Diffractive devices based on cholesteric liquid crystals.

Abstract

To provide a preferred cholesteric liquid crystal based diffractive device. [Solution] An embodiment of a diffractive device includes a cholesteric liquid crystal (CLC) layer having a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction and continuously rotated in a first rotation direction by at least a certain helical pitch. The alignment of the liquid crystal molecules in the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction, providing a diffraction grating. The diffractive device can be configured to reflect light having a specific wavelength range and circular polarization orientation. The diffractive device can be used in waveguides and imaging systems in augmented or virtual reality systems.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of priority to U.S. Provisional Patent Application No. 62 / 431,752, filed December 8, 2016, entitled "DIFFRACTIVE DEVICES BASED ON CHOLESTERIC LIQUID CRYSTAL," and to U.S. Provisional Patent Application No. 62 / 431,745, filed December 8, 2016, entitled "DIFFRACTIVE DEVICES BASED ON CHOLESTERIC LIQUID CRYSTAL," the contents of which are incorporated herein by reference in their entireties. (Field) The present disclosure relates to display systems, and more particularly to augmented reality display systems that include diffractive devices based on cholesteric liquid crystals. [Background technology]

[0002] 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 may 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 inputs, while augmented reality or "AR" scenarios typically involve the presentation of digital or virtual image information as an extension to the visualization of the real world around the user. Mixed reality or "MR" scenarios are a type of AR scenario that typically involve virtual objects that are integrated into and respond to the natural world. For example, in MR scenarios, AR image content may be perceived to appear blocked by or otherwise interact with objects in the real world.

[0003] 1, an augmented reality scene 1 is depicted in which a user of the AR technology sees a real-world park-like setting 1100 featuring people, trees, buildings in the background, and a concrete platform 1120. In addition to these items, the user of the AR technology also perceives that they are "seeing" "virtual content," such as a robotic figure 1110 standing on the real-world platform 1120 and a flying cartoon-like avatar character 1130 that appears to be an anthropomorphic bumblebee, even though these elements 1130, 1110 do not exist in the real world. The human visual perception system is complex, making it difficult to produce AR technology that facilitates a pleasing, natural-feeling, and rich presentation of virtual image elements among other virtual or real-world image elements.

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

[0005] In one aspect, a diffraction grating comprises a cholesteric liquid crystal (CLC) layer comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction and successively rotated in a first rotation direction by at least a helical pitch. The helical pitch is a length in the layer depth direction that corresponds to a net rotation angle of the liquid crystal molecules of the chiral structures through one full rotation in the first rotation direction. The alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction.

[0006] In another aspect, a head mounted display device (HMD) is configured to project light to a user's eye and display augmented reality image content. The HMD comprises a head mounted display device comprising a frame configured to be supported on the user's head. The HMD comprises a display disposed on the frame, at least a portion of the display comprising one or more waveguides. The display is disposed at a location in front of the user's eye when the user wears the head mounted display such that the transparent portion transmits light from the location in front of the user's eye to the user's eye to provide a view of the portion of the environment in front of the user. The display further comprises one or more light sources and at least one diffraction grating configured to couple light from the light sources into or out of the one or more waveguides, the at least one diffraction grating comprising a diffraction grating according to any aspect described herein.

[0007] In another aspect, a waveguiding device includes one or more cholesteric liquid crystal (CLC) layers each including a plurality of chiral structures, each chiral structure including a plurality of liquid crystal molecules extending in a layer depth direction and rotated successively in a first rotation direction, and the alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to Bragg-reflect incident light. One or more waveguides are formed across the one or more CLC layers and configured to optically couple the Bragg-reflected light such that the Bragg-reflected light travels in a lateral direction perpendicular to the layer depth direction by total internal reflection (TIR). The one or more CLC layers and the one or more waveguides are configured to be in the same optical path.

[0008] In another aspect, a wavelength-selective cholesteric liquid crystal reflector (CLCR) comprises one or more cholesteric liquid crystal (CLC) layers each comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction and sequentially rotated in a first rotation direction, the alignment of the liquid crystal molecules of the chiral structures varying periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to substantially Bragg-reflect a first incident light having a first wavelength while substantially transmitting a second incident light having a second wavelength.

[0009] In another aspect, a head mounted display (HMD) configured to be worn on a user's head includes a frame including a pair of ear hooks, a pair of optical elements supported by the frame such that each of the pair of optical elements can be positioned in front of the user's eyes, a forward-facing imager mounted on one of the pair of ear hooks, and a cholesteric liquid crystal (CLC) off-axis mirror including one or more cholesteric liquid crystal (CLC) layers each including a plurality of chiral structures. Each chiral structure includes a plurality of liquid crystal molecules extending in a layer depth direction and rotated continuously in a first rotation direction, and the alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to Bragg-reflect incident light. The cholesteric liquid crystal (CLC) off-axis mirror is disposed in or on one of the pair of optical elements and configured to reflect infrared light toward a forward-facing imager configured to receive infrared light reflected by the reflecting element.

[0010] In another aspect, a waveguiding device includes one or more cholesteric liquid crystal (CLC) layers each having a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction and rotated successively in a first rotation direction, and an alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to Bragg-reflect incident light. The waveguiding device additionally includes one or more waveguides formed across the one or more CLC layers and configured to optically couple Bragg-reflected light from the one or more CLC layers such that the Bragg-reflected light travels in a lateral direction perpendicular to the layer depth direction by total internal reflection (TIR). The waveguiding device includes one or more waveguides formed across the one or more CLC layers and configured to optically couple Bragg-reflected light from the one or more CLC layers such that the Bragg-reflected light travels in a lateral direction perpendicular to the layer depth direction by total internal reflection (TIR). o The diffraction efficiency is greater than 25%.

[0011] In yet another aspect, a display device includes a waveguide and an incoupling optical element formed on the waveguide. The incoupling optical element is configured to incoupling light incident thereon into a first side of the waveguide, and the incoupling optical element and the waveguide are configured such that light incoupling into the waveguide propagates within the waveguide in an in-plane direction of the waveguide by total internal reflection (TIR). The display device additionally includes an outcoupling optical element formed on the waveguide and configured to outcoupling light incident thereon from the waveguide. The light outcoupling element includes a cholesteric liquid crystal (CLC) layer having a plurality of chiral structures, each of the chiral structures comprising a plurality of liquid crystal molecules extending in a layer depth direction of the CLC layer and being continuously rotated in a first rotation direction, and an alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction such that one or more of the CLC layers are configured to Bragg-reflect light incident thereon from the waveguide toward the first side.

[0012] Details of one or more implementations of the subject matter described herein are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages will become apparent from the description, drawings, and claims. Neither this summary nor the following detailed description purports to define or limit the scope of the inventive subject matter. The present specification also provides, for example, the following items: (Item 1) A diffraction grating comprising: A cholesteric liquid crystal (CLC) layer comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules, the plurality of liquid crystal molecules extending in a layer depth direction with at least a helical pitch and being continuously rotated in a first rotation direction. Equipped with the helical pitch is a length in the layer depth direction corresponding to a net rotation angle of the liquid crystal molecules of the chiral structure through one complete rotation in the first rotation direction; The alignment of the liquid crystal molecules of the chiral structure varies periodically in a lateral direction perpendicular to the layer depth direction. Diffraction grating. (Item 2) Item 2. The diffraction grating of item 1, wherein each chiral structure comprises at least three calamitic liquid crystal molecules stretched along different stretching directions. (Item 3) 2. The diffraction grating of item 1, wherein the CLC layer is configured to substantially Bragg reflect elliptically or circularly polarized light having a handedness of polarization that matches the first rotation direction when viewed in the layer normal direction, while substantially transmitting elliptically or circularly polarized light having a handedness of polarization opposite to the first rotation direction when viewed in the layer depth direction. (Item 4) The alignment of the liquid crystal molecules which varies periodically in the lateral direction is such that the liquid crystal molecules having chiral structures which are consecutively adjacent to each other at substantially the same depth in the layer depth direction are aligned in a 360° pattern. o 2. The diffraction grating of item 1, wherein the diffraction grating is continuously rotated in the second rotation direction by n, where n is an integer. (Item 5) 2. The diffraction grating of item 1, wherein the alignment of the liquid crystal molecules that varies periodically in the lateral direction is such that elliptically or circularly polarized light Bragg-reflected by the laterally adjacent chiral structures is phase-shifted by an angle proportional to the angle of rotation of the second rotation direction between the laterally adjacent chiral structures. (Item 6) Item 2. The diffraction grating of item 1, wherein the chiral structures have substantially the same helical pitch. (Item 7) The chiral structure is a first plurality of chiral structures, each of the first plurality of chiral structures comprising a plurality of first liquid crystal molecules, the first plurality of first liquid crystal molecules extending in a layer depth direction by at least a first helical pitch and being continuously rotated in the first rotation direction; a second plurality of chiral structures, each of the second plurality of chiral structures comprising a plurality of second liquid crystal molecules, the second plurality of liquid crystal molecules extending in the layer depth direction by at least a second helical pitch and being continuously rotated in the first rotation direction; Equipped with 2. The diffraction grating of item 1, wherein the first helical pitch and the second helical pitch are such that the first chiral structure and the second chiral structure are configured to Bragg reflect light having different off-axis angles of incidence. (Item 8) 8. The diffraction grating of item 7, wherein the first plurality of chiral structures are formed in a first cholesteric liquid crystal (CLC) layer, and the second plurality of chiral structures are formed in a second cholesteric liquid crystal (CLC) layer, the second cholesteric liquid crystal (CLC) layer being formed across the first CLC layer and stacked in the layer depth direction. (Item 9) 8. The diffraction grating of item 7, wherein the first plurality of chiral structures are formed in a first region of the cholesteric liquid crystal (CLC) layer and the second plurality of chiral structures are formed in a second region of the cholesteric liquid crystal (CLC) layer formed across the first region in the layer depth direction. (Item 10) 8. The diffraction grating of claim 7, wherein the first plurality of chiral structures are formed in a first region of the cholesteric liquid crystal (CLC) layer and the second plurality of chiral structures are formed in a second region of the cholesteric liquid crystal (CLC) layer, the first and second regions being laterally adjacent regions in the lateral direction. (Item 11) 11. The diffraction grating of any one of items 7-10, wherein one or both of the first and second chiral structures form a gradient of the helical pitch in one or both of the layer depth direction and the lateral direction. (Item 12) 1. A waveguide device comprising: one or more cholesteric liquid crystal (CLC) layers, each of the one or more cholesteric liquid crystal (CLC) layers comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules, the plurality of liquid crystal molecules extending in a layer depth direction and being continuously rotated in a first rotation sense, an alignment of the liquid crystal molecules of the chiral structures varying periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to Bragg reflect incident light; one or more waveguides formed across the one or more CLC layers, the one or more waveguides configured to optically couple Bragg-reflected light from the one or more CLC layers such that the Bragg-reflected light travels in a lateral direction perpendicular to the layer depth direction by total internal reflection (TIR); Equipped with A waveguide device, wherein the one or more CLC layers and the one or more waveguides are configured to be in the same optical path. (Item 13) 13. The waveguiding device of claim 12, wherein each of the plurality of chiral structures extends in a layer depth direction with at least a helical pitch, the helical pitch being a length in the layer depth direction corresponding to a net rotation angle of the liquid crystal molecules of the chiral structure through one complete rotation in the first rotation direction. (Item 14) Item 13. The waveguide device of item 12, comprising a plurality of CLC layers, each one of the CLC layers having differently arranged chiral structures configured to selectively Bragg-reflect incident light having a different wavelength than the others of the CLC layers at a different Bragg-reflection angle than the others of the CLC layers. (Item 15) Item 13. The waveguide device of item 12, wherein the periodically varying lateral alignment of the liquid crystal layers is characterized by a period, each one of the CLC layers having a different period than the other of the CLC layers. (Item 16) Item 13. The waveguide device of item 12, wherein each one of the CLC layers is configured to selectively Bragg reflect incident light having a wavelength within the visible spectrum. (Item 17) Item 13. The waveguiding device of item 12, wherein each one of the CLC layers is configured to selectively Bragg reflect incident light having wavelengths in the infrared spectrum while transmitting light having wavelengths in the visible spectrum. (Item 18) Item 13. The waveguide device of item 12, comprising a plurality of waveguides, each waveguide optically coupled to one of the CLC layers formed thereon. (Item 19) Item 13. The waveguide device of item 12, wherein the multiple CLC layers form a stack and a single waveguide is optically coupled to each one of the CLC layers in the stack. (Item 20) 20. The waveguiding device according to any one of claims 12-19, further comprising a polarizing reflector, the one or more waveguides being interposed between the one or more CLC layers and the polarizing reflector, such that elliptically or circularly polarized incident light transmitted through the one or more CLC layers and further through the waveguide is reflected by the polarizing reflector as reflected light having the opposite polarization handedness to the elliptically or circularly polarized incident light. (Item 21) 13. The waveguide device of claim 12, comprising a first CLC layer and a second CLC layer forming a stack with a waveguide, the chiral structures of the first CLC layer and the second CLC layer being successively rotated in opposite rotational directions. (Item 22) 22. The waveguide device of claim 21, wherein the first and second CLC layers are stacked on the waveguide. (Item 23) 22. The waveguide device of claim 21, wherein the first and second CLC layers are interposed by the waveguide. [Brief description of the drawings]

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

[0014] [Diagram 2] FIG. 2 illustrates an example of a wearable display system.

[0015] [Diagram 3] FIG. 3 illustrates a conventional display system for simulating a three-dimensional image for a user.

[0016] [Figure 4] FIG. 4 illustrates aspects of an approach for simulating a three-dimensional image using multiple depth planes.

[0017] [Diagram 5] 5A-5C illustrate the relationship between the radius of curvature and the radius of focus.

[0018] [Figure 6] FIG. 6 illustrates an embodiment of a waveguide stack for outputting image information to a user.

[0019] [Figure 7] FIG. 7 illustrates an example of an output beam output by a waveguide.

[0020] [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.

[0021] [Figure 9A] FIG. 9A illustrates a cross-sectional side view of an example of a set of stacked waveguides, each of which includes an internal coupling optical element.

[0022] [Figure 9B] FIG. 9B illustrates a perspective view of the multiple stacked waveguide embodiment of FIG. 9A.

[0023] [Figure 9C] FIG. 9C illustrates a top-down plan view of the multiple stacked waveguide embodiment of FIGS. 9A and 9B.

[0024] [Figure 10]FIG. 10 illustrates a cross-sectional side view of an embodiment of a cholesteric liquid crystal grating (CLCG) having a plurality of uniform chiral structures.

[0025] [Figure 11] FIG. 11 illustrates a cross-sectional side view of an embodiment of a CLCG having chiral structures that are differently aligned in the lateral direction.

[0026] [Figure 12] FIG. 12 illustrates a cross-sectional side view of an embodiment of a CLC layer configured for Bragg reflection at off-axis angles of incidence.

[0027] [Figure 13A] FIG. 13A illustrates a cross-sectional side view of an example CLC layer having a first helical pitch and configured for Bragg reflection at a first off-axis angle of incidence.

[0028] [Figure 13B] FIG. 13B illustrates a cross-sectional side view of an example CLC layer having a second helical pitch and configured for Bragg reflection at a second off-axis angle of incidence.

[0029] [Figure 13C] FIG. 13C illustrates a cross-sectional side view of an example CLCG including the CLC layers of FIGS. 13A and 13B having different helical pitches in a stacked configuration to provide Bragg reflection at multiple off-axis angles of incidence and high diffraction bandwidth.

[0030] [Figure 14] FIG. 14 illustrates a cross-sectional side view of an example CLCG including a CLC layer having vertical regions with different helical pitches along the depth direction for Bragg reflection at multiple off-axis angles of incidence and high diffraction bandwidth.

[0031] [Figure 15]FIG. 15 illustrates a cross-sectional side view of an example of a CLCG that includes a CLC layer having lateral regions with different helical pitches along the lateral direction to spatially vary the Bragg reflection.

[0032] [Figure 16] FIG. 16 illustrates an example of an optical waveguiding device comprising a waveguide coupled to a CLCG and configured to propagate light by total internal reflection (TIR).

[0033] [Figure 17A] FIG. 17A illustrates an example of an optical waveguiding device comprising a waveguide coupled to a CLCG and configured to selectively propagate light having certain wavelengths by total internal reflection (TIR).

[0034] [Figure 17B] FIG. 17B illustrates an example of multiple optical waveguiding devices in the same optical path, each comprising a waveguide coupled to a CLCG and configured to selectively propagate light having certain wavelengths by total internal reflection (TIR).

[0035] [Figure 17C] FIG. 17C illustrates an example of multiple optical waveguiding devices in the same optical path, each comprising a waveguide coupled to a CLCG and configured to selectively propagate light having certain wavelengths by total internal reflection (TIR).

[0036] [Figure 18] FIG. 18 illustrates an example of an optical waveguiding device comprising a common waveguide coupled to multiple CLCGs and configured to selectively propagate light having multiple wavelengths by total internal reflection (TIR).

[0037] [Figure 19] FIG. 19 illustrates an example of an optical waveguiding device comprising a waveguide coupled to a CLCG and configured to propagate light by total internal reflection (TIR).

[0038] [Figure 20] FIG. 20 illustrates an example of an optical waveguiding device comprising a waveguide coupled to a CLCG and a polarization converting reflector, where the CLCG is configured to receive incident light and the waveguide is configured to propagate light Bragg reflected from the CLCG by total internal reflection (TIR).

[0039] [Figure 21A] FIG. 21A illustrates the optical waveguide device of FIG. 20, where the CLCG is configured to receive incident light that is linearly polarized or unpolarized, and the waveguide is configured to propagate light that is Bragg reflected from the CLCG and light reflected by the reflector by total internal reflection (TIR).

[0040] [Figure 21B] FIG. 21B illustrates the optical waveguide device of FIG. 20, where the CLCG is configured to receive incident light that has been changed into an orthogonal elliptically or circularly polarized beam, and the waveguide is configured to propagate light that is Bragg reflected from the CLCG and light reflected by the reflector by total internal reflection (TIR).

[0041] [Figure 22A] FIG. 22A illustrates an example of an optical waveguide device comprising multiple CLC layers coupled to a common waveguide, the CLC layer including a first CLC layer having a chiral structure with a first rotation direction and a second CLC layer having a chiral structure with a second rotation direction opposite to the first rotation direction, under conditions where an incident light beam is linearly polarized or unpolarized.

[0042] [Figure 22B] FIG. 22B illustrates the optical waveguide device of FIG. 22A under conditions where the incident light is polarized into orthogonal elliptically or circularly polarized beams.

[0043] [Figure 22C]FIG. 22C illustrates an example of an optical waveguide device comprising multiple CLC layers coupled to a common waveguide interposed between two CLC layers, including a first CLC layer having a chiral structure with a first rotation direction and a second CLC layer having a chiral structure with a second rotation direction opposite to the first rotation direction, under conditions where an incident light beam is linearly polarized or unpolarized.

[0044] [Diagram 23] FIG. 23 illustrates an example of an imaging system comprising a forward-facing camera configured to image the wearer's eye using a cholesteric liquid crystal (CLC) off-axis mirror.

[0045] [Figure 24A] 24A-24F illustrate an example of an imaging system comprising a forward-facing camera configured to image a wearer's eye using a CLC off-axis mirror. [Figure 24B] 24A-24F illustrate an example of an imaging system comprising a forward-facing camera configured to image a wearer's eye using a CLC off-axis mirror. [Figure 24C] 24A-24F illustrate an example of an imaging system comprising a forward-facing camera configured to image a wearer's eye using a CLC off-axis mirror. [Figure 24D] 24A-24F illustrate an example of an imaging system comprising a forward-facing camera configured to image a wearer's eye using a CLC off-axis mirror. [Figure 24E] 24A-24F illustrate an example of an imaging system comprising a forward-facing camera configured to image a wearer's eye using a CLC off-axis mirror. [Figure 24F] 24A-24F illustrate an example of an imaging system comprising a forward-facing camera configured to image a wearer's eye using a CLC off-axis mirror.

[0046] [Figure 24G] 24G and 24H illustrate an example of an imaging system comprising a forward-facing camera configured to image a wearer's eye using a diffractive optical element comprising multiple segments including one or more CLC off-axis mirrors, each of which can have different optical properties. [Fig. 24H] 24G and 24H illustrate an example of an imaging system comprising a forward-facing camera configured to image a wearer's eye using a diffractive optical element comprising multiple segments including one or more CLC off-axis mirrors, each of which can have different optical properties.

[0047] [Diagram 25] FIG. 25 illustrates an example optical waveguiding device optimized over a wide field of view, comprising a waveguide coupled to a CLCG and configured to propagate light by total internal reflection (TIR).

[0048] [Figure 26] FIG. 26 illustrates an example optical waveguiding device configured as an outcoupling optical element that comprises a waveguide coupled to a CLCG and configured to propagate light by total internal reflection (TIR). DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0049] 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.

[0050] 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 that projects image information to the user's eyes, for example as part of eyewear. In addition, the display may also transmit light from the surrounding environment to the user's eyes, providing a view of the surrounding environment. As used herein, it should be understood that a "head-mounted" display is a display that may be mounted on the viewer's head.

[0051] FIG. 2 illustrates an example of a wearable display system 80. The display system 80 includes a display 62 and various mechanical and electronic modules and systems to support the functionality of the display 62. The display 62 may be coupled to a frame 64, which is wearable by a display system user or viewer 60 and configured to position the display 62 in front of the user's 60 eye. The display 62 may be considered eyewear in some embodiments. In some embodiments, a speaker 66 is coupled to the frame 64 and positioned adjacent to the ear canal of the user 60 (in some embodiments, another speaker, not shown, is positioned adjacent to the user's other ear canal to provide stereo / adjustable sound control). In some embodiments, the display system may also include one or more microphones 67 or other devices to detect sound. In some embodiments, the microphones may be configured to allow the user to provide input or commands (e.g., voice menu command selections, natural language questions, etc.) to the system 80 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 continuously collect audio data (e.g., to passively collect from the user and / or the environment). Such audio data may include user sounds, such as heavy breathing, or environmental sounds, such as commotion, indicative of a nearby event. The display system may also include an ambient sensor 30a, which may be separate from the frame 64 and attached to the body of the user 60 (e.g., on the head, torso, limbs, etc. of the user 60). The ambient sensor 30a may be configured to obtain data characterizing a physiological state of the user 60 in some embodiments, as described further herein. For example, the sensor 30a may be an electrode.

[0052] 2, the display 62 is operably coupled by a communication link 68, such as wired or wireless connectivity, to a local data processing module 70, which may be mounted in a variety of configurations, such as fixedly attached to the frame 64, fixedly attached to a helmet or hat worn by the user, built into headphones, or otherwise removably attached to the user 60 (e.g., in a backpack configuration, in a belt-coupled configuration). Similarly, the sensor 30a may be operably coupled to the local processor and data module 70 by a communication link 30b, such as wired or wireless connectivity. The local processing and data module 70 may include a hardware processor and digital memory, such as non-volatile memory (e.g., flash memory or hard disk drive), both of which may be utilized to aid in processing, caching, and storing data. The data includes a) captured from sensors (e.g., which may be operatively coupled to the frame 64 or otherwise attached to the user 60), such as image capture devices (such as cameras), microphones, inertial measurement units, accelerometers, compasses, GPS units, wireless devices, gyroscopes, and / or other sensors disclosed herein, and / or b) data obtained and / or processed using a remote processing module 72 and / or a remote data repository 74 (including data related to the virtual content), as the case may be, for passing through the display 62 after processing or retrieval. The local processing and data module 70 may be operatively coupled to the remote processing module 72 and the remote data repository 74 by communications links 76, 78, such as via wired or wireless communication links, such that these remote modules 72, 74 are operatively coupled to each other and available as resources to the local processing and data module 70. In some embodiments, the local processing and data module 70 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, etc.In some other embodiments, one or more of these sensors may be mounted on the frame 64 or may be stand-alone structures that communicate with the local processing and data module 70 via wired or wireless communication paths.

[0053] 2, in some embodiments, the remote processing module 72 may comprise one or more processors configured to analyze and process the data and / or image information. In some embodiments, the remote data repository 74 may comprise a digital data storage facility, which may be available through the Internet or other networking configurations in a "cloud" resource configuration. In some embodiments, the remote data repository 74 may include one or more remote servers, which provide information, e.g., information for generating augmented reality content, to the local processing and data module 70 and / or the remote processing module 72. In some embodiments, all data is stored and all calculations are performed in the local processing and data module, allowing for fully autonomous use from the remote modules.

[0054] The perception of an image as being "three-dimensional" or "3-D" may be achieved by providing a slightly different presentation of the image to each eye of the viewer. FIG. 3 illustrates a conventional display system for simulating a three-dimensional image for a user. Two distinct images 5, 7, one for each eye 4, 6, are output to the user. The images 5, 7 are spaced apart from the eyes 4, 6 by a distance 10 along an optical or z-axis parallel to the viewer's line of sight. The images 5, 7 are flat and the eyes 4, 6 may focus on the images by assuming a single accommodation state. Such a system relies on the human visual system to combine the images 5, 7 and provide the perception of depth and / or scale for the combined image.

[0055] However, it will be appreciated that the human visual system is more complex and more difficult to provide a realistic perception of depth. For example, many viewers of conventional "3-D" display systems may find such systems uncomfortable or may not perceive any sensation of depth at all. 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 vergence and accommodation. Vergence of the two eyes relative to one another (i.e., rotation of the eyes such that the pupils move toward or away from one another, converging the gaze of the eyes and fixating on the object) is closely linked to the focusing (or "accommodation") of the lenses and pupils of the eye. Under normal conditions, a change in focus of the lenses of the eye or accommodation of the eye to change focus from one object to another at a different distance will automatically produce a matching change in vergence at the same distance, a relationship known as the "accommodation-vergence-divergence reflex" and pupil dilation or constriction. Similarly, changes in vergence-divergence will induce matching changes in accommodation of lens shape and pupil size under normal conditions. As described herein, many stereoscopic, or "3-D," display systems display a scene to each eye using a slightly different presentation (and therefore a slightly different image) so that a three-dimensional perspective is perceived by the human visual system. However, such systems are uncomfortable for many viewers because, among other things, they simply provide a different presentation of the scene but counter the "accommodation-vergence-divergence reflex" in which the eyes view all image information in a single accommodation state. Display systems that provide better matching between accommodation and vergence-divergence may form a more realistic and comfortable simulation of a three-dimensional image and contribute to increased wearing duration and thus compliance with diagnostic and therapy protocols.

[0056] FIG. 4 illustrates aspects of an approach for simulating a three-dimensional image using multiple depth planes. With reference to FIG. 4, objects at various distances from the eyes 4, 6 on the z-axis are accommodated by the eyes 4, 6 such that the objects are in focus. The eyes (4 and 6) assume a particular accommodated state and focus objects at different distances along the z-axis. As a result, a particular accommodated state may be said to be associated with a particular one of the depth planes 14 having an associated focal length such that an object or part of an object at a particular depth plane is in focus when the eye is in an accommodated state relative to that depth plane. In some embodiments, a three-dimensional image may be simulated by providing a different presentation of an image for each eye 4, 6, and by providing a different presentation of an image corresponding to each of the depth planes. Although shown as separate for clarity of illustration, it should be understood that the fields of view of the eyes 4, 6 may overlap, for example, as the distance along the z-axis increases. Additionally, while shown to be flat for ease of illustration, it will be understood that the contour of the depth plane may be curved in physical space such that all features within the depth plane are in focus with the eye in a particular accommodated state.

[0057] The distance between an object and the eye 4 or 6 may also change the amount of light emitted from the object as viewed by that eye. Figures 5A-5C illustrate the relationship between distance and divergence of light rays. The distance between the object and the eye 4 is represented in the order of decreasing distances R1, R2, and R3. As shown in Figures 5A-5C, the light rays become more divergent as the distance to the object decreases. As the distance increases, the light rays become more collimated. In other words, the light field generated by a point (an object or part of an object) may be said to have a spherical wavefront curvature that is a function of the distance the point is away from the user's eye. As the curvature increases, the distance between the object and the eye 4 decreases. As a result, at different depth planes, the degree of divergence of the light rays is also different, and the degree of divergence increases with decreasing distance between the depth plane and the viewer's eye 4. Only a single eye 4 is shown in Figures 5A-5C and other figures herein for clarity of illustration, but it will be understood that the discussion regarding eye 4 may apply to both eyes 4 and 6 of a viewer.

[0058] 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. The different presentations may be focused separately by the viewer's eye, thereby serving to provide depth cues to the user based on the ocular accommodation required to focus on different image features for a scene located on different depth planes and / or based on the observation of different image features on different depth planes that are out of focus.

[0059] FIG. 6 illustrates an example of a waveguide stack for outputting image information to a user. The display system 1000 includes a stack of waveguides or a stacked waveguide assembly 1178 that may be utilized to provide a three-dimensional perception to the eye / brain using multiple waveguides 1182, 1184, 1186, 1188, 1190. In some embodiments, the display system 1000 is the system 80 of FIG. 2, of which FIG. 6 illustrates several portions in greater detail. For example, the waveguide assembly 1178 may be part of the display 62 of FIG. 2. It will be appreciated that the display system 1000 may be considered a light field display in some embodiments.

[0060] Continuing with reference to FIG. 6, the waveguide assembly 1178 may also include a number of features 1198, 1196, 1194, 1192 between the waveguides. In some embodiments, the features 1198, 1196, 1194, 1192 may be one or more lenses. The waveguides 1182, 1184, 1186, 1188, 1190 and / or the number of lenses 1198, 1196, 1194, 1192 may be configured to transmit image information to the eye with various levels of wavefront curvature or ray divergence. Each waveguide level may be associated with a particular depth plane and may be configured to output image information corresponding to that depth plane. The image input devices 1200, 1202, 1204, 1206, 1208 may act as light sources for the waveguides and may be utilized to input image information into the waveguides 1182, 1184, 1186, 1188, 1190, each of which may be configured to distribute incident light across each respective waveguide for output towards the eye 4, as described herein. Light exits output surfaces 1300, 1302, 1304, 1306, 1308 of the image input devices 1200, 1202, 1204, 1206, 1208 and is input into corresponding input surfaces 1382, 1384, 1386, 1388, 1390 of the waveguides 1182, 1184, 1186, 1188, 1190. In some embodiments, each of the input surfaces 1382, 1384, 1386, 1388, 1390 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 144 or the viewer's eye 4). In some embodiments, a single beam of light (e.g., a collimated beam) may be launched into each waveguide and output a total field of cloned collimated beams that are directed towards the eye 4 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 1200, 1202, 1204, 1206, 1208 may be associated with and launch light into multiple (e.g., three) waveguides 1182, 1184, 1186, 1188, 1190.

[0061] In some embodiments, each of the image input devices 1200, 1202, 1204, 1206, 1208 is a discrete display that generates image information for input into the corresponding waveguides 1182, 1184, 1186, 1188, 1190, respectively. In some other embodiments, the image input devices 1200, 1202, 1204, 1206, 1208 are the output of a single multiplexed display that may, for example, send image information to each of the image input devices 1200, 1202, 1204, 1206, 1208 via one or more optical conduits (such as fiber optic cables). It should be understood that the image information provided by the image input devices 1200, 1202, 1204, 1206, 1208 may include light of different wavelengths or colors (e.g., different primary colors as discussed herein).

[0062] In some embodiments, the light injected into the waveguides 1182, 1184, 1186, 1188, 1190 is provided by a light projector system 2000, which includes a light module 2040, which may include light emitters such as light emitting diodes (LEDs). Light from the light module 2040 may be directed and modified by a light modulator 2030, e.g., a spatial light modulator, via a beam splitter 2050. The light modulator 2030 may be configured to vary the perceived intensity of the light injected into the waveguides 1182, 1184, 1186, 1188, 1190. The light modulator 2030 may be configured to vary the perceived intensity of the light injected into the waveguides 1182, 1184, 1186, 1188, 1190. Examples of spatial light modulators include liquid crystal displays (LCDs), including liquid crystal on silicon (LCOS) displays.

[0063] In some embodiments, the display system 1000 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 patterns, etc.) into one or more waveguides 1182, 1184, 1186, 1188, 1190 and ultimately to a viewer's eye 4. In some embodiments, the illustrated image injection devices 1200, 1202, 1204, 1206, 1208 may diagrammatically represent a single scanning fiber or a bundle of scanning fibers configured to inject light into one or more waveguides 1182, 1184, 1186, 1188, 1190. In some other embodiments, the illustrated image injection devices 1200, 1202, 1204, 1206, 1208 may diagrammatically represent a plurality of scanning fibers or a plurality of bundles of scanning fibers, each configured to inject light into an associated one of the waveguides 1182, 1184, 1186, 1188, 1190. It should be understood that one or more optical fibers may be configured to transmit light from the optical module 2040 into one or more of the waveguides 1182, 1184, 1186, 1188, 1190. It should be understood that one or more intervening optical structures may be provided between the scanning fiber or fibers and one or more of the waveguides 1182, 1184, 1186, 1188, 1190, for example, to redirect light exiting the scanning fiber into one or more of the waveguides 1182, 1184, 1186, 1188, 1190.

[0064] The controller 1210 controls the operation of one or more of the stacked waveguide assemblies 1178, including the operation of the image input devices 1200, 1202, 1204, 1206, 1208, the light source 2040, and the light modulator 2030. In some embodiments, the controller 1210 is part of the local data processing module 70. The controller 1210 includes programming (e.g., instructions in a non-transient medium) that coordinates the timing and provision of image information to the waveguides 1182, 1184, 1186, 1188, 1190, 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. The controller 1210 may be part of the processing module 70 or 72 (FIG. 1) in some embodiments.

[0065] Continuing with reference to FIG. 6, the waveguides 1182, 1184, 1186, 1188, 1190 may be configured to propagate light within each individual waveguide by total internal reflection (TIR). Each of the waveguides 1182, 1184, 1186, 1188, 1190 may be planar or have another shape (e.g., curved) with major top and bottom surfaces and edges extending between their major top and bottom surfaces. In the illustrated configuration, the waveguides 1182, 1184, 1186, 1188, 1190 may each include an external coupling optical element 1282, 1284, 1286, 1288, 1290 configured to extract light from the waveguide by redirecting light propagating within each individual waveguide out of the waveguide and outputting image information to the eye 4. The extracted light may also be referred to as out-coupled light, and the out-coupling optical element may also be referred to as a light extraction optical element. The extracted light beam is output by the waveguide at the location where the light propagating in the waveguide strikes the light extraction optical element. The out-coupling optical element 1282, 1284, 1286, 1288, 1290 may be a grating, for example, including diffractive optical features as further discussed herein. Although shown disposed on the bottom major surface of the waveguides 1182, 1184, 1186, 1188, 1190 for ease of explanation and clarity of the drawings, in some embodiments, the out-coupling optical element 1282, 1284, 1286, 1288, 1290 may be disposed on the top and / or bottom major surfaces and / or directly within the volume of the waveguides 1182, 1184, 1186, 1188, 1190, as further discussed herein. In some embodiments, the outcoupling optical elements 1282, 1284, 1286, 1288, 1290 may be formed in a layer of material that is attached to a transparent substrate and forms the waveguides 1182, 1184, 1186, 1188, 1190. In some other embodiments, the waveguides 1182, 1184, 1186, 1188, 1190 may be monolithic pieces of material and the outcoupling optical elements 1282, 1284, 1286, 1288, 1290 may be formed on and / or within the material pieces.

[0066] With continued reference to FIG. 6, as discussed herein, each waveguide 1182, 1184, 1186, 1188, 1190 is configured to output light and form an image corresponding to a particular depth plane. For example, the waveguide 1182 closest to the eye may be configured to deliver collimated light (injected into such waveguide 1182) to the eye 4. The collimated light may represent an optical infinity focal plane. The next upper waveguide 1184 may be configured to send collimated light that passes through a first lens 1192 (e.g., a negative lens) before it can reach the eye 4. Such a first lens 1350 may be configured to generate a slight convex wavefront curvature such that the eye / brain interprets the light originating from the next upper waveguide 1184 as originating from a first focal plane closer inward from optical infinity toward the eye 4. Similarly, the third upper waveguide 1186 passes its output light through both the first 1192 and second 1194 lenses before reaching the eye 4. The combined refractive power of the first 1192 and second 1194 lenses may be configured to produce another incremental amount of wavefront curvature such that the eye / brain interprets the light emerging from the third upper waveguide 1186 as emerging from a second focal plane that is closer inward towards the person from optical infinity where the light from the next waveguide 184 was.

[0067] The other waveguide layers 1188, 1190 and lenses 1196, 1198 are similarly configured, with the highest waveguide 1190 in the stack sending its output through all of the lenses between it and the eye for an aggregate focal force that represents the focal plane closest to the person. To compensate for the stack of lenses 1198, 1196, 1194, 1192 when viewing / interpreting light originating from the world 1144 on the other side of the stacked waveguide assembly 1178, a compensating lens layer 1180 may be placed on top of the stack to compensate for the aggregate force of the lens stacks 1198, 1196, 1194, 1192 below. Such a configuration provides as many perceived focal planes as there are waveguide / lens pairs available. Both the outcoupling optical elements of the waveguides and the focusing sides of the lenses may be static (i.e., not dynamic or electroactive). In some alternative embodiments, one or both may be dynamic using electroactive features.

[0068] In some embodiments, two or more of the waveguides 1182, 1184, 1186, 1188, 1190 may have the same associated depth plane. For example, multiple waveguides 1182, 1184, 1186, 1188, 1190 may be configured to output images set at the same depth plane, or multiple subsets of the waveguides 1182, 1184, 1186, 1188, 1190 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.

[0069] Continuing with reference to FIG. 6, the out-coupling optical elements 1282, 1284, 1286, 1288, 1290 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 the waveguide. As a result, waveguides with different associated depth planes may have different configurations of out-coupling optical elements 1282, 1284, 1286, 1288, 1290 that output light with different amounts of divergence depending on the associated depth plane. In some embodiments, the light extraction optical elements 1282, 1284, 1286, 1288, 1290 may be volume or surface features that may be configured to output light at specific angles. For example, the light extraction optical elements 1282, 1284, 1286, 1288, 1290 may be volume holograms, surface holograms, and / or diffraction gratings. In some embodiments, features 1198, 1196, 1194, 1192 may not be lenses. Rather, they may simply be spacers (e.g., cladding layers and / or structures for forming air gaps).

[0070] In some embodiments, the outcoupling optical elements 1282, 1284, 1286, 1288, 1290 are diffractive features that form a diffraction pattern or "diffractive optical elements" (also referred to herein as "DOEs"). Preferably, the DOEs have a sufficiently low diffraction efficiency (ratio of diffracted beam intensity to incident beam intensity) such that only a portion of the light of the beam is deflected toward the eye 4 with each intersection point of the DOE, while the remainder continues to travel through the waveguide via total internal reflection. The light carrying the image information is thus split into several related exit beams that exit the waveguide at various locations, resulting in a very uniform pattern of exit emission toward the eye 4 for this particular collimated beam bouncing within the waveguide.

[0071] 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).

[0072] In some embodiments, a camera assembly 500 (e.g., a digital camera, including visible and infrared light cameras) is provided to capture images of the eye 4 and / or tissue surrounding the eye 4, 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 500 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 500 may be mounted on a frame 64 (FIG. 2) and may be in electrical communication with a processing module 70 and / or 72, which may process image information from the camera assembly 500 and make various determinations regarding the physiological state of the user, for example, as discussed herein. It should be understood that information regarding the physiological state of the user may be used to determine the behavior or emotional state of the user. Examples of such information include the user's movements and / or the user's facial expressions. The user's behavior or emotional state may then be triangulated with the collected environmental and / or virtual content data to determine relationships between the behavior or emotional state, the physiological state, and the environmental or virtual content data. In some embodiments, one camera assembly 500 may be utilized per eye to monitor each eye separately.

[0073] 7, an example of an output beam output by a waveguide is shown. Although one waveguide is shown, it should be understood that other waveguides in the waveguide assembly 1178 (FIG. 6) may function similarly and that the waveguide assembly 1178 includes multiple waveguides. Light 400 is launched into the waveguide 1182 at the input surface 1382 of the waveguide 1182 and propagates within the waveguide 1182 by TIR. At the point where the light 400 impinges on the DOE 1282, a portion of the light exits the waveguide as an output beam 402. The output beam 402 is shown as approximately parallel, but may be redirected to propagate to the eye 4 at an angle (e.g., divergent output beam formation) as discussed herein and depending on the depth plane associated with the waveguide 1182. 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 4. Other waveguides or other sets of outcoupling optics may output an exit beam pattern that is more divergent, which would require the eye 4 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 4 than optical infinity.

[0074] In some embodiments, a full color image may be formed at each depth plane by overlaying an image on each of the primary colors, for example, three or more primary colors. FIG. 8 illustrates an example of a stacked waveguide assembly, where each depth plane includes an image formed using multiple different primary colors. The illustrated embodiment shows depth planes 14a-14f, but more or less depths are also contemplated. Each depth plane may have three or more primary color images associated with a first image of a first color G, a second image of a second color R, and a third image of a third color B. The different depth planes are indicated in the figure by different numbers for diopters (dpt) following the letters G, R, and B. By way of example only, the numbers following each of these letters indicate the diopters (1 / m), i.e., the inverse distance of the depth plane from the viewer, and each box in the figure represents an individual primary color image. In some embodiments, the exact location of the depth planes for the different primary colors may be varied to account for differences in the eye's focusing of different wavelengths of light. For example, different primary color images for a given depth plane may be placed on depth planes corresponding to different distances from the user. Such an arrangement may increase visual acuity and user comfort and / or reduce chromatic aberration.

[0075] In some embodiments, the light of 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 figure containing the letter G, R, or B may be understood to represent an individual waveguide, and three waveguides may be provided per depth plane, with three primary color images provided per depth plane. The waveguides associated with each depth plane are shown adjacent to each other in this drawing for ease of illustration, but 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.

[0076] 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 also be used in addition to or replace one or more of the red, green, or blue colors. In some embodiments, features 198, 196, 194, and 192 may be active or passive optical filters configured to selectively block light from the surrounding environment to the viewer's eye.

[0077] It should be appreciated that references throughout this disclosure to a given color of light will be understood to encompass one or more wavelengths of light 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.

[0078] In some embodiments, the light source 2040 (FIG. 6) may be configured to emit light at one or more wavelengths outside the range of visual perception of a viewer, e.g., infrared and / or ultraviolet wavelengths. Additionally, the waveguide in-coupling, out-coupling, and other light redirecting structures of the display 1000 may be configured to direct and emit this light from the display toward the user's eye 4, e.g., for imaging and / or user stimulation applications.

[0079] 9A, in some embodiments, light impinging on a waveguide may need to be redirected to in-couple the light into the waveguide. An in-coupling optical element may be used to redirect and in-couple the light into its corresponding waveguide. FIG. 9A illustrates a cross-sectional side view of an example of a plurality or set 1200 of stacked waveguides, each including an in-coupling optical element. Each of the waveguides may be configured to output light of one or more different wavelengths or one or more different wavelength ranges. The stack 1200 may correspond to the stack 1178 (FIG. 6), and the illustrated waveguides of the stack 1200 may correspond to a portion of the plurality of waveguides 1182, 1184, 1186, 1188, 1190, but it should be understood that light from one or more of the image input devices 1200, 1202, 1204, 1206, 1208 is input into the waveguide from a position that requires the light to be redirected for in-coupling.

[0080] The illustrated set 1200 of stacked waveguides includes waveguides 1210, 1220, and 1230. Each waveguide includes an associated incoupling optical element (which may also be referred to as the light input area on the waveguide), e.g., incoupling optical element 1212 is disposed on a major surface (e.g., the top major surface) of waveguide 1210, incoupling optical element 1224 is disposed on a major surface (e.g., the top major surface) of waveguide 1220, and incoupling optical element 1232 is disposed on a major surface (e.g., the top major surface) of waveguide 1230. In some embodiments, one or more of the incoupling optical elements 1212, 1222, 1232 may be disposed on a bottom major surface of the respective waveguides 1210, 1220, 1230 (particularly, one or more of the incoupling optical elements are reflective polarizing optical elements). As shown, the incoupling optical elements 1212, 1222, 1232 may be disposed on the upper major surface of their respective waveguides 1210, 1220, 1230 (or on top of the next lower waveguide), and in particular, the incoupling optical elements are transmissive turning optical elements. In some embodiments, the incoupling optical elements 1212, 1222, 1232 may be disposed within the body of the respective waveguides 1210, 1220, 1230. In some embodiments, as discussed herein, the incoupling optical elements 1212, 1222, 1232 are wavelength selective such that they selectively redirect one or more wavelengths of light while transmitting other wavelengths of light. Although illustrated on one side or corner of the respective waveguides 1210, 1220, 1230, it should be understood that the internal coupling optical elements 1212, 1222, 1232 may be disposed within other areas of the respective waveguides 1210, 1220, 1230 in some embodiments.

[0081] As shown, the in-coupling optical elements 1212, 1222, 1232 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 1212, 1222, 1232 may be configured to receive light from different image input devices 1200, 1202, 1204, 1206, and 1208 as shown in FIG. 6, and may be separated (e.g., laterally spaced) from the other in-coupling optical elements 1212, 1222, 1232 so as to not substantially receive light from others of the in-coupling optical elements 1212, 1222, 1232.

[0082] Each waveguide also includes an associated optically dispersive element, for example, optically dispersive element 1214 is disposed on a major surface (e.g., the top major surface) of waveguide 1210, optically dispersive element 1224 is disposed on a major surface (e.g., the top major surface) of waveguide 1220, and optically dispersive element 1234 is disposed on a major surface (e.g., the top major surface) of waveguide 1230. In some other embodiments, optically dispersive elements 1214, 1224, 1234 may be disposed on the bottom major surfaces of the associated waveguides 1210, 1220, 1230, respectively. In some other embodiments, the optically dispersive elements 1214, 1224, 1234 may be disposed on both the top and bottom major surfaces of the associated waveguides 1210, 1220, 1230, respectively, or the optically dispersive elements 1214, 1224, 1234 may be disposed on different ones of the top and bottom major surfaces in different associated waveguides 210, 1220, 1230, respectively.

[0083] The waveguides 1210, 1220, 1230 may be spaced apart and separated by, for example, gas, liquid, and / or solid layers of material. For example, as shown, layer 1218a may separate waveguides 1210 and 1220, and layer 1218b may separate waveguides 1220 and 1230. In some embodiments, layers 1218a and 1218b are formed from a low index material (i.e., a material having a lower index of refraction than the material forming the immediate neighbors of waveguides 1210, 1220, 1230). Preferably, the index of refraction of the material forming layers 1218a, 1218b is 0.05 or more, or 0.10 or less than the index of refraction of the material forming waveguides 1210, 1220, 1230. Advantageously, the lower refractive index layers 1218a, 1218b may act as cladding layers to promote total internal reflection (TIR) ​​of light through the waveguides 1210, 1220, 1230 (e.g., TIR between the top and bottom major surfaces of each waveguide). In some embodiments, the layers 1218a, 1218b are formed from air. Although not shown, it should be understood that the top and bottom of the illustrated set of waveguides 1200 may include immediate cladding layers.

[0084] Preferably, for ease of manufacturing and other considerations, the materials forming the waveguides 1210, 1220, 1230 are similar or the same, and the materials forming the layers 1218a, 1218b are similar or the same. In some embodiments, the materials forming the waveguides 1210, 1220, 1230 may differ between one or more of the waveguides, and / or the materials forming the layers 1218a, 1218b may differ while still maintaining the various refractive index relationships discussed above.

[0085] 9A, light rays 1240, 1242, 1244 are incident on the set of waveguides 1200. It should be understood that light rays 1240, 1242, 1244 may be injected into the waveguides 1210, 1220, 1230 by one or more image injection devices 1200, 1202, 1204, 1206, 1208 (FIG. 6).

[0086] In some embodiments, the light beams 1240, 1242, 1244 have different properties, e.g., different wavelengths or different wavelength ranges, that may correspond to different colors. The internal coupling optical elements 1212, 1222, 1232 each deflect the incident light such that the light propagates through a respective one of the waveguides 1210, 1220, 1230 by TIR.

[0087] For example, incoupling optical element 1212 may be configured to deflect light ray 1240 having a first wavelength or range of wavelengths. Similarly, transmitted light ray 1242 impinges on and is deflected by incoupling optical element 1222, which is configured to selectively deflect light of a second wavelength or range of wavelengths. Similarly, light ray 1244 is deflected by incoupling optical element 1232, which is configured to selectively deflect light of a third wavelength or range of wavelengths.

[0088] 9A, the deflected light rays 1240, 1242, 1244 are deflected to propagate through the corresponding waveguides 1210, 1220, 1230. That is, the in-coupling optical element 1212, 1222, 1232 of each waveguide deflects the light into its corresponding waveguide 1210, 1220, 1230 and in-couples the light into the corresponding waveguide. The light rays 1240, 1242, 1244 are deflected at an angle that causes the light to propagate through the respective waveguides 1210, 1220, 1230 by TIR. The light rays 1240, 1242, 1244 propagate through the respective waveguides 1210, 1220, 1230 by TIR until they strike the corresponding optical dispersive element 1214, 1224, 1234 of the waveguide.

[0089] 9B, a perspective view of the multiple stacked waveguide embodiment of FIG. 9A is illustrated. As previously described, the in-coupled light rays 1240, 1242, 1244 are deflected by the in-coupling optical elements 1212, 1222, 1232, respectively, and then propagate by TIR within the waveguides 1210, 1220, 1230, respectively. The light rays 1240, 1242, 1244 then impinge on the optically dispersive elements 1214, 1224, 1234, respectively. The optically dispersive elements 1214, 1224, 1234 deflect the light rays 1240, 1242, 1244 to propagate towards the out-coupling optical elements 1250, 1252, 1254, respectively.

[0090] In some embodiments, the optically dispersive elements 1214, 1224, 1234 are orthogonal pupil expanders (OPEs). In some embodiments, the OPEs both deflect or disperse the light into the out-coupling optical elements 1250, 1252, 1254 and also increase the beam or spot size of this light as it propagates into the out-coupling optical elements. In some embodiments, for example, if the beam size is already the desired size, the optically dispersive elements 1214, 1224, 1234 may be omitted and the in-coupling optical elements 1212, 1222, 1232 may be configured to deflect the light directly into the out-coupling optical elements 1250, 1252, 1254. For example, referring to FIG. 9A, the optically dispersive elements 1214, 1224, 1234 may be replaced with the out-coupling optical elements 1250, 1252, 1254, respectively. In some embodiments, the outcoupling optical elements 1250, 1252, 1254 are exit pupils (EP) or exit pupil expanders (EPE) that direct light into the viewer's eye 4 (FIG. 7).

[0091] Thus, referring to Figures 9A and 9B, in some embodiments, a set of waveguides 1200 includes, for each primary color, a waveguide 1210, 1220, 1230, an in-coupling optical element 1212, 1222, 1232, an optically dispersive element (e.g., OPE) 1214, 1224, 1234, and an out-coupling optical element (e.g., EP) 1250, 1252, 1254. The waveguides 1210, 1220, 1230 may be stacked with an air gap / cladding layer between each one. The in-coupling optical element 1212, 1222, 1232 redirects or deflects the incoming light into that waveguide (different in-coupling optical elements receive different wavelengths of light). The light then propagates at an angle that will result in TIR within the individual waveguides 1210, 1220, 1230. In the example shown, light ray 1240 (e.g., blue light) is deflected by the first in-coupling optical element 1212 in the manner previously described, then continues bouncing back down the waveguide, interacting with the optically dispersive element (e.g., OPE) 1214 and then the out-coupling optical element (e.g., EP) 1250. Light rays 1242 and 1244 (e.g., green and red light, respectively) pass through the waveguide 1210, and light ray 1242 will impinge on and be deflected by the in-coupling optical element 1222. Light ray 1242 then continues through the TIR, bouncing back down the waveguide 1220, its optically dispersive element (e.g., OPE) 1224 and then the out-coupling optical element (e.g., EP) 1252. Finally, light ray 1244 (e.g., red light) passes through waveguide 1220 and impinges on light in-coupling optical element 1232 of waveguide 1230. Light in-coupling optical element 1232 deflects light ray 1244 such that it propagates by TIR to light dispersive element (e.g., OPE) 1234 and then by TIR to out-coupling optical element (e.g., EP) 1254. Out-coupling optical element 1254 then finally out-couples light ray 1244 to a viewer, who also receives light out-coupled from the other waveguides 1210, 1220.

[0092] 9C illustrates a top-down plan view of the multiple stacked waveguide embodiment of FIGS. 9A and 9B. As shown, the waveguides 1210, 1220, 1230 may be vertically aligned with each waveguide's associated optical dispersion elements 1214, 1224, 1234 and associated external coupling optical elements 1250, 1252, 1254. However, as discussed herein, the internal coupling optical elements 1212, 1222, 1232 are not vertically aligned. Rather, the internal 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 that include non-overlapping, spatially separated incoupling optical elements may be referred to as shifted pupil systems, and the incoupling optical elements in these arrays may correspond to sub-pupils. (Liquid crystal based Bragg reflective or diffractive structures)

[0093] 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 some structural order. Different types of liquid crystals include thermotropic, lyotropic, and polymeric liquid crystals. The thermotropic liquid crystals disclosed herein can be implemented into a variety of physical states, e.g., phases, including nematic states / phases, smectic states / phases, chiral nematic states / phases, or chiral smectic states / phases.

[0094] 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 approximately parallel. Thus, the organic molecules can flow freely with their center of mass positions randomly distributed as in a liquid, while still maintaining their long-range directional order. In some implementations, liquid crystals in the nematic phase can be uniaxial; that is, the liquid crystal has one axis that is longer and preferred, and the other two are approximately equal. In other implementations, the liquid crystal can be biaxial; that is, in addition to the orientation of its long axis, the liquid crystal can also be oriented along a secondary axis.

[0095] 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 along a direction 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 a direction approximately normal to the plane of the layer.

[0096] As used herein and throughout this disclosure, nematic liquid crystals consist of rod-like 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, may be used to describe the direction of preferred orientation of the liquid crystal molecules.

[0097] As used herein, throughout this disclosure, tilt angle or pre-tilt angle Φ may refer to the angle measured in a plane perpendicular to the major surface (xy plane) of the liquid crystal layer or substrate, e.g., the xz plane, and measured between the alignment direction and a direction parallel to the major surface or to the major surface, e.g., the x-direction.

[0098] As used herein and throughout this disclosure, the azimuthal angle or rotation angle φ is used to describe the angle of rotation about an axis normal to the layer normal direction or to the major surfaces of the liquid crystal layer, which is measured in a plane parallel to the major surfaces of the liquid crystal layer or substrate, e.g., the xy plane, and is measured between an alignment direction, e.g., the height direction or director direction, and a direction parallel to the major surfaces, e.g., the y-direction.

[0099] It should be understood that, as used herein and throughout this disclosure, when alignment angles, such as rotation angle φ or pre-tilt angle Φ, are referred to as being substantially the same between different regions, the average alignment angles 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.

[0100] As used herein and throughout the specification, a duty cycle may refer, for example, to the ratio between a first lateral dimension of a first region having liquid crystal molecules aligned in a first alignment direction and the grating period of a zone having the first region. Where applicable, the first region corresponds to a region where the alignment of the liquid crystal does not vary between different zones.

[0101] As described herein, liquid crystals in the nematic or smectic state can also exhibit chirality. Such liquid crystals are said to be in the chiral or cholesteric phase. In the chiral or cholesteric phase, the liquid crystal can exhibit a twist of the molecules perpendicular to the director, with the molecular axes parallel to the director. The finite twist angle between adjacent molecules results from their asymmetric packing, which leads to a longer-range chiral order.

[0102] As described herein, liquid crystals in a chiral smectic state or phase can be configured such that the liquid crystal molecules have positional order in a layered structure, with the molecules tilted by a finite angle relative to the layer normal. In addition, the chirality can induce a continuous azimuthal twisting of the liquid crystal molecules from one liquid crystal layer to the next in the layer normal direction, perpendicular to the layer normal, thereby producing a helical twisting of the molecular axes along the layer normal.

[0103] As described herein, throughout this disclosure, a chiral structure refers to a plurality of liquid crystal molecules in a cholesteric phase that extend perpendicular to a director, such as a layer depth direction, and are continuously rotated or twisted in a rotational direction, such as clockwise or counterclockwise. In one aspect, the director of the liquid crystal molecules in the chiral structure can be characterized as a helix having a helical pitch.

[0104] As described herein, liquid crystals in the cholesteric phase exhibiting chirality can be described as having a chiral pitch or helical pitch (p), which corresponds to the length in the layer depth direction that corresponds to the net rotation angle of the liquid crystal molecules in the chiral structure by one full turn in the first rotation direction. In other words, the helical pitch refers to the distance over which the liquid crystal molecules undergo a full 360° twist. The helical pitch (p) can change, for example, when the temperature is altered or when other molecules are added to the liquid crystal host (an achiral liquid host material can form a chiral phase when doped with a chiral material), allowing the helical pitch (p) of a given material to be tailored accordingly. In some liquid crystal systems, the helical pitch is in the same order as the wavelength of visible light. As described herein, liquid crystals that exhibit chirality may also be described as having a twist angle or rotation angle (φ), which may refer, for example, to the relative azimuthal rotation between successive liquid crystal molecules in the layer normal direction, and as having a net twist angle or net rotation angle, 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 length of the chiral structure or the thickness of the liquid crystal layer.

[0105] According to various embodiments described herein, liquid crystals, having various states or phases as described above, can be configured to provide various desirable material properties, including, for example, birefringence, optical anisotropy, and manufacturability using thin film processes. For example, by varying the surface conditions of the liquid crystal layer and / or mixing different liquid crystal materials, grating structures can be fabricated that exhibit spatially variable diffractive properties, for example, gradient diffraction efficiency.

[0106] As described herein, "polymerizable liquid crystal" may refer to a liquid crystal material that can be polymerized, e.g., photopolymerized in situ, and may also be described herein as a reactive mesogen (RM).

[0107] It should be understood that the liquid crystal molecules may be polymerizable in some embodiments and, once polymerized, may form extensive networks with other liquid crystal molecules. For example, the 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. For ease of explanation, the term "liquid crystal molecules" is used herein to refer to both the liquid crystal molecules before polymerization and the liquid crystal domains formed by these molecules after polymerization.

[0108] According to certain embodiments described herein, photopolymerizable liquid crystal materials can be configured to form Bragg reflective or diffractive structures, e.g., diffraction gratings, and their material properties, including birefringence, chirality, and ease of multiple coatings, can be exploited to create diffraction gratings with different material properties, e.g., birefringence, chirality, and thickness, which can result in different optical properties, e.g., diffraction efficiency, wavelength selectivity, and off-axis diffraction angle selectivity, to name a few.

[0109] As described herein, it should be understood that a "transmissive" or "transparent" structure, e.g., a transparent substrate, may allow at least a portion, e.g., at least 20, 30, or 50%, of incident light to pass therethrough. Thus, the transparent substrate may be a glass, sapphire, or polymer substrate in some embodiments. In contrast, a "reflective" structure, e.g., a reflective substrate, may reflect and have reflected therefrom at least a portion, e.g., at least 20, 30, 50, 70, 90%, or more, of incident light.

[0110] The optical properties of the grating are determined by the physical structure of the grating (e.g., periodicity, depth, and duty cycle) and the material properties of the grating (e.g., refractive index, absorptivity, and birefringence). When liquid crystals are used, the optical properties of the grating can be controlled, for example, by controlling the molecular orientation or distribution of the liquid crystal material. For example, by varying the molecular orientation or distribution of the liquid crystal material across the grating area, the grating can exhibit graded diffraction efficiency. Such an approach is described below with reference to the figures. (Cholesteric Liquid Crystal Grating (CLCG))

[0111] As described above with reference to Figures 6 and 7, a display system according to various embodiments described herein may include optical elements, such as an in-coupling optical element, an out-coupling optical element, and a light dispersive element, which may include a diffraction grating. For example, as described above with reference to Figure 7, light 400 launched into the waveguide 1182 at the input surface 1382 of the waveguide 1182 propagates within the waveguide 1182 by total internal reflection (TIR). At the point where the light 400 impinges on the out-coupling optical element 1282, a portion of the light exits the waveguide as an exit beam 402. In some implementations, any of the optical elements 1182, 1282, or 1382 may be configured as a diffraction grating.

[0112] Efficiently in-coupling light into (or out-coupling light from) the waveguide 1182 can be a challenge in designing a waveguide-based see-through display, for example, for virtual / augmented / mixed reality display applications. For these and other applications, it is desirable to have a diffraction grating formed from a material whose structure can be configured to optimize various optical properties, including diffractive properties. Desirable diffractive properties include, among other properties, polarization selectivity, spectral selectivity, angular selectivity, high spectral bandwidth, and high diffraction efficiency. To address these and other needs, in various embodiments disclosed herein, the optical element 1282 is configured as a cholesteric liquid crystal grating (CLCG). As described below, CLCGs according to various embodiments can be configured to optimize, among other properties, polarization selectivity, bandwidth, phase profile, spatial variation of diffractive properties, spectral selectivity, and high diffraction efficiency.

[0113] In the following, various embodiments of cholesteric liquid crystals (CLCs) configured as reflective liquid crystal gratings are described, which comprise CLCs optimized for various optical properties. Generally, a grating has a periodic structure that splits and diffracts light into several beams traveling in different directions. The direction of these beams depends, among other things, on the period of the periodic structure and the wavelength of the light. For certain applications, such as the outcoupling optical element 1282 (FIGS. 6, 7), various material properties of the CLCs can be optimized, as described below, to optimize certain optical properties, e.g., diffraction efficiency.

[0114] As explained above, the liquid crystal molecules of a cholesteric liquid crystal (CLC) layer in the chiral (nematic) or cholesteric phase are characterized by a plurality of liquid crystal molecules arranged to have a continuous azimuthal twist of the director as a function of film position in the normal or depth direction of the liquid crystal layer. Liquid crystal molecules arranged to have a continuous azimuthal twist as explained herein are collectively referred to herein as a chiral structure. As explained herein, the angle of azimuthal twist or rotation (φ) is described as the angle between the directors of the liquid crystal molecules with respect to a direction parallel to the layer normal as explained above. The spatially variable directors of the liquid crystal molecules in the chiral structure may be described as forming a helical pattern, and the helical pitch (p) is the angle between the directors 360° apart as explained above. o The grating period is defined as the distance rotated (e.g., in the layer normal direction of the liquid crystal layer). As described herein, a CLC layer configured as a diffraction grating has a lateral dimension in which the molecular structure of the liquid crystal repeats periodically in a lateral direction normal to the depth direction. This periodicity in the lateral direction is referred to as the grating period (∧).

[0115] According to various embodiments described herein, a diffraction grating comprises a cholesteric liquid crystal (CLC) layer comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction and rotated continuously in a first rotation direction by at least a helical pitch. The helical pitch is a length in the layer depth direction that corresponds to a net rotation angle of the liquid crystal molecules of the chiral structures through one full rotation in the first rotation direction. The alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction.

[0116] 10 illustrates a cross-sectional side view of a cholesteric liquid crystal (CLC) layer 1004 comprising a plurality of uniform chiral structures, according to an embodiment. The CLC 1004 comprises a CLC layer 1008 comprising liquid crystal molecules arranged as a plurality of chiral structures 1012-1, 1012-2, ... 1012-i, where each chiral structure comprises a plurality of liquid crystal molecules, where i is any suitable integer greater than 2. For example, the chiral structure 1012-1 comprises a plurality of liquid crystal molecules 1012-1-1, 1012-1-2, ... 1012-1-j, where j is any suitable integer greater than 2, arranged to extend in a layer normal direction, e.g., in the illustrated embodiment, the z-direction. The liquid crystal molecules of each chiral structure are rotated successively in a first rotation direction. In the illustrated embodiment, the liquid crystal molecules are continuously rotated in a clockwise direction when viewed in the positive direction of the z-axis (i.e., the direction of the axis arrow) or the propagation direction of the incident light beams 1016-L, 1016-R. For example, in the illustrated embodiment, the liquid crystal molecules 1012-1-1, 1012-1-2, ... 1012-1-j of the chiral structure 1012-1 are continuously rotated, for example, by rotation angles φ1, φ2, ... φj, relative to the positive x-direction. In the illustrated embodiment, for illustrative purposes, the liquid crystal molecules of each of the chiral structures 1012-1, 1012-2, ... 1012-i between opposite ends in the z-direction are rotated such that the net rotation angle of the liquid crystal molecules is approximately 360°. o As a result, the chiral structures 1012-1, 1012-2, ... 1012-i have a length L in the z-direction that is the same as the helical pitch p. However, embodiments are not so limited and the chiral structures 1012-1, 1012-2, ... 1012-i may be rotated any number of full rotations, greater than or less than one, such as 360 o The chiral structure can have any suitable net rotation angle, lower or higher, and / or any suitable length L in the z-direction, shorter or longer than the helical pitch p. For example, in various embodiments described herein, the number of complete turns of the chiral structure can be 1-3, 2-4, 3-5, 4-6, 5-7, 6-8, 7-9, or 8-10, among other numbers.

[0117] 10, the successive rotation angles φ, φ, ... φ between adjacent liquid crystal molecules in the z-direction can be the same according to some embodiments, or different according to some other embodiments. By way of example, in the illustrated embodiment, the length of the chiral structures 1012-1, 1012-2, ... 1012-i is about p, and the net rotation angle is about 360° between adjacent liquid crystal molecules in the z-direction. o / (m-1) so that it is rotated 360 o where m is the number of liquid crystal molecules in the chiral structure. For example, for illustrative purposes, each of the chiral structures 1012-1, 1012-2, ... 1012-i has adjacent liquid crystal molecules in the z-direction spaced apart from each other by approximately 30 degrees. o As rotated, it has 13 liquid crystal molecules. Of course, the chiral structures in various embodiments can have any suitable number of liquid crystal molecules.

[0118] 10, adjacent chiral structures in a lateral direction, e.g., in the x-direction, have liquid crystal molecules that are similarly aligned. In the illustrated embodiment, the chiral structures 1012-1, 1012-2, ... 1012-i are similarly configured such that liquid crystal molecules of different chiral structures at approximately the same depth, e.g., the liquid crystal molecules closest to the light incidence surface 1004S, have approximately the same rotation angle at the same depth, and the successive rotation angles of successive liquid crystal molecules, and the net rotation angle of the liquid crystal molecules of each chiral structure.

[0119] In the following, the CLC layer 1004 illustrated in FIG. 10 will be further described in operation according to an embodiment. As described, the CLC layer 1004 comprises chiral structures 1012-1, 1012-2, ... 1012-i with uniform alignment in a lateral direction, e.g., in the x-direction. In operation, when incident light having a combination of a light beam with left-handed circular polarization and a light beam with right-handed circular polarization is incident on the surface 1004S of the CLC layer 1008 by Bragg reflection or diffraction, the light with one of the circular polarization handedness is reflected by the CLC layer 1004, while the light with the opposite polarization handedness is transmitted through the CLC layer 1008 without substantial interference. As described herein, throughout this disclosure, handedness is defined as seen in the propagation direction. According to an embodiment, when the direction of polarization or handedness of polarization of the light beams 1016-L, 1016-R is matched to have the same rotational direction as the liquid crystal molecules of the chiral structures 1012-1, 1012-2, ... 1012-i, the incident light is reflected. As shown, incident on the surface 1004S is a light beam 1016-L with left-handed circular polarization and a light beam 1016-R with right-handed circular polarization. In the illustrated embodiment, the liquid crystal molecules of the chiral structures 1012-1, 1012-2, ... 1012-i are continuously rotated in a clockwise direction in the direction in which the incident light beams 1016-L, 1016-R travel, i.e. in the positive x-direction, which is the same rotational direction as the light beam 1016-R with right-handed circular polarization. As a result, the light beam 1016 -R having right-handed circular polarization is substantially reflected, while the light beam 1016 -L having left-handed circular polarization is substantially transmitted through the CLC layer 1004 .

[0120] Without being bound by any theory, under Bragg reflection or diffraction conditions, the wavelength (λ) of the incident light can be proportional to the representative or average refractive index (n) and helical pitch (p) of the CLC layer, and under some circumstances can be expressed as satisfying the following condition: [ka]

[0121] In addition, the bandwidth (Δλ) of the Bragg reflection or diffraction wavelength may be proportional to the birefringence Δn (e.g., the difference in refractive index between different polarizations of light) and the helical pitch (p) of the CLC layer 1004, and under some circumstances may be expressed as satisfying the following condition: Δλ=Δn p [2]

[0122] In various embodiments described herein, the bandwidth Δλ is about 60 nm, about 80 nm, or about 100 nm.

[0123] According to various embodiments, the peak reflection intensity in the visible wavelength range, for example, from about 390 nm to about 700 nm, or in the near infrared wavelength range, for example, from about 700 nm to about 2500 nm, can be greater than about 60%, about 70%, about 80%, or about 90%. Additionally, according to various embodiments, the full width at half maximum (FWHM) can be less than about 100 nm, less than about 70 nm, less than about 50 nm, or less than about 20 nm.

[0124] 11 illustrates a cross-sectional side view of a CLC grating (CLCG) 1150 having chiral structures that are arranged differently in the lateral direction, e.g., vary the twist angle in the lateral direction, according to an embodiment. Similar to the CLC layer 1004 of FIG. 10, the diffraction grating 1150 comprises a cholesteric liquid crystal (CLC) layer 1158 comprising liquid crystal molecules arranged as a plurality of chiral structures 1162-1, 1162-2, ... 1162-i, each chiral structure comprising a plurality of liquid crystal molecules. For example, the chiral structure 1162-1 comprises a plurality of liquid crystal molecules 1162-1-1, 1162-1-2, ... 1162-1-j arranged to extend in a layer normal direction, represented as the z-direction in the illustrated embodiment. The liquid crystal molecules of each chiral structure are rotated successively in a first rotation direction in a similar manner as described with respect to FIG. 10. In addition, various other parameters of the chiral structure, including the length L, the number of complete rotations made by the liquid crystal molecules, and the number of liquid crystal molecules per chiral structure, are similar to the chiral structure described above with respect to FIG.

[0125] However, in contrast to the illustrated embodiment of Fig. 10, in the illustrated embodiment of Fig. 11, adjacent chiral structures in a lateral direction, e.g., in the x-direction, have liquid crystal molecules that are arranged differently. The chiral structures 1162-1, 1162-2, ... 1162-i are arranged differently in the x-direction, such that liquid crystal molecules of different chiral structures at approximately the same depth have different rotation angles. For example, in the illustrated embodiment, the liquid crystal molecules 1162-1-1, 1162-2-1, ... 1162-i-1 that are closest to the entrance surface 1158S of the chiral structures 1162-1, 1162-2, ... 1162-i are successively rotated by rotation angles φ1, φ2, ... φi, respectively, in the positive x-axis direction, e.g., with respect to the positive x-direction. In the illustrated embodiment, the net rotation angle of the liquid crystal molecules 1162-1-1, 1162-2-1, ... 1162-i-1 closest to the entrance surface 1158S across the lateral length ∧, which corresponds to the period of the diffraction grating 1150, is approximately 180°. o In addition, liquid crystal molecules of different chiral structures that are disposed at approximately the same depth level are rotated by approximately the same rotation angle relative to the liquid crystal molecules closest to the respective surfaces.

[0126] 11, the successive rotation angles φ, φ, ... φ of liquid crystal molecules at the same depth level in the x-direction across the period ∧ can be the same according to some embodiments, or different according to some other embodiments. In the illustrated embodiment, for a period ∧, the net rotation angle is 360° as in the illustrated embodiment. o When the liquid crystal molecules are adjacent in the x-direction, o / (m-1), where m is the number of liquid crystal molecules that span the x-direction by the period ∧. For example, for illustrative purposes, adjacent liquid crystal molecules at the same vertical level in the x-direction are rotated approximately 30 degrees relative to each other. o As rotated, there are seven liquid crystal molecules spanning across the period . Of course, the chiral structures in various embodiments can have any suitable number of liquid crystal molecules.

[0127] It should be understood that for illustrative purposes, the CLC layer 1158 is shown as having only one period ∧. Of course, embodiments are not so limited and the CLC layer 1158 can have any suitable number of periods, as determined by the lateral dimension of the CLCG in the x-direction.

[0128] As illustrated by CLCG 1150, when a chiral structure in a lateral direction, e.g., the x-direction, is arranged differently, e.g., continuously rotated, the continuously rotated chiral structure induces a shift in the relative phase of the light reflected along the x-direction. This is illustrated with respect to graph 1170, which plots the phase change φ resulting from a chiral structure being continuously rotated by rotation angles φ1, φ2, ... φi in one period ∧ in the x-axis direction. Without being bound by any theory, the relative phase difference (ΔΦ) of the reflected light 1018 may be expressed as ΔΦ(x) = (2πx / Λ), where x is the position along the lateral direction and ∧ is the period. The bandwidth may be expressed as Δλ ≒ Δn·p.

[0129] Referring back to Figures 10-11 and equations [1] and [2], according to various embodiments, the Bragg reflected wavelength can be varied by varying the helical pitch p of the chiral structure. In various embodiments, without being bound by any theory, the helical pitch p can be varied by increasing or decreasing the helical twisting power (HTP), which refers to the ability of the chiral compound to induce a rotation or twist angle as explained above. The HTP can in turn be varied by changing the amount of chiral compound relative to the amount of non-chiral compound. In various embodiments, by chemically and / or mechanically mixing chiral compounds with non-chiral compounds, e.g., nematic compounds, the Bragg reflected wavelength, and therefore the color, can be varied based on the inverse relationship between the relative proportions of the chiral compounds and the helical pitch. In various embodiments disclosed herein, the ratio of the amount of chiral conjugate to the amount of non-chiral conjugate can be about 20:1, 10:1, 5:1, 4:1, 3:1, 2:1, 1:1, 1:2, 1:3, 1:4, 1:5, 1:10, or about 1:20 by weight.

[0130] In the discussion above with respect to Figures 10 and 11, the incident light beams 1016-L, 1016-R are illustrated as propagating parallel to the layer normal, e.g., in the z-direction. However, for various applications, e.g., as described above with respect to Figures 6 and 7, light propagating in the waveguide 1182, e.g., by total internal reflection (TIR), impinges on the outcoupling optical elements 1282, 1284, 1286, 1288, 1290, e.g., diffraction gratings, at some off-axis angle. Diffraction gratings as described herein can be configured to maximize bandwidth and diffraction efficiency for such configurations, as described below.

[0131] In the description above with respect to Figures 10 and 11, the liquid crystal molecules are illustrated as not being pretilted. However, the embodiments are not so limited, and the liquid crystal molecules may have a pretilt angle Φ, according to some embodiments, with respect to a direction parallel to the major surface of the CLCG, e.g., with respect to the xy plane, of about + / -60 degrees to about + / -90 degrees or about + / -65 degrees to about + / -85 degrees, e.g., about + / -75 degrees, about + / -35 degrees to about + / -65 degrees or about + / -40 degrees to about + / -60 degrees, e.g., about + / -50 degrees, about + / -10 degrees to about + / -40 degrees or about + / -15 degrees to about + / -35 degrees, e.g., about + / -25 degrees. According to some other embodiments, the pretilt angle Φ may be about ±15 degrees or about ±10 degrees or about ±5, e.g., 0 degrees. (CLCG configured for high bandwidth reflection at off-axis angles of incidence)

[0132] 12 illustrates a cross-sectional side view of a CLC layer 1158 configured for high reflection bandwidth at off-axis angles of incidence, according to an embodiment. As described herein, an off-axis angle of incidence is an angle of incidence θ of an incident beam 1216 relative to the direction of the layer normal (e.g., in FIG. 12, the z-direction) that has a non-zero value and results in a Bragg-reflected beam 1220 at a reflection angle θ. inc In some circumstances, the reflection angle can be varied to a limited extent by varying λ / Λ. Without being limited by any theory, in some circumstances, the off-axis reflection can be explained based on the following relationship: n sin(θ) = λ / Λ + sin(θ) inc ) [3] In the formula, θ incwhere θ is the angle of incidence relative to the direction of the layer normal θ, θ is the angle of reflection relative to the direction of the layer normal, and n is the reflectivity of the medium through which the reflected beam propagates. When the CLC layer 1158 is illuminated with an incident beam 1216 at an off-axis angle, the reflection spectrum can be shifted towards shorter wavelengths. According to various embodiments disclosed herein, the ratio λ / Λ can have a value of 0.5-0.8, 0.6-0.9, 0.7-1.0, 0.8-1.1, 0.9-1.2, 1.0-1.6, 1.1-1.5, or 1.2-1.4.

[0133] Without being bound by any theory, the off-axis angle at which the CLC layer 1158 is configured to Bragg reflect efficiently may also depend on the helical pitch p of the chiral structure.

[0134] 13A and 13B illustrate cross-sectional side views of a CLC layer configured for reflection at off-axis incidence angles, according to an embodiment. Referring to FIG. 13A, a first cholesteric liquid crystal (CLC) layer 1358A comprises a first plurality of chiral structures having a first helical pitch (p1). The first CLC layer 1358A is configured such that a first incident light beam 1316A strikes an incident surface of the CLC layer 1358A at a first off-axis angle θ inc,1 1, which results in a first reflected light beam 1320A at a first reflection angle θ1. As shown, the CLC layer 1358A is further configured to have a first range 1324A of off-axis incidence angles, outside of which a relatively high diffraction efficiency may be obtained. The first range 1324A may correspond to a range of off-axis incidence angles outside of which the intensity of the first reflected light beam 1320A falls off, for example, by more than 1 / e. For example, the first range 1324A may be oriented at a first angle θ1, which results in a first reflected light beam 1320A at a first reflection angle θ1. inc,1 ±3°, θ inc,1 ±5°, θ inc,1 ±7°, θ inc,1 ±10°, or θ inc,1 It can have a value of ±20°.

[0135] Referring to Figure 13B, the second cholesteric liquid crystal (CLC) layer 1358B is different from the first CLC layer 1358A and has a second plurality of chiral structures having a second helical pitch (p2) different from the first helical pitch p1 of the first CLC layer 1358A in Figure 13A.

[0136] As shown, the second CLC layer 1358B is configured such that the second incident light beam 1316B is incident on the incident surface of the CLC layer 1358B at a first off-axis angle θ inc,1 A second off-axis angle θ inc,2 When directed at the CLC layer 1358B, a second reflected light beam 1320B is generated having a second reflection angle θ2 that is different from the first reflection angle θ1. As shown, the CLC layer 1358B is further configured to have a second range of off-axis angles 1324B similar to the first range 1324A described above with respect to FIG.

[0137] 13C illustrates a cross-sectional side view of a CLCG 1358 including multiple CLC layers having different helical pitches in a stacked configuration to Bragg reflect at multiple off-axis angles of incidence and high diffraction bandwidth, according to an embodiment. The CLCG 1358 includes CLC layers 1358A, 1358B, as described above with respect to FIGS. 13A and 13B, respectively, formed over one another, e.g., in a stacked configuration and / or in contact with one another. Various parameters of the multiple CLC layers 1358A, 1358B, including different helical pitches, can be modified or optimized such that the CLCG 1358 is configured for efficient reflection at multiple off-axis angles of incidence and high diffraction efficiency over a wider range of off-axis angles than can be obtained using only one CLC. For example, in the illustrated embodiment, p1 and p2 can be selected such that the resulting first and second ranges 1324A and 1324B at least partially overlap to provide high diffraction efficiency over a continuous wavelength range that includes the first and second ranges 1324A and 1324B. However, in other embodiments, p1 and p2 can be selected such that the first and second ranges 1324A and 1324B do not overlap.

[0138] In operation, the first and second CLC layers 1358A, 1358B are oriented at first and second off-axis angles θ inc,1 , θ inc,2 When the first and second incident light beams 1316A, 1316B in are directed toward an incident surface of the first CLC layer 1358A, they are formed across one another such that the first incident light beam 1316A is substantially reflected by the first CLC layer 1358A at a first reflection angle θ1, while the second incident light beam 1358B is substantially transmitted through the first CLC layer 1358A toward the incident surface of the second CLC layer 1358B and is substantially reflected by the second CLC layer 1358B at a second reflection angle θ2. Although not shown for clarity, it should be understood that the concepts described above can be extended to any suitable number of CLC layers.

[0139] As described herein, throughout this specification, a light beam that is "substantially transmitted" through a layer can refer to light that has at least 20%, 30%, 50%, 70%, or 90% of the incident light intensity remaining as the light exits the layer. Similarly, a light beam that is "substantially reflected" by a layer can refer to light that has at least 20, 30, 50%, 70%, or 90% of the incident light intensity remaining in the reflected light.

[0140] Still referring to FIG. 13C, in various embodiments, the liquid crystal molecules of the first and second CLC layers 1358A, 1358B can include different amounts of the same chiral compound such that the CLC layers 1358A, 1358B have different helical twisting powers (HTPs), as described above. For example, the second CLC layer 1358B can have a higher relative amount of the same chiral compound compared to the first CLC layer 1358A. In some embodiments, the pitch p can be inversely proportional to the proportion of the chiral compound to the total liquid crystal compound, including chiral and non-chiral compounds. However, the embodiments are not so limited and the first and second CLC layers 1358A, 1358B can have different chiral compounds.

[0141] Additionally, in various embodiments, the liquid crystal molecules of the first and second CLC layers 1358A, 1358B are oriented such that the CLC layers 1358A, 1358B have different ratios λ / Λ and λ / Λ, respectively, such that the CLC layers 1358A, 1358B are oriented at different incidence angles θ, e.g., according to equation [3]. inc,1 , θ inc,2 The chiral compounds may contain the same or different chiral compounds such that they can be configured for high diffraction efficiency.

[0142] Still referring to FIG. 13C, the first and second CLC layers 1358A, 1358B can be processed directly on top of each other, according to some embodiments. For example, the first CLC layer 1358A can be deposited on a matching layer that provides matching conditions for the first CLC layer 1358A, and then the second CLC layer 1358B can be deposited on the first CLC layer 1358B. Under these processing conditions, the surface of the first CLC layer 1358A can provide matching conditions for the second CLC layer 1358B. In some other embodiments, the CLC layers 1358A, 1358B can each be processed using a separate matching layer. For example, a first CLC layer 1358A can be formed on the first matching layer, a second matching layer can be formed on the first CLC layer 1358A, and a second CLC layer 1358B can be formed on the second matching layer. An isolation layer, e.g., a thin oxide layer, can be formed on the first CLC layer 1358A prior to forming the second matching layer and / or the second CLC layer 1358B, according to some embodiments. In still other embodiments, the two CLC layers 1358A, 1358B can be individually fabricated on different substrates and subsequently stacked. In various embodiments, an intermediate layer can be formed between the two CLC layers 1358A, 1358B, for example, to improve adhesion.

[0143] The concepts described above with respect to a CLCG having multiple CLC layers optimized for optimal diffraction efficiency at different off-axis angles can be extended to other alternative embodiments. In particular, in some embodiments, instead of forming multiple layers, a single CLC layer can be configured to have different regions optimized for optimal diffraction efficiency at different off-axis angles.

[0144] 14 illustrates a cross-sectional side view of a CLCG 1400 including a single CLC layer 1404 having vertical regions with different helical pitches along the depth direction to Bragg reflect in different vertical regions with high diffraction bandwidth at multiple off-axis incidence angles, according to an embodiment. The CLC layer 1404 has multiple vertical regions with different parameters, e.g., different helical pitches, optimized so that high diffraction efficiency can be obtained over a wider range of off-axis angles than can be obtained using only one CLC layer with a uniform pitch in the depth direction. In the illustrated embodiment, the single CLC layer 1404 includes multiple vertical regions 1404A, 1404B, 1404C, and 1404D, which can have different helical pitches p1, p2, p3, and p4, respectively. Similar to that described above with respect to FIG. 13C, the helical pitches p1, p2, p3, and p4 are determined by the angle of incidence θ incA , θ incB , θ incC , and θ incD , which are configured for optimal diffraction efficiency at the corresponding reflection angles θA, θB, and θ C , and θD can be selected to result in the reflected light beam at different vertical depths. Further, as described above with respect to FIG. 13C, the CLC layer 1404 is further configured to have a discrete range of off-axis angles at which relatively high diffraction efficiency can be obtained. Of course, although four vertical regions are illustrated for clarity, any suitable number of regions can be included within the CLC layer 1404. Additionally, the different variations described above with respect to the CLCG 1358 of FIG. 13C having multiple CLC layers may also be applicable to the CLCG 1400.

[0145] In the illustrated embodiment of FIG. 14, the values ​​of helical pitches p1, p2, p3, and p4 decrease with increasing depth from the incident surface 1404S such that a decrease in the gradient of helical pitch is created in the depth direction (negative z-direction). When the rate of decrease of helical pitch as a function of layer depth in the z-direction is uniform across the thickness of the CLC layer 1404, a graph 1408 representing a linear relationship between depth and helical pitch can be obtained. However, the embodiment is not so limited. By way of example, the helical pitches p1, p2, p3, and p4 can increase or decrease at any depth and can change at different rates as a function of layer depth according to some other embodiments.

[0146] A CLC layer 1404 with a gradient of helical pitch can be fabricated by varying, e.g., increasing or decreasing, the helical twisting power (HTP) of the liquid crystal molecules at different depths in the CLC layer. The HTP, in turn, can be spatially varied by changing the relative amount of chiral compounds. In various embodiments, by chemically and / or mechanically mixing chiral compounds with non-chiral compounds, e.g., nematic compounds, at different vertical depths, the helical pitch of vertical regions 1404A, 1404B, 1404C, and 1404D can be varied at different incidence angles θ, respectively, based on the inverse relationship between the relative proportions of chiral compounds and the helical pitch. incA , θ incB , θ incC , and θ incDFor example, a mixture of different chemical components (e.g., chiral diacrylate monomers and nematic / chiral monoacrylate monomers) that undergo polymerization processes at different reaction rates under UV irradiation can be used. Additionally or alternatively, the HTP can be spatially varied by changing the irradiation conditions, including the exposure intensity and / or exposure time of UV irradiation at different depths of the CLC layer. The HTP can also be spatially varied by varying pre / post treatments of the UV polymerization process, including heat treatments before, after, and / or during UV irradiation. For example, when a UV absorbing dye is added to the mixture, an intensity gradient of UV light at different depths of the CLC layer can be created. For example, due to the UV intensity gradient, polymerization near the surface can proceed faster compared to the bottom region of the CLC layer. For example, when the cholesteric component is a diacrylate, the probability of incorporation into the resulting polymer can be much higher, e.g., twice as high, than the probability of a nematic monoacrylate being incorpo- rated into the polymer. In some circumstances, the overall polymerization rate is controlled so that the depletion of the chiral diacrylate near the surface region of the CLC layer creates a diacrylate concentration gradient in the depth direction of the CLC layer. This in turn initiates the diffusion of diacrylate toward the surface region of the CLC layer. After full photopolymerization, the surface region of the CLC layer may contain more chiral material and therefore have a shorter helical pitch compared to the bottom region of the CLC layer, which contains a relatively larger amount of non-chiral compounds. In some other circumstances, heat treatment before / after or during UV irradiation is added to the polymerization process to control the helical pitch gradient. Thus, by controlling the ratio between two different liquid crystal monomers and / or the dose of UV irradiation at different depths, with or without heat treatment, a helical pitch gradient can be achieved along the depth direction of the CLC layer.

[0147] For some applications, it may be desirable to have certain optical properties of the grating, such as off-angle diffraction efficiency, refractive index, wavelength selectivity, polarization selectivity, and phase selectivity, among other parameters, to vary along a lateral direction orthogonal to the layer normal direction. Lateral variations are desired, for example, when the grating is stacked with a waveguide, as illustrated, for example, with respect to Figures 6 and 7 above, so that light propagates in a lateral direction. However, under such a configuration, the intensity of the light may attenuate as it propagates within the waveguide (e.g., 1182 in Figure 7). Such a configuration may also be desirable, for example, to intentionally distort the light intensity across the grating (e.g., 1282 in Figure 7) to match the spatial and / or angular variations in sensing efficiency associated with the human eye and maximize the user experience. Thus, there is a need for optical elements, e.g., gratings, with spatially variable optical properties.

[0148] 15 illustrates a cross-sectional side view of a CLCG including a CLC layer having lateral regions with different helical pitches along the lateral direction to spatially vary Bragg reflection, according to an embodiment. The CLC layer 1424 has multiple lateral regions with different liquid crystal material parameters, e.g., helical pitches, such that laterally variable properties, e.g., laterally variable off-axis incidence angles for Bragg reflection, can be obtained. In the illustrated embodiment, the CLC layer 1424 includes multiple lateral regions 1424A, 1424B, and 1424C, each with a period ∧ and with individual helical pitches p1, p2, and p3. The helical pitches p1, p2, and p3 are determined so that multiple vertical regions 1424A, 1424B, and 1424C, each with different off-axis incidence angles θ incA , θ incB , and θ incC , which are configured for optimal diffraction efficiency at the corresponding reflection angles θ A , θ B , and θ C13C, the different lateral regions of the CLC layer 1424 can be further configured to have similar respective ranges of off-axis angles at which relatively high diffraction efficiency can be obtained. Of course, although three vertical regions are illustrated for clarity, any suitable number of regions can be included within the CLC layer 1424.

[0149] In the illustrated embodiment of FIG. 15, the magnitude of helical pitch p1, p2, and p3 can vary monotonically in the lateral direction such that a gradient of helical pitch is created. When the rate of change of helical pitch in the x-direction is uniform across the width or length of the CLC layer 1424, a linear relationship between length or width and helical pitch can be obtained, as illustrated in graph 1428. However, the embodiments are not so limited. By way of example, helical pitch p1, p2, and p3 can increase or decrease at any lateral location and can vary at different rates in the x-direction along the length or width according to various other embodiments.

[0150] According to various embodiments, the CLC layer can be engineered to have laterally variable diffractive properties, for example, by spatially varying the alignment properties or other material properties of the liquid crystal molecules. For example, in a similar manner as described above with respect to Figure 14, a lateral helical pitch gradient can be achieved along the lateral dimension, for example, by controlling the ratio between two different liquid crystal monomers and / or the dose of UV radiation in different lateral regions. (Waveguide combined with CLCG for wavelength selective optical coupling)

[0151] As described above, for various applications, including incoupling and outcoupling of light, the waveguide device can be configured to propagate light by total internal reflection (TIR). Figure 16 illustrates an example of an optical waveguide device 1600 comprising a waveguide 1604 coupled to a CLCG 1150. The CLCG 1150 comprises liquid crystal molecules arranged in a plurality of chiral structures in a manner similar to the chiral structures 1162-1, 1162-2, ... 1162-i described above with respect to Figure 11. The waveguide 1604 is disposed across the CLCG 1150 and optically coupled to the CLCG 1150. When the elliptically / circularly polarized incident light 1016-R / L has a polarization handedness that matches the rotation direction of the chiral structured liquid crystal molecules, the incident light 1016-R / L is Bragg reflected by the CLCG 1150 and coupled into the waveguide 1604 at an angle such that the coupled light travels in a lateral direction (e.g., x-direction) by total internal reflection (TIR). Without being bound by any theory, the TIR condition is: C In some circumstances, the TIR condition may be expressed as: sin(θ C )=1 / n t [4] In the formula, n t is the refractive index of the waveguide 1604. According to various embodiments, n t may be from about 1 to about 2, from about 1.4 to about 1.8, or from about 1.5 to about 1.7. For example, the waveguide may be made of a polymer, such as polycarbonate or glass.

[0152] FIG. 17A shows a first CLCG 1750A coupled to a first CLCG 1750B, where θ>θ c31 illustrates a first optical guiding device 1700A comprising a first waveguide 1704A configured to propagate light having a third wavelength λ3 by total internal reflection (TIR) ​​when λ 3 = 1 . The first CLCG 1750A has a first period ∧1 and a first helical pitch p1. According to some embodiments, the first guiding device 1700A may be configured to propagate light in the visible spectrum (e.g., with wavelengths between about 400 nm and 700 nm) by TIR. According to some other embodiments, the first guiding device 1700A may be configured to propagate light in the infrared spectrum (e.g., in the near-infrared portion of the spectrum with wavelengths between about 700 nm and 1400 nm) by TIR. As described above with respect to FIGS. 10 and 11, Bragg reflection occurs at wavelengths represented by the aforementioned equation [1] and within a bandwidth of wavelengths Δλ represented by the aforementioned equation [2]. For example, the first CLCG 1750A may be designed to couple, by TIR, a third incident light 1736 having a third wavelength λ3 within one of blue (e.g., about 450 nm), green (e.g., about 550 nm), red (e.g., about 650 nm), or infrared. As shown, when Δλ is about 60 nm, about 80 nm, or about 100 nm, as described above, the first and second lights 1716 and 1726 having first and second wavelengths λ1, λ2 are substantially transmitted because equation [1] is not satisfied for these colors, which is not coupled into the first waveguide 1704 because equation [4] is not satisfied.

[0153] FIG. 17B illustrates a second optical guiding device 1700B combined with the first optical guiding device 1700A illustrated above with respect to FIG. 17A. The optical guiding device 1700B comprises a second waveguide 1704B disposed in the optical path following the optical guiding device 1700A and coupled to a second CLCG 1750B and configured to propagate a second light 1726 having a second wavelength λ2 by total internal reflection (TIR) ​​when θ>θc2. The second CLCG 1750B has a second period ∧2 and a second helical pitch p2. As described above with respect to FIG. 17A, the first and second lights 1716 and 1726 having the first and second wavelengths λ1, λ2 are substantially transmitted through the first optical guiding device 1700A. Of the transmitted first and second lights 1716 and 1726, the second CLCG 1750B may be designed to couple, by TIR, a second incident light 1726 having a second wavelength λ2 within the transmitted ones of blue (e.g., about 450 nm), green (e.g., about 550 nm), red (e.g., about 650 nm), or infrared when θ>θc2. Thus, as shown, the first light 1716 having a first wavelength λ1 is substantially transmitted further through the second waveguiding device 1700B when Δλ is about 60 nm, about 80 nm, or about 100 nm, as described above.

[0154] FIG. 17C illustrates a third optical guiding device 1700C combined with the first and second optical guiding devices 1700A and 1700B illustrated above with respect to FIG. 17B. The third optical guiding device 1700C comprises a third waveguide 1704C disposed in the optical path following the first and second optical guiding devices 1700A and 1700B and coupled to a third CLCG 1750C and configured to propagate a first light 1716 having a first wavelength λ2 by total internal reflection (TIR) ​​when θ>θc1. The third CLCG 1750C has a third period ∧3 and a third helical pitch p3. As described above with respect to FIG. 17B, the first light 1716 having a first wavelength λ1 is substantially transmitted through the first and second guiding devices 1700A and 1700B. The third CLCG 1750C may be designed to couple a first incident light 1716 having a first wavelength λ1 within a transmitted one of blue (e.g., about 450 nm), green (e.g., about 550 nm), red (e.g., about 650 nm), or infrared by TIR when θ>θc1. Thus, as shown, when Δλ is about 60 nm, about 80 nm, or about 100 nm, as described above, the first light 1716 having the first wavelength λ1 is substantially coupled into the third waveguide 1704C because equation [4] is satisfied.

[0155] Thus, as described above with respect to Figures 17A-17C, by placing one or more of the first, second, and third optical wave-guiding devices 1700A, 1700B, and 1700C within the same optical path, one or more of the first, second, and third lights 1716, 1726, and 1736 having different wavelengths λ1, λ2, and λ3 can be coupled to propagate by TIR within one of the first, second, and third waveguides 1704A, 1704B, and 1704C, respectively. In each of Figures 17A-17C, the first to third optical waveguiding devices 1704A, 1704B, and 1704C each have a dedicated first to third waveguide 1704A, 1704B, and 1704C, respectively, and a dedicated first to third CLCG 1750A, 1750B, and 1750C, respectively, although the embodiments are not so limited. For example, a single waveguide can combine light Bragg reflected from a stack of multiple CLCGs by TIR, as illustrated below with respect to Figure 18. In addition, any suitable number of optical waveguiding devices greater than or less than three can also be combined for further selective coupling by Bragg reflection.

[0156] 18 illustrates an optical waveguiding device 1800 comprising a common waveguide 1704 coupled to a plurality of CLCGs 1750. The plurality of CLCGs 1750 are configured as a stack comprising first-third CLCGs 1750A-1750C, configured to propagate third, second, and first lights 1736, 1726, and 1716 having third, second, and first wavelengths λ3, λ2, and λ1, respectively, by total internal reflection (TIR). TIR occurs when one or more of the third, second, and first lights 1736, 1726, and 1716, respectively, satisfy the conditions θ>θc3, θ>θc2, and θ>θc1, respectively, in a similar manner as described above with respect to FIGS. 17A-17C. Also in a similar manner, the first, second, and third CLCGs 1750A, 1750B, and 1750C are configured to selectively Bragg-reflect the third, second, and first lights 1736, 1726, and 1716 when θ>θc3, θ>θc2, and θ>θc1, respectively. Of course, any suitable number of CLCGs, less than three or more (or less than three), can be stacked to further selectively couple by Bragg reflection. Thus, compared to the embodiment described above with respect to Figs. 17B and 17C, a more compact waveguiding device 1800 can be obtained by employing a common waveguide 1704. Also, instead of three distinct CLCG layers (as shown in Fig. 18), the stack of CLCG layers can be arranged as a single (or multiple) layer with a helical pitch gradient, including a range of p1 to p3.

[0157] As described above with respect to Figures 17A-18, the first to third CLCGs 1750, 1750B, 1750C have first to third periods Λ1, Λ2, and Λ3, respectively, and first to third helical pitches p1, p2, and p3, respectively. In various embodiments, the CLCGs can each be configured such that the wavelength / period ratio λ / Λ is about 0.3 to 2.3, about 0.8 to 1.8, or about 1.1 to about 1.5, e.g., about 1.3. Alternatively, the period (Λ) can be configured to be about 1 nm to 250 nm smaller, about 50 nm to 200 nm smaller, or about 80 nm to 170 nm smaller than the individual wavelengths (λ) at which the CLCGs are configured for Bragg reflection. For example, when λ1, λ2, and λ3 are within the visible range, e.g., about 620 nm to about 780 nm, e.g., about 650 nm (red), about 492 nm to about 577 nm, e.g., about 550 nm (green), and about 435 nm to about 493 nm, e.g., about 450 nm (blue), the corresponding periods Λ1, Λ2, and Λ3 can be about 450 nm to about 550 nm, e.g., about 500 nm, about 373 nm to about 473 nm, e.g., about 423 nm, and about 296 nm to about 396 nm, e.g., about 346 nm, respectively. Alternatively, when λ1, λ2, and λ3 are within the infrared range, e.g., the near infrared range, about 750 nm to about 1400 nm, e.g., about 850 nm, the corresponding periods Λ1, Λ2, and Λ3 can be about 975 nm to about 1820 nm, e.g., about 1105 nm. In addition, in various embodiments, the CLCGs can be configured such that the wavelength / helical pitch ratio λ / p is about 0.6 to 2.6, about 1.1 to 2.1, or about 1.4 to about 1.8, e.g., about 1.6, respectively. Alternatively, the helical pitch (p) can be configured to be about 50 nm to 350 nm smaller, about 100 nm to 300 nm smaller, or about 140 nm to 280 nm smaller than the individual wavelengths (λ) at which the CLCGs are configured for Bragg reflection.For example, when λ1, λ2, and λ3 are about 620 nm to about 780 nm, for example, about 650 nm (red), about 492 nm to about 577 nm, for example, 550 nm (green), and about 435 nm to about 493 nm, for example, about 450 nm (blue), the corresponding helical pitches p1, p2, and p3 can be about 350 nm to about 450 nm, for example, about 400 nm, about 290 nm to about 390 nm, for example, about 340 nm, about 230 nm to about 330 nm, for example, about 280 nm, respectively. Alternatively, when λ1, λ2, and λ3 are in the infrared range, e.g., the near infrared range from about 750 nm to about 1400 nm, e.g., about 850 nm, the corresponding periods Λ1, Λ2, and Λ3 can be from about 1200 nm to about 2240 nm, e.g., about 1360 nm. (Waveguide combined with CLCG and mirror for wavelength selective optical coupling)

[0158] FIG. 19 illustrates an optical waveguiding device 1900 comprising a waveguide 1604 coupled to a CLCG 1150, similar to the optical waveguiding device described above with respect to FIG. 16. As described above with respect to FIGS. 10 and 11, in operation, the CLCG 1150 substantially reflects the incident light when the handedness of the polarization of the elliptically / circularly polarized incident light has the same rotation sense as the chiral structured liquid crystal molecules of the CLCG 1150. As shown, incident on the surface 1050S are a light beam 1016-L having a left-handed circular polarization and a light beam 1016-R having a right-handed circular polarization. In the illustrated embodiment, the chiral structured liquid crystal molecules are continuously rotated in a clockwise direction when viewed in the direction in which the incident light beams 1016-L, 1016-R travel, i.e., in the negative z-direction, such that the rotation sense of the liquid crystal molecules matches the handedness of the light beam 1016-R having a right-handed circular polarization. As a result, the light beam 1016 -R having right-handed circular polarization is substantially reflected by the CLCG 1150 , while the light beam 1016 -L having left-handed circular polarization is substantially transmitted through the CLCG 1150 .

[0159] For some applications, it may be desirable to invert the polarization handedness of elliptically or circularly polarized light prior to coupling into a waveguiding device similar to that described above with respect to FIG. 19. This may be the case, for example, when the polarization handedness of the incident elliptically or circularly polarized light does not match the rotation direction of the chiral structures in the CLCG, such that the CLCG is not configured to Bragg-reflect the light for coupling into the waveguide, as discussed above. For certain other applications, it may be desirable to recycle light transmitted through the CLCG due to a lack of match between the polarization handedness of the incident elliptically or circularly polarized light and the rotation direction of the chiral structures in the CLCG. To address these and other needs, various embodiments of waveguiding devices employing polarization-converting reflectors and addressing these needs are disclosed below.

[0160] 20 illustrates an optical guiding device 2000 comprising a waveguide 1150 coupled to a CLCG 1604 and a polarization converting reflector 2004, according to an embodiment, where the CLCG 1604 is configured to receive incident light and the waveguide 1150 is configured to propagate light Bragg reflected from the CLCG by total internal reflection (TIR). The polarization converting reflector 2004 is configured such that upon reflection therefrom, the polarization handedness of the incident elliptical or circularly polarized light is flipped to the opposite polarization handedness (e.g., from left-handed to right-handed or right-handed to left-handed). The guiding device 2000 is similar to the guiding device 1900 described above with respect to FIG. 19, but instead of being configured to first receive the incident light beam through the waveguide 1150, the guiding device 2000 is configured to first receive the incident light beam 2016-L, e.g., having left-handed circular polarization, through the CLCG 1604. The incident light beam 2016-L has a polarization handedness that does not match the rotation direction of the chiral structures in the CLCG 1604 when viewed in the propagation direction of the incident light beam 2016-L (negative z-direction) so that it is not Bragg reflected by the CLCG 1604. As a result, the incident light beam 2016-L is substantially transmitted through the CLCG 1604 and subsequently reflected by the polarization converting reflector 2004. For example, the reflected light beam 2016-R having right-handed circular polarization thereby becomes the incident light beam on the surface 1150S of the waveguide 1150. Due to the inverted polarization handedness, the reflected light beam 2016-R now incident on the surface 1150S of the waveguide 1150 has a polarization handedness that matches the rotation direction of the chiral structures in the CLCG 1604 when viewed in the propagation direction of the reflected light beam 2016-R (positive z-direction) so that it is Bragg reflected by the CLCG 1604. Further, as the reflected beam 2018 is reflected at an angle θ>θc relative to the layer normal (z-axis), the reflected light beam 2016-R couples into the waveguide 1150 and travels therethrough in a lateral direction (e.g., x-direction).

[0161] FIG. 21A illustrates the optical waveguiding device 2000, described above with respect to FIG. 20, under conditions where the incident light beam 2116 is linearly polarized or unpolarized, which may be processed to include both left-handed and right-handed circularly polarized components, respectively. Under such conditions, the incident light beam 2116 can be coupled into the waveguide in both lateral directions by TIR. For example, similar to what was described above with respect to FIG. 20, the components of the incident light beam 2116 having a polarization handedness, e.g., left-handedness, that does not match the rotational direction of the chiral structure in the CLCG 1604 are substantially transmitted through the CLCG 1604, subsequently reflected by the polarization converting reflector 2004, have their polarization handedness inverted, e.g., to right-handedness, and are coupled into the waveguide 1150 and travel therethrough in a first lateral direction (e.g., positive x-direction). On the other hand, similar to that described above with respect to FIG. 19, the component of the incident light beam 2116 having a polarization handedness, e.g., right-handedness, that matches the rotation direction of the chiral structure in the CLCG 1604 is substantially reflected directly by the CLCG 1604 and subsequently coupled into the waveguide 1150 and travels therethrough in a second lateral direction opposite to the first lateral direction (e.g., the negative x-direction).

[0162] FIG. 21B illustrates the optical waveguiding device 2000 described above with respect to FIG. 21A under conditions where the incident light is polarized into two orthogonal elliptically or circularly polarized beams, e.g., a light beam 1016-L having a left-handed circular polarization and a light beam 1016-R having a right-handed circular polarization. Under such conditions, the incident light beams 1016-L, 1016-R can be coupled into the waveguides by TIR to propagate in both lateral directions in a similar manner as described above with respect to FIG. 21A. For example, the light beam 1016-L having a polarization handedness, e.g., left-handedness, that does not match the rotation direction of the chiral structure in the CLCG 1604 is substantially transmitted through the CLCG 1604 and subsequently reflected by the polarization converting reflector 2004, where the polarization handedness is inverted, e.g., to right-handedness, and coupled into the waveguide 1150 and travels therethrough in a first lateral direction (e.g., positive x-direction). On the other hand, an incident light beam 1016-R having a polarization handedness, e.g., right-handedness, that matches the rotation direction of the chiral structure in CLCG 1604 is substantially reflected directly by CLCG 1604 and subsequently coupled into waveguide 1150 through which it travels in a second lateral direction opposite to the first lateral direction (e.g., the negative x-direction).

[0163] 22A illustrates an optical guiding device 2200 with a common waveguide 2204 coupled to multiple CLCGs arranged in a stack, including, for example, a first CLCG 2204 having a chiral structure with a first rotation direction and a second CLCG 2208 having a chiral structure with a second rotation direction opposite to the first rotation direction, according to an embodiment. As described above with respect to various embodiments, in operation, the incident light is reflected when the direction of the polarization direction of the incident light beam is aligned with the direction of rotation of the liquid crystal molecules of the chiral structure of the CLCG. The illustrated optical guiding device 2200 is under conditions in which the incident light beam 2116 is linearly polarized or unpolarized. Under such conditions, the incident light beam 2116 can be coupled into the waveguide in both bilateral directions (positive and negative x-directions) by TIR. In the illustrated embodiment, when viewed in the direction of travel of the incident light 2116, i.e., the negative z-direction, the liquid crystal molecules of the chiral structure of the first CLCG 2204 are continuously rotated in a clockwise direction, while the liquid crystal molecules of the chiral structure of the second CLCG 2204 are continuously rotated in the opposite counterclockwise direction.

[0164] Still referring to FIG. 22A, a component of an elliptical or circular incident light beam 2116 having a first polarization handedness, e.g., a right-handed polarization component, that matches the rotation direction, e.g., clockwise direction, of the chiral structure of the first CLCG 2204 is substantially reflected by the first CLCG 2204, thereby resulting in a first reflected beam 2118A at an angle θ>θc1 with respect to the layer normal direction (z-axis) which couples to the common waveguide 2204 and travels therethrough in a first lateral direction (e.g., positive x-direction).

[0165] 22A , on the other hand, a component of the elliptical or circular incident light beam 2116 having a second polarization handedness, e.g., a left-handed polarization component, that does not match the rotation direction of the chiral structure of the first CLCG 2204 is substantially transmitted through the first CLCG 2204. After being transmitted through the first CLCG 2204, an elliptical or circular incident light beam 2116 having a second polarization handedness 2116 that matches the rotation direction of the chiral structure of the second CLCG 2208, e.g., a counterclockwise direction, is substantially reflected by the second CLCG 2208, thereby resulting in a second reflected beam 2118B at an angle θ>θc2 with respect to the layer normal direction (z-axis) that couples into the common waveguide 2204 and travels therethrough in a second lateral direction (e.g., negative x-direction).

[0166] Figure 22B illustrates the optical wave-guiding device 2000, described above with respect to Figure 22A, in a different condition where the incident light is polarized into two orthogonal elliptical or circularly polarized beams, e.g., light beam 1016-L having a left-handed elliptical / circular polarization, and light beam 1016-R having a right-handed elliptical / circular polarization. Under such conditions, the incident light beams 1016-L, 1016-R can be coupled into a common waveguide 2204 in both lateral directions by TIR in a similar manner as described above with respect to Figure 22A to combine the incident light beams 1016-L, 1016-R having first and second polarization handedness, e.g., left-handedness and right-handedness.

[0167] 21B and 22B may be particularly advantageous in certain applications, for example, where different optical signals (i.e., images) are encoded in orthogonal circular polarizations. Under such circumstances, light can be coupled in opposite directions (e.g., positive and negative x-directions) depending on the polarization handedness.

[0168] 22C illustrates an optical wave-guiding device 2220 with a common waveguide 2250 coupled to multiple CLCGs arranged as a stack, including, for example, a first CLCG 2204 having a chiral structure with a first rotation sense and a second CLCG 2208 having a chiral structure with a second rotation sense opposite to the first rotation sense, according to an embodiment. Unlike the embodiment described with respect to FIGS. 22A and 22B, in the wave-guiding device 2220, the common waveguide 2250 is interposed between the first and second CLCG layers 2204, 2208. For illustrative purposes, the illustrated optical wave-guiding device 2220 is under conditions where the incident light beam 2116 is linearly polarized or unpolarized. Under such conditions, the incident light beam 2116 can be coupled into the waveguide in both lateral directions by TIR. In the illustrated embodiment, when viewed in the direction of travel of the incident light 2116, i.e., in the negative z-direction, the liquid crystal molecules of the chiral structure of the first CLCG 2204 are continuously rotated in a clockwise direction, while the liquid crystal molecules of the chiral structure of the second CLCG 2204 are continuously rotated in an opposite counterclockwise direction. Of course, the opposite alignment is also possible.

[0169] Still referring to FIG. 22C, a component of an elliptical or circular incident light beam 2116 having a first polarization handedness, e.g., a right-handed polarization component, that matches the rotation direction, e.g., clockwise direction, of the chiral structure of the first CLCG 2204 is substantially reflected by the first CLCG 2204, thereby resulting in a first reflected beam 2118A at an angle θ>θc1 with respect to the layer normal direction (z-axis), which in turn reflects from the outer surface of the first CLCG 2204 before coupling into and traveling in a first lateral direction (e.g., negative x-direction) through the common waveguide 2250 by TIR.

[0170] Still referring to FIG. 22C, on the other hand, a component of the elliptical or circular incident light beam 2116 having a second polarization handedness, e.g., a left-handed polarization component, that does not match the rotation direction, e.g., clockwise direction, of the chiral structure of the first CLCG 2204 is substantially transmitted through the first CLCG 2204 and further through the common waveguide 2204, and then is substantially reflected by the second CLCG 2208, thereby resulting in a second reflected beam 2218B at an angle θ>θc2 with respect to the layer normal direction (z-axis), which by TIR couples into the common waveguide 2250 and travels therethrough in a second lateral direction (e.g., the positive x-direction). (Cholesteric Liquid Crystal Off-Axis Mirror)

[0171] As described above with respect to various embodiments, by matching the handedness of the polarization of the incident elliptically or circularly polarized light with the liquid crystal molecular rotation direction of the chiral structure of the CLC layer, the CLC layer can be configured as a Bragg reflector. Furthermore, one or more CLC layers with different helical pitches can be configured as wavelength-selective Bragg reflectors with high bandwidth. Based on the concepts described herein with respect to various embodiments, the CLC layer can be configured as an off-axis mirror configured to selectively reflect a first range of wavelengths, e.g., infrared wavelengths (e.g., near-infrared), while transmitting another range of wavelengths, e.g., visible wavelengths. In the following, applications of various embodiments of the CLC off-axis mirror implemented in an eye tracking system according to embodiments are disclosed.

[0172] FIG. 23 illustrates an example of an eye tracking system 2300 employing a cholesteric liquid crystal reflector (CLCR), e.g., a wavelength selective CLCR 1150, configured to image a viewer's eye 302, according to various embodiments. Eye tracking may be an important feature in two-way vision or control systems, including wearable displays for virtual / augmented / mixed reality display applications, e.g., the wearable display system 200 in FIG. 2 or the system 700 described in FIGS. 24A-24H, among other applications. To achieve good eye tracking, it may be desirable to obtain an image of the eye 302 at a low viewing angle, and therefore, to position the eye tracking camera 702b near the center position of the viewer's eye. However, such a position of the camera 702b may interfere with the user's view. Alternatively, the eye tracking camera 702b may be positioned at a lower position or to the side. However, such a position of the camera may increase the difficulty of obtaining robust and accurate eye tracking because eye images are captured at steeper angles. Optionally, by configuring the CLCR 1150 to reflect infrared (IR) light 2308 (e.g., having a wavelength of 850 nm) from the eye 302 while transmitting visible light 2304 from the world as shown in FIG. 4, the camera 702b can be placed away from the user's view while capturing eye images at a normal or low viewing angle. Such a configuration does not interfere with the user's view because visible light is not reflected. The same CLCR 1150 can also be configured as the IR illumination source 2320 as shown. The low viewing angle of the IR illuminator may result in less occlusion from, for example, eyelashes, and the configuration allows for more robust detection of specular reflections, which may be an important feature in modern eye tracking systems.

[0173] 23, according to various embodiments, the CLCR 1150 comprises one or more cholesteric liquid crystal (CLC) layers each comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction (e.g., z-direction) and being rotated successively in a first rotation direction, as described above. The alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to substantially Bragg-reflect a first incident light having a first wavelength (λ1) while substantially transmitting a second incident light having a second wavelength (λ2). Each of the one or more CLC layers is configured to substantially Bragg reflect elliptically or circularly polarized first and second incident light having a handedness of polarization that is aligned with a first rotation direction when viewed in the layer depth direction, while substantially transmitting elliptically or circularly polarized first and second incident light having a handedness of polarization that is opposite to the first rotation direction when viewed in the layer depth direction, as described elsewhere herein. According to an embodiment, the alignment of the liquid crystal molecules that periodically vary in the lateral direction is aligned to have a period in the lateral direction such that the ratio between the first wavelength and the period is about 0.5 to about 2.0. According to an embodiment, the first wavelength is within the near infrared range of about 600 nm to about 1.4 μm, e.g., about 850 nm, as described elsewhere herein, and the second wavelength is within the visible range having one or more colors. According to an embodiment, the liquid crystal molecules in the chiral structure are pretilted with respect to a direction normal to the layer depth direction. As configured, the one or more CLC layers may be configured such that the first incident light is incident at an angle (θR) relative to the layer depth direction (z-direction), e.g., at an angle of about 50° relative to the layer depth direction based on Equation [3] described above. o , about 60 o , about 70 o , or about 80 o It is configured to be reflected over a degree.

[0174] Referring back to Figure 2, the eyes of a wearer of a head mounted display (HMD) (e.g., wearable display system 200 in Figure 2) can be imaged using a reflective off-axis diffractive optical element (DOE), which can be, for example, a holographic optical element (HOE). The resulting images can be used to track one or both eyes, image the retina, reconstruct eye shape in three dimensions, extract biometric information from the eye (e.g., iris identification), etc.

[0175] There are various reasons why a head mounted display (HMD) may use information about the state of the wearer's eyes. For example, this information can be used to estimate the wearer's gaze direction or for biometric identification. However, this problem is difficult due to the short distance between the HMD and the wearer's eyes. This is further complicated by the fact that gaze tracking requires a larger field of view, while biometric identification requires a relatively high number of pixels on the target on the iris. For an imaging system that would attempt to accomplish both of these objectives, the requirements of the two tasks largely conflict. Finally, both problems are further complicated by occlusion by the eyelids and eyelashes. The embodiments of the imaging system described herein address some or all of these problems. Various embodiments of the imaging system 700 described herein with reference to Figures 24A-24F can be used in conjunction with HMDs, including display devices described herein (e.g., the wearable display system 200 shown in Figure 2 and / or the display system 1000 shown in Figure 6).

[0176] FIG. 24A diagrammatically illustrates an example of an imaging system 700 comprising an imager 702b used to view eye 304 and mounted adjacent to the wearer's temple (e.g., on frame 64 of wearable display system 200, FIG. 2, e.g., on an ear piece). In other embodiments, a second imager is used for the wearer's other eye 302 such that each eye is imaged separately. Imager 702b may include an infrared digital camera sensitive to infrared radiation. Imager 702b is mounted to face forward (in the direction of the wearer's vision) rather than facing backward and directed toward eye 304 (similar to camera 500 shown in FIG. 6). By placing the imager 702b closer to the wearer's ear, the weight of the imager 702b will also be closer to the ear, and the HMD may be easier to wear compared to an HMD in which the imager faces rearward and is located closer to the front of the HMD (e.g., closer to the display 62 in FIG. 2). In addition, by placing the forward-facing imager 702b near the wearer's temple, the distance from the wearer's eye 304 to the imager is approximately doubled compared to a rear-facing imager located near the front of the HMD (e.g., compared to the camera 500 shown in FIG. 4). Since the depth of field of the image is approximately proportional to this distance, the depth of field for the forward-facing imager 702b is approximately doubled compared to a rear-facing imager. The greater depth of field for the imager 702b may be advantageous for imaging the eye region of wearers with large or prominent noses, brow ridges, etc.

[0177] The imager 702b is positioned to view an inner surface 704 of an otherwise transparent optical element 706. The optical element 706 can be part of a display 708 of an HMD (or a lens in a pair of glasses). The optical element 706 can be transmissive to at least 10%, 20%, 30%, 40%, 50%, or more of the visible light incident on the optical element. In other embodiments, the optical element 706 need not be transparent (e.g., in a virtual reality display). The optical element 706 can comprise a CLC off-axis mirror 708. The CLC off-axis mirror 708 can be a surface that reflects a first range of wavelengths while being substantially transmissive to a second range of wavelengths (different from the first range of wavelengths). The first range of wavelengths can be in the infrared, and the second range of wavelengths can be in the visible. For example, the CLC off-axis mirror 708 can comprise a hot mirror, which reflects infrared light while transmitting visible light. In such an embodiment, infrared light 710a, 712a, 714a from the wearer propagates to and reflects from the optical element 706, resulting in reflected infrared light 710b, 712b, 714b, which can be imaged by imager 702b. In some embodiments, imager 702b may be sensitive to or capable of capturing at least a subset (such as a non-empty subset and / or a subset less than all) of the wavelengths in the first range reflected by the CLC off-axis mirror 708. For example, the CLC off-axis mirror 708 may reflect infrared light in the range of 700 nm to 1.5 μm, and imager 702b may be sensitive to or capable of capturing near-infrared light in wavelengths between 700 nm and 900 nm. As another example, CLC off-axis mirror 708 may reflect infrared light in the range of 700 nm to 1.5 μm, and imager 702b may include a filter that filters out infrared light in the range of 900 nm to 1.5 μm such that imager 702b may capture near-infrared light at wavelengths between 700 nm and 900 nm.

[0178] Visible light from the outside world (1144, FIG. 6) can be transmitted through the optical element 706 and perceived by the wearer. In effect, the imaging system 700 shown in FIG. 24A acts as if there is a virtual imager 702c directed back toward the wearer's eye 304. The virtual imager 702c can image virtual infrared light 710c, 712c, 714c (shown as dotted lines) propagating from the wearer's eye 704 through the optical element 706. The hot mirror (or other DOE described herein) may be disposed on the inner surface 704 of the optical element 706, but this is not a limitation. In other embodiments, the hot mirror or DOE may be disposed on the outer surface of the optical element 706 or within the optical element 706 (e.g., a volumetric HOE).

[0179] FIG. 24B diagrammatically illustrates another example of an imaging system 700. In this embodiment, viewpoint distortion can be reduced or eliminated by use of a viewpoint control lens assembly 716b (e.g., a shifting lens assembly, a tilting lens assembly, or a tilt-shifting lens assembly) with a visual imager 702b. In some embodiments, the viewpoint control lens assembly 716b may be part of the lens of the imager 702b. The viewpoint control lens 716b can be configured such that the normal to the imager 702b is approximately parallel to the normal to the region of the surface 704 that includes the DOE (or HOE) or hot mirror. In effect, the imaging system 700 shown in FIG. 24B acts as if it were a virtual imager 702c with a virtual viewpoint control lens assembly 716c pointed back toward the wearer's eye 304.

[0180] Additionally or alternatively, as shown diagrammatically in FIG. 24C, the CLC off-axis mirror 708 of the optical element 706 may have an off-axis holographic mirror (OAHM) on its surface 704, which is used to reflect light 710a, 712a, 714a and facilitate viewing of the eye 304 by the camera imager 702b, which captures the reflected light 710b, 712b, 714b. The OAHM 708 may also have refractive power, in which case it may be an off-axis volumetric diffractive optical element (OAVDOE), as shown diagrammatically in FIG. 24D. In the embodiment shown in FIG. 24D, the effective location of the virtual camera 702c is at infinity (and is not shown in FIG. 24D).

[0181] In some embodiments, the HOE (e.g., OAHM or OAVDOE) can be divided into multiple segments. Each of these segments can have different optical properties or characteristics, including, for example, the reflective angle or refractive power at which the segment reflects incident (infrared) light. The segments can be configured such that light is reflected from each segment toward the imager 702b. As a result, the image acquired by the imager 702b is also divided into a corresponding number of segments, each effectively viewing the eye from a different angle. FIG. 24E diagrammatically illustrates an example of a display system 700 having an OAHM with three segments 718a1, 718a2, 718a3, acting as individual virtual cameras 702c1, 702c2, 702c3, respectively, that image the eye 304 at different angular locations.

[0182] FIG. 24F diagrammatically illustrates another example of a display system 700 having an OAHM with three segments 718a1, 718a2, 718a3, each having refractive power (e.g., a segmented OAVDOE) that creates a virtual camera at infinity, with each segment imaging the eye 304 at a different angular location. Although three segments are diagrammatically illustrated in FIGS. 24E and 24F, this is for illustration and not limitation. In other embodiments, two, four, five, six, seven, eight, nine, or more segments can be utilized. None of the segments of the HOE can have refractive power, or some or all of them can have refractive power.

[0183] The three segments 718a1, 718a2, 718a3 are shown in Figures 24E and 24F as being horizontally spaced apart across the optical element 706. In other embodiments, the segments can be vertically spaced apart on the optical element 706. For example, Figure 24G diagrammatically shows a DOE 718 having two vertically spaced apart segments 718a1 and 718a2, where segment 718a1 comprises a CLC off-axis mirror configured to reflect light towards imager 702b (which may be in the same approximate horizontal plane as segment 718a1), and segment 718a2 is configured to reflect light upward towards imager 702b. Similar to a bifocal lens, the arrangement shown in FIG. 24G may be advantageous in enabling the imaging system 700 to use a reflected image obtained by the imager 702b from the upper segment 718a1 when the wearer is looking forward through the upper portion of the HMD (schematically shown via solid arrow lines), and to use a reflected image from the lower segment 718a2 when the wearer is looking downward through the lower portion of the HMD (schematically shown via dashed arrow lines).

[0184] A mix of horizontally and vertically spaced segments can be used in other embodiments. For example, FIG. 24H shows another example of HOE718 with an array of 3×3 segments, each with a CLC off-axis mirror. Imager702b can obtain reflection data from each of these nine segments, representing rays originating from different areas of the eye region and angular directions therefrom. Two example rays propagating from the eye region to HOE718 and reflecting to imager702b are shown as solid and dashed lines. Imaging system700 (or processing module224 or 228) can analyze the reflection data from multiple segments and calculate the three-dimensional shape of the eye or the gaze direction of the eye (e.g., eye posture) in a multi-perspective manner.

[0185] An embodiment of the optical system 700 utilizing segments may have several advantages. For example, the segments can be used individually by selecting the particular segment that is best for a particular task, or they can be used collectively to estimate the 3D shape or pose of the eye multi-viewwise. In the former case, this selectivity can be used, for example, to select an image of the wearer's iris that has at least an occlusion by the eyelid or eyelashes. In the latter case, the 3D reconstruction of the eye can be used to estimate the orientation (e.g., by estimating the location of the corneal collaterals) or the accommodation state (e.g., by estimating the lens-induced distortion on the apparent location of the pupil). (Waveguide combined with CLCG optimized for field of view)

[0186] A medium that has a refractive index that depends on the polarization and propagation direction of light is referred to as 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 usually experiences a refractive index (n o ), and light whose polarization is parallel to the optical axis of the birefringent medium is usually affected by the external refractive index (n e ) and the refractive index difference observed in a birefringent medium material, ne -n o is described as having a birefringence Δn. As described herein, the average refractive index n LC can be expressed as follows: [ka]

[0187] According to various embodiments described herein, a cholesteric liquid crystal (CLC) layer can have a representative, local, average, median, maximum, or minimum birefringence (Δn) of 0.05-0.10, 0.15-0.20, 0.20-0.25, 0.25-0.30, 0.30-0.35, 0.35-0.40, 0.40-0.45, 0.45-0.50, 0.50-0.55, 0.55-0.60, 0.60-0.65, 0.65-0.70, or a value within a range defined by any of these values.

[0188] As described herein, the phase retardation (Γ) of light in a material medium having birefringence Δn can be expressed as Γ=2πΔnd / λ, where λ is the wavelength of light and d is the thickness of the medium. In addition, the diffraction efficiency (η) of a birefringent medium, such as a layer with liquid crystal, can be expressed as η=sin 2 (πΔnd / λ), where Δn is the birefringence, λ is the wavelength, and d is the thickness of the medium. Because the phase deceleration of light propagating through a diffractive component varies with wavelength for conventional birefringent media, some diffractive components, including diffraction gratings, may exhibit a limited range of wavelengths, or bandwidth, within the visible spectrum over which the diffraction efficiency is relatively high.

[0189] According to various embodiments, the various CLC layers and CLCGs described herein may be configured such that they diffract light incident thereon with relatively high efficiency within a certain range of angles of incidence, sometimes referred to as the range of acceptance angles or field of view (FOV). As described herein, the FOV may include an angular range that spans angles of incidence of negative and positive values ​​relative to the centerline wavelength of the FOV, outside which the diffraction efficiency drops off by more than 10%, more than 25%, more than 50%, more than 75%, or a value within a range defined by any of these values, relative to the diffraction efficiency at the centerline wavelength of the FOV or at a wavelength corresponding to the peak efficiency within the FOV. In other words, inside the FOV, the CLC layers and CLCGs are configured such that the diffraction efficiency is more than 25%, more than 50%, more than 75%, more than 90%, or a value within a range defined by any of these values, relative to the diffraction efficiency at the centerline wavelength of the FOV or at a wavelength corresponding to the peak efficiency within the FOV. It may be desirable to have an FOV in which the diffraction efficiency is relatively constant, for example if diffracted light of uniform intensity is desired within the FOV.

[0190] Applicant recognizes that the FOV of the CLC layer and CLCG can be increased or optimized for various embodiments of the waveguide coupled with the CLC layer and CLCG as described above by selecting a CLC layer and CLCG with appropriate birefringence (see, e.g., Equation [6]). FIG. 25 illustrates an exemplary optical waveguide device 2500 optimized for a relatively high FOV, according to an embodiment. The optical waveguide device 2500 comprises a waveguide 1604 coupled to a CLCG 1150. As with various embodiments described herein, the CLCG 1150 comprises liquid crystal molecules arranged in a plurality of chiral structures, e.g., in a manner similar to the chiral structures 1162-1, 1162-2, ... 1162-i described above with respect to FIG. 11. The waveguide 1604 is disposed across and optically coupled to the CLCG 1150.

[0191] An elliptically / circularly polarized incident light 2504 having right / left (R / L) handedness is incident at an angle θ with respect to the layer normal of the waveguide 1604. inc When incident on the waveguide 1604 at θ 2504 , the incident light 2504 is coupled into the waveguide 1604 as light 2508 , which is at an angle θ incWG When light 2508 has a polarization handedness (R / L) that matches the rotation direction of the chiral liquid crystal molecules in the CLCG 1150, the light 2508 is coupled into the waveguide 1604 and is rotated by the CLCG 1150 at an angle θ to the layer normal. LC The reflected light 2512 is then Bragg-reflected into light 2512 having an angle θ with respect to the layer normal as light 2516, such that light 2516 travels under total internal reflection (TIR) ​​in a lateral direction (e.g., the x-direction). WG 1604. Without being bound by any theory, the TIR condition is WG is greater than the critical angle.

[0192] Without being bound by any theory, it is assumed that the angle of incidence is symmetrical |sinθ inc |<(n-1) / 2 and the minimum refractive index for a given FOV is [ka] When satisfies, the range of propagation angles can be limited by the material refractive index of the propagation medium as follows: [ka] This condition can also be valid within a CLCG layer as light diffracts and propagates through the layer. CLCG layers are birefringent, so that the propagating light is diffracted through the LC material at the average refractive index n LC to suffer from o Assuming that is fixed (not required), the minimum birefringence Δn is related to the angle of incidence in the FOV as follows: [ka]

[0193] The LC material of the CLCG layer can be selected based on Equation [6] to provide a desired FOV. The FOV is 20 o 30 o , 36 o , 40 o , 44 o , 50 o or within the range of angles defined by any of these values. For example, the FOV incidence angles: [ka] As another example, n LC When is about 1.35 to about 1.85, the complete FOV is about 20 o ~about 50 o Can be, or 50 o It can exceed.

[0194] In various embodiments, the above disclosed values ​​of FOV are set when the waveguide 1604 has a refractive index n t When formed from a suitable material, a refractive index of about 1 to about 2, about 1.4 to about 1.8, or about 1.5 to about 1.7 can be obtained. For example, the waveguide may be made of a polymer, such as polycarbonate or glass. (Waveguide coupled with CLCG configured as external coupling optical element)

[0195] As described above with respect to Figures 9B and 9C, various embodiments of the display device disclosed herein include external coupling optical elements 1250, 1252, 1254, which may be configured as an exit pupil expander (EPE) to direct light into the viewer's eye 4 (Figure 7). In various embodiments described herein, various optical components such as lenses, mirrors, and gratings may be configured to be specific to a certain light propagation direction and / or a certain polarization of light, for example, right-handed or left-handed circular polarization. As described herein, in various embodiments, the CLC layer and CLCG comprise a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules that extend in the layer depth direction by at least a helical pitch and are rotated successively in a rotation direction. The CLC layer or CLCG can be advantageously configured to substantially Bragg reflect elliptically or circularly polarized light with a handedness of polarization that matches the rotation direction of the liquid crystal molecules, while substantially transmitting elliptically or circularly polarized light with a handedness of polarization that is opposite to the rotation direction of the liquid crystal molecules. Based on these properties of CLC layers and CLCGs, various embodiments of display devices disclosed herein have optical elements 1250, 1252, 1254 that comprise one or more CLC layers or CLCGs.

[0196] 26 illustrates an exemplary optical waveguiding device 2600 configured as an outcoupling optical element, such as an EPE, according to an embodiment. The waveguiding device 2600 comprises a waveguide 1604 coupled to the CLCG 1150 and configured to propagate light by total internal reflection (TIR). As with various embodiments described herein, the CLCG 1150 comprises liquid crystal molecules arranged in a plurality of chiral structures, e.g., in a manner similar to the chiral structures 1162-1, 1162-2, ... 1162-i described above with respect to FIG.

[0197] 26, the CLCG 1150 coupled to the waveguide 1604 may represent any one of the external coupling optical elements 1250, 1252, 1254 coupled to an individual one of the waveguides 1210, 1220, 1230 as illustrated in FIGS. 9B, 9C, however, unlike the external coupling optical elements 1250, 1252, 1254 which are formed on the light output side of the individual waveguides 1210, 1220, 1230, the CLCG 1150 is formed on the opposite side of the light output side of the waveguide 1604. Thus, according to some embodiments, each of the external coupling optical elements 1250, 1252, 1254 and the corresponding one of the internal coupling optical elements 1212, 1222, 1232 is formed on the opposite side of the corresponding one of the waveguides 1210, 1220, 1230. In operation, for example, light incoupled by the incoupling optical elements 1212, 1222, 1232 (FIGS. 9A-9C) propagates in the in-plane direction within the waveguides 1210, 1220, 1230 (FIGS. 9A-9C) by TIR, respectively. The incoupling light may then impinge on the optical dispersive elements 1214, 1224, 1234 (FIGS. 9A-9C), when present, which may deflect the light to propagate towards the outcoupling optical elements 1250, 1252, 1254. Light approaching the outcoupling optical elements 1250, 1252, 1254 may be represented in FIG. 26 by light 2604. Upon impinging on the CLCG 1150, at least a portion of the light 2604 may be diffracted by the CLCG 1150 as diffracted light 2608, which may be directed, for example, into the viewer's eye 4 (FIG. 7).

[0198] Still referring to FIG. 26, the liquid crystal molecules of the illustrated CLCG1150 are continuously rotated in a certain rotation direction, and the alignment of the liquid crystal molecules of the chiral structure periodically varies in a lateral direction perpendicular to the layer depth direction. Due to the rotation alignment of the liquid crystal molecules, when the light 2604 is elliptically / circularly polarized light with one of the polarization handedness, e.g., left-handed or right-handed, that matches the rotation direction of the liquid crystal molecules of the chiral structure, the light 2604 is Bragg-reflected by the CLCG1150. That is, the rotation alignment of the liquid crystal molecules in the CLCG1150 is such that the CLCG1150 selectively Bragg-reflects light with one handedness, while non-Bragg-reflecting or transmitting light with the opposite handedness. In addition, since the Bragg reflection occurs under a diffraction condition, the Bragg-reflected light 2608 is unidirectional (e.g., most of the light is directed toward one direction in the external coupling, such as the direction indicated by the arrow 2608 in FIG. 26). The out-coupled light can preserve a uniform polarization state, which corresponds to the chirality of the CLC material. Thus, when configured as an optical out-coupling element, the CLCG 1150 acts as a polarizer and a unidirectional reflector, which allows for efficient integration with other optical components in various display systems described herein. For example, the optical element 2600 can be used in a waveguide-based AR display as an exit pupil expander to project a virtual image with a controlled polarization state in a single direction. (Additional Aspects)

[0199] In a first aspect, a diffraction grating comprises a cholesteric liquid crystal (CLC) layer comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction and successively rotated in a first rotation direction by at least a helical pitch. The helical pitch is a length in the layer depth direction that corresponds to a net rotation angle of the liquid crystal molecules of the chiral structures through one full rotation in the first rotation direction. The alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction.

[0200] In a second aspect, in the grating of the first aspect, each chiral structure comprises at least three calamitic liquid crystal molecules stretched along different stretch directions.

[0201] In a third aspect, in a diffraction grating of any one of the first to second aspects, the CLC layer is configured to substantially Bragg reflect elliptically or circularly polarized light having a handedness of polarization that matches the first rotation direction when viewed in the layer normal direction, while being configured to substantially transmit elliptically or circularly polarized light having a handedness of polarization opposite to the first rotation direction when viewed in the layer depth direction.

[0202] In a fourth aspect, in the diffraction grating of any one of the first to third aspects, the alignment of the liquid crystal molecules that varies periodically in the lateral direction is such that the liquid crystal molecules having chiral structures that are continuously adjacent to each other in the lateral direction and at substantially the same depth in the layer depth direction are arranged in a 360° pattern. o / n, where n is an integer, as being continuously rotated in a second rotation direction.

[0203] In a fifth aspect, in the diffraction grating of any one of the first to fourth aspects, the arrangement of the liquid crystal molecules that varies periodically in the laterally direction is such that elliptically or circularly polarized light Bragg-reflected by a laterally adjacent chiral structure is phase-shifted by an angle proportional to the angle of rotation in the second rotation direction between the laterally adjacent chiral structures.

[0204] In a sixth aspect, in the diffraction grating of any one of the first to fifth aspects, the chiral structures have substantially the same helical pitch.

[0205] In a seventh aspect, in the diffraction grating of any one of the first to fourth aspects, the chiral structures comprise a first plurality of chiral structures each comprising a first plurality of liquid crystal molecules extending in a layer depth direction and continuously rotated in a first rotation direction by at least a first helical pitch, and a second plurality of chiral structures each comprising a second plurality of liquid crystal molecules extending in a layer depth direction and continuously rotated in the first rotation direction by at least a second helical pitch, the first helical pitch and the second helical pitch being such that the first chiral structure and the second chiral structure are configured to Bragg reflect light having different off-axis angles of incidence.

[0206] In an eighth aspect, in the diffraction grating of the seventh aspect, a first plurality of chiral structures are formed in a first cholesteric liquid crystal (CLC) layer and a second plurality of chiral structures are formed in a second cholesteric liquid crystal (CLC) layer formed across the first CLC layer and stacked in the layer depth direction.

[0207] In a ninth aspect, in the diffraction grating of the seventh aspect, a first plurality of chiral structures are formed in a first region of a cholesteric liquid crystal (CLC) layer and a second plurality of chiral structures are formed in a second region of the cholesteric liquid crystal (CLC) layer formed across the first region in a layer depth direction.

[0208] In a tenth aspect, in the diffraction grating of the seventh aspect, a first plurality of chiral structures are formed in a first region of the cholesteric liquid crystal (CLC) layer and a second plurality of chiral structures are formed in a second region of the cholesteric liquid crystal (CLC) layer, the first and second regions being laterally adjacent regions in a lateral direction.

[0209] In an eleventh aspect, in a diffraction grating of any one of the seventh to tenth aspects, one or both of the first and second chiral structures form a gradient of helical pitch in one or both of the depth direction and the lateral direction.

[0210] In a twelfth aspect, a waveguiding device comprises one or more cholesteric liquid crystal (CLC) layers each comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction and being rotated successively in a first rotation direction. The alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to Bragg-reflect incident light. The waveguiding device additionally comprises one or more waveguides formed across the one or more CLC layers and configured to optically couple Bragg-reflected light from the one or more CLC layers such that the Bragg-reflected light travels in a lateral direction perpendicular to the layer depth direction by total internal reflection (TIR). The one or more CLC layers and the one or more waveguides are configured to be in the same optical path.

[0211] In a thirteenth aspect, in a waveguide device of the twelfth aspect, each of the plurality of chiral structures extends in a layer depth direction by at least a helical pitch, the helical pitch being a length in the layer depth direction corresponding to a net rotation angle of the liquid crystal molecules of the chiral structure through one full rotation in a first rotation direction.

[0212] In a fourteenth aspect, the waveguide device of any one of aspects twelfth-thirteenth comprises a plurality of CLC layers, each one of the CLC layers having differently arranged chiral structures configured to selectively Bragg-reflect incident light having a different wavelength than the other of the CLC layers at a different Bragg-reflection angle than the other of the CLC layers.

[0213] In a fifteenth aspect, in a waveguide device of any one of aspects twelfth to fourteenth, the periodically varying lateral alignment of the liquid crystal layers is characterized by a period, each one of the CLC layers having a different period than the other of the CLC layers.

[0214] In a sixteenth aspect, in the waveguide device of any one of the twelfth to fifteenth aspects, each one of the CLC layers is configured to selectively Bragg reflect incident light having a wavelength within the visible spectrum.

[0215] In a seventeenth aspect, in a waveguide device of any one of aspects twelfth to fifteenth, each one of the CLC layers is configured to selectively Bragg reflect incident light having wavelengths in the infrared spectrum while transmitting light having wavelengths in the visible spectrum.

[0216] In an eighteenth aspect, the waveguide device of any one of aspects 12-17 comprises a plurality of waveguides, each waveguide being optically coupled to one of the CLC layers formed thereon.

[0217] In a nineteenth aspect, in the waveguide device of any one of aspects twelfth to eighteenth, a plurality of CLC layers form a stack and a single waveguide is optically coupled to each one of the CLC layers in the stack.

[0218] In a twentieth aspect, the waveguide device of any one of aspects 12-19 further comprises a polarizing reflector, wherein one or more waveguides are interposed between the one or more CLC layers and the polarizing reflector, and wherein elliptically or circularly polarized incident light transmitting through the one or more CLC layers and further through the waveguides is reflected by the polarizing reflector as reflected light having the opposite polarization handedness to the elliptically or circularly polarized incident light.

[0219] In a twenty-first aspect, the waveguide device of any one of aspects twelve to twentieth comprises a first CLC layer and a second CLC layer forming a stack with a waveguide, the chiral structures of the first CLC layer and the second CLC layer being sequentially rotated in opposite rotational directions.

[0220] In a twenty-second aspect, in the waveguide device of the twenty-first aspect, first and second CLC layers are stacked on a waveguide.

[0221] In a twenty-third aspect, in the waveguide device of the twenty-first aspect, the first and second CLC layers are interposed by a waveguide.

[0222] In a twenty-fourth aspect, in the waveguide device of any one of aspects 12-23, the one or more CLC layers each have an average refractive index (n LC ), n LC is the usual refractive index (n o ) and the normal refractive index (n e ) is the average of

[0223] In a twenty-fifth aspect, in the waveguide device of the twenty-fourth aspect, the one or more waveguides are configured to optically couple light Bragg reflected from the one or more CLC layers when the incident light is incident on the one or more CLC layers at an angle of incidence relative to a layer depth direction, the angle of incidence being within a field of view (FOV) within which the diffraction efficiency is greater than 25% and at least 20%. o This ranges from...

[0224] In a twenty-sixth aspect, in the waveguide device of any one of aspects twenty-four to twenty-fifth, the one or more CLC layers each have a birefringence (Δn) of about 0.05 to 0.70. In any one of aspects twenty-four to twenty-six, the one or more CLC layers each have a birefringence (Δn) of about 0.05 to 0.70. [ka] and inc is the angle of incidence of the field of view (FOV) of the waveguide device, and n o is the ordinary refractive index of one or more CLC layers.

[0225] In a twenty-seventh aspect, a head mounted display device is configured to project light to a user's eye and display augmented reality image content. The head mounted display device comprises a frame configured to be supported on the user's head. The head mounted display device additionally comprises a display disposed on the frame, at least a portion of the display comprising one or more waveguides. The one or more waveguides are transparent and disposed at a location in front of the user's eye when the user wears the head mounted display device such that the transparent portion transmits light from the portion of the environment in front of the user to the user's eye to provide a view of the portion of the environment in front of the user. The display further comprises one or more light sources and at least one diffraction grating configured to couple light from the light sources into or out of the one or more waveguides, the at least one diffraction grating comprising a diffraction grating according to any one of the first to eleventh aspects.

[0226] In a twenty-eighth aspect, in the head-mounted device of the twenty-seventh aspect, the one or more light sources comprise a fiber scanning projector.

[0227] In a twenty-ninth aspect, the head-mounted device of any one of aspects twenty-seventh to twenty-eighth is configured to project light into the user's eye so as to present image content to the user at multiple depth planes.

[0228] In a thirtieth aspect, a wavelength-selective cholesteric liquid crystal reflector (CLCR) comprises one or more cholesteric liquid crystal (CLC) layers each comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction and successively rotated in a first rotation direction, the alignment of the liquid crystal molecules of the chiral structures varying periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to substantially Bragg-reflect a first incident light having a first wavelength while substantially transmitting a second incident light having a second wavelength.

[0229] In a thirty-first aspect, in the wavelength-selective CLCR of the thirty-two aspect, one or more CLC layers are each configured to substantially Bragg-reflect first or second incident light of elliptically or circularly polarized light having a handedness of polarization that matches a first rotation direction when viewed in the layer depth direction, while being configured to substantially transmit first or second incident light of elliptically or circularly polarized light having a handedness of polarization opposite to the first rotation direction when viewed in the layer depth direction.

[0230] In a thirty-second aspect, in a wavelength-selective CLCR of any one of the thirty-first to thirty-first aspects, the arrangement of the liquid crystal molecules that periodically vary in the lateral direction is arranged so as to have a period in the lateral direction such that the ratio between the first wavelength and the period is from about 1.1 to about 1.5.

[0231] In a thirty-third aspect, in the wavelength-selective CLCR of any one of the thirty-first to thirty-second aspects, the first wavelength is in the near-infrared range of about 750 nm to about 1400 nm, and the second wavelength is in the visible range.

[0232] In a thirty-fourth aspect, in the wavelength-selective CLCR of any one of the thirty-first to thirty-second aspects, the one or more CLC layers are configured such that the first incident light is reflected at an angle greater than 60 degrees relative to the layer depth direction.

[0233] In a thirty-fifth aspect, in the wavelength-selective CLCR of any one of the thirty-first to thirty-second aspects, the plurality of liquid crystal molecules in the chiral structure are pretilted with respect to a direction normal to the layer depth direction.

[0234] In a thirty-sixth aspect, a head mounted display (HMD) configured to be worn on a user's head comprises a frame comprising a pair of ear hooks. The HMD additionally comprises a pair of optical elements supported by the frame such that each of the pair of optical elements can be positioned in front of an eye of the user. The HMD additionally comprises a forward-facing imager mounted on one of the pair of ear hooks. The HMD further comprises a cholesteric liquid crystal (CLC) off-axis mirror according to any one of the thirty-fifth aspects. The cholesteric liquid crystal (CLC) off-axis mirror is disposed within or on one of the pair of optical elements and configured to reflect infrared light towards a forward-facing imager configured to receive infrared light reflected by the reflective element.

[0235] In a thirty-seventh aspect, in the HMD of the thirty-sixth aspect, the CLC off-axis mirror comprises a plurality of CLC layers, each one of which has a differently arranged chiral structure configured to selectively Bragg-reflect incident light having a different wavelength than the other of the CLC layers at a different Bragg reflection angle than the other of the CLC layers.

[0236] In a thirty-eighth aspect, in an HMD of any one of aspects thirty-six to thirty-seven, the periodically varying lateral alignment of the liquid crystal layers is characterized by a period, each one of the CLC layers having a different period than the other of the CLC layers.

[0237] In a thirty-ninth aspect, in an HMD of any one of aspects thirty-six to thirty-eight, each one of the CLC layers is configured to selectively Bragg reflect incident light having wavelengths in the infrared spectrum while transmitting incident light having wavelengths in the visible spectrum.

[0238] In a fortieth aspect, in the HMD of any one of the thirty-sixth to thirty-ninth aspects, each of the pair of optical elements is transparent to visible light.

[0239] In a forty-first aspect, in an HMD of any one of the thirty-sixth to fortieth aspects, each of the pair of optical elements is configured to display an image to a user.

[0240] In a forty-second aspect, a waveguiding device includes one or more cholesteric liquid crystal (CLC) layers each having a plurality of chiral structures, each chiral structure including a plurality of liquid crystal molecules extending in a layer depth direction and rotated successively in a first rotation direction, and an alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to Bragg-reflect incident light. The waveguiding device additionally includes one or more waveguides formed across the one or more CLC layers and configured to optically couple Bragg-reflected light from the one or more CLC layers such that the Bragg-reflected light travels in a lateral direction perpendicular to the layer depth direction by total internal reflection (TIR). The waveguiding device includes one or more waveguides formed across the one or more CLC layers and configured to optically couple Bragg-reflected light from the one or more CLC layers such that the Bragg-reflected light travels in a lateral direction perpendicular to the layer depth direction by total internal reflection (TIR). o The diffraction efficiency is greater than 25%.

[0241] In a forty-third aspect, in the waveguide device of the forty-second aspect, the one or more CLC layers each have an average refractive index (n LC ), n LC is the usual refractive index (n o ) and the normal refractive index (n e ) is the average of

[0242] In a forty-fourth aspect, in the waveguide device of any one of the forty-second to forty-third aspects, the one or more CLC layers each have a birefringence (Δn) of about 0.05 to 0.70.

[0243] In a forty-fifth aspect, a display device comprises a waveguide and an incoupling optical element formed on the waveguide and configured to incoupling light incident thereon into a first side of the waveguide, the incoupling optical element and the waveguide configured such that light incoupling into the waveguide propagates within the waveguide in an in-plane direction of the waveguide by total internal reflection (TIR). The display device additionally comprises an outcoupling optical element formed on the waveguide and configured to outcoupling light incident thereon from the waveguide. The light outcoupling element comprises a cholesteric liquid crystal (CLC) layer comprising a plurality of chiral structures, each of the chiral structures comprising a plurality of liquid crystal molecules extending in a layer depth direction of the CLC layer and being continuously rotated in a first rotation direction, an alignment of the liquid crystal molecules of the chiral structures periodically varying in a lateral direction perpendicular to the layer depth direction, such that the one or more CLC layers are configured to Bragg-reflect light incident thereon from the waveguide towards the first side.

[0244] In a forty-sixth aspect, in the display device of the forty-fifth aspect, the outcoupling optical element and the incoupling optical element are formed on opposite sides of the waveguide.

[0245] In a forty-seventh aspect, in the display device of the forty-fifth aspect, the light out-coupling optical elements are configured to selectively Bragg reflect light having one of right-handed circular polarization or left-handed circular polarization.

[0246] In a forty-eighth aspect, in the display device of the forty-fifth aspect, the light out-coupling optical element is configured to selectively Bragg reflect light having a polarization direction that is the same as the first rotation direction.

[0247] In a forty-ninth aspect, in the display device of the forty-fifth aspect, the light in-coupling optical elements comprise a liquid crystal layer.

[0248] In a 50th aspect, in the display device of the 49th aspect, the liquid crystal layer comprises a second CLC layer having a plurality of chiral structures, each of the chiral structures comprising a plurality of liquid crystal molecules extending in a layer depth direction of the second CLC layer and being continuously rotated in a first rotation direction, and the arrangement of the liquid crystal molecules of the chiral structures varies periodically in the lateral direction. (Additional Considerations)

[0249] In the above described embodiments, the augmented reality display system, more specifically, the spatially variable diffraction grating, is described in relation to a specific embodiment. However, it will be understood that the principles and advantages of the embodiments can be used for any other system, device, or method involving the need for a spatially variable diffraction grating. In the foregoing, it should be understood that any feature of any one of the embodiments can be combined with and / or substituted for any other feature of any other one of the embodiments.

[0250] Unless otherwise clearly required by context, throughout the description and claims, the words "comprises," "comprises," "includes," "including," and the like, should be interpreted in an inclusive sense, i.e., "including but not limited to," as opposed to an exclusive or inclusive sense. The word "coupled," as generally used herein, refers to two or more elements that may be either directly connected or continued via one or more intermediate elements. Similarly, the word "connected," as generally used herein, refers to two or more elements that may be either directly connected or continued via one or more intermediate elements. In addition, the words "herein," "above," "below," "hereinafter," "above," and words of similar import, when used in this application, shall refer to this application as a whole and not to any particular portions of this application. Where permitted by context, words in the above detailed description using the singular or plural form may also include the plural or singular form, respectively. When the word "or" refers to a list of two or more items, the word encompasses all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of one or more of the items in the list. Additionally, the articles "a," "an," and "the," as used in this application and the appended claims, should be interpreted to mean "one or more" or "at least one," unless otherwise specified.

[0251] As used herein, a phrase referring to a list of items "at least one of" refers to any combination of those items, including single elements. As an example, "at least one of A, B, or C" is intended to cover A, B, C, A and B, A and C, B and C, and A, B, and C. Transitive phrases such as "at least one of X, Y, and Z" are generally understood differently in the context in which they are used to convey that an item, term, etc. may be at least one of X, Y, or Z, unless specifically stated otherwise. Thus, such transitive phrases are generally not intended to suggest that an embodiment requires that at least one of X, at least one of Y, and at least one of Z, respectively, be present.

[0252] Additionally, it should be understood that conditional statements used herein, such as, among others, "can," "could," "might," "may," "eg," "for example," "such as," and the like, are generally intended to convey that certain embodiments include certain features, elements, and / or conditions 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 suggest that features, elements, and / or conditions are in any way required for one or more embodiments, or whether or not these features, elements, and / or conditions should be included or implemented in any particular embodiment.

[0253] Although certain embodiments have been described, these embodiments are presented as examples only and are not intended to limit the scope of the disclosure. Indeed, the novel apparatus, methods, and systems described herein may be embodied in a variety of other forms. Furthermore, various omissions, substitutions, and changes in the form of the methods and systems described herein may be made without departing from the spirit of the disclosure. For example, although blocks are presented in a given arrangement, alternative embodiments may implement similar functionality using different components and / or circuit topologies, and some blocks may be deleted, moved, added, sub-divided, combined, and / or modified. Each of these blocks may be implemented in a variety of different ways. Any suitable combination of elements and acts of the various embodiments described above can be combined to provide further embodiments. The various features and processes described above may be implemented independently of one another or may be combined in various ways. No element or combination of elements is necessary or essential for all embodiments. All suitable combinations and sub-combinations of features of the present disclosure are intended to be within the scope of the present disclosure.

Claims

1. 1. A diffraction grating, the diffraction grating comprising a cholesteric liquid crystal (CLC) layer, the CLC layer comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules, the plurality of liquid crystal molecules extending in a layer depth direction with at least a helical pitch and being continuously rotated in a first rotation direction; the helical pitch is a length in the layer depth direction corresponding to a net rotation angle of the liquid crystal molecules of the chiral structure through one complete rotation in the first rotation direction; the alignment of the liquid crystal molecules of the chiral structure varies periodically in a lateral direction perpendicular to the layer depth direction; the chiral structure comprises a plurality of first liquid crystal molecules in a first layer stacked across a plurality of second liquid crystal molecules in a second layer, the first liquid crystal molecules and the second liquid crystal molecules extending in the layer depth direction with different helical pitches such that the second liquid crystal molecules have a reduced helical pitch relative to the first liquid crystal molecules; A diffraction grating, wherein the length of the first layer along the layer depth direction is constant along the lateral direction, and the length of the second layer along the layer depth direction is constant along the lateral direction.

2. The diffraction grating of claim 1 , wherein each chiral structure comprises at least three calamitic liquid crystal molecules stretched along different stretch directions.

3. 2. The diffraction grating of claim 1, wherein the CLC layer is configured to substantially Bragg reflect elliptically or circularly polarized light having a handedness of polarization that is aligned with the first rotation direction when viewed in the layer depth direction, while substantially transmitting elliptically or circularly polarized light having a handedness of polarization opposite to the first rotation direction when viewed in the layer depth direction.

4. The alignment of the liquid crystal molecules that periodically varies in the lateral direction is such that the liquid crystal molecules having chiral structures that are consecutively adjacent to each other at substantially the same depth in the layer depth direction are aligned in a 360° pattern. ｏ 2. The diffraction grating of claim 1, wherein the grating is successively rotated in the second rotation direction by n, n being an integer.

5. 2. The diffraction grating of claim 1, wherein the alignment of the liquid crystal molecules that varies periodically in the lateral direction is such that elliptically or circularly polarized light Bragg-reflected by the laterally adjacent chiral structures is phase-shifted by an angle proportional to the angle of rotation of a second rotation direction between the laterally adjacent chiral structures.

6. 2. The diffraction grating of claim 1, wherein the chiral structures comprising the plurality of first liquid crystal molecules have substantially identical first helical pitches and the chiral structures comprising the plurality of second liquid crystal molecules have substantially identical second helical pitches.

7. 1. A waveguide device, comprising: one or more cholesteric liquid crystal (CLC) layers, each of the one or more CLC layers comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction and being continuously rotated in a first rotation direction, an alignment of the liquid crystal molecules of the chiral structures varying periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to Bragg reflect incident light; one or more waveguides formed across the one or more CLC layers, the one or more waveguides configured to optically couple the Bragg-reflected light from the one or more CLC layers such that the Bragg-reflected light travels in a lateral direction perpendicular to the layer depth direction by total internal reflection (TIR); Equipped with the one or more CLC layers and the one or more waveguides are configured to be in the same optical path; the chiral structure comprises a plurality of first liquid crystal molecules in a first layer stacked across a plurality of second liquid crystal molecules in a second layer, the first liquid crystal molecules and the second liquid crystal molecules extending in the layer depth direction with different helical pitches such that the second liquid crystal molecules have a reduced helical pitch relative to the first liquid crystal molecules; A waveguide device, wherein the length of the first layer along the layer depth direction is constant along the lateral direction, and the length of the second layer along the layer depth direction is constant along the lateral direction.

8. 8. The waveguiding device of claim 7, wherein each of the plurality of chiral structures extends in the layer depth direction by at least a helical pitch, the helical pitch being a length in the layer depth direction corresponding to a net rotation angle of liquid crystal molecules of the chiral structure through one full rotation in the first rotation direction.

9. A plurality of CLC layers, 8. The waveguide device of claim 7, wherein each one of the CLC layers has differently arranged chiral structures configured to selectively Bragg-reflect incident light having a different wavelength than other ones of the CLC layers at a different Bragg-reflection angle than the other ones of the CLC layers.

10. A plurality of CLC layers, 8. The waveguide device of claim 7, wherein the periodically varying lateral alignment of the liquid crystal layers is characterized by a period, each one of the CLC layers having a different period than other ones of the CLC layers.

11. 8. A waveguide device according to claim 7, wherein each one of the CLC layers is configured to selectively Bragg reflect incident light having a wavelength within the visible spectrum.

12. 8. A waveguiding device according to claim 7, wherein each one of the CLC layers is configured to selectively Bragg reflect incident light having wavelengths in the infrared spectrum while transmitting light having wavelengths in the visible spectrum.

13. A plurality of waveguides are provided, 8. The waveguide device of claim 7, wherein each waveguide is optically coupled to one of the CLC layers formed thereon.

14. A plurality of CLC layers, 8. The waveguide device of claim 7, wherein the plurality of CLC layers form a stack, and a single waveguide is optically coupled to each one of the CLC layers in the stack.

15. A waveguide device, comprising: one or more cholesteric liquid crystal (CLC) layers, each of the one or more CLC layers comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction and being continuously rotated in a first rotation direction, an alignment of the liquid crystal molecules of the chiral structures varying periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to Bragg reflect incident light; one or more waveguides formed across the one or more CLC layers, the one or more waveguides configured to optically couple the Bragg-reflected light from the one or more CLC layers such that the Bragg-reflected light travels in a lateral direction perpendicular to the layer depth direction by total internal reflection (TIR); Polarizing reflector Equipped with the one or more CLC layers and the one or more waveguides are configured to be in the same optical path; the chiral structure comprises a plurality of first liquid crystal molecules stacked across a plurality of second liquid crystal molecules, the first liquid crystal molecules and the second liquid crystal molecules extending in the layer depth direction with different helical pitches such that the second liquid crystal molecules have a reduced helical pitch relative to the first liquid crystal molecules; at least one of the one or more waveguides is interposed between one of the one or more CLC layers and the polarizing reflector; The waveguide device is configured such that elliptically or circularly polarized incident light transmitted through the one or more CLC layers and further through the waveguide is reflected by the polarizing reflector as reflected light having the opposite polarization handedness to the elliptically or circularly polarized incident light.

16. 8. The waveguide device of claim 7, comprising a first CLC layer and a second CLC layer forming a stack with a waveguide, the chiral structures of the first CLC layer and the second CLC layer being successively rotated in opposite rotational directions.

17. 17. The waveguide device of claim 16, wherein the first and second CLC layers are stacked on the waveguide.

18. A waveguide device, comprising: a first cholesteric liquid crystal (CLC) layer and a second CLC layer, each of the first CLC layer and the second CLC layer comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules, the plurality of liquid crystal molecules extending in a layer depth direction and being continuously rotated in a first rotation direction, an alignment of the liquid crystal molecules of the chiral structures varying periodically in a lateral direction perpendicular to the layer depth direction such that the first CLC layer and the second CLC layer are configured to Bragg reflect incident light; one or more waveguides formed across the first and second CLC layers, the one or more waveguides configured to optically couple the Bragg-reflected light from the first and second CLC layers such that the Bragg-reflected light travels in a lateral direction perpendicular to the layer depth direction by total internal reflection (TIR); Equipped with the first CLC layer and the second CLC layer form a stack with a waveguide; the first and second CLC layers are sandwiched by the waveguide; the first CLC layer, the second CLC layer and the one or more waveguides are configured to be in the same optical path; the chiral structure comprises a plurality of first liquid crystal molecules stacked across a plurality of second liquid crystal molecules; the chiral structures of the first and second CLC layers are successively rotated in counter-rotating directions; A waveguiding device, wherein the first liquid crystal molecules and the second liquid crystal molecules extend in the layer depth direction with different helical pitches such that the second liquid crystal molecules have a reduced helical pitch relative to the first liquid crystal molecules.

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