image," which is an unintended image or an image visible to a user at an unintended depth plane. The inventors recognize that such leakage light can result, among other causes, from a waveplate lens or waveplate formed from a liquid crystal configured to have a relatively high diffraction efficiency within a relatively narrow wavelength range within the visible spectrum. Accordingly, in another aspect, the inventors recognize a need for a broadband adaptive waveplate lens assembly that can generate images at multiple depth planes over a wide range of wavelengths within the visible spectrum with little undesirable effects resulting from leakage light. To address these and other needs, various embodiments include a broadband adaptive waveplate lens assembly comprising a liquid crystal-based switchable waveplate lens or switchable waveplate configured to provide variable refractive power. Waveplate lenses and waveplates formed from liquid crystals can offer various advantages toward achieving these goals, including thin thickness, light weight, and a high degree of configurability at the molecular level.In various embodiments described herein, a display device is configured to form images at different virtual depth planes using a waveguide assembly configured to direct light in a lateral direction parallel to an output surface of the waveguide and outcouple the light directed through the output surface into one or more broadband adaptive waveplate lens assemblies. In various embodiments, the broadband adaptive waveplate lens assemblies are configured to incouple and diffract the outcoupled light from the waveguide therethrough. The broadband adaptive lens assemblies include a first waveplate lens comprising a liquid crystal (LC) layer arranged to have birefringence (Δn) that varies radially outward from a central region of the first waveplate lens, where the waveplate lens is configured to diffract the outcoupled light within a broadband wavelength range including at least 450 nm to 630 nm with a diffraction efficiency greater than 90%, greater than 95%, or even greater than 99%. In some embodiments, broadband adaptive waveplate lens assemblies according to embodiments are significantly lighter and thinner (a few microns) than conventional lenses and can advantageously provide variable optical power over a broadband wavelength range. Advantageously, such broadband adaptive lens assemblies can reduce the number, thickness, and weight of waveguide assemblies, such as waveguide assembly 260 (FIG. 6), and can reduce or eliminate undesirable effects resulting from leaking light.

[0122] As used herein, optical power (P, also referred to as refractive power, focusing power, or convergence power) refers to the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device: P=1 / f. That is, high optical power corresponds to short focal lengths. The SI unit for optical power is per meter (m -1 ), which is commonly called diopter (D).

[0123] As described herein, a converging lens, which focuses light passing through it, is described as having positive refractive power, while a diverging lens, which defocuses light passing through it, is described as having negative power. Without being bound by theory, when light passes through two or more thin lenses that are relatively close to one another, the refractive power of the combined lenses can be approximated as the sum of the refractive powers of the individual lenses. Thus, when light passes through a first lens having a first refractive power P1 and further passes through a second lens having a second refractive power P2, the light can be understood to converge or diverge according to the sum of the refractive powers Pnet = P1 + P2.

[0124] A medium that has a refractive index that depends on the polarization and direction of propagation of light is called birefringent (or double refractive). As explained throughout this specification and understood in the relevant industry, light whose polarization is perpendicular to the optical axis of the birefringent medium experiences an ordinary refractive index (n o ), and light whose polarization is parallel to the optic axis of the birefringent medium will have an extraordinary refractive index (n e ) and the refractive index difference observed in the birefringent medium material is n e -n o is described as having birefringence Δn. The phase delay of light in a material medium with birefringence Δn can be expressed as Γ=2πΔnd / λ at different λ, where d is the thickness of the medium.

[0125] Generally, optically anisotropic materials, such as liquid crystals, exhibit a positive dispersion of birefringence (Δn), which decreases with increasing wavelength λ of light. Positive dispersion of Δn results in different phase retardations Γ=2πΔnd / λ at different λ, where d is the thickness of the medium. As disclosed herein, anisotropic materials that exhibit a negative dispersion of birefringence (Δn) refer to materials whose birefringence increases with increasing wavelength λ of light.

[0126] As explained above, the wavelength dependence of the diffraction efficiency of a waveplate lens or waveplate can be an important consideration in reducing or minimizing various undesirable optical effects. As explained herein, the diffraction efficiency (η) of a birefringent medium, such as a layer of liquid crystal, is given by η=sin 2 (πΔnd / λ), where Δn is the birefringence, λ is the wavelength, and d is the thickness. Because the phase retardation of light propagating through a diffractive component varies with wavelength as compared to conventional birefringent media, some diffractive components, including waveplate lenses and waveplates, exhibit a relatively narrow range of wavelengths or bandwidths within the visible spectrum over which the diffraction efficiency is sufficiently high. In contrast, waveplate lenses and waveplates, according to embodiments, exhibit a relatively wide range of wavelengths or bandwidths within the visible spectrum over which the diffraction efficiency is sufficiently high for the various applications described herein.

[0127] According to various embodiments, a broadband waveplate lens or waveplate has a normalized bandwidth (Δλ / λ o ), where λ o is a center wavelength within the visible spectrum spanning a wavelength range of about 400 to 800 nm, including one or more of a red spectrum having a wavelength range of about 620 to 780 nm, a green spectrum having a wavelength range of about 492 to 577 nm, and a blue spectrum having a wavelength range of about 435 to 493 nm; and Δλ is a wavelength at which the diffraction efficiency exceeds 70%, 80%, 90%, 95%, 99%, or any value within a range defined by these values. o It is a range of wavelengths centered around

[0128] According to various embodiments, when a waveplate lens or waveplate is described as being a broadband waveplate lens or broadband waveplate, it will be understood to have an average, instantaneous, mean, median, or minimum diffraction efficiency of greater than 70%, 80%, 90%, 95%, 99%, or a percentage within any of these values within at least a portion of the visible spectrum spanning a wavelength range of about 400-800 nm, including one or more of: a red spectrum comprising a range of wavelengths from about 620-780 nm; a green spectrum comprising wavelengths from about 492-577 nm; a blue spectrum within a range of wavelengths from about 435-493 nm; or any wavelength within the visible spectrum from about 400-800 nm, e.g., 400-700 nm, 430-650 nm, or 450-630 nm.

[0129] The relationship η = sin 2 Based on (πΔnd / λ), a broadband waveplate lens or waveplate can have an efficiency for a fixed d when the ratio of Δn / λ has a positive and relatively constant value. As described herein, a medium with a positive ratio value of Δn / λ is said to have negative dispersion. According to embodiments, the broadband waveplate lens or broadband waveplate described herein has negative dispersion, i.e., a birefringence (Δn) that increases with increasing wavelength (λ) within the wavelength range described above.

[0130] According to various embodiments, a broadband waveplate lens or waveplate may be described as having an instantaneous, mean, median, minimum, or maximum value of the ratio Δn / λ that is a positive value within any range of the visible spectrum described above. o and Δλ is a wavelength range within any of the visible spectrum described above, o is the center wavelength within Δλ. According to various embodiments, the high normalized bandwidth Δλ / λ ocan have a value of about 0.3 to 1.0, 0.3 to 0.7, 0.4 to 0.7, 0.5 to 0.7, 0.6 to 0.7, or any value within a range defined by these values. In addition, the broadband waveplate lens or waveplate has a ratio Δn / λ that is relatively constant within the various wavelength ranges within the visible spectrum described above. For example, the ratio Δn / λ can have a deviation, e.g., standard deviation, from the mean, median, minimum, or maximum value of the ratio Δn / λ that does not exceed 30%, 20%, 10%, 5%, 1%, or a percentage within any of these values.

[0131] As described herein, a "transmissive" or "transparent" structure, e.g., a transparent substrate, may allow at least a portion, e.g., at least 20, 30, 50, 70, or 90%, of incident light to pass therethrough. Thus, a transparent substrate may, in some embodiments, be a glass, sapphire, or polymer substrate. In contrast, a "reflective" structure, e.g., a reflective substrate, may reflect at least a portion, e.g., at least 20, 30, 50, 70, 90%, or more, of incident light for reflection therefrom.

[0132] FIG. 10 illustrates an example of a display device 1000, e.g., a wearable display device, including one or more broadband adaptive lens assemblies, e.g., a pair of broadband adaptive lens assemblies 1004, 1008, in an optical path 1016 interposed by a waveguide assembly 1012. As described above, the waveguide assembly includes a waveguide configured to propagate light (e.g., visible light) under total internal reflection and to outcouple the light in an optical axis extending from (e.g., in a direction normal to) the waveguide's light output surface (e.g., a major surface of the waveguide). The light may, in some embodiments, be outcoupled by a diffraction grating. Each of the broadband adaptive lens assemblies 1004, 1008 may be configured to at least partially transmit the outcoupled light therethrough. In the illustrated embodiment, each of the broadband adaptive lens assemblies may be configured to receive light outcoupled from the waveguide assembly 1012 and converge or diverge the outcoupled light along an optical axis. Each of the broadband adaptive lens assemblies 1004, 1008 comprises a waveplate lens comprising liquid crystals arranged such that the waveplate lens has a birefringence (Δn) that varies radially from a central region of the waveplate lens and decreases with increasing wavelength (λ) within the visible spectrum. The broadband adaptive lens assemblies are configured to be selectively switched between a plurality of states having different refractive powers. When activated (e.g., electrically activated), the broadband adaptive lens assemblies are configured to alter the polarization state of outcoupled light passing therethrough.

[0133] As used herein, an adaptive lens assembly refers to a lens assembly having at least one optical property that can be adjusted, e.g., reversibly activated and deactivated using an external stimulus. Exemplary optical properties that can be reversibly activated and deactivated, among other properties, include refractive power (focal length), phase, polarization, polarization selectivity, transmittance, reflectance, birefringence, and diffractive properties, among other properties. In various embodiments, an adaptive lens assembly is capable of electrically varying the refractive power and polarization state of light passing therethrough.

[0134] In the illustrated embodiment, the pair of wideband adaptive lens assemblies 1004, 1008 are each configured to be selectively switched between at least two states, where in a first state, each is configured to pass outcoupled light therethrough without altering its polarization state, while in a second state, each is configured to alter the polarization state of the outcoupled light passing therethrough. For example, in the second state, each wideband adaptive lens assemblies 1004, 1008 reverses the handedness of circularly polarized light, while in the first state, each wideband adaptive lens assemblies 1004, 1008 preserves the handedness of circularly polarized light.

[0135] Still referring to Figure 10, display device 1000 further comprises a waveguide assembly 1012 interposed between the pair of adaptive lens assemblies 1004, 1008. Waveguide assembly 1012 may be similar to waveguide assembly 260, described above with respect to Figure 6, which comprises one or more waveguides similar to one or more of waveguides 270, 280, 290, 300, 310 in Figure 6. For example, as described above with respect to Figures 6 and 7, the waveguides may be configured to propagate light in a lateral direction parallel to the major surfaces of the waveguide under total internal reflection. The waveguides may further be configured to outcouple light, for example, in a direction normal to the major surfaces of the waveguide.

[0136] Still referring to FIG. 10 , a first adaptive lens assembly 1004 of the paired adaptive lens assembly is positioned on a first side of a waveguide assembly 1012, e.g., the side of the world 510 observed by the user, and a second adaptive lens assembly 1008 of the paired lens assembly is positioned on a second side of the waveguide assembly 1012, e.g., the side of the user's eye 210. As described below, the paired adaptive lens assembly as configured provides the user with virtual content from the waveguide assembly 1012 in multiple virtual depth planes along with a view of the real world. In some embodiments, there is little or no distortion due to the presence of the adaptive lens assemblies. The virtual content and views of the real world are provided to the user in response to activation of the first and second adaptive lens assemblies 1004, 1008, as described below with respect to FIGS. 11A and 11B .

[0137] 11A and 11B illustrate examples of display devices 1100A / 1100B, each including an adaptive lens assembly, that, in operation, output image information to a user. Display devices 1100A and 1100B are structurally identical in an unpowered state. Display device 1100A is used herein to describe outputting a virtual image to a user, while display device 1100B is used herein to describe transmitting a real-world image to a user through display device 1100B. Display devices 1100A / 1100B include a pair of switchable lens assemblies 1004, 1008 configured to be electrically activated, for example, by application of a voltage or current. In some embodiments, in a deactivated state, for example, when no voltage or current is applied, first and second switchable lens assemblies 1004, 1008 each have low, e.g., approximately zero, optical power. In some embodiments, in an activated state, e.g., when a voltage or current is applied, the world-side first adaptive lens assembly 1004 may provide a first net refractive power (Pnet1) having a first sign, e.g., positive refractive power, and the user-side second adaptive lens assembly 1008 may provide a second net refractive power (Pnet2) having a second sign, e.g., negative refractive power, when in the activated state.

[0138] 11A illustrates an example of the display system of FIG. 10 displaying virtual content to a user in a virtual depth plane, according to some embodiments. As described above, the waveguide assembly 1012 interposed between the pair of adaptive lens assemblies 1004, 1008 comprises a waveguide configured to receive light containing virtual image information and propagate the light under total internal reflection. The waveguide assembly 1012 is further configured to outcouple the light toward the eye 210, for example, through a diffraction grating. The outcoupled light passes through the second adaptive lens assembly 1008 prior to entering the eye 210. When activated, the second adaptive lens assembly 1008 has a second net refractive power Pnet2, which may have a negative value such that the user sees a virtual image in the virtual depth plane 1104.

[0139] In some embodiments, the second net refractive power Pnet2 may be electronically adjusted to adjust the second net refractive power (Pnet2) of the second adaptive lens assembly 1008, thereby adjusting the distance to the virtual depth plane 1104. For example, as a virtual object “moves” closer and farther relative to the eye 210 in virtual three-dimensional space, the second net refractive power Pnet2 of the second adaptive lens assembly 1008 may be correspondingly adjusted such that the virtual depth plane 1104 is adjusted to track the virtual object. Thus, the user may experience relatively little or no accommodation / vergence-divergence mismatch beyond an acceptable threshold. In some embodiments, the magnitude of the distance to the virtual depth plane 1104 may be adjusted in discrete steps, while in some other embodiments, the magnitude of the distance to the virtual depth plane 1104 may be continuously adjusted.

[0140] 11B illustrates an example of the display system of FIG. 10 providing a user with a view of real-world content, according to some embodiments. When the second adaptive lens assembly 1008 is activated to have a second net refractive power (Pnet2) for displaying virtual content in the virtual depth plane 1104, light from the real world passing through the second adaptive lens assembly 1008 may also converge or diverge according to the Pnet2 of the activated second adaptive lens assembly 1008. Thus, objects in the real world may appear out of focus. To mitigate such distortion, according to an embodiment, the first and second adaptive lens assemblies 1004, 1008 may be configured to have refractive powers with opposite signs when activated. In some embodiments, light passing through the first and second adaptive lens assemblies 1004, 1008 converges or diverges according to a combined refractive power having a magnitude that is approximately the difference in magnitude of the first and second net refractive powers Pnet1, Pnet2 of the first and second adaptive lens assemblies 1004, 1008, respectively. In some embodiments, the waveguide assembly 1012 may also have a refractive power, and the adaptive lens assembly 1008 may be configured to account for distortion caused by both the lens assembly 1004 and the waveguide assembly 1012. For example, the refractive power of the adaptive lens assembly 1008 may be of the opposite sign to the sum of the refractive powers of the lens assembly 1004 and the waveguide assembly 1012.

[0141] In some embodiments, the first adaptive lens assembly 1004 is configured to have a first net refractive power Pnet1 having a magnitude that is close to or identical to the magnitude of the second net refractive power Pnet2 of the second adaptive lens assembly 1008. As a result, when both the first and second adaptive lens assemblies 1004, 1008 are activated simultaneously, objects in the real world appear relatively unaffected by the refractive power of the second adaptive lens assembly 1008, which is provided to display virtual content.

[0142] In some embodiments, the first adaptive lens assembly 1004 may be configured, upon activation, to dynamically match the first net refractive power Pnet1 to the second net refractive power Pnet2 of the second adaptive lens assembly 1008. For example, as the second net refractive power Pnet1 of the second switchable lens assembly 1008 is adjusted to track a moving virtual object in virtual three-dimensional space, the first net refractive power Pnet1 of the first adaptive lens assembly 1004 may be dynamically adjusted such that the magnitude of the combined refractive power P=Pnet1+Pnet2 may be kept below a predetermined value. Thus, according to embodiments, an object in the real world may be positioned such that the magnitude of the combined refractive power P=Pnet1+Pnet2 is small, e.g., approximately 0 m -1 By compensating the second net refractive power (Pnet2) of the second adaptive lens assembly 1008, which may have a negative value, with the first net refractive power (Pnet1) of the first adaptive lens assembly 1004 so that the second net refractive power (Pnet2) of the second adaptive lens assembly 1008 remains negative, unacceptable defocusing can be prevented. Switchable Waveplates and Switchable Waveplate Lenses for Broadband Adaptive Waveplate Lens Assemblies

[0143] As discussed above, one of the advantages of using fewer waveguides to form images at multiple depth planes is an overall reduction in the thickness and weight of a display device (e.g., display device 1000 in FIG. 10). Accordingly, various embodiments described herein provide adaptive waveplate lens assemblies that are compact and lightweight and provide a variety of optical functionality, such as high bandwidth capabilities and variable optical power. In addition, various embodiments described herein provide adaptive lens assemblies with relatively low leakage light.

[0144] To provide images at multiple depth planes with high efficiency across a wide range of the visible spectrum, a broadband adaptive lens assembly according to various embodiments includes a waveplate lens (1154A, 1154B in FIGS. 12A and 12B, respectively) comprising liquid crystals arranged such that the waveplate lens has a birefringence (Δn) that varies radially from a central region of the first waveplate lens and decreases with increasing wavelength (λ) within the visible spectrum. As described above, according to various embodiments, the broadband adaptive waveplate lens assembly can be configured to be selectively switched between multiple states with different refractive powers, thereby generating images at multiple depth planes. Selective switching of the broadband lens assembly can, in turn, be implemented by switching the waveplate lens or waveplate included within the broadband adaptive waveplate lens assembly according to embodiments, as discussed herein.

[0145] 12A, in some embodiments, a broadband adaptive lens assembly 1150A is configured to be switched between different optical power states by employing a switchable waveplate 1158 comprising a liquid crystal in the same optical path as a waveplate lens 1154A. The waveplate lens 1154A may be a passive lens, and the broadband adaptive lens assembly 1150A may be selectively switched between different states by electrically activating and deactivating the switchable waveplate 1158.

[0146] 12A , in operation, the waveplate lens 1154A is configured to diverge or converge incident light 1162A, 1162B passing therethrough depending on the polarization of the light, e.g., circular polarization, according to various embodiments. The illustrated waveplate lens 1154A, which may be a passive waveplate lens when configured as a half-waveplate (HWP) lens, is configured to converge a right-handed circularly polarized (RHCP) light beam 1162B incident on the waveplate lens 1154A into a left-handed circularly polarized (LHCP) beam 1166A. On the other hand, the waveplate lens 1154A is configured to diverge an LHCP light beam 1162A incident on the waveplate lens 1154A into a right-handed circularly polarized (RHCP) beam 1166B.

[0147] 12A , after being focused or defocused by waveplate lens 1154A depending on the circular polarization of the light incident thereon, LHCP light beam 1166A or RHCP light beam 1166B is incident on switchable waveplate 1158. The liquid crystal of switchable waveplate 1158 is configured such that, when activated, e.g., electrically activated, the polarization of the circularly polarized light passing therethrough is preserved (not shown). That is, LHCP light beam 1166A and RHCP light beam 1166B pass through switchable waveplate 1158 unaffected. On the other hand, when deactivated, e.g., electrically deactivated, the polarization of the circularly polarized light passing therethrough is inverted (as shown). That is, LHCP light beam 1166A is converted to RHCP light beam 1170A, and RHCP light beam 1166B is converted to LHCP light beam 1170B.

[0148] 12B, in some other embodiments, a broadband adaptive lens assembly 1150B is configured to be switched between different optical power states by employing a switchable waveplate lens 1154B comprising a liquid crystal. The adaptive lens assembly 1150B may be selectively switched between different states by electrically activating and deactivating the switchable waveplate lens 1154B.

[0149] In operation, the liquid crystals of the waveplate lens 1154B are configured, according to various embodiments, so that the waveplate lens 1154B diverges or converges incident light 1162A, 1162B passing therethrough depending on its polarization, e.g., circular polarization. When configured as a half-waveplate lens, when deactivated, e.g., electrically deactivated, the illustrated waveplate lens 1154B is configured to converge an RHCP light beam 1162B incident on the waveplate lens 1160B into an LHCP beam 1166A. Conversely, when deactivated, the waveplate lens 1154B is configured to diverge a left-handed polarized (LHCP) light beam 1162A incident on the waveplate lens 1154B into an RHCP beam 1166B. On the other hand, when activated, e.g., electrically activated, the polarization of the circularly polarized light passing therethrough is preserved (not shown), and the LHCP light beam 1162A and the RHCP light beam 1162B incident thereon pass through the waveplate lens 1154B substantially without converging or diverging. In various embodiments, by configuring the liquid crystals to realign in response to a switching signal, e.g., an electric field, the waveplate lens assemblies 1150A, 1150B may be activated or deactivated to converge or diverge, and convert or preserve the polarization of the circularly polarized light, depending on its polarization. (Broadband switchable waveplate)

[0150] As described above, according to various embodiments, a broadband adaptive waveplate lens assembly can be used to generate images at multiple depth planes by selectively switching the broadband waveplate lens assembly between multiple lens states having different refractive powers. As described above, in some embodiments, the broadband adaptive waveplate lens assembly may be configured to be selectively switched between multiple lens states by electrically activating a broadband switchable waveplate included within the broadband adaptive waveplate lens assembly. Below, embodiments of the broadband switchable waveplate are disclosed.

[0151] In some embodiments, the broadband switchable waveplate comprises a layer of unpolymerized twisted nematic (TN) liquid crystal (LC) and is configured to switch in response to application of an electric field across the thickness of the TN LC layer. Without being bound by any theory, switching may be achieved in response to altering the orientation of the unpolymerized LC molecules across the thickness of the TN LC layer.

[0152] 13A-13F, according to various embodiments, a broadband switchable waveplate comprises a layer of twisted nematic (TN) liquid crystal (LC). Figure 13A illustrates a cross-sectional view of an example switchable waveplate comprising a layer of TN LC. The TN LC switchable waveplate 1300A comprises a layer of TN LC 1302 disposed between a pair of transparent substrates 1312. The transparent substrates 1312 each have conductive transparent electrodes 1316, 1320 formed on their inner surfaces.

[0153] The surfaces of the transparent electrodes 1316, 1320 and / or substrate 1312 may be configured such that the TN LC molecules in contact with or directly adjacent to the upper electrode 1316 tend to align with their long axes extending in a first lateral direction, while the TN LC molecules in contact with or directly adjacent to the lower electrode 1320 tend to align with their long axes extending in a second lateral direction that may intersect, e.g., form an approximately 90-degree angle with the first lateral direction. The TN LC molecules between the TN LC molecules directly adjacent to the lower electrode 1320 and the TN LC molecules directly adjacent to the upper electrode 1316 undergo a twist. As configured, the TN LC switchable waveplate 1300A is configured as a broadband waveplate.

[0154] Still referring to FIG. 13A , in operation, in the absence of an electric field across the TN LC layer 1302 (deactivated state), the nematic director of the TN LC molecules undergoes a smooth 90-degree twist across the thickness of the TN LC layer 1302. In this state, incident light 1308 polarized in a first direction (the same direction as the LC molecules closest to the bottom electrode 1312) is incident on the TN LC layer 1302. The twisted arrangement of the TN LC molecules within the TN LC layer 1302 then acts as an optical waveguide, rotating the plane of polarization by a quarter-turn (90 degrees) prior to reaching the top electrode 1316. In this state, the TN LC layer 1302 serves to shift the polarization direction of linearly polarized light passing therethrough from one linear polarization direction to another. Thus, the transmitted light 1304 is polarized in a second direction opposite to the first direction (the same direction as the LC molecules adjacent to the top electrode 1316).

[0155] On the other hand, when a voltage exceeding the threshold voltage (V>Vth) of the TN LC switchable waveplate 1300A is applied across the electrodes 1316, 1320 (activated state), the TN LC molecules in the TN LC layer 1306 tend to align with the resulting electric field, and the optical wave-guiding properties of the TN LC layer 1304 described above with respect to the deactivated state are lost. In this state, the TN LC layer 1306 serves to preserve the polarization direction of light passing through it. Thus, the incident light 1308 and the transmitted light 1304B are polarized in the same first direction (the same direction as the LC molecules closest to the bottom electrode 1312).

[0156] When the electric field is turned off, the TN LC molecules relax and return to their twisted state, and the TN LC molecules of TN LC layer 1306 in the activated state return to the configuration of the TN LC molecules of TN LC layer 1302 in the deactivated state.

[0157] As explained above, the TN LC switchable waveplate 1300A described with respect to Figure 13A serves to shift the polarization direction of linearly polarized light. However, various broadband waveplate lens assemblies described herein include a switchable waveplate configured as a switchable half-waveplate for reversing the handedness of circularly polarized light. Accordingly, below with respect to Figures 13B-13D, a switchable waveplate configured as a switchable half-waveplate is described according to an embodiment.

[0158] 13B illustrates a cross-sectional view of a switchable broadband waveplate 1300B configured as a half-waveplate, according to an embodiment. The switchable broadband waveplate 1300B includes the TN LC switchable waveplate 1300A illustrated with respect to FIG. 13A. In addition, to serve as a broadband half-waveplate for circularly polarized light, the switchable broadband waveplate 1300B also includes a pair of achromatic quarter-waveplates (QWPs) 1324, 1326.

[0159] In operation, in an activated state of the switchable broadband waveplate 1300B, an input circularly polarized beam 1324 having a first handedness, e.g., a left-handed circularly polarized (LHCP) light beam, passes through the first QWP 1324, which converts the circularly polarized beam 1324 into a first linearly polarized beam 1328 having a first linear polarization. Subsequently, in response to passing through the activated TN LC switchable waveplate 1300A, the first linearly polarized beam 1328 is converted into a second linearly polarized beam 1332 having a second linear polarization. Subsequently, in response to passing through the second QWP 1326, the second linearly polarized beam 1332 is converted into an outgoing circularly polarized beam 1340 having a second handedness opposite to the first handedness, e.g., an RHCP light beam. Thus, when activated, the switchable broadband waveplate 1300B acts as a half-waveplate, reversing the polarization of the circularly polarized beam.

[0160] On the other hand, when the switchable broadband waveplate 1300B is deactivated, the polarization of the first linearly polarized beam 1328 is preserved after the incident circularly polarized beam 1324 passes through the first QWP 1324, as described above, and subsequently through the deactivated TN LC switchable waveplate 1300A. Then, in response to passing through the second QWP 1326, the first linearly polarized beam 1328 is converted into an outgoing circularly polarized beam 1340, e.g., an LHCP light beam, having a first handedness. Thus, when deactivated, the broadband waveplate 1300B acts as a transparent medium, which preserves the polarization of the circularly polarized beam.

[0161] In various embodiments described herein, the first and / or second QWPs 1324, 1326 are broadband quarter-wave plates having similar bandwidths as the TN LC switchable waveplate 1300A. According to embodiments, the quarter-wave plates can be formed using polymerized TN LC layers. To provide broadband capability, the QWPs, according to various embodiments, include multiple TN LC layers. If each TN LC layer were formed on its own substrate, the resulting broadband quarter-wave plate and / or the optical absorption of the resulting stack could become unacceptably thick. Therefore, below, embodiments of QWPs comprising multiple TN LC layers formed on a single substrate are described with respect to efficient integration with the TN LC switchable waveplate 1300A.

[0162] 13C illustrates a cross-sectional view of a broadband QWP 1300C, which can be the first and / or second QWPs 1324, 1326 illustrated above with respect to FIG. 13B , comprising multiple (M) TN LC layers 1302-1, 1302-2, ... 1302-M stacked on a matching layer 1302-0 formed on a substrate 1312. The matching layer 1302-0, described in more detail elsewhere herein, is configured to induce the elongation direction of LC molecules in the first TN LC layer 1302-1 directly adjacent to the matching layer 1302-0 to be aligned in a first direction. LC molecules above the LC molecules aligned by the matching layer 1302-0 experience a first twist such that the LC molecules in the first TN LC layer 1302-1 directly adjacent to the second TN LC layer 1302-2 are elongated in a second direction. The alignment of the LC molecules in each of the subsequent TN LC layers 1302-2 through 1302-M is similar to that of the first TN LC layer 1302-1, except that the LC molecules closest to the previous layer are aligned in the same direction as the topmost LC molecules of the previous layer. For example, the topmost LC molecules in the first TN LC layer 1302-1 and the bottommost LC molecules in the second TN LC layer 1302-1 are aligned in the same second direction. The LC molecules in the second TN LC layer 1302-2 undergo a second twist such that the topmost LC molecules in the second TN LC layer 1302-2 are stretched in a third direction. Such alignment of the LC molecules in a given TN LC layer as a result of the alignment of the LC molecules in the adjacent layer in contact with it is sometimes referred to as self-alignment, since no intervening alignment layer is interposed therebetween. Thus, in some embodiments, a broadband QWP comprises multiple TN LC layers, with two or more self-aligned TN LC layers each having a non-zero twist.

[0163] In embodiments, the TN LC layer comprises polymerized LC molecules (LCP), formed, for example, using reactive mesogens. As explained above, reactive mesogens are initially low-molecular-weight LCs that can be aligned by surface and twist to have complex profiles, similar to conventional LCs, but can then be hardened into solid polymer films by photopolymerization.

[0164] Figure 13D illustrates a cross-sectional view of an integrated switchable broadband waveplate 1300D in which a TN LC switchable waveplate 1300A similar to that described above with respect to Figure 13A is integrated into a single stack with a pair of broadband QWPs 1324, 1326 similar to that described above with respect to Figure 13C. In the illustrated embodiment, the TN LC switchable waveplate 1300A is integrated into a single stack by attaching a pair of broadband quarter-waveplates 1324, 1326 to opposite sides thereof using adhesive layer 1348.

[0165] FIG. 13E illustrates a cross-sectional view of an integrated switchable broadband waveplate 1300E in which a TN LC switchable waveplate 1300A similar to that described above with respect to FIG. 13A is integrated into a single stack with a pair of broadband quarter-waveplates 1324, 1326 in a manner similar to that described above with respect to FIG. 13D, except that instead of using an adhesive to form the integrated stack, one of the pair of broadband quarter-waveplates 1324, 1326 serves as a substrate onto which the TN LC switchable waveplate 1300A ( FIG. 13A ) can be formed directly. For example, the different layers of the TN LC switchable waveplate 1300A may be formed directly on one surface of the QWPs 1324, 1326. Advantageously, one or both of the substrates 1312 of the TN LC switchable waveplate 1300A may be omitted. Thus, the TN LC switchable waveplate 1300A is integrated into a compact single stack by forming directly on one of the pair of wideband QWPs 1324, 1326, on top of which the other of the pair of wideband QWPs 1324, 1326 is formed.

[0166] In each of the embodiments illustrated above with respect to Figures 13D and 13E, the broadband QWP can be formed from a liquid crystal-based material, such as quartz and MgF2, or other non-liquid crystal-based materials. Below with respect to Figure 13F, embodiments in which the broadband QWP comprises a liquid crystal are particularly advantageously integrated with a TN LC switchable waveplate into a single stack, serving not only as a QWP but also as a matching layer for the TN LC switchable waveplate.

[0167] Figure 13F illustrates a cross-sectional view of an integrated switchable broadband waveplate 1300F that integrates a TN LC switchable waveplate 1300A similar to that described above with respect to Figure 13A. The switchable broadband waveplate 1300F includes a pair of broadband QWPs 1324, 1326 arranged in a manner similar to that described above with respect to Figure 13E, except that instead of broadband QWPs 1324, 1326 as substrates for the TN LC layer 1302, the broadband QWPs 1324, 1326 comprise thin polymerized LC layers formed on respective surfaces of a substrate 1312, and the LC molecules of the TN LC layer 1302 are inserted into a gap formed between the opposing surfaces of the broadband QWPs 1324, 1326 by a spacer 1350 that defines the thickness of the TN LC layer 1302. Methods for inserting the LC molecules are described elsewhere herein. Additionally, the different layers of the TN LC switchable waveplate 1300A and the different layers of the wideband QWPs 1324, 1326 are integrally formed into a single stack. For example, the first wideband QWP 1324 includes a substrate 1312 on which a lower transparent electrode 1316 is formed, followed by a matching layer 1302-2 and multiple TN LC layers 1302-1, 1302-2. Similarly, the second wideband QWP 1326 includes a substrate 1312 on which an upper transparent electrode 1320 is formed, followed by a matching layer 1302-0 and multiple TN LC layers 1302-1, 1302-2.

[0168] 13F, advantageously, the outermost LC molecules of the TN LC layer 1302-2 of the first wideband QWP 1324 facing the gap and the outermost LC molecules of the TN LC layer 1302-2 of the second wideband QWP 1326 facing the gap are arranged to serve as matching layers for the switchable TN LC layer 1302, such that the outermost LC molecules of the TN LC layer 1302 are self-aligned, in a manner similar to that described above with respect to FIG. 13C. Additionally, by integrally stacking the different layers of the TN LC switchable waveplate 1300A and the different layers of the wideband QWPs 1324, 1326, the total thickness of the entire stack can be substantially reduced. For example, mechanically joining a TN LC switchable waveplate 1300A as shown in FIG. 13A and broadband quarter-waveplates 1324, 1326 as shown in FIG. 13C would result in as many as four substrates, whereas the entire stack of switchable broadband waveplate 1300F has only two substrates.

[0169] 13F and various embodiments throughout the specification, the switchable LC layer, e.g., TN LC layer 1302 inserted in the gap, has a thickness of about 1 μm to 50 μm, 1 to 10 μm, 10 to 20 μm, 20 to 30 μm, 30 to 40 μm, 40 to 50 μm, or any range defined by these values. In addition, the passive LC layers, e.g., TN LC layers 1302-1 and 1302-2, can have a thickness of about 0.1 μm to 50 μm, 0.1 to 1 μm, 1 to 10 μm, 10 to 20 μm, 20 to 30 μm, 30 to 40 μm, 40 to 50 μm, or any range defined by these values.

[0170] In various embodiments described herein, a matching layer (e.g., 1302-2 in Figures 13C and 13F) is used to align LC molecules, e.g., align the elongation direction of LC molecules along a particular direction. For example, as described above with respect to Figures 13A-13F, a matching layer can be used to define the director (n), i.e., the local average elongation direction of elongated LC molecules in a given direction. In some other embodiments, the matching layer may be formed from mechanically rubbed organic polymers such as polyimides and polyamides, obliquely deposited inorganic oxides such as SiO2, or long-chain aliphatic siloxanes. In some embodiments, a non-contact matching layer may be formed from an organic polymer using plane-polarized light to create surface anisotropy, which in turn defines the director. For example, the use of cis-trans photoisomerization of azo dyes, which can be directly deposited or dissolved in standard alignment layers (e.g., polyimides) or LC mixtures, can produce alignment effects in the matching layer without rubbing. Non-contact matching layers that use azo chromophores sometimes employ high intensity laser light to induce isomerization of the dye molecules.

[0171] In some other embodiments, the nanostructure pattern can serve as a matching layer for aligning the LC molecules. Advantageously, in some embodiments, the nanostructure pattern is formed as part of the electrode layer, improving optical transparency, reducing process steps, and further reducing the overall thickness of the broadband waveplate, e.g., as described above with respect to Figures 13A-13F. To this end, Figure 14A illustrates a perspective view of a pattern of nanostructures 1400A, e.g., nanowires, formed on a transparent substrate 1312, that serves the dual functions of a matching layer and an electrode layer, according to an embodiment. The pattern of nanostructures 1400A can be patterned on the substrate 1312, e.g., using lithography or nanoimprinting techniques, as described in detail elsewhere herein. The nanostructures can be formed from a sufficiently thin conductive material that is patterned as elongated metal wires. For example, the conductive material can be gold, silver, copper, aluminum, or ITO, or any suitable conductive material having a thickness and electrical resistivity such that the resulting pattern of nanostructures can simultaneously serve as a matching layer and an electrode layer. In the illustrated embodiment, the pattern of nanostructures 1400A comprises periodic conductive lines 1404A extending in a first direction, e.g., the x-direction, connected to rails 1408A to supply current or voltage to the periodic conductive lines 1404A. In various embodiments, the periodic conductive lines 1404A can have a pitch of 1 μm to 1000 μm, 5 μm to 500 μm, 10 μm to 100 μm, or any value within a range defined by these values. The conductive lines 1404A can have a width of 10 nm to 1 μm, 100 nm to 1000 nm, 100 nm to 500 nm, 200 nm to 300 nm, or any value within a range defined by these values. The periodic conductive lines 1404 can have a thickness of 10 nm to 1 μm, 100 nm to 1000 nm, 100 nm to 500 nm, 400 nm to 500 nm, or any value within the ranges defined by these values.The combination of material, thickness, and width of the periodic conductive lines 1404A can be selected so that the resulting sheet resistance of the periodic conductive lines 1404A is approximately 1 ohm / sq to 100 ohm / sq, 2 ohm / sq to 50 ohm / sq, 5 ohm / sq to 20 ohm / sq, or any value within the range defined by these values, for example, approximately 10 ohm / sq. Additionally, the combination of material and thickness of the conductive lines 1404A can be selected so that the resulting transmittance within the visible spectrum is 80% to 99%, 90% to 99%, 95% to 99%, 97% to 99%, or any value within the range defined by these values, for example, approximately 98%. Other dimensions, configurations, and values are also possible.

[0172] FIG. 14B illustrates a perspective view of a pattern of nanostructures 1400B similar to the pattern of nanostructures 1400A described above with respect to FIG. 14A, except that the pattern of nanostructures 1400B comprises periodic conductive lines 1404B extending in a second direction, e.g., the y-direction, that are connected to rails 1408B for supplying current to the periodic conductive lines 1404B.

[0173] 14C illustrates a perspective view of a pair of electrodes 1400C, according to an embodiment. The pair of electrodes 1400C includes a pattern of nanostructures 1400A and a pattern of nanostructures 1400B arranged such that the periodic conductive lines 1404A and the periodic conductive lines 1404B face and cross each other and are separated by gaps 1412 configured to accommodate one or more LC layers, e.g., TN LC layers, disposed therein. Advantageously, it has been found that the patterns of nanostructures 1400A and 1400B can each act as an alignment layer similar to alignment layer 1302-0 described above with respect to Figures 13C and 13F, such that when nematic LC molecules, e.g., reactive mesogens, are formed thereon, the LC molecules directly adjacent to each of the patterns of nanostructures 1400A and 1400B can be aligned with the directors of the nematic LC molecules, e.g., generally aligned in the same direction as the extension direction of the periodic conductive lines 1404A and 1404B. Additionally, the LC molecules between the LC molecules immediately adjacent the periodic conductive lines 1404A, 1404B can be configured to undergo twisting using a twisting agent such that an unpolymerized TN LC layer similar to the TN LC layer 1302 described above with respect to FIG. 13A and a polymerized TN LC layer similar to the TN LC layers 1302-1, 1302-2, ... 1302-M described above with respect to FIG. 13C can be formed.

[0174] Referring back to FIG. 13F, it should be appreciated that in some embodiments, by combining the functionality of the electrodes and matching layers, the pattern of nanostructures 1400A can replace the combination of transparent electrode 1316 and matching layer 1302-0 of broadband QWP 1324, and the pattern of nanostructures 1400B can replace the combination of transparent electrode 1320 and matching layer 1302-0 of broadband QWP 1326, thereby enabling a more compact overall stack.

[0175] Still referring to FIG. 14C, in operation, the alignment of the LC molecules and the corresponding effects on the polarization of light with and without an electric field are similar to those described above with respect to FIG. 13A.

[0176] 15A and 15B illustrate plan and cross-sectional views of a TN LC switchable broadband waveplate 1500 according to an embodiment. Unlike the broadband waveplates illustrated above with reference to FIGS. 13A and 13F , which have vertically separated electrodes for switching, the TN LC switchable broadband waveplate includes in-plane laterally separated electrodes for switching. The TN LC switchable broadband waveplate 1500 includes a matching electrode stack 1524 and a matching layer stack 1526. Similarly, as described above with reference to FIG. 13F , LC molecules are inserted into the gap formed by the spacer 1350 between the opposing surfaces of the matching electrode stack 1524 and the matching layer stack 1526. Methods for inserting LC molecules are described elsewhere herein. The matching electrode stack 1524 includes first and second electrodes 1500A and 1500B formed on the upper transparent substrate 1312, and further includes an optional upper matching layer 1302-0. The matching layer stack 1526 includes a lower matching layer 1302-0 formed on a lower transparent substrate 1312.

[0177] 15A, a matching electrode stack 1524 includes first and second electrodes 1500A, 1500B, each including a respective one of first and second periodic conductive lines 1504A, 1504B. The periodic conductive lines 1504A are interdigitated or intertwined and alternating with the periodic conductive lines 1504B. The first and second periodic conductive lines 1504A, 1504B are each strapped to rails 1508A, 1508B, respectively, in a manner similar to that described above with respect to the patterned nanostructures 1400A (FIG. 14A), 1400B (FIG. 14B). The material, thickness, width, and pitch of the alternating periodic conductive lines 1504A, 1504B can be similar to those described above with respect to the patterned nanostructures 1400A ( FIG. 14A ), 1400B ( FIG. 14B ). However, unlike the paired electrodes 1400C described above with respect to FIG. 14C , which are vertically separated, the periodic conductive lines 1504A alternate with the periodic conductive lines 1504B in a lateral direction, e.g., the x-direction, such that the electric field between the periodic conductive lines 1504A and 1504B is directed in the lateral direction.

[0178] Referring to the cross-sectional view of TN LC switchable cell 1500 in Figure 15B, in a manner similar to that described above with respect to Figure 13F, LC molecules are inserted into the gap formed between opposing surfaces of matching electrode stack 1524 and matching layer stack 1526 so that a TN LC layer (not shown) similar to TN LC layer 1302 (Figure 13A) can be formed. Methods for inserting LC molecules are described elsewhere herein.

[0179] In some embodiments, in a manner similar to that described above with respect to FIG. 14C , the alternating periodic conductive lines 1504A, 1504B in the matching electrode stack 1524 and / or the upper matching layer 1302-0 can serve as a matching layer for the outermost LC molecules of the TN LC layer 1302 formed in the gap 1412, in a manner similar to the matching layer 1316 described above with respect to FIG. 13A and the conductive line 1404B described above with respect to FIG. 14C . When the alternating periodic conductive lines 1504A, 1504B serve as matching layers, in some embodiments, the upper matching layer 1302-0 may be omitted. Similar to the matching layer 1320 described above with respect to FIG. 13A and the conductive line 1404A described above with respect to FIG. 14C , the lower matching layer 1302-0 can serve to match the LC molecules in the gap 1412 directly adjacent thereto.

[0180] Although not shown, in some embodiments, the illustrated TN LC switchable broadband waveplate 1500 can integrate multiple TN LC layers similar to TN LC layers 1302-1, 1302-2, ... 1302-M (Figure 13F, not shown) between the alternating periodic conductive lines 1504A, 1504B and the LC molecules in the gaps 1412 and / or between the lower matching layer 1302-0 and the LC molecules in the gaps 1412, in a manner similar to that described above with respect to Figure 1300F, thereby providing integrated QWP functionality in a manner similar to that described above with respect to Figure 13F.

[0181] 15A and 15B, in operation, in the absence of an electric field, the alternating periodic conductive lines 1504A, 1504B act as matching layers for the LC molecules directly adjacent to the periodic conductive lines 1504A, 1504B such that the LC molecules have directors that generally extend parallel to the periodic conductive lines 1504A, 1504B. In a deactivated state, the switchable broadband waveplate 1500 is configured to invert the polarization of linearly polarized light in a manner similar to that described above with respect to FIG. On the other hand, when an electric field is applied in a lateral direction, e.g., the y-direction, between the periodic conductive lines 1504A and 1504B, the LC molecules between immediately adjacent periodic conductive lines 1504A, 1504B align their elongation direction, e.g., away from parallel, between parallel and perpendicular, or perpendicular to the periodic conductive lines 1504A, 1504B. In an activated state, in a manner similar to that described above with respect to FIG. 13A , the switchable broadband waveplate 1500 is configured to preserve the polarization of linearly polarized light.

[0182] In some embodiments, in addition to combining the functionality of the electrodes and matching layers, the first and second electrodes 1500A, 1500B can replace, for example, the combination of transparent electrodes 1316, 1320 and upper and lower matching layers 1302-0 of the broadband waveplate 1300F (FIG. 13F), thereby allowing for an even more compact overall stack and even more improved transparency due to halving the electrode layers. (Liquid crystal based wave plate lens)

[0183] 12A , to provide images at multiple depth planes with high efficiency across a wide range of the visible spectrum, some broadband adaptive waveplate lens assemblies, according to embodiments, include a switchable waveplate and one or more waveplate lenses, which may be passive or switchable, formed from thin films of birefringent liquid crystals. Below, exemplary waveplate lenses are disclosed that comprise liquid crystals whose orientation in the plane of the waveplate is adapted to focus and / or modify the polarization state of light transmitted therethrough. Below, various embodiments of lenses and waveplates are formed from liquid crystals.

[0184] One example of a liquid crystal-based waveplate lens is illustrated with respect to Figures 16A and 16B.

[0185] 16A and 16B illustrate examples of wave plate lenses 1200A and 1200B, respectively, each comprising a transparent substrate 1204, e.g., a glass substrate, having formed thereon liquid crystal molecules 1208 that are elongated along different elongation directions relative to a direction parallel to an axial direction (e.g., x-direction or y-direction) along a major surface of the substrate 1204. That is, the liquid crystal molecules 1208 are rotated by different rotation angles (φ) about a direction normal to the major surface of the substrate 1204 (e.g., z-direction), where φ is described as the angle between the elongation directions of the liquid crystal molecules relative to a layer normal and a direction parallel to the layer normal (e.g., x-direction or y-direction).

[0186] In the illustrated implementation, the liquid crystal molecules 1208 at a given radius from the central axis C or center of the lens have substantially the same rotation angle (φ). As arranged, the liquid crystal molecules 1208 are configured to focus a collimated beam of light to a point at a certain focal length. Without being bound by any theory, the rotation angle (φ) of the liquid crystal molecules 1208 may be proportional to a power of r, where r is the radial distance from C and has a value of about 1 to 3, e.g., 2. In one implementation, the angle (φ) is + / - k0r 2 / f, where r is the radial distance from C, k0=2π / λ is the wave number of the light to be focused by the diffractive wave plate lens, λ is the wavelength of the light, and f is the focal length of the wave plate lenses 1200A, 1200B. The + and − signs may correspond to the rotation direction of the liquid crystal molecules 1208 relative to the liquid crystal molecules 1208 nearest to the center C of the wave plate lenses 1200A, 1200B.

[0187] It should be understood that the patterns of liquid crystal molecules 1208 in waveplate lenses 1200A and 1200B represent inverted images of each other. That is, one of waveplate lenses 1200A and 1200B can be obtained by rotating the other of waveplate lenses 1200A and 1200B by 180 degrees about an axial direction (e.g., the x-direction or the y-direction). As configured, the focal lengths and refractive powers of waveplate lenses 1200A and 1200B are identical in magnitude but opposite in sign.

[0188] In some implementations, waveplate lenses 1200A and 1200B can each function as a half-waveplate lens. When configured as a half-waveplate lens, waveplate lenses 1200A and 1200B each rotate the plane of linear polarization by an angle 2α relative to the polarization of the input beam, where α is the angle between the input polarization direction and the waveplate axis. For a circularly polarized beam, this change in angle translates into a phase shift and a reversal of polarization handedness. Thus, a ±2α phase shift can be generated in the circularly polarized beam, with the sign of the phase shift depending on the polarization handedness.

[0189] 16C illustrates an example of a waveplate lens that diverges or converges light passing through it depending on the polarization of the light and the side the light is incident on, according to some embodiments. When configured as a half-waveplate lens, the illustrated waveplate lens 1200A may be configured to diverge a right-handed circularly polarized (RHCP) light beam 1212 incident on a first side into a left-handed circularly polarized (LHCP) beam 1216. On the other hand, the waveplate lens 1200A may be configured to converge a RHCP light beam 1220 incident on a second side opposite the first side into a left-handed circularly polarized (LHCP) beam 1224.

[0190] 16D , when configured as a half-wave plate, waveplate lens 1200B may be configured to converge LHCP light beam 1228 incident on a first side into RHCP beam 1232. On the other hand, waveplate lens 1200B may be configured to diverge LHCP light beam 1236 incident on a second side opposite the first side into RHCP beam 1240.

[0191] Therefore, by controlling the rotation angle direction and radial distribution of the liquid crystal 1208, the waveplate lens can be configured to converge or diverge circularly polarized light of either handedness. It should be understood that the refractive power can be increased or decreased based on the relationship between the rotation angles of the liquid crystal. Additionally, in some embodiments, the liquid crystals may be aligned and misaligned by applying an electric field. It should be understood that, in the limit where the refractive power is approximately zero, the waveplate lens can be used as a waveplate, for example, a switchable waveplate. (Broadband adaptive waveplate lens assembly including switchable waveplates)

[0192] As described above with respect to Figure 12A, to provide images at multiple depth planes with high efficiency across a wide range of the visible spectrum, some broadband adaptive waveplate lens assemblies, according to embodiments, include a switchable waveplate and one or more waveplate lenses, which may be passive or switchable, formed from a thin film of birefringent material, e.g., liquid crystal. Below, embodiments of broadband adaptive waveplate lens assemblies are disclosed that include a switchable broadband waveplate. For example, the switchable broadband waveplate may be one of the broadband switchable waveplates described above with respect to Figures 13A-13F, 14A-14C, and 15A-15B. (Polarization switch configured to provide a wide field of view)

[0193] A wide variety of examples of adaptive lens assemblies comprising a waveplate lens and a switchable waveplate that receives light from a wide field of view are discussed above. As described above with reference to Figures 13A-13F, various implementations of such adaptive lens assemblies may include one or more layers of twisted nematic (TN) liquid crystal (LC) molecules. However, the efficiency of the optical wave-guiding properties of TN LC molecules depends, at least in part, on the angle at which light is incident thereon. Thus, increasing the angle of incidence of light on a TN LC layer (e.g., in a switchable waveplate) may result in a reduction in its ability to alter, e.g., rotate, the polarization state of the incident light. This characteristic may cause light directed from an object widely off-axis within the field of view to differ from light propagating directly along the optical axis of the adaptive lens assembly normal to the switchable waveplate and waveplate lens.

[0194] FIG. 17 illustrates an example of an adaptive lens assembly 3800 comprising a liquid crystal lens (e.g., a waveplate lens) 3802, such as a liquid crystal (LC) diffractive lens, and a polarization switch (e.g., a switchable waveplate including at least one layer of TN LC molecules) 3804 that receives light 3806 from a wide field of view. Light from an object 3808 on the periphery 3810 of the field of view is shown incident on the switchable waveplate 3804 at an angle θ. This angle of incidence θ is measured relative to a normal 3812 to the switchable waveplate 3804. The polarization switch 3800 may be configured such that, when the polarization switch is in a certain state, the polarization switch rotates the polarization of light incident thereon. For example, right-handed circularly polarized light (RHCP) incident on a polarization switch, such as a switchable waveplate, may be rotated to left-handed circularly polarized light (LHCP). Such an effect may occur, for example, with light incident normally to the polarization switch or switchable waveplate 3804. With a larger incident angle θ, the light cannot be completely converted from right-handed polarization to left-handed polarization.

[0195] Thus, for example, light from an off-axis object 3808 in the periphery 3810 of the field of view that is incident on the polarization switch 3804 at an angle θ greater than zero may not undergo a complete conversion of polarization (e.g., from right-handed to left-handed circular polarization). The result may be non-uniform processing of light directed from different regions of the field of view onto the polarization switch 3804 and adaptive lens assembly 3800. The present adaptive lens produces afterimage images at the wrong depth plane when such elements are used as variable-focus elements for augmented reality devices. Therefore, a need exists to increase the field of view of switchable waveplates such as those shown in FIG. 17 .

[0196] Figure 18 shows an example of this non-uniformity. Figure 18 is a plot 3900 illustrating the efficiency with which an exemplary LC layer of a switchable waveplate 3804 converts the polarization of light at different angles of incidence on it. This contour plot is the simulated percentage of light leaking through parallel circular polarizers with an electrically controlled birefringence (ECB) LC cell between them. An ECB LC cell is a simple switchable waveplate in which the LC molecules are all aligned in the same direction, i.e., parallel along the X axis in the coordinate system shown. Typically, the thickness (d) of the LC layer is proportional to Δn * The LC cell is chosen to be d=λc / 2, where Δn is the LC birefringence and λc is the center wavelength. When no external voltage is applied, this LC cell can convert right-handed circularly polarized light to left-handed circularly polarized light, and vice versa. The amount of conversion can be measured as the % of light leakage through a parallel circular polarizer across the field of view. The coordinate system is a polar coordinate system that maps the polarization conversion or rotation efficiency for different angles of light incident on the polarization switch or switchable waveplate 3804. The center 3906 corresponds to light normally incident on the polarization switch or switchable waveplate 3804, for example, along the center or optical axis through the polarization switch or switchable waveplate. Azimuthal angles of 45, 135, 225, and 315 degrees are marked. The polar grid also has circles 3908 a , 3908 b , and 3908 c that represent elevation angles of 10, 20, and 30 degrees relative to a central or optical axis through the exemplary TN LC layer of the polarization switch or switchable waveplate 3804 .

[0197] The substantially dark regions 3902 of the plot indicate the amount of light at different angles whose polarization is efficiently converted or rotated. However, some bright regions 3904 of the plot indicate that for some of the light at higher angles, corresponding to off-center regions of the field of view, the polarization is not efficiently converted or rotated. The various polarization switch or switchable waveplate designs disclosed herein are configured to provide more efficient polarization conversion / rotation for various higher angles, corresponding to more peripheral locations 3810 within the field of view.

[0198] FIG. 19 illustrates one such design configured to increase the efficiency of polarization conversion or rotation for light from objects on the periphery of the field of view. In particular, FIG. 19 shows an example of an adaptive lens assembly 4000 comprising a liquid crystal lens (e.g., a waveplate lens) 4002, such as a liquid crystal (LC) diffractive lens, and a polarization switch (e.g., a switchable waveplate) 4004 (wherein the switchable waveplate is curved). That is, the polarization switch or switchable waveplate 4004 is curved so that light 4006 from a wide field of view is incident on the switchable waveplate near the normal, or closer to the normal (compared to a flat switchable waveplate). Light from an object 4008 on the periphery 4010 of the field of view is shown incident on the switchable waveplate 4004 at an angle θ. This angle of incidence θ is measured relative to the normal 4012 to the switchable waveplate 4004. A polarization switch or switchable waveplate 4004 is shown to receive this light incident at an angle θ such that it is at normal or substantially normal incidence on the polarization switch.

[0199] The polarization switch or switchable waveplate 4004 has first and second surfaces 4014, 4016 (e.g., outer and inner surfaces) and a liquid crystal layer 4018 disposed therebetween. The first and second surfaces 4014, 4016, in this example, are concave from the perspective of the viewer's eye 2020 and convex with respect to the world 2022. The first and second surfaces 4014, 4016 may be spherically shaped or may have other curved shapes. The first and second surfaces 4014, 4016 may have the same or similar curvatures in some implementations, but are not limited to such. Other curvatures and shapes are also possible.

[0200] 19 shows a liquid crystal layer 4018 disposed between the first and second curved surfaces 4014, 4016, which are similarly curved. The liquid crystal layer 4018 may also be curved so that the LC layer is concave relative to the viewer's eye 4020 and convex relative to the world 4022. The liquid crystal layer 4018 may be spherically shaped in some implementations, but need not be so limited.

[0201] The curvature of the polarization switch or switchable waveplate 4004 shown in FIG. 19 is such that the angle of incidence θ of light incident is normal or substantially normal on the first outer surface 4014 of the polarization switch 4004. Similarly, the liquid crystal layer 4018 may comprise a liquid crystal comprising a plurality of liquid crystal molecules that are longer than they are wide along their length, and the direction of the incident light may be perpendicular to the length of the molecules on which the light is incident. Similarly, the liquid crystal molecules may have a side along their length that faces the incident light. In some cases, the side of the liquid crystal molecules on which the light is incident may be normal or nearly normal to the incident light. With light more consistently incident at the same or similar angles on the polarization switch 4004 and the liquid crystal molecules, the polarization conversion or rotation may be more uniform across the polarization switch. The polarization conversion or rotation of light incident along a central axis 4024 (e.g., the optical axis) through the polarization switch (e.g., through the first and second surfaces 4014, 4016 and the liquid crystal layer 4018) may be similar to the polarization conversion or rotation for off-axis light arising from objects 4008 located at the periphery 4010 of the field of view. This result may be a result of the curvature of the polarization switch 4004 and the liquid crystal layer 4018, which increases the likelihood that the angles of incidence of light from different objects in the field of view will be substantially the same (e.g., near normal).

[0202] In various implementations, the first and second curved surfaces 4014, 4016 on the switchable waveplate 4004 comprise curved surfaces on curved substrates (not shown). For example, the liquid crystal layer 4018 may be disposed between a first curved substrate and a second curved substrate. These curved substrates may provide the first and second (outer and inner) curved surfaces 4014, 4016 referenced above. The substrates may comprise glass or a plastic material. The substrates may, in some implementations, comprise optical elements such as quarter-wave plates.

[0203] The polarization switch or switchable waveplate 4004 may further comprise a plurality of electrodes (not shown) for applying an electrical signal across the curved liquid crystal layer 4018. This electrical signal may be used to switch the state of the liquid crystal and the polarization switch or switchable waveplate 4004. Thus, the polarization switch 4004 may be configured such that when the polarization switch is in one state, the polarization of light incident thereon is rotated or otherwise converted to a different polarization state. For example, right-handed circularly polarized light (RHCP) incident on the polarization switch or switchable waveplate 4004 may be converted to left-handed circularly polarized light (LHCP). However, when the polarization switch 4004 is in another state, such conversion or rotation generally does not occur.

[0204] 20 illustrates another exemplary design for a switchable waveplate configured to increase the efficiency of polarization rotation for light from objects on the periphery of the field of view. However, the switchable waveplate is not curved, but rather flat or planar. Such a configuration may make the switchable waveplate more compact and / or easier to fabricate. To provide increased efficiency of polarization conversion or rotation, the polarization switch comprises a liquid crystal with molecules that are tilted with increasing outward radial distance so that light is incident on the molecules closer to normal with respect to off-axis objects.

[0205] 20 shows an example of an adaptive lens assembly 4100 comprising, among other things, a liquid crystal lens (e.g., a waveplate lens) 4102, such as a liquid crystal (LC) diffractive lens, and a polarization switch (e.g., a switchable waveplate) 4104 (the switchable waveplate is flat or planar instead of curved). Light from an object 4108 on the periphery 4110 of the field of view is shown incident on the switchable waveplate 4104 at an angle θ. This angle of incidence θ is measured relative to a normal 4112 to the switchable waveplate 4104.

[0206] The polarization switch or switchable waveplate 4104 has first and second surfaces 4114, 4116 (e.g., outer and inner surfaces) and disposed therebetween a liquid crystal layer 4118. The first and second surfaces 4114, 4116 are flat or planar in this example.

[0207] 20 shows a liquid crystal layer 4118 comprising a plurality of layers 4107 of molecules 4105 disposed between first and second curved surfaces 4114, 4116. As shown schematically, the plurality of liquid crystal molecules 4105 can be oriented at an angle 4128 that varies with outward radial distance 4130 from a central axis or optic axis 4124 passing through the first and second surfaces 4114, 4116 and the liquid crystal layer 4118 in a plurality of radial directions. In particular, the plurality of liquid crystal molecules 4105 can vary, e.g., increase, a tilt angle relative to the first and second surfaces 4114, 4116 with outward radial distance 4130 from the central axis or optic axis 4124 in a plurality of radial directions. In various implementations such as that shown in FIG. 20 , the central axis or optic axis 4124 is normal to the first and second surfaces.

[0208] In some configurations, for example, an adaptive lens assembly 4100 is configured to transmit light to a viewer's eye 4120 located a distance d from the adaptive lens assembly, and a plurality of liquid crystal molecules 4105 each have a tilt angle 4128 that matches the angle of incidence θ of light propagating from a location 4108 in the field of view of the viewer's eye along a path 4130 to the viewer's eye. Similarly, the molecules 4105 may be longer than they are wide in a longitudinal direction 4132. This longitudinal direction 4132 may be tilted at an angle 4128 relative to the first and / or second surfaces 4114, 4116 that matches the angle of incidence θ of the incident light or the path 4130 from an object 4108 in the field of view to the eye 4120. Alternatively, in some implementations, the longitudinal direction 4132 of the molecules 4105 may be tilted at an angle 4128 that increases with outward radial distance 4130 from the central axis 4124 in multiple radial directions.

[0209] For example, in some designs, such as those illustrated in Figures 19 and 20, the liquid crystal molecules, having the tilt angle, which may increase radially with outward radial distance from the central axis, may be spaced at least 1, 2, 3, 4, 5, 6, 8, 10, 12 cm across the liquid crystal layer and / or wave plate. 2 , 60%, 70%, 80%, 90%, 95%, or more of the molecules (or a percentage within any range defined by any of these values) extending over a range of 100°, 150°, 200°, 300°, 400°, 500°, 600°, 700°, 800°, 900°, 950°, or more (or any range defined by any of these values). In various implementations, the alignment of the liquid crystal molecules with the longitudinal direction forms a pattern that is axially symmetric. The pattern may have, for example, at least 3-, 4-, 5-, 6-, 7-, 8-, 9-, 10-, 11-, 12-, or 20-fold rotational symmetry about an axis (e.g., a central axis), or may include a range between any of these values.

[0210] FIG. 20 is a cross-sectional view showing a cross section of the polarization switch and liquid crystal layer 4118 in the y-z plane. The liquid crystal molecules 4105 are therefore shown tilted with respect to a plane parallel to the y-z plane. This tilt angle increases with outward radial distance 4130 from the central axis 4124, for example, in a radial direction parallel to the y-axis. However, in various implementations, the tilt angle of the liquid crystal molecules 4105 increases with outward radial distance 4130 from the central axis 4124 in other radial directions. For example, the tilt angle of the liquid crystal molecules 4105 may increase with outward radial distance 4130 from the central axis 4124 in radial directions that are oblique (non-parallel and non-perpendicular) angles (e.g., 20°, 30°, 40°) to the y-axis (and orthogonal x-axis), e.g., partially outward from the paper.

[0211] Thus, the liquid crystal molecules 4105 may have a side along the longitudinal direction 4132 facing the incident light. In some cases, the side of the liquid crystal molecules 4105 on which light is incident may be normal or near normal to the incident light. As discussed above, in some cases, the direction of the incident light may be orthogonal to the longitudinal direction 3132 of the molecules on which the light is incident. With light more consistently incident on the liquid crystal molecules 4105 at the same or at least similar angles (e.g., if the molecules are oriented in the same direction for all outward radial distances 4130 from the central axis 4124), polarization conversion or rotation may be more uniform across the polarization switch 4104. The polarization conversion or rotation of light incident along a central axis 4124 (e.g., optical axis) through the polarization switch 4104 (e.g., through the first and second surfaces 4114, 4116 and the liquid crystal layer 4118) may be similar to the polarization conversion or rotation for off-axis light originating from objects 4108 located at the periphery 4110 of the field of view. This result may be a result of the tilted orientation of the liquid crystal molecules 4105 (e.g., tilt angle that increases with radial distance from the central axis 4124), which increases the likelihood that the angle of incidence of light from different objects 4108 in the field of view will be substantially the same (e.g., near normal).

[0212] In various implementations, the first and second surfaces 4114, 4116 on the switchable waveplate 4104 comprise surfaces on substrates 4115, 4117. For example, a liquid crystal layer 4118 may be disposed between the first and second substrates 4115, 4117. In various implementations, such as the design shown in FIG. 20 , the first and second surfaces 4114, 4116 comprise planar surfaces on planar substrates 4115, 4117. These substrates 4115, 4117 may provide the first and second (outer and inner) surfaces 4114, 4116 referenced above. The substrates 4115, 4117 may comprise glass or a plastic material. The substrates 4115, 4117 may, in some implementations, comprise optical elements such as quarter-wave plates.

[0213] The polarization switch or switchable waveplate 4104 may further comprise a plurality of electrodes (not shown) to apply an electrical signal across the liquid crystal layer 4118. This electrical signal may be used to switch the state of the liquid crystal and the polarization switch or switchable waveplate 4104. Thus, the polarization switch 4104 may be configured such that when the polarization switch is in one state, the polarization of light incident thereon is rotated or otherwise converted to a different polarization state. For example, right-handed circularly polarized light (RHCP) incident on the polarization switch or switchable waveplate 4104 may be rotated or converted to left-handed circularly polarized light (LHCP). However, when the polarization switch 4104 is in another state, such conversion or rotation generally does not occur.

[0214] Various methods may be employed to fabricate optical elements comprising liquid crystals, such as the switchable waveplate 4104 shown in FIG. 20 having tilted liquid crystal molecules 4105. As further illustrated in FIG. 20, the liquid crystal molecules 4105 may be tilted at a variable amount of tilt relative to substrates 4115 and 4117 on either side of the liquid crystal layer 4118. Various methods may be used to orient such liquid crystal molecules 4104 to provide a desired amount of tilt angle 4128 relative to the substrates 4115 and 4117. Examples of such fabrication methods are disclosed in U.S. Patent Application Publication Nos. 2018 / 0143470 and 2018 / 0143485, both of which are incorporated herein by reference in their entireties.

[0215] Additionally, the present methods can be used to vary the orientation of the LC molecules and create a wide variety of optical elements comprising liquid crystals, including waveplates such as switchable waveplates (e.g., equipped with electrodes and applying an electrical signal to switch the state of the waveplate), broadband waveplates, and waveplate lenses. Additionally, while such methods can be used to vary the orientation of LC molecules within optical elements such as waveplates, the methods can be used for other types of optical elements. Variations in methods for fabricating optical elements are also possible. For example, imprinting techniques such as nanoimprinting techniques, variations in fabrication techniques, and other approaches and fabrication techniques may be employed. (Example)

[0216] Various examples are provided below.

[0217] Example 1 1. A switchable optical assembly comprising: A switchable waveplate configured to be electrically activated and deactivated to selectively alter the polarization state of light incident thereon, first and second curved surfaces; a liquid crystal layer disposed between the first curved surface and the second curved surface such that the liquid crystal layer is curved; a plurality of electrodes for applying electrical signals across the curved liquid crystal layer; 1. A switchable optical assembly comprising a switchable waveplate comprising:

[0218] Example 2 10. The switchable optical assembly of example 1, wherein the first and second curved surfaces on the switchable waveplate comprise curved surfaces on a curved substrate.

[0219] Example 3 10. A switchable optical assembly according to any of the preceding examples, wherein the first and second curved surfaces have the same curvature.

[0220] Example 4 The switchable optical assembly further comprises a first waveplate lens comprising a liquid crystal layer, the first waveplate lens having different refractive powers for different polarizations of light incident thereon, the switchable optical assembly further comprising: a first lens state configured to have a first refractive power; and a second lens state configured to have a second optical power different from the first optical power.

[0221] Example 5 5. The switchable optical assembly of example 4, wherein the second optical power is zero optical power.

[0222] Example 6 1. A switchable optical assembly comprising: A switchable waveplate configured to be electrically activated and deactivated to selectively alter the polarization state of light incident thereon, first and second surfaces; a liquid crystal layer disposed between the first and second surfaces, the liquid crystal layer comprising a plurality of liquid crystal molecules whose tilt angles relative to the first and second surfaces vary with outward radial distance from an axis passing through the first and second surfaces and the liquid crystal layer in a plurality of radial directions; and a plurality of electrodes for applying an electric signal across the liquid crystal layer; 1. A switchable optical assembly comprising a switchable waveplate comprising:

[0223] Example 7 10. The switchable optical assembly of example 6, wherein the first and second surfaces comprise planar surfaces.

[0224] Example 8 The switchable optical assembly of any of Examples 6-7, wherein the first and second surfaces comprise planar surfaces on a planar substrate.

[0225] Example 9 The switchable optical assembly of any of Examples 6-8, wherein the axis is normal to the first and second surfaces.

[0226] Example 10 A switchable optical assembly described in any of Examples 6-9, wherein the plurality of liquid crystal molecules have tilt angles relative to the first and second surfaces that increase with outward radial distance from the axis in the plurality of radial directions.

[0227] Example 11 A switchable optical assembly described in any of Examples 6-10, configured to transmit light to a viewer's eye located at a certain distance from the switchable optical assembly, and wherein the plurality of liquid crystal molecules each have a tilt angle that matches the angle of incidence of light propagating along a path from a location within the viewer's field of view to the viewer's eye.

[0228] Example 12 12. A switchable optical assembly according to any of Examples 6-11, wherein the liquid crystal molecules have an orientation such that the liquid crystal molecules are arranged in a symmetrical array that is rotatable about the axis.

[0229] Example 13 12. The switchable optical assembly of any of Examples 6-11, wherein the plurality of liquid crystal molecules have an orientation such that the plurality of liquid crystal molecules have at least four-fold rotational symmetry about the axis.

[0230] Example 14 The switchable optical assembly further comprises a first waveplate lens comprising a liquid crystal layer, the first waveplate lens having different refractive powers for different polarizations of light incident thereon, the switchable optical assembly further comprising: a first lens state configured to have a first refractive power; A switchable optical assembly described in any of Examples 6-13, configured to be selectively switched between at least two lens states, including a second lens state configured to have a second refractive power different from the first refractive power.

[0231] Example 15 15. The switchable optical assembly of claim 14, wherein the second optical power is zero optical power.

[0232] Example 16 a plurality of liquid crystal molecules having tilt angles relative to the first and second surfaces that vary with outward radial distance from the axis in a plurality of radial directions, the plurality of liquid crystal molecules being spaced at least 1 cm across the first layer; 2 16. The switchable optical assembly of Examples 6-15, comprising at least 50% of the molecules extending over a range of

[0233] Example 17 a plurality of liquid crystal molecules having tilt angles relative to the first and second surfaces that vary with outward radial distance from the axis in a plurality of radial directions, the plurality of liquid crystal molecules being spaced at least 2 cm across the first layer; 2 16. The switchable optical assembly of Examples 6-15, comprising at least 50% of the molecules extending over a range of

[0234] Example 18 a plurality of liquid crystal molecules having tilt angles relative to the first and second surfaces that vary with outward radial distance from the axis in a plurality of radial directions, the plurality of liquid crystal molecules being spaced at least 1 cm across the first layer; 2 16. The switchable optical assembly of Examples 6-15, comprising at least 80% of the molecules extending over a range of

[0235] Example 19 a plurality of liquid crystal molecules having tilt angles relative to the first and second surfaces that vary with outward radial distance from the axis in a plurality of radial directions, the plurality of liquid crystal molecules being spaced at least 2 cm across the first layer; 216. The switchable optical assembly of Examples 6-15, comprising at least 80% of the molecules extending over a range of

[0236] Example 20 The switchable optical assembly of any one of Examples 6-19, wherein the axis comprises a central axis passing through the first and second surfaces and the liquid crystal layer.

[0237] Various additional examples are provided below.

[0238] Example 21 1. An optical assembly comprising: A waveplate comprising: first and second curved surfaces; a liquid crystal layer disposed between the first curved surface and the second curved surface such that the liquid crystal layer is curved; 1. An optical assembly comprising a wave plate comprising:

[0239] Example 22 22. The optical assembly of example 21, wherein the first and second curved surfaces on the waveplate comprise curved surfaces on a curved substrate.

[0240] Example 23 23. The optical assembly of Examples 21-22, wherein the first and second curved surfaces have the same curvature.

[0241] Example 24 The optical assembly of Examples 21-23, further comprising a first wave plate lens having a liquid crystal layer, the first wave plate lens having different refractive powers for different polarizations of light incident thereon.

[0242] Example 25 1. An optical assembly comprising: A waveplate comprising: first and second surfaces; an optical assembly comprising: a wave plate; and a liquid crystal layer disposed between the first and second surfaces, the liquid crystal layer comprising a plurality of liquid crystal molecules that vary in tilt angle relative to the first and second surfaces with outward radial distance from an axis passing through the first and second surfaces and the liquid crystal layer in a plurality of radial directions.

[0243] Example 26 26. The optical assembly of example embodiment 25, wherein the first and second surfaces comprise planar surfaces.

[0244] Example 27 27. The optical assembly of any of Examples 25-26, wherein the first and second surfaces comprise planar surfaces on a planar substrate.

[0245] Example 28 28. The optical assembly of any of Examples 25-27, wherein the axis is normal to the first and second surfaces.

[0246] Example 29 An optical assembly described in any of Examples 25-28, wherein the liquid crystal molecules have tilt angles relative to the first and second surfaces that increase with outward radial distance from the axis in the radial directions.

[0247] Example 30 An optical assembly described in any of Examples 25-29, configured to transmit light to a viewer's eye located at a certain distance from the optical assembly, and wherein the plurality of liquid crystal molecules each have a tilt angle that matches the angle of incidence of light propagating along a path from a location within the field of view of the viewer's eye to the viewer's eye.

[0248] Example 31 An optical assembly described in any of Examples 25-30, wherein the plurality of liquid crystal molecules have an orientation such that the plurality of liquid crystal molecules are arranged in a symmetrical array that can rotate around the axis.

[0249] Example 32 The optical assembly of any of Examples 25-30, wherein the plurality of liquid crystal molecules are oriented such that the plurality of liquid crystal molecules have at least four-fold rotational symmetry about the axis.

[0250] Example 33 An optical assembly described in any of Examples 25-32, wherein the optical assembly further comprises a first wave plate lens having a liquid crystal layer, the first wave plate lens having different refractive powers for different polarizations of light incident thereon.

[0251] Example 34 a plurality of liquid crystal molecules having tilt angles relative to the first and second surfaces that vary with outward radial distance from the axis in a plurality of radial directions, the plurality of liquid crystal molecules being spaced at least 1 cm across the first layer; 2 The optical assembly of Examples 25-33, comprising at least 50% of the molecules extending over a range of

[0252] Example 35 a plurality of liquid crystal molecules having tilt angles relative to the first and second surfaces that vary with outward radial distance from the axis in a plurality of radial directions, the plurality of liquid crystal molecules being spaced at least 2 cm across the first layer; 2 The optical assembly of Examples 25-33, comprising at least 50% of the molecules extending over a range of

[0253] Example 36 a plurality of liquid crystal molecules having tilt angles relative to the first and second surfaces that vary with outward radial distance from the axis in a plurality of radial directions, the plurality of liquid crystal molecules being spaced at least 1 cm across the first layer; 2 The optical assembly of Examples 25-33, comprising at least 80% of the molecules extending over a range of

[0254] Example 37 a plurality of liquid crystal molecules having tilt angles relative to the first and second surfaces that vary with outward radial distance from the axis in a plurality of radial directions, the plurality of liquid crystal molecules being spaced at least 2 cm across the first layer; 2The optical assembly of Examples 25-33, comprising at least 80% of the molecules extending over a range of

[0255] Example 38 The optical assembly of any one of Examples 25-37, wherein the axis comprises a central axis passing through the first and second surfaces and the liquid crystal layer. Additional Considerations

[0256] In the foregoing specification, the invention has been described with reference to specific embodiments thereof. It will, however, be apparent that various modifications and changes can be made therein without departing from the broader spirit and scope of the invention. The specification and drawings are, therefore, to be regarded in an illustrative rather than a restrictive sense.

[0257] Indeed, it should be understood that the systems and methods of the present disclosure each have several innovative aspects, none of which is solely responsible for or required for the desirable attributes disclosed herein. The various features and processes described above may be used independently of one another or may be combined in various ways. All possible combinations and subcombinations are intended to fall within the scope of the present disclosure. For example, with reference to FIG. 15, it should be understood that one or more adaptive lens assemblies 1504-1-1504-3 may be disposed between individual ones of waveguides 1012a, 1012b, and / or 1012c.

[0258] Certain features described herein in the context of separate embodiments may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented in multiple embodiments separately or in any suitable subcombination. Furthermore, while features may be described above as operative in a combination and may even be initially claimed as such, one or more features from the claimed combination may, in some cases, be deleted from the combination, and the claimed combination may be directed to a subcombination or variation of the subcombination. No single feature or group of features is required or essential to every embodiment.

[0259] It should be understood that conditional statements used herein, such as "can," "could," "might," "may," "eg," and the like, in particular, are generally intended to convey that certain embodiments include certain features, elements, and / or steps, while other embodiments do not, unless specifically stated otherwise or understood otherwise within the context as used. Thus, such conditional statements are generally not intended to imply that features, elements, and / or steps are in any way required for one or more embodiments, or that one or more embodiments necessarily include logic for determining whether those features, elements, and / or steps are to be included or performed in any particular embodiment, with or without authorial input or prompting. The terms "comprising," "including," "having," and the like, are synonymous and used inclusively in a non-limiting manner and do not exclude additional elements, features, acts, operations, etc. Also, the term "or" is used in its inclusive sense (and not its exclusive sense); thus, for example, when used to connect a list of elements, the term "or" means one, some, or all of the elements in the list. Additionally, the articles "a," "an," and "the," as used in this application and the appended claims, shall be interpreted to mean "one or more" or "at least one," unless otherwise specified. Similarly, while operations may be depicted in the figures in a particular order, it should be recognized that such operations need not be performed in the particular order shown, or in sequential order, or that all of the depicted operations need not be performed to achieve desirable results. Furthermore, the figures may diagrammatically depict one or more exemplary processes in the form of a flowchart. However, other operations not depicted may also be incorporated within the diagrammatically depicted exemplary methods and processes. For example, one or more additional operations may be performed before, after, concurrently with, or during any of the depicted operations.Additionally, operations may be rearranged or reordered in other embodiments. In some situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system components in the above-described embodiments should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems may generally be integrated together in a single software product or packaged into multiple software products. Additionally, other implementations are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results.

[0260] Thus, the claims are not intended to be limited to the embodiments shown herein but are to be accorded the widest scope consistent with the present disclosure, the principles and novel features disclosed herein.

Claims

1. A switchable optical assembly, comprising:

1. A switchable waveplate configured to be electrically activated and deactivated to selectively alter the polarization state of light incident thereon, said switchable waveplate comprising: first and second surfaces; a liquid crystal layer disposed between the first and second surfaces, the liquid crystal layer comprising a plurality of liquid crystal molecules having tilt angles relative to the first and second surfaces that increase with outward radial distance from an axis passing through the first and second surfaces and the liquid crystal layer in a plurality of radial directions; a plurality of electrodes for applying electrical signals across the liquid crystal layer; A switchable waveplate comprising: Equipped with a switchable optical assembly, wherein the plurality of liquid crystal molecules having increasing tilt angles relative to the first and second surfaces with outward radial distance from the axis comprise at least 50% of the molecules extending across the liquid crystal layer over an area of at least 1 cm 2 .

2. A switchable optical assembly as described in claim 1, wherein the first and second surfaces have planar surfaces.

3. A switchable optical assembly as described in claim 1, wherein the first and second surfaces comprise planar surfaces on a planar substrate.

4. A switchable optical assembly as described in claim 1, wherein the axis is normal to the first and second surfaces.

5. A switchable optical assembly as described in claim 1, configured to transmit light to the eye of a viewer located at a certain distance from the switchable optical assembly, and wherein the plurality of liquid crystal molecules each have a tilt angle that matches the angle of incidence of light propagating along a path from a location within the field of view of the viewer's eye to the viewer's eye.

6. A switchable optical assembly as described in claim 1, wherein the plurality of liquid crystal molecules have an orientation such that the plurality of liquid crystal molecules are arranged in a rotationally symmetric array around the axis.

7. A switchable optical assembly as described in claim 1, wherein the plurality of liquid crystal molecules have an orientation such that the plurality of liquid crystal molecules have at least four-fold rotational symmetry around the axis.

8. The switchable optical assembly further comprises a first waveplate lens comprising a liquid crystal layer, the first waveplate lens having different refractive powers for different polarizations of light incident thereon; The switchable optical assembly comprises: a first lens state configured to have a first refractive power; a second lens state configured to have a second refractive power different from the first refractive power; and 10. The switchable optical assembly of claim 1, configured to be selectively switched between at least two lens states comprising:

9. A switchable optical assembly as described in claim 8, wherein the second refractive power is zero refractive power.

10. A switchable optical assembly as described in claim 1, wherein the axis includes a central axis passing through the first and second surfaces and the liquid crystal layer.

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