Eyepieces for augmented reality display system

Abstract

To provide eyepieces for an augmented reality display system.SOLUTION: An augmented reality display system can include a first eyepiece waveguide with a first input coupling grating (ICG) region. The first ICG region can receive a set of input beams of light corresponding to an input image having a corresponding field of view (FOV), and can internally couple a first subset of the input beams. The first subset of the input beams can correspond to a first sub-portion of the FOV. The system can also include a second eyepiece waveguide with a second ICG region. The second ICG region can receive and internally couple at least a second subset of the input beams. The second subset of the input beams can correspond to a second sub-portion of the FOV. The first and second sub-portions of the FOV can be at least partially different from each other but together include the complete FOV of the input image.SELECTED DRAWING: Figure 27A

Description

Technical Field

[0001] (Incorporation by reference to any priority application) This application claims the benefit of U.S. Provisional Patent Application No. 62 / 863,871, filed Jun. 20, 2019, and entitled "EYEPIECES FOR AUGMENTED REALITY DISPLAY SYSTEM", and U.S. Provisional Patent Application No. 63 / 024,343, filed May 13, 2020, and entitled "EYEPIECES FOR AUGMENTED REALITY DISPLAY SYSTEM". Each of these applications and any other applications identified within the application data sheet for which a claim of foreign or domestic priority is filed together with this application are hereby incorporated by reference into this specification under 37 CFR 1.57.

[0002] The present disclosure relates to eyepieces for virtual reality, augmented reality, and mixed reality systems.

Background Art

[0003] Modern computing and display technologies have facilitated the development of virtual reality, augmented reality, and mixed reality systems. A virtual reality, or "VR", system creates a simulated environment for a user to experience. This can be done by presenting computer-generated image data to the user through a head-mounted display. This image data creates a sensory experience that immerses the user within the simulated environment. Virtual reality scenarios typically involve the presentation of only computer-generated image data and not also actual real-world image data.

[0004] An augmented reality system generally complements the real-world environment with simulated elements. For example, an augmented reality, i.e., "AR" system, can provide a user with a view of the surrounding real-world environment via a head-mounted display. However, computer-generated image data can also be presented on the display to enhance the real-world environment. This computer-generated image data can include elements that are contextually relevant to the real-world environment. Such elements can include simulated text, images, objects, etc. A mixed reality, i.e., "MR" system, is a type of AR system that also introduces simulated objects into the real-world environment, but these objects typically feature a greater degree of interaction. The simulated elements can often be bidirectional in real time.

[0005] Figure 1 depicts an exemplary AR scene 1, where a user can see a real-world park setting 6 featuring people, trees, buildings in the background, and a concrete platform 20. In addition to these items, computer-generated image data is also presented to the user. The computer-generated image data can include, for example, a robot image 10 standing on the real-world platform 20 and an avatar character 2 in the form of a flying comic that appears anthropomorphic like a honeybee, but these elements 2, 10 do not actually exist within the real-world environment. SUMMARY OF THE INVENTION MEANS FOR SOLVING THE PROBLEM

[0006] In some embodiments, the augmented reality display system comprises a first eyepiece waveguide comprising a first optically transmissive substrate, and a first input coupling grating (ICG) region formed on or within the first eyepiece waveguide, the first ICG region receiving a set of input light beams corresponding to an input image having a corresponding field of view and configured to couple a first subset of the input light beams into the substrate as a first set of guided beams, the first subset of the input light beams corresponding to a first sub-portion of the field of view of the input image, a first ICG region, a second eyepiece waveguide comprising a second optically transmissive substrate, and a second input coupling grating (ICG) region formed on or within the second eyepiece waveguide, the second ICG region receiving at least a second subset of the input light beams corresponding to the input image and configured to couple the second subset of the input light beams into the substrate as a second set of guided beams, the second subset of the input light beams corresponding to a second sub-portion of the field of view of the input image, the second ICG region, wherein the first and second sub-portions of the field of view are at least partially different but together include the entire field of view of the input image.

[0007] In some embodiments, an augmented reality display system includes a first ocular waveguide having a first optically transparent substrate, and a first input coupling grating (ICG) region formed on or within the first ocular waveguide, where the first ICG region receives a set of input light beams associated with a set of k-vectors in k-space corresponding to an input image, and is configured to translate the set of k-vectors to a location in k-space such that a first subset of the k-vectors is inside a first k-space loop associated with the first ocular waveguide, and the first k-space loop corresponds to a region in k-space associated with guided propagation within the first ocular waveguide; a second ocular waveguide having a second optically transparent substrate, and a second input coupling grating (ICG) region formed on or within the second ocular waveguide, where the second ICG region receives at least a portion of the set of input light beams, and is configured to translate the set of k-vectors to a location in k-space such that a second subset of the k-vectors is inside a second k-space loop associated with the second ocular waveguide, and the second k-space loop corresponds to a region in k-space associated with guided propagation within the second ocular waveguide, and the first and second subsets of k-vectors are at least partially different, but together include the complete set of k-vectors corresponding to the input image. The present invention provides, for example, the following. (Item 1) An augmented reality display system comprising a first ocular waveguide having a first optically transparent substrate, and A first input coupling grating (ICG) region formed on or within the first eyepiece waveguide, the first ICG region receiving a set of input beams of light corresponding to an input image having a corresponding field of view and configured to couple a first subset of the input beams into the substrate as a first set of guiding beams, the first subset of the input beams corresponding to a first sub-portion of the field of view of the input image, the first ICG region, and A second eyepiece waveguide comprising a second optically transmissive substrate, and A second input coupling grating (ICG) region formed on or within the second eyepiece waveguide, the second ICG region receiving at least a second subset of the input beams of light corresponding to the input image and configured to couple the second subset of the input beams into the substrate as a second set of guiding beams, the second subset of the input beams corresponding to a second sub-portion of the field of view of the input image, the second ICG region and Comprising, An augmented reality display system in which the first and second sub-portions of the field of view are at least partially different but together include the entire field of view of the input image. (Item 2) The augmented reality display system according to item 1, wherein the field of view of the input image is larger than a range of total internal reflection propagation angles in the thickness direction of the first and second eyepiece waveguides in at least one dimension. (Item 3) A third eyepiece waveguide comprising a third optically transmissive substrate, and A third input coupling grating (ICG) region formed on or within the third eyepiece waveguide, the third ICG region receiving at least a third subset of the input beams of light corresponding to the input image and configured to couple the third subset of the input beams into the substrate as a third set of guiding beams, the third subset of the input beams corresponding to a third sub-portion of the field of view of the input image, the third ICG region and further comprising, The first, second, and third sub - portions of the field of view are at least partially different but together include the entire field of view of the input image, the augmented reality display system according to item 1. (Item 4) The first ICG region has a periodic diffraction feature with a first spatial period, The second ICG region has a periodic diffraction feature with a second spatial period, The third ICG region has a periodic diffraction feature with a third spatial period, The first spatial period is smaller than the second spatial period, The second spatial period is smaller than the third spatial period, The augmented reality display system according to item 3. (Item 5) For a refractive index n ≤ 1.5, the first spatial period is < 336 nm, the second spatial period is 408 - 458 nm, and the third spatial period is > 546 nm, For a refractive index 1.5 < n ≤ 1.6, the first spatial period is < 325 nm, the second spatial period is 380 - 454 nm, and the third spatial period is > 521 nm, For a refractive index 1.6 < n ≤ 1.7, the first spatial period is < 318 nm, the second spatial period is 359 - 427 nm, and the third spatial period is > 492 nm, For a refractive index 1.7 < n ≤ 1.8, the first spatial period is < 314 nm, the second spatial period is 338 - 403 nm, and the third spatial period is > 463 nm, For a refractive index 1.8 < n ≤ 1.9, the first spatial period is < 308 nm, the second spatial period is 321 - 382 nm, and the third spatial period is > 440 nm, For a refractive index 1.9 < n ≤ 2.0, the first spatial period is < 302 nm, the second spatial period is 306 - 362 nm, and the third spatial period is > 419 nm, or Regarding the refractive index 2.0 < n ≤ 2.1, the first spatial period is < 298 nm, the second spatial period is 298 - 346 nm, and the third spatial period is > 397 nm. The augmented reality display system according to item 4. (Item 6) The projector system is further configured to project the set of input beams corresponding to the input image towards the first, second, and third ocular lens waveguides. The first ocular lens waveguide is located in front of the second ocular lens waveguide along the optical path of the set of input beams. The second ocular lens waveguide is located in front of the third ocular lens waveguide along the optical path of the set of input beams. The augmented reality display system according to item 4. (Item 7) The first and second sub - portions of the visual field partially overlap. The second and third sub - portions of the visual field partially overlap. The augmented reality display system according to item 3. (Item 8) The first, second, and third ICG regions are laterally aligned. The augmented reality display system according to item 3. (Item 9) The first, second, and third ICG regions are configured to receive input beams of light corresponding to a plurality of color components of the input image. The first ICG region is configured to couple, as a first set of induced beams, a first subset of the input beams for two or more of the color components into the first substrate. The first subset of the input beams corresponds to the first sub - portion of the visual field of the color components of the input image. The second ICG region is configured to couple a second subset of the input beams for two or more of the color components into the second substrate. The second subset of the input beams corresponds to the second sub - portion of the visual field of the color components of the input image. The third ICG region is configured to couple a third subset of the input beam for two or more of the color components into the third substrate, and the third subset of the input beam corresponds to a third sub - portion of the field of view of the color components of the input image. The first, second, and third sub - portions of the field of view of the individual color components of the input image are at least partially different, but together include the entire field of view of the color components of the input image. The augmented reality display system according to item 3. (Item 10) The first ICG region comprises a plurality of spatially separated sub - sections, each corresponding to one of the color components. The second ICG region comprises a plurality of spatially separated sub - sections, each corresponding to one of the color components. The third ICG region comprises a plurality of spatially separated sub - sections, each corresponding to one of the color components. The augmented reality display system according to item 9. (Item 11) The third ICG region has a second - order diffraction efficiency of less than 10%, and is the augmented reality display system according to item 9. (Item 12) Further comprising an optical filter positioned after the second eyepiece waveguide along the optical path of the input beam, the optical filter being configured to selectively absorb the input beam related to the color component having the shortest wavelength, and is the augmented reality display system according to item 9. (Item 13) The optical filter is a yellow filter that absorbs at least 90% of blue light, and is the augmented reality display system according to item 12. (Item 14) The optical filter is configured to selectively absorb the input beam related to the two color components having the two shortest wavelengths, and is the augmented reality display system according to item 12. (Item 15) The augmented reality display system according to item 14, wherein the optical filter is a red filter that absorbs at least 90% of green and blue light. (Item 16) The augmented reality display system according to item 12, wherein the optical filter is a component provided between the second ocular lens waveguide and the third ocular lens waveguide. (Item 17) The augmented reality display system according to item 12, wherein the optical filter is a dye provided within the third ocular lens waveguide. (Item 18) The augmented reality display system according to item 1, wherein the first and second ICG regions have a first-order diffraction efficiency of 5 to 90%. (Item 19) The augmented reality display system according to item 18, wherein the first ICG region is configured such that a second subset of the input beam passes through it without being diffracted. (Item 20) The augmented reality display system according to item 1, wherein the first and second ocular lens waveguides have a refractive index of 1.5 to 2.1. (Item 21) For a refractive index n ≤ 1.5, the field of view of the input image in at least one direction is greater than 29.0° but less than or equal to 44.5°. For a refractive index 1.5 < n ≤ 1.6, the field of view of the input image in at least one direction is greater than 34.9° but less than or equal to 50.4°. For a refractive index 1.6 < n ≤ 1.7, the field of view of the input image in at least one direction is greater than 41.0° but less than or equal to 54.2°. For a refractive index 1.7 < n ≤ 1.8, the field of view of the input image in at least one direction is greater than 47.2° but less than or equal to 57.5°. For a refractive index 1.8 < n ≤ 1.9, the field of view of the input image in at least one direction is greater than 53.5° but less than or equal to 60.9°. Regarding a refractive index of 1.9 < n ≤ 2.0, the field of view of the input image in at least one direction is greater than 60.0° but 64.7° or less, or Regarding a refractive index of 2.0 < n ≤ 2.1, the field of view of the input image in at least one direction is greater than 66.7° but 68.0° or less. The augmented reality display system according to item 1. (Item 22) The augmented reality display system according to item 1, wherein the first and second ocular lens waveguides have the same dimensions. (Item 23) The augmented reality display system according to item 1, wherein the first and second ocular lens waveguides are laterally aligned and vertically separated by a gap. (Item 24) A first orthogonal pupil expander (OPE) region, or a first multi-directional pupil expander (MPE) region, or a first combined pupil expander - extractor (CPE) region formed on or within the first ocular lens waveguide, wherein the first OPE, MPE, or CPE region is configured to receive a first set of the guiding beams and replicate them across a spatially dispersed portion of the first ocular lens waveguide, and a first OPE region, a first MPE region, or a first combined CPE region, A second OPE region, or a second MPE region, or a second CPE region formed on or within the second ocular lens waveguide, wherein the second OPE, MPE, or CPE region is configured to receive a second set of the guiding beams and replicate them across a spatially dispersed portion of the second ocular lens waveguide, and a second OPE region, a second MPE region, or a second combined CPE region The augmented reality display system according to item 1, further comprising (Item 25) A first output coupling grating region formed on or within the first eyepiece waveguide, the first output coupling grating region being configured to output a first set of the guiding beams from the first eyepiece waveguide as a first set of output beams. A second output coupling grating region formed on or within the second eyepiece waveguide, the second output coupling grating region being configured to output a second set of the guiding beams from the second eyepiece waveguide as a second set of output beams further comprising The augmented reality display system according to item 1, wherein both the first and second sets of the output beams include a full field of view of the input image. (Item 26) An augmented reality display system, a first eyepiece waveguide including a first optically transparent substrate; a first input coupling grating (ICG) region formed on or within the first eyepiece waveguide, the first ICG region being configured to receive a set of input beams of light, the set of input beams being associated with a set of k-vectors in k-space corresponding to an input image, and to translate the set of k-vectors to a location in k-space such that a first subset of the k-vectors is inside a first k-space ring associated with the first eyepiece waveguide, the first k-space ring corresponding to a region in k-space associated with guided propagation within the first eyepiece waveguide, the first ICG region; a second eyepiece waveguide including a second optically transparent substrate; A second input coupling grating (ICG) region formed on or within the second eyepiece waveguide, the second ICG region receiving at least a portion of a set of input beams of light and configured to translate a set of k-vectors to a location in k-space such that a second subset of the k-vectors is inside a second k-space ring associated with the second eyepiece waveguide, the second k-space ring corresponding to a region in k-space associated with guided propagation within the second eyepiece waveguide, the second ICG region and comprising an augmented reality display system, wherein the first and second subsets of the k-vectors are at least partially different but together include the complete set of k-vectors corresponding to the input image. (Item 27) The augmented reality display system according to item 26, wherein the set of k-vectors corresponding to the input image has at least one dimension in k-space that is larger than the widths of the first and second k-space rings. (Item 28) a third eyepiece waveguide comprising a third optically transmissive substrate, and a third input coupling grating (ICG) region formed on or within the third eyepiece waveguide, the third ICG region receiving at least a portion of a set of input beams of light and configured to translate a set of k-vectors to a location in k-space such that a third subset of the k-vectors is inside a third k-space ring associated with the third eyepiece waveguide, the third k-space ring corresponding to a region in k-space associated with guided propagation within the third eyepiece waveguide, the third ICG region and further comprising the augmented reality display system according to item 26, wherein the first, second, and third subsets of the k-vectors are at least partially different but together include the complete set of k-vectors corresponding to the input image. (Item 29) The display system is an equation [Number] is satisfied, where n is the refractive index of the first, second, and third eyepiece waveguide, and λ Blue is the central wavelength of the blue input light, Λ2 is the period of the second ICG region, and k FoV is the k-space dimension of the input image in the direction of the ICG vector. The augmented reality display system according to item 28. (Item 30) The display system satisfies the equation [Number] is satisfied, where n is the refractive index of the first, second, and third eyepiece waveguide, and λ Green is the central wavelength of the green input light, Λ1 is the period of the first ICG region, and Λ2 is the period of the second ICG region. The augmented reality display system according to item 28. (Item 31) The display system satisfies the equation [Number] is satisfied, where n is the refractive index of the first, second, and third eyepiece waveguide, and λ Red is the central wavelength of the red input light, Λ1 is the period of the first ICG region, and Λ2 is the period of the second ICG region. The augmented reality display system according to item 28. (Item 32) The display system satisfies the equation [Number] is satisfied, where n is the refractive index of the first, second, and third eyepiece waveguide, and λ Blueis the central wavelength of the blue input light, Λ1 is the period of the first ICG region, and k FoV is the k-space dimension of the input image in the direction of the ICG vector, The augmented reality display system according to item 28. (Item 33) The display system satisfies the equation [Number] wherein n is the refractive index of the first, second, and third eyepiece waveguide, and λ Red is the central wavelength of the red input light, Λ3 is the period of the third ICG region, and k FoV is the k-space dimension of the input image in the direction of the ICG vector, The augmented reality display system according to item 28. (Item 34) The display system satisfies the equation [Number] wherein n is the refractive index of the first, second, and third eyepiece waveguide, and λ Blue is the central wavelength of the blue input light, Λ2 is the period of the second ICG region, and k FoV is the k-space dimension of the input image in the direction of the ICG vector, The augmented reality display system according to item 28. (Item 35) The display system satisfies the equation [Number] wherein n is the refractive index of the first, second, and third eyepiece waveguide, and λ Green is the central wavelength of the green input light, Λ2 is the period of the second ICG region, and k FoVThe augmented reality display system according to item 28, which is the k-space dimension of the input image in the direction of the ICG vector. (Item 36) The display system satisfies the equation

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Brief Description of the Drawings

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[0123] Detailed Description Overview The present disclosure describes various eyepiece waveguides that can be used within an AR display system to project an image onto a user's eye. The eyepiece waveguides are described both in physical terms and in terms of the use of k-space representations. Exemplary HMD Device

[0124] Figure 2 illustrates an exemplary wearable display system 60. The display system 60 includes a display or an eyepiece 70 and various mechanical and electronic modules and systems to support the functions of the display 70. The display 70 may be coupled to a frame 80, which is wearable by a display system user 90 and configured to position the display 70 in front of the user 90's eyes. The display 70 may be considered eyewear in some embodiments. In some embodiments, a speaker 100 is coupled to the frame 80 and positioned adjacent to the user 90's external ear canal. The display system may also include one or more microphones 110 that may detect sound. The microphones 110 can enable the user to provide an input or a command to the system 60 (e.g., selection of an audio menu command, natural language question, etc.) and / or enable audio communication with other persons (e.g., other users of a similar display system). The microphones 110 can also collect audio data (e.g., sound from the user and / or the environment) from around the user. In some embodiments, the display system may also include a peripheral sensor 120a, which is separate from the frame 80 and may be attached to the user 90's body (e.g., on the head, torso, limbs, etc.). The peripheral sensor 120a may, in some embodiments, acquire data characterizing the physiological state of the user 90.

[0125] The display 70 is operatively coupled to the local data processing module 140 by a communication link 130 such as a wired conductor or wireless connectivity, which may be mounted in various configurations, such as fixedly attached to a frame 80, fixedly attached to a helmet or hat worn by a user, built into headphones, or removably attached to the user 90 (e.g., in a backpack configuration or in a belt attachment configuration). Similarly, the sensor 120a may be operatively coupled to the local processor and data module 140 by a communication link 120b (e.g., a wired conductor or wireless connectivity). The local processing and data module 140 may include a digital memory such as a hardware processor and a non-volatile memory (e.g., flash memory or hard disk drive), both of which may be utilized to assist in the processing, caching, and storage of data. The data may include 1) data captured from sensors such as an image capture device (e.g., a camera), microphone, inertial measurement unit, accelerometer, compass, GPS unit, wireless device, gyroscope, and / or other sensors disclosed herein (e.g., operatively coupled to the frame 80 or otherwise attachable to the user 90), and / or 2) potentially data obtained and / or processed using the remote processing module 150 and / or remote data repository 160 (including data related to virtual content) for passage to the display 70 after processing or retrieval. The local processing and data module 140 may be operatively coupled to the remote processing module 150 and the remote data repository 160 by communication links 170, 180 via a wired or wireless communication link or the like such that these remote modules 150, 160 are operatively coupled to each other and available as resources to the local processing and data module 140.In some embodiments, the local processing and data module 140 may include one or more of an image capture device, a microphone, an inertial measurement unit, an accelerometer, a compass, a GPS unit, a wireless device, and / or a gyroscope. In some other embodiments, one or more of these sensors may be attached to the frame 80 or may be independent devices that communicate with the local processing and data module 140 via a wired or wireless communication path.

[0126] The remote processing module 150 may include one or more processors for analyzing and processing data such as image and audio information. In some embodiments, the remote data repository 160 may be 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 160 may include one or more remote servers that provide information (e.g., information for generating augmented reality content) to the local processing and data module 140 and / or the remote processing module 150. In other embodiments, all data is stored and all calculations are performed in the local processing and data module, enabling fully autonomous use from the remote module.

[0127] Perception of an image as "three-dimensional" or "3-D" can be achieved by providing slightly different presentations of the image to each of the user's eyes. FIG. 3 illustrates a conventional display system for simulating three-dimensional image data for a user. Two distinct images 190, 200, one for each eye 210, 220, are output to the user. Images 190, 200 are separated from eyes 210, 220 by a distance 230 along an optical axis or z-axis parallel to the user's line of sight. Images 190, 200 are flat, and eyes 210, 220 can be focused on the images by taking a single focused state. Such a 3-D display system relies on the human visual system to combine images 190, 200 and provide a perception of depth and / or scale of the combined images.

[0128] However, the human visual system is complex and it is difficult to provide a realistic perception of depth. For example, many users of conventional "3-D" display systems find such systems uncomfortable or may not perceive a sense of depth at all. Objects can be perceived as "three-dimensional" due to a combination of convergence-divergence movements and accommodation. The movement of the convergence-divergence of the two eyes relative to each other (e.g., the pupils move towards each other or away from each other, rotating the pupils to converge the individual lines of sight of the eyes and fixate on an object) is closely associated with the focusing (or "accommodation") of the eye's lens. Under normal conditions, the change in the focus of the eye's lens or the eye's accommodation to change the focus from one object to another object at a different distance will automatically cause a coordinated change in convergence-divergence at the same distance under the relationship known as the "accommodation-convergence-divergence reflex" and pupillary dilation or constriction. Similarly, under normal conditions, a change in convergence-divergence will induce a coordinated change in accommodation of the lens shape and pupil size. As described herein, many stereoscopic or "3-D" display systems use slightly different presentations (and thus slightly different images) to each eye so that a three-dimensional viewpoint is perceived by the human visual system to display a scene. However, such systems can be uncomfortable for some users because they simply provide image information in a single accommodated state and function against the "accommodation-convergence-divergence reflex". A display system that provides a better match between accommodation and convergence-divergence can form a more realistic and comfortable simulation of three-dimensional image data.

[0129] FIG. 4 illustrates aspects of an approach for simulating 3D image data using a plurality of depth planes. Referring to FIG. 4, eyes 210, 220 take on different focused states and focus an object at various distances along the z-axis. As a result, a particular focused state is associated with a particular one of the illustrated depth planes 240 having a focal length such that an object or a portion of an object in that particular depth plane is in focus when the eye is in the focused state with respect to that depth plane. In some embodiments, the 3D image data may be simulated by providing different presentations of the image for each of the eyes 210, 220 and also by providing different presentations of the image corresponding to the plurality of depth planes. Although shown as separate for clarity of illustration, the individual fields of view of the eyes 210, 220 may overlap, for example, as the distance along the z-axis increases. Additionally, although the depth planes are shown as flat for ease of illustration, it should 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 focused state.

[0130] The distance between an object and an eye 210 or 220 can also vary the amount of divergence of light from that object as viewed by that eye. FIGS. 5A-5C illustrate the relationship between distance and divergence of light rays. The distances between the object and the eye 210 are represented in the order of decreasing distances R1, R2, and R3. As shown in FIGS. 5A-5C, the light rays diverge more as the distance to the object decreases. As the distance increases, the light rays become more collimated. In other words, it can be said that the light field generated by a point (object or part of an object) has a spherical wavefront curvature that is a function of the distance the point is away from the user's eye. The curvature increases as the distance between the object and the eye 210 decreases. As a result, at different depth planes, the divergence of the light rays also differs, and the divergence increases as the distance between the depth plane and the user's eye 210 decreases. Only the monocular 210 is illustrated in FIGS. 5A-5C and other figures in this specification for clarity of illustration, but it should be understood that the discussion regarding the eye 210 can apply to both of the user's eyes 210 and 220.

[0131] A realistic simulation of the perceived depth altitude can be achieved by providing different presentations of images corresponding to each of a limited number of depth planes to the eyes. The different presentations are separately focused by the user's eyes, thereby based on the amount of eye accommodation required to focus on different image features for scenes located on different depth planes and / or based on the observation of different out-of-focus image features on different depth planes, which may help to provide depth cues to the user. Example of a waveguide stack assembly for an AR or MR eyepiece

[0132] FIG. 6 illustrates an example of a waveguide stack for outputting image information to a user within an AR eyepiece. Display system 250 includes a stack of waveguides or a stacked waveguide assembly 260 that can be utilized to provide three-dimensional perception to the eye / brain using a plurality of waveguides 270, 280, 290, 300, 310. In some embodiments, display system 250 is the system 60 of FIG. 2, and FIG. 6 schematically shows some parts of that system 60 in more detail. For example, waveguide assembly 260 may be part of display 70 of FIG. 2. It should be understood that display system 250 may be regarded as a light field display in some embodiments.

[0133] The waveguide assembly 260 may also include a plurality of features 320, 330, 340, 350 between the waveguides. In some embodiments, the features 320, 330, 340, 350 may be one or more lenses. The waveguides 270, 280, 290, 300, 310 and / or the plurality of lenses 320, 330, 340, 350 may be configured to transmit image information to the eye using various levels of wavefront curvature or ray divergence. Each waveguide level may be associated with a particular depth plane and may be configured to output image information corresponding to that depth plane. The image input devices 360, 370, 380, 390, 400 may function as light sources for the waveguides and may be utilized to input image information into the waveguides 270, 280, 290, 300, 310, and may each be configured to disperse incident light across the respective waveguide to output it towards the eye 210, as described herein. Light exits from the output surfaces 410, 420, 430, 440, 450 of each individual image input device 360, 370, 380, 390, 400 and is input into the corresponding input surfaces 460, 470, 480, 490, 500 of the individual waveguides 270, 280, 290, 300, 310. In some embodiments, the input surfaces 460, 470, 480, 490, 500 may each be an edge of the corresponding waveguide or a part of the major surface of the corresponding waveguide (i.e., one of the waveguide surfaces facing directly towards the world 510 or the user's eye 210). In some embodiments, a beam of light (e.g., a collimated beam) may be input into each waveguide and replicated by refraction within the waveguide, such as by sampling into beamlets, and then directed towards the eye 210 with an amount of refractive power corresponding to the depth plane associated with that particular waveguide. In some embodiments, a single one of the image input devices 360, 370, 380, 390, 400 may be associated with and input light into a plurality (e.g., three) of the waveguides 270, 280, 290, 300, 310.

[0134] In some embodiments, the image input devices 360, 370, 380, 390, 400 are discrete displays that each generate image information for input into their respective waveguides 270, 280, 290, 300, 310. In some other embodiments, the image input devices 360, 370, 380, 390, 400 are the output ends of a single multiplexed display that can send image information to each of the image input devices 360, 370, 380, 390, 400 via one or more optical waveguides (such as optical fiber cables). It should be understood that the image information provided by the image input devices 360, 370, 380, 390, 400 may include light of different wavelengths or colors.

[0135] In some embodiments, the light input into the waveguides 270, 280, 290, 300, 310 is provided by an optical projector system 520, which may include an optical module 530 that may include a light source or emitter such as a light-emitting diode (LED). The light from the optical module 530 may be directed and modulated by an optical modulator 540 (such as a spatial light modulator) via a beam splitter (BS) 550. The optical modulator 540 may spatially and / or temporally vary the perceived intensity of the light input into the waveguides 270, 280, 290, 300, 310. Examples of spatial light modulators include liquid crystal displays (LCDs) and digital light processing (DLP) displays, including liquid crystal on silicon (LCOS) displays.

[0136] In some embodiments, the optical projector system 520 or one or more of its components may be attached to the frame 80 (FIG. 2). For example, the optical projector system 520 may be part of a vine portion (such as the earhook portion 82) of the frame 80 or may be disposed at the edge of the display 70. In some embodiments, the optical module 530 may be separate from the BS 550 and / or the optical modulator 540.

[0137] In some embodiments, the display system 250 may be a scanning fiber display that includes one or more scanning fibers for projecting light in various patterns (e.g., raster scan, helical scan, Lissajous pattern, etc.) into one or more waveguides 270, 280, 290, 300, 310 and ultimately into the user's eye 210. In some embodiments, the illustrated image input devices 360, 370, 380, 390, 400 may schematically represent a single scanning fiber or a bundle of scanning fibers configured to input light into one or more waveguides 270, 280, 290, 300, 310. In some other embodiments, the illustrated image input devices 360, 370, 380, 390, 400 may schematically represent a plurality of scanning fibers or a plurality of bundles of scanning fibers, each configured to input light into an associated one of the waveguides 270, 280, 290, 300, 310. One or more optical fibers may transmit light from the optical module 530 to one or more of the waveguides 270, 280, 290, 300, and 310. Additionally, one or more intervening optical structures may be provided between the scanning fiber or fibers and the one or more waveguides 270, 280, 290, 300, 310, for example, to redirect light exiting the scanning fiber into one or more of the waveguides 270, 280, 290, 300, 310.

[0138] The controller 560 controls the operation of the stacked waveguide assembly 260, including the operation of the image input devices 360, 370, 380, 390, 400, the light source 530, and the optical module 540. In some embodiments, the controller 560 is part of the local data processing module 140. The controller 560 includes programming (e.g., instructions in a non-transitory medium) that adjusts the timing and provision of image information to the waveguides 270, 280, 290, 300, 310. In some embodiments, the controller may be a single integrated device or a distributed system connected by a wired or wireless communication channel. The controller 560 may, in some embodiments, be part of the processing module 140 or 150 (FIG. 2).

[0139] Waveguides 270, 280, 290, 300, 310 may be configured to propagate light within each individual waveguide by total internal reflection (TIR). Each of waveguides 270, 280, 290, 300, 310 may be planar or have another shape (e.g., curved), with a major top and bottom surface and an edge extending between those major top and bottom surfaces. In the illustrated configuration, waveguides 270, 280, 290, 300, 310 each include external coupling optical elements 570, 580, 590, 600, 610 configured to extract light from the waveguide by redirecting light propagating within each individual waveguide out of the waveguide and outputting image information to eye 210. The extracted light may also be referred to as external coupled light, and the optical elements that externally couple the light may also be referred to as light extraction optical elements. The beam of extracted light may be output by the waveguide at the location where the light propagating within the waveguide impinges on the light extraction optical element. External coupling optical elements 570, 580, 590, 600, 610 may be diffractive optical features, including, for example, diffraction gratings as further discussed herein. External coupling optical elements 570, 580, 590, 600, 610 are shown disposed on the bottom major surface of waveguides 270, 280, 290, 300, 310, but in some embodiments they may be disposed on the top and / or bottom major surfaces and / or directly within the volume of waveguides 270, 280, 290, 300, 310, as further discussed herein. In some embodiments, external coupling optical elements 570, 580, 590, 600, 610 may be attached to a transparent substrate and formed within a layer of material that forms waveguides 270, 280, 290, 300, 310. In some other embodiments, waveguides 270, 280, 290, 300, 310 may be a monolithic piece of material, and external coupling optical elements 570, 580, 590, 600, 610 may be formed on and / or within the surface of that piece of material.

[0140] Each waveguide 270, 280, 290, 300, 310 may output light and form an image corresponding to a specific depth plane. For example, the waveguide 270 closest to the eye may deliver a collimated light beam to the eye 210. The collimated light beam may represent an optically infinite focal plane. The next upper waveguide 280 may output a collimated light beam that passes through a first lens 350 (e.g., a negative lens) before reaching the eye 210. The first lens 350 may add some convex wavefront curvature to the collimated beam so that the eye / brain interprets the light arising from that waveguide 280 as arising from a first focal plane that is closer inwardly from the optically infinite towards the eye 210. Similarly, the third upper waveguide 290 passes its output light through both the first lens 350 and the second lens 340 before reaching the eye 210. The combined refractive power of the first lens 350 and the second lens 340 may add another incremental amount of wavefront curvature so that the eye / brain interprets the light arising from the third waveguide 290 as arising from a second focal plane that is even closer inwardly from the optically infinite than the light from the second waveguide 280.

[0141] The other waveguide layers 300, 310 and lenses 330, 320 are similarly configured, and the top waveguide 310 in the stack sends its output through all of the lenses between it and the eye for the converging focal power representing the focal plane closest to the person. When viewing / interpreting light arising from the world 510 on the other side of the stacked waveguide assembly 260, a compensation lens layer 620 may be disposed on top of the stack to compensate for the combined refractive power of the lower lens stack 320, 330, 340, 350. Such a configuration provides the same number of perceived focal planes as there are available waveguide / lens pairs. Both the external coupling 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.

[0142] In some embodiments, two or more of the waveguides 270, 280, 290, 300, 310 may have the same associated depth plane. For example, a plurality of waveguides 270, 280, 290, 300, 310 may output images set to the same depth plane, or a plurality of subsets of the waveguides 270, 280, 290, 300, 310 may output images set to the same plurality of depth planes, with one set per depth plane. This can provide the advantage of forming tiled images to provide an expanded field of view at those depth planes.

[0143] The external coupling optical elements 570, 580, 590, 600, 610 may be configured to redirect light from their respective waveguides for a particular depth plane associated with the waveguide and output the light with an appropriate amount of divergence or collimation. As a result, waveguides having different associated depth planes may have different configurations of external coupling optical elements 570, 580, 590, 600, 610 that output light with different amounts of divergence depending on the associated depth plane. In some embodiments, the light extraction optical elements 570, 580, 590, 600, 610 may be three-dimensional or surface features configured to output light at a specific angle. For example, the light extraction optical elements 570, 580, 590, 600, 610 may be volume holograms, surface holograms, and / or diffraction gratings. In some embodiments, the features 320, 330, 340, 350 may not be lenses. Rather, they may simply be spacers (e.g., cladding layers and / or structures for forming voids).

[0144] In some embodiments, the external coupling optical elements 570, 580, 590, 600, 610 are diffraction features with a sufficiently low diffraction efficiency such that only a portion of the refractive power of the light within the beam is redirected towards the eye 210 with each interaction, while the remainder continues to travel through the waveguide via TIR. Thus, the exit pupil of the optical module 530 is replicated across the waveguide, creating multiple output beams that carry image information from the light source 530 and effectively expanding the number of locations where the eye 210 can capture the replicated light source exit pupil. These diffraction features may also have a variable diffraction efficiency across their geometry and may improve the uniformity of the light output by the waveguide.

[0145] In some embodiments, one or more diffraction features 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 diffraction feature may comprise a layer of polymer-dispersed liquid crystal in which microdroplets have a diffraction pattern within a host medium, and the refractive index of the microdroplets may be switched to substantially match that of the host material (in which case the pattern does not significantly diffract the 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 the incident light).

[0146] In some embodiments, a camera assembly 630 (e.g., a digital camera including visible light and IR light cameras) is provided to capture an image of the eye 210, a part of the eye 210, or at least a part of the tissue surrounding the eye 210, and may, for example, detect user input, extract biometric information from the eye, estimate and track the line of sight direction of the eye, monitor the physiological state of the user, and the like. In some embodiments, the camera assembly 630 may include an image capture device and a light source for projecting light (e.g., IR or near-IR light) onto the eye (which may then be reflected by the eye and detected by the image capture device). In some embodiments, the light source includes a light emitting diode ("LED") that emits IR or near-IR thereof. In some embodiments, the camera assembly 630 may be attached to the frame 80 (FIG. 2) and may communicate electrically with the processing module 140 or 150, which may process the image information from the camera assembly 630 and make various determinations regarding, for example, the physiological state of the user, the line of sight direction of the wearer, iris identification, and the like. In some embodiments, one camera assembly 630 may be utilized for each eye to monitor each eye separately.

[0147] FIG. 7A illustrates an example of an output beam output by a waveguide. One waveguide is shown (using a perspective view), but other waveguides within the waveguide assembly 260 (FIG. 6) can function similarly. Light 640 is input into the waveguide 270 at the input surface 460 of the waveguide 270 and propagates within the waveguide 270 by TIR. Through interaction with the diffraction features, the light exits the waveguide as an output beam 650. The output beam 650 replicates the exit pupil from a projector device that projects an image into the waveguide. Any one of the output beams 650 contains a sub - portion of the total energy of the input light 640. Also, in a perfectly efficient system, the sum of the energy within all the output beams 650 would be equal to the energy of the input light 640. The output beams 650 are shown in FIG. 7A as being substantially parallel, but as discussed herein, some amount of refractive power may be imparted depending on the depth plane associated with the waveguide 270. The parallel output beams can represent a waveguide with an external - coupling optical element that forms an image that externally couples the light and appears to be set on a depth plane at a long distance (e.g., optical infinity) from the eye 210. Another set of waveguides or other external - coupling optical elements may output a more divergent output - beam pattern, as shown in FIG. 7B, which would require the eye 210 to focus at a closer distance and would be interpreted by the brain as light from a distance closer to the eye 210 than optical infinity.

[0148] In some embodiments, a full-color image may be formed on each depth plane by overlaying an image on each of the primary colors (e.g., three or more primary colors such as red, green, and blue). FIG. 8 illustrates an example of a stacked waveguide assembly, and each depth plane includes an image formed using a plurality of different primary colors. The illustrated embodiment shows depth planes 240a-240f, but more or fewer depths may also be considered. Each depth plane may have three or more primary color images associated therewith, including a first image of a first color G, a second image of a second color R, and a third image of a third color B. Different depth planes are shown in the figure by different diopter numbers following the letters G, R, and B. The numbers following each of these letters indicate the diopter (1 / m), i.e., the inverse distance of the depth plane from the user, and each box in the figure represents an individual primary color image. In some embodiments, to account for differences in the focusing of light of different wavelengths by the eye, the exact location of the depth plane for different primary colors may vary. For example, different primary color images for a given depth plane may be disposed on a depth plane corresponding to different distances from the user. Such an arrangement may increase visual acuity and user comfort, or may reduce chromatic aberration.

[0149] In some embodiments, the light of each primary color may be output by a single dedicated waveguide, and as a result, each depth plane may have a plurality of waveguides associated therewith. In such embodiments, each box in the figure may be understood to represent an individual waveguide, and three waveguides may be provided for each depth plane to display three primary color images for each depth plane. The waveguides associated with each depth plane are shown adjacent to each other in this figure for ease of illustration, but it should be understood that in a physical device, all of the waveguides may be arranged in a stack with one waveguide per level. In some other embodiments, a plurality of primary colors may be output by the same waveguide, such that, for example, only a single waveguide may be provided for each depth plane.

[0150] Continuing to refer to FIG. 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 yellow, magenta, and cyan, may also be used in addition, or may replace one or more of red, green, or blue. In some embodiments, features 320, 330, 340, and 350 may be active or passive optical filters configured to selectively block or pass light from the surrounding environment to the user's eyes.

[0151] It should be understood that references to the color of a given light throughout this disclosure encompass light of one or more wavelengths within the range of wavelengths of the light that is perceived by the user as that given color. For example, red light may include light of one or more wavelengths within the range of about 620 - 780 nm, green light may include light of one or more wavelengths within the range of about 492 - 577 nm, and blue light may include light of one or more wavelengths within the range of about 435 - 493 nm.

[0152] In some embodiments, the light source 530 (FIG. 6) may be configured to emit light of one or more wavelengths outside the user's visual perception range, such as IR and / or ultraviolet wavelengths. IR light can include light with wavelengths in the range of 700 nm to 10 μm. In some embodiments, the IR light can include near - IR light with wavelengths in the range of 700 nm to 1.5 μm. Additionally, the internal coupling, external coupling, and other light redirection structures of the waveguide of the display 250 may be configured to direct and emit this light from the display towards the user's eyes 210, for example, for imaging and / or user stimulation purposes.

[0153] Referring now to FIG. 9A, in some embodiments, light impinging on the waveguide may need to be redirected to internally couple the light into the waveguide. An internal coupling optical element may be used to redirect and internally couple the light into its corresponding waveguide. FIG. 9A illustrates a cross-sectional side view of an example of a set 660 of stacked waveguides, each including an internal coupling optical element. Each waveguide may be configured to output light of one or more different wavelengths or one or more different wavelength ranges. Stack 660 may correspond to stack 260 (FIG. 6), and the illustrated waveguides of stack 660 may correspond to a portion of the plurality of waveguides 270, 280, 290, 300, 310, but it should be understood that light from one or more of the image input devices 360, 370, 380, 390, 400 is input into the waveguide from a position or orientation that requires the light to be redirected for internal coupling.

[0154] The illustrated set 660 of stacked waveguides includes waveguides 670, 680, and 690. Each waveguide includes an associated internal coupling optical element (which may also be referred to as an optical input area on the waveguide). For example, internal coupling optical element 700 is disposed on a major surface (e.g., the upper major surface) of waveguide 670, internal coupling optical element 710 is disposed on a major surface (e.g., the upper major surface) of waveguide 680, and internal coupling optical element 720 is disposed on a major surface (e.g., the upper major surface) of waveguide 690. In some embodiments, one or more of the internal coupling optical elements 700, 710, 720 may be disposed on the bottom major surface of the respective waveguide 670, 680, 690 (in particular, one or more of the internal coupling optical elements are reflective optical elements). As illustrated, the internal coupling optical elements 700, 710, 720 may be disposed on the upper major surface (or the upper part of the next lower waveguide) of their respective waveguides 670, 680, 690. In particular, those internal coupling optical elements are transmissive optical elements. In some embodiments, the internal coupling optical elements 700, 710, 720 may be disposed within the body of the respective waveguides 670, 680, 690. In some embodiments, as discussed herein, the internal coupling optical elements 700, 710, 720 are wavelength selective 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 their respective waveguides 670, 680, 690, it should be understood that the internal coupling optical elements 700, 710, 720 may be disposed within other areas of their respective waveguides 670, 680, 690 in some embodiments.

[0155] As shown, the internally coupled optical elements 700, 710, 720 may be laterally offset from each other. In some embodiments, each internally coupled optical element may be offset such that its light is received without passing through another internally coupled optical element. For example, each internally coupled optical element 700, 710, 720 may be configured to receive light from different image input devices 360, 370, 380, 390, and 400, as shown in FIG. 6, and may be separated (e.g., laterally spaced) from other internally coupled optical elements 700, 710, 720 such that it receives substantially no light from other internally coupled optical elements 700, 710, 720.

[0156] Each waveguide also includes an associated light dispersing element. For example, the light dispersing element 730 is disposed on a major surface (e.g., upper major surface) of the waveguide 670, the light dispersing element 740 is disposed on a major surface (e.g., upper major surface) of the waveguide 680, and the light dispersing element 750 is disposed on a major surface (e.g., upper major surface) of the waveguide 690. In some other embodiments, the light dispersing elements 730, 740, 750 may each be disposed on a bottom major surface of the associated waveguides 670, 680, 690. In some other embodiments, the light dispersing elements 730, 740, 750 may each be disposed on both the upper and bottom major surfaces of the associated waveguides 670, 680, 690, or the light dispersing elements 730, 740, 750 may each be disposed on different ones of the upper and bottom major surfaces within different associated waveguides 670, 680, 690.

[0157] Waveguides 670, 680, 690 may be separated and isolated, for example, by gas, liquid, and / or solid layers of material. For example, as shown, layer 760a may separate waveguides 670 and 680, and layer 760b may separate waveguides 680 and 690. In some embodiments, layers 760a and 760b are formed from a low refractive index material (i.e., a material having a refractive index lower than the material forming the immediate waveguides 670, 680, 690). Preferably, the refractive index of the material forming layers 760a, 760b is at least 0.05 or at least 0.10 lower than the refractive index of the material forming waveguides 670, 680, 690. Advantageously, the lower refractive index layers 760a, 760b may function as cladding layers that facilitate TIR of light through waveguides 670, 680, 690 (e.g., TIR between the upper and bottom major surfaces of each waveguide). In some embodiments, layers 760a, 760b are formed from air. It should be understood that although not shown, the top and bottom of the illustrated set 660 of waveguides may include an immediate cladding layer.

[0158] Preferably, for ease of manufacture and other considerations, the materials forming waveguides 670, 680, 690 are similar or identical, and the materials forming layers 760a, 760b are similar or identical. In other embodiments, the materials forming waveguides 670, 680, 690 may be different between one or more waveguides, or the materials forming layers 760a, 760b may still be different while maintaining the various refractive index relationships described above.

[0159] Continuing to refer to FIG. 9A, light rays 770, 780, 790 are incident on the set 660 of waveguides. Light rays 770, 780, 790 may be introduced into waveguides 670, 680, 690 by one or more image input devices 360, 370, 380, 390, 400 (FIG. 6).

[0160] In some embodiments, the light rays 770, 780, 790 may have different properties (e.g., different wavelengths or different wavelength ranges) corresponding to different colors. Each of the internal coupling optical elements 700, 710, 720 redirects the incident light so that the light propagates through an individual one of the waveguides 670, 680, 690 by TIR.

[0161] For example, the internal coupling optical element 700 may be configured to selectively redirect the light ray 770 having a first wavelength or wavelength range. Similarly, the transmitted light ray 780 impinges on the internal coupling optical element 710 configured to redirect light of a second wavelength or wavelength range, thereby being redirected. Similarly, the light ray 790 is redirected by the internal coupling optical element 720 configured to selectively redirect light of a third wavelength or wavelength range.

[0162] Continuing to refer to FIG. 9A, the light rays 770, 780, 790 are redirected to propagate through the corresponding waveguides 670, 680, 690. That is, the internal coupling optical elements 700, 710, 720 of each waveguide redirect the light into its corresponding waveguide 670, 680, 690 and internally couple the light into the corresponding waveguide. The light rays 770, 780, 790 are redirected at an angle that causes the light to propagate through the individual waveguides 670, 680, 690 by TIR. The light rays 770, 780, 790 propagate through the individual waveguides 670, 680, 690 by TIR until they interact with the corresponding light dispersion elements 730, 740, 750 of the waveguides.

[0163] Referring now to FIG. 9B, a perspective view of an embodiment of the plurality of stacked waveguides of FIG. 9A is illustrated. As described above, light rays 770, 780, 790 are internally coupled by internal coupling optical elements 700, 710, 720, respectively, and then propagate by TIR within waveguides 670, 680, 690, respectively. Light rays 770, 780, 790 then interact with light dispersing elements 730, 740, 750, respectively. Light dispersing elements 730, 740, 750 redirect light rays 770, 780, 790 so as to propagate towards external coupling optical elements 800, 810, and 820, respectively.

[0164] In some embodiments, light dispersing elements 730, 740, 750 are orthogonal pupil expanders (OPEs). In some embodiments, the OPEs perform both redirecting light to external coupling optical elements 800, 810, 820 and expanding the pupil associated with this light by sampling light rays 770, 780, 790 at many locations across light dispersing elements 730, 740, 750 as they propagate towards the external coupling optical elements. In some embodiments (e.g., when the exit pupil is already of a desired size), light dispersing elements 730, 740, 750 may be omitted and internal coupling optical elements 700, 710, 720 may be configured to redirect light directly to external coupling optical elements 800, 810, 820. For example, referring to FIG. 9A, light dispersing elements 730, 740, 750 may be replaced by external coupling optical elements 800, 810, 820, respectively. In some embodiments, external coupling optical elements 800, 810, 820 are exit pupils (EPs) or exit pupil expanders (EPEs) that redirect light from the waveguide towards the user's eye 210 (FIG. 7). The OPE may be configured to increase the size of the eyebox in at least one axis, and the EPE may be configured to increase the eyebox in an axis that intersects (e.g., is orthogonal to) the axis of the OPE.

[0165] Thus, referring to FIGS. 9A and 9B, in some embodiments, a set of waveguides 660 includes, for each primary color, waveguides 670, 680, 690, internal coupling optical elements 700, 710, 720, light dispersion elements (e.g., OPE) 730, 740, 750, and external coupling optical elements (e.g., EPE) 800, 810, 820. The waveguides 670, 680, 690 may be stacked with a gap / cladding layer between each one. The internal coupling optical elements 700, 710, 720 direct incident light into the corresponding waveguides (using different internal coupling optical elements that receive light of different wavelengths). The light then propagates at an angle that aids TIR within the individual waveguides 670, 680, 690. Since TIR occurs only over a certain angular range, the range of propagation angles of the light rays 770, 780, 790 is limited. The range of angles that aid TIR can be considered the angular limit of the field of view that can be presented by the waveguides 670, 680, 690 in such embodiments. In the illustrated embodiment, the light ray 770 (e.g., blue light) is internally coupled by the first internal coupling optical element 700 in the manner described above and then continues to reciprocally reflect from the surface of the waveguide as it travels through the waveguide. The light dispersion element (e.g., OPE) 730 then gradually samples it and creates additional replicated light rays that are directed towards the external coupling optical element (e.g., EPE) 800. The light rays 780 and 790 (e.g., green and red light, respectively) pass through the waveguide 670. The light ray 780 impinges on the internal coupling optical element 710 and is thereby internally coupled. The light ray 780 then propagates through the waveguide 680 via TIR and will proceed to its light dispersion element (e.g., OPE) 740 and then to the external coupling optical element (e.g., EPE) 810. Finally, the light ray 790 (e.g., red light) passes through the waveguides 670, 680 and impinges on the internal coupling optical element 720 of the waveguide 690. The internal coupling optical element 720 internally couples the light ray 790 such that the light ray propagates via TIR to the light dispersion element (e.g., OPE) 750 and then via TIR to the external coupling optical element (e.g., EPE) 820. The external coupling optical element 820 then finally externally couples the light ray 790 to the user, and the viewer also receives the externally coupled light from the other waveguides 670, 680.

[0166] FIG. 9C illustrates top and bottom plan views of an example of a plurality of stacked waveguides of FIGS. 9A and 9B. As shown, waveguides 670, 680, 690 may be vertically aligned with associated optical dispersion elements 730, 740, 750 and associated external coupling optical elements 800, 810, 820 of each waveguide. However, as discussed herein, internal coupling optical elements 700, 710, 720 are not vertically aligned. Rather, the internal coupling optical elements may be non-overlapping (e.g., laterally spaced as seen in the top and bottom views). This non-overlapping spatial arrangement may facilitate the injection of light from different sources into different waveguides on a one-to-one basis, thereby enabling a particular light source to be optically coupled uniquely to a particular waveguide. In some embodiments, an array including non-overlapping spatially separated internal coupling optical elements may be referred to as an offset pupil system, and the internal coupling optical elements within these arrays may correspond to sub-pupils.

[0167] FIG. 10 is a perspective view of an exemplary AR eyepiece waveguide stack 1000. The eyepiece waveguide stack 1000 may include a world-side cover window 1002 and an eye-side cover window 1006 that protect one or more eyepiece waveguides 1004 positioned therebetween. In other embodiments, one or both of the cover windows 1002, 1006 may be omitted. As already discussed, the eyepiece waveguides 1004 may be arranged in a stratified configuration. The eyepiece waveguides 1004 may be coupled together. For example, each individual eyepiece waveguide may be coupled to one or more adjacent eyepiece waveguides. In some embodiments, the waveguides 1004 may be coupled with edge seals (such as edge seal 1108 shown in FIG. 11) such that adjacent eyepiece waveguides 1004 do not contact each other directly.

[0168] Each of the eyepiece waveguide 1004 can be made from a substrate material that is at least partially transparent, such as glass, plastic, polycarbonate, sapphire, etc. The selected material may have a refractive index greater than 1.4, for example, greater than 1.6 or 1.8, and may facilitate optical guiding. The thickness of each eyepiece waveguide substrate may be, for example, 325 microns or less, although other thicknesses can also be used. Each eyepiece waveguide can include one or more internal coupling regions, an optical dispersion region, an image expansion region, and an external coupling region, which may consist of diffraction features formed on or within each waveguide substrate 902.

[0169] Although not shown in FIG. 10, the eyepiece waveguide stack 1000 can include a physical support structure for supporting it in front of the user's eye. In some embodiments, the eyepiece waveguide stack 1000 is part of a head-mounted display system 60 as shown in FIG. 2. Generally, the eyepiece waveguide stack 1000 is supported such that the external coupling region is directly in front of the user's eye. It should be understood that FIG. 10 shows only a portion of the eyepiece waveguide stack 1000 corresponding to one of the user's eyes. The completed eyepiece may include a mirror image of the same structure with two halves that are potentially separated by a nose piece.

[0170] In some embodiments, the eyepiece waveguide stack 1000 can project color image data into the user's eye from multiple depth planes. The image data displayed by each individual eyepiece waveguide 1004 within the eyepiece 1000 may correspond to a selected color component of the image data for a selected depth plane. For example, since the eyepiece waveguide stack 1000 includes six eyepiece waveguides 1004, it can project color image data (e.g., consisting of red, green, and blue components) corresponding to two different depth planes, i.e., one eyepiece waveguide 1004 per color component per depth plane. Other embodiments can include more or fewer color components and / or more or fewer eyepiece waveguides 1004 for more or fewer depth planes.

[0171] FIG. 11 is a partial cross-sectional view of an exemplary eyepiece waveguide stack 1100 with an edge seal structure 1108 for supporting the stacked configuration of the eyepiece waveguides 1104. The edge seal structure 1108 aligns the eyepiece waveguides 1104 and separates them from each other using an air space or another material disposed therebetween. Although not shown, the edge seal structure 1108 can extend around the entire perimeter of the stacked waveguide configuration. In FIG. 11, the separation between each eyepiece waveguide is 0.027 mm, although other distances are also possible.

[0172] In the illustrated embodiment, there are two eyepiece waveguide 1104 designed to display red image data, one for a 3m depth plane and the other for a 1m depth plane. (Again, the divergence of the light beam output by the eyepiece waveguide 1104 can be made to appear to originate from a depth plane located at a specific distance for the image data.) Similarly, there are two eyepiece waveguide 1104 designed to display blue image data, one for a 3m depth plane and the other for a 1m depth plane, and two eyepiece waveguide 1104 designed to display green image data, one for a 3m depth plane and the other for a 1m depth plane. These six eyepiece waveguide 1104 are each illustrated as being 0.325 mm thick, although other thicknesses are also possible as considerations.

[0173] The world-side cover window 1102 and the eye-side cover window 1106 are also shown in FIG. 11. These cover windows can be, for example, 0.330 mm thick. Considering the thicknesses of the six eyepiece waveguide 1104, the seven air gaps, the two cover windows 1102, 1106, and the edge seal 1108, the total thickness of the illustrated eyepiece waveguide stack 1100 is 2.8 mm. k-space Representation of the AR Eyepiece Waveguide

[0174] Figures 12A and 12B illustrate top views of the eyepiece waveguide 1200 during operation when projecting an image towards the user's eye 210. The image can first be projected from the image plane 1207 towards the entrance pupil 1208 of the eyepiece waveguide 1200 using a projection lens 1210 or some other projector device. Each image point (e.g., an image pixel or a part of an image pixel) has a corresponding input beam of light (e.g., 1202a, 1204a, 1206a), which propagates in a specific direction at the entrance pupil 1208 (e.g., a specific angle with respect to the optical axis of the projector lens 1210). Although shown as light rays, the input beams of light 1202a, 1204a, 1206a may be collimated beams with a diameter of a few millimeters or less when they enter the eyepiece waveguide 1200.

[0175] In FIGS. 12A and 12B, the central image point corresponds to the input beam 1204a, which is illustrated using a solid line. The right-side image point corresponds to the input beam 1202a, which is illustrated using a dashed line. The left-side image point, illustrated using a dotted line, corresponds to the input beam 1206a. For clarity of illustration, only three input beams 1202a, 1204a, 1206a are shown at the entrance pupil 1208, but a typical input image will include many input beams that propagate within an angular range in both the x - direction and the y - direction corresponding to different image points within a two - dimensional image plane.

[0176] There is a unique correspondence between the various propagation angles of the input beams (e.g., 1202a, 1204a, 1206a) in the entrance pupil 1208 and the individual image points in the image plane 1207. The eyepiece waveguide 1200 can all internally couple the input beams (e.g., 1202a, 1204a, 1206a), replicate them through space in a distributed pattern while substantially maintaining the correspondence between the image points and the beam angles, guide them, and be designed to form an exit pupil 1210 that is larger than the entrance pupil 1208 and consists of the replicated beams. The eyepiece waveguide 1200 can convert to a given input beam of light (e.g., 1202a), which propagates into a number of replicated beams (e.g., 1202b) at a specific angle and is output across the exit pupil 1210 at an angle that is substantially uniquely correlated with that specific input beam and its corresponding image point. For example, the replicated output beams corresponding to each input beam can exit the eyepiece waveguide 1200 at substantially the same angle as their corresponding input beam.

[0177] As shown in FIGS. 12A and 12B, the input beam of light 1204a corresponding to the central image point in the image plane 1207 is converted into a set of replicated output beams 1204b shown by solid lines, which are aligned with the optical axis perpendicular to the exit pupil 1210 of the eyepiece waveguide 1200. The input beam of light 1202a corresponding to the right image point in the image plane 1207 is converted into a set of replicated output beams 1202b shown by dashed lines, which exit the eyepiece waveguide 1200 at a propagation angle such that they appear to originate from a location within the right portion of the user's field of view. Similarly, the input beam of light 1206a corresponding to the left image point in the image plane 1207 is converted into a set of replicated output beams 1206b shown by chain lines, which exit the eyepiece waveguide 1200 at a propagation angle such that they appear to originate from a location within the left portion of the user's field of view. The larger the range of the input beam angle and / or the output beam angle, the larger the field of view (FOV) of the eyepiece waveguide 1200.

[0178] For each image, there is a set of replicated output beams (e.g., 1202b, 1204b, 1206b), i.e., one set of replicated beams per image point, which are output at different angles across the exit pupil 1210. Each individual output beam (e.g., 1202b, 1204b, 1206b) can be collimated. The set of output beams corresponding to a given image point may consist of beams that propagate along a parallel path (as shown in FIG. 12A) or a diverging path (as shown in FIG. 12B). In either case, the specific propagation angles of the set of replicated output beams depend on the location of the corresponding image point on the image plane 1207. FIG. 12A illustrates the case where each set of output beams (e.g., 1202b, 1204b, 1206b) consists of beams that propagate along a parallel path. This results in a projection such that the image appears as if it is originating from optical infinity. This is represented in FIG. 12A by thin lines extending from the peripheral output beams 1202b, 1204b, 1206b towards optical infinity on the world side of the eyepiece waveguide 1200 (the side opposite to where the user's eye 210 is located). FIG. 12B illustrates the case where each set of output beams (e.g., 1202b, 1204b, 1206b) consists of beams that propagate along a diverging path. This results in a projection such that the image appears as if it is originating from a virtual depth plane having a distance closer than optical infinity. This is represented in FIG. 12B by thin lines extending from the peripheral output beams 1202b, 1204b, 1206b towards a point on the world side of the eyepiece waveguide 1200.

[0179] Again, each set of replicated output beams (e.g., 1202b, 1204b, 1206b) has a propagation angle corresponding to a specific image point on the image plane 1207. In the case of a set of replicated output beams propagating along a parallel path (see FIG. 12A), the propagation angles of all the beams are the same. However, in the case of a set of replicated output beams propagating along a diverging path, the individual output beams can propagate at different angles, but those angles are related to each other in that they appear to create a converging diverging wavefront and originate from a common point along the axis of the beam set (see FIG. 12B). This axis defines the angle of propagation for the set of diverging output beams and corresponds to a specific image point on the image plane 1207.

[0180] All the various light beams that enter the eyepiece waveguide 1200, propagate through the eyepiece waveguide, and exit the eyepiece waveguide can be described using one or more wave vectors, i.e., k-vectors, which describe the propagation direction of the beam. k-space is an analytical framework that relates k-vectors to geometric points. In k-space, each point in space corresponds to a unique k-vector, which can, in turn, represent a beam or ray of light with a specific propagation direction. This allows the input and output beams with their corresponding propagation angles to be understood as a set of points (e.g., a rectangle) in k-space. While passing through the eyepiece, the diffraction features that change the propagation direction of the light beam can be understood in k-space as simply translating the location of the set of k-space points that make up the image. This newly translated k-space location corresponds to a new set of k-vectors, which, in turn, represent the new propagation angles of the beam or ray after interacting with the diffraction features.

[0181] The operation of an eyepiece waveguide can be understood in terms of a mode of moving a set of points within a k-space rectangle, such as points inside the k-space rectangle corresponding to the projected image, within k-space. This is in contrast to a more complex ray trace diagram that could alternatively be used to illustrate the beam and its propagation angle. k-space is thus an effective tool for explaining the design and operation of an eyepiece waveguide. The following discussion explains the k-space representation of the features and functions of various AR eyepiece waveguides.

[0182] FIG. 13A illustrates a k-vector 1302 that can be used to represent the propagation direction of a ray or light beam. The particular k-vector 1302 shown represents a plane wave with a plane wavefront 1304. The k-vector 1302 points in the direction of propagation of the ray or beam that it represents. The magnitude of the k-vector 1302, i.e., its length, is defined by the wave number k. The dispersion relation ω = ck relates the angular frequency ω of light, the speed of light c, and the wave number k. (In a vacuum, the speed of light is equal to the constant c of the speed of light. However, in a medium, the speed of light is inversely proportional to the refractive index of the medium. Thus, in a medium, the equation becomes k = nω / c.) It should be noted that by definition, k = 2π / λ and ω = 2πf, where f is the frequency of light (e.g., in Hertz). As is clear from this equation, a light beam with a higher angular frequency ω has a larger wave number and thus a k-vector of larger magnitude (assuming the same propagation medium). For example, assuming the same propagation medium, a blue light beam has a k-vector of larger magnitude than a red light beam.

[0183] FIG. 13B illustrates a ray 1301 corresponding to a k-vector 1302 within a planar waveguide 1300. The waveguide 1300 may represent any of the waveguides described herein and may be part of an eyepiece lens for an AR display system. The waveguide 1300 can guide a ray having a certain k-vector via total internal reflection (TIR). For example, as shown in FIG. 13B, the ray 1301 illustrated by the k-vector 1302 is directed towards the upper surface of the waveguide 1300 at an angle. If the angle is not too steep such that it is controlled by Snell's law, the ray 1301 will reflect at the upper surface of the waveguide 1300 at an angle equal to the angle of incidence and then propagate downward towards the lower surface of the waveguide 1300 where it will again reflect back towards the upper surface. The ray 1301 will propagate in a guided mode within the waveguide 1300 and continue to reflect back and forth between its upper and lower surfaces.

[0184] FIG. 13C illustrates the allowed k-vectors for light of a given angular frequency ω propagating within a non-bound homogeneous medium with refractive index n. The length of the illustrated k-vector 1302, i.e., the magnitude k, is equal to the refractive index n of the medium multiplied by the angular frequency ω of the light divided by the constant c of the speed of light. For a ray or beam of light with a given angular frequency ω propagating within a homogeneous medium with refractive index n, the magnitude of all allowed k-vectors is the same. Also, for non-guided propagation, all propagation directions are allowed. Thus, the manifold in k-space that defines all allowed k-vectors is a hollow sphere 1306, and the size of the sphere depends on the angular frequency of the light and the refractive index of the medium.

[0185] FIG. 13D illustrates the allowed k-vectors for light of a given angular frequency ω propagating in a homogeneous planar waveguide medium with refractive index n. In the unbounded medium, all allowed k-vectors lie on the hollow sphere 1306, but to determine the allowed k-vectors within the planar waveguide, the sphere 1306 of allowed k-vectors in a plane (e.g., the x-y plane) can be projected. This results in a solid disk 1308 in the projected k-space that represents the k-vectors that can propagate within the planar waveguide. As shown in FIG. 13D, all k-vectors that can propagate within the planar waveguide (e.g., waveguide 1300) in the x-y plane are such that the components of the k-vector in the x-y plane are less than or equal to the refractive index n of the medium divided by the constant c of the speed of light times the angular frequency ω of the light.

[0186] All points within the solid disk 1308 correspond to the k-vectors of waves that can propagate within the waveguide (although not all of these k-vectors result in guided propagation within the waveguide as discussed below with respect to FIG. 13E). At each point within the solid disk 1308, there are two allowed waves. That is, one has a z-component of propagation into the page and the other has a z-component of propagation out of the page. Thus, the out-of-plane component k z of the k-vector is given by the equation

Chemical Formula

[0187] FIG. 13E illustrates a loop 1310 in k-space corresponding to the k-vector of an optical wave that can be induced within a waveguide having a refractive index n2 (e.g., n2 = 1.5). The waveguide is physically surrounded by a medium (e.g., air) having a lower refractive index n1 (e.g., n1 ≈ 1). As just discussed with respect to FIG. 13D, all of the k-vectors corresponding to the allowed waves within the planar waveguide medium in the x-y plane are those k-vectors whose individual x-y components lie within the solid disk 1308 in k-space. The radius of the solid disk 1308 is proportional to the refractive index of the waveguide medium. Thus, referring back to FIG. 13E, the k-vectors corresponding to optical waves that can propagate within the planar waveguide medium having a refractive index n2 = 1.5 are those whose individual x-y components lie within the larger disk 1308a. On the other hand, the k-vectors corresponding to optical waves that can propagate within the surrounding medium having a refractive index n1 = 1 are those whose individual x-y components lie within the smaller disk 1308b. All k-vectors whose individual x-y components lie inside the loop 1310 correspond to those optical waves that can propagate within the waveguide medium but not within the surrounding medium (e.g., air). These are the optical waves that are induced within the waveguide medium via total internal reflection, as explained with respect to FIG. 13B. Thus, a ray or beam can only undergo guided propagation within the waveguide of the AR eyepiece if they have a k-vector that lies within the k-space loop 1310. Note that propagating optical waves having k-vectors outside the larger disk 1308a are prohibited. That is, there are no propagating waves whose k-vectors lie within that region (the waves within that region have an evanescently decaying amplitude and are not constant along their direction of propagation).

[0188] The various AR eyepiece waveguides described herein use diffractive features such as diffractive structures to internally couple light and direct the k-vector of an optical beam propagating in free space (e.g., from a projector) with n1≈1 into the k-space ring 1310 of the eyepiece waveguide. Any optical wave whose k-vector lies within the ring 1310 can propagate in a guided mode within the eyepiece waveguide. The width of the ring 1310 determines the range of k-vectors, and thus the range of propagation angles, that can be guided within the eyepiece waveguide. Thus, the width of the k-space ring 1310 is typically thought to determine the maximum field of view (FOV) that can be projected by the eyepiece waveguide. Since the width of the ring 1310 depends in part on the radius of the larger disk 1308a, which itself depends on the refractive index n2 of the eyepiece waveguide medium, one technique for increasing the eyepiece FOV is to use an eyepiece waveguide medium with a larger refractive index (compared to the refractive index of the medium surrounding the eyepiece waveguide). However, there are practical limits on the refractive index of waveguide media that can be used within an AR eyepiece, such as material cost. This is thought to impose practical limits on the FOV of the AR eyepiece. However, as described herein, there are techniques that can be used to overcome these limits to enable a larger FOV.

[0189] The radius of the larger disk 1308a in FIG. 13E also depends on the angular frequency ω of the light and the width of the ring 1310, and thus on the color of the light, but this does not imply that the FOV supported by the eyepiece waveguide is larger for light with a higher angular frequency, since any given angular range corresponding to the FOV scales linearly with the angular frequency as well.

[0190] FIG. 13F shows a k-space diagram similar to that depicted in FIG. 13E. The k-space diagram shows a smaller disk 1308b corresponding to allowable k-vectors in a first medium of refractive index n1, a larger disk 1308a corresponding to allowable k-vectors in a second medium of refractive index n2 (n2 > n1), and a ring 1310 between the outer boundaries of the smaller disk 1308a and the larger disk 1308b. All k-vectors within the width 1342 of the ring 1310 correspond to the guided propagation angle, although it is also possible that less than all of the k-vectors within the width 1342 of the ring 1310 may be sufficient for use in displaying an image.

[0191] FIG. 13F also shows a waveguide 1350 with two guided beams shown in comparison to each other. The first optical beam has a first k-vector 1344a near the outer edge of the ring 1310. The first k-vector 1344a corresponds to a first TIR propagation path 1344b shown in a cross-section of the waveguide 1350 having a refractive index n2 surrounded by air having a refractive index n1. A second optical beam having a second k-vector 1346a closer to the center of the k-space ring 1310 is also shown. The second k-vector 1346a corresponds to a second TIR propagation path 1346b within the waveguide 1350. The waveguide 1350 may include a diffraction grating 1352 on or within the waveguide 1350. When an optical beam encounters the surface of the waveguide 1350 with the diffraction grating 1352, an interaction occurs, which can send a sample of the optical beam energy out of the waveguide while the beam continues to TIR within the waveguide. The angle at which the optical beam propagates through the waveguide by TIR determines the density of reflection events per unit length with respect to the surface of the waveguide 1350 with the diffraction grating 1352, i.e., the number of bounces. Returning to the example of the optical beam comparison, the first optical beam within the first TIR propagation path 1344b reflects four times from the waveguide surface with the diffraction grating 1352, producing four exit pupils 1354 (illustrated using solid lines) over the length of the diffraction grating 1352, while the second optical beam within the second TIR propagation path 1346b reflects ten times from the waveguide surface with the diffraction grating 1352 over the same or a similar distance, producing ten exit pupils 1356 (illustrated using dashed lines) across the length of the diffraction grating 1352.

[0192] In practice, it may be desirable to ensure that the output beam, i.e., the inter-pupil distance, is equal to or constrained within a preselected range, and that the content projected to the user will be visible from any position within a predefined eye box. By using this information, the width 1342 of the ring 1310 can be limited to a subset of the k-vectors 1344 for which this constraint applies, excluding angles of incidence that are too grazing and not included in the design calculations. More or fewer angles than the subset 1344 may also be acceptable depending on the desired performance, diffraction grating design, and other optimization factors. Similarly, in some embodiments, k-vectors corresponding to propagation angles that are too steep with respect to the surface of the waveguide and provide too much interaction with the diffraction grating 1352 may also be excluded from use. In such embodiments, the width 1342 of the ring 1310 can be reduced by effectively moving the boundary of the usable angles radially outward from the boundary between the larger disk 1308a and the smaller disk 1308b. The design of any of the eyepiece waveguides disclosed herein can be adjusted by thus constraining the width 1310 of the k-space ring.

[0193] As described above, the k-vectors within the annulus 1310 corresponding to the quasi-optimal TIR propagation paths can be omitted from use in the eyepiece design calculations. Alternatively, k-vectors corresponding to TIR propagation paths with overly large grazing angles, and thus overly low reflection event densities on the surface of the waveguide with the diffraction grating, may be compensated using the various techniques described herein. One technique is to use an internal coupling grating to direct a portion of the field of view (FOV) of the incident image to two different areas of the k-space annulus 1310. In particular, it may be advantageous to direct the incident image to a first side of the k-space annulus 1310 represented by a first group of k-vectors and a second side of the k-space annulus 1310 represented by a second group of k-vectors, where the first and second sides of the k-space annulus 1310 are substantially opposed to each other. For example, the first group of k-vectors may correspond to the FOV rectangle of the k-vectors on the left side of the annulus 1310, and the second group of k-vectors may correspond to the FOV rectangle of the k-vectors on the right side of the annulus 1310. The left FOV rectangle has its left edge near the outer edge of the larger disc 1308a and corresponds to the k-vector angle near the grazing incidence angle. Light at the left edge will produce a sparse exit pupil. However, the same left edge of the right FOV rectangle, located on the right side of the annulus 1310, will be closer to the center of the larger disc 1308a. Light at the same left edge of the right FOV rectangle will have a high density of exit pupils. Thus, when the left and right FOV rectangles are recombined and exit the waveguide towards the user's eye to produce an image, a sufficient number of exit pupils are produced across all areas of the field of view.

[0194] Diffraction features such as diffraction gratings can be used to couple light into and out of an eyepiece waveguide and / or change the propagation direction of light within the eyepiece waveguide. In k-space, the effect of a diffraction grating on a ray or beam of light represented by a particular k-vector is determined by the vector addition of the k-vector components in the plane of the diffraction grating with a certain lattice vector. The magnitude and direction of the lattice vector depend on the specific nature of the diffraction grating. FIGS. 13G, 13H, and 13I illustrate the action of a diffraction grating on the k-vectors in k-space.

[0195] FIG. 13G shows a top view of diffraction grating 1320 and some of its associated k-space diffraction grating vectors (G -2 , G -1 , G1, G2). Diffraction grating 1320 is oriented in the x-y plane, and FIG. 13G shows a view of the grating from the perspective of a ray or beam of light incident on it from the z-direction. Diffraction grating 1320 has an associated set of k-space diffraction grating vectors (e.g., G -2 , G -1 , G1, G2) that are oriented in the same plane as the diffraction grating. The G1 and G -1 lattice vectors each correspond to a ±1 diffraction order, while the G2 and G -2The lattice vectors each correspond to ±2 diffraction orders. The lattice vectors for the ±1 diffraction orders point in opposite directions (along the periodic axes of the lattice) and have equal magnitudes that are inversely proportional to the period Λ of the diffraction grating 1320. Thus, a diffraction grating with a finer pitch has larger lattice vectors. The lattice vectors for the ±2 diffraction orders also point in opposite directions and have equal magnitudes that are twice those of the lattice vectors for the ±1 diffraction orders. Additional higher diffraction order lattice vectors may also exist, but they are not shown. For example, the magnitude of the lattice vectors for the ±3 diffraction orders is three times that of the lattice vectors for the ±1 diffraction orders, and so on. The fundamental lattice vector G1 is simply determined by the periodicity (direction and pitch) of the lattice, while it should be noted that the composition of the lattice (e.g., surface profile, material, layer structure) can affect other properties of the lattice such as diffraction efficiency and diffraction phase. All harmonics of the fundamental lattice vectors (e.g., G -1 , G2, G -2 etc.) are simply integer multiples of the fundamental G1, so all diffraction directions of the lattice are simply determined by the periodicity of the lattice. The function of the diffraction grating 1320 is to add the lattice vectors to the in-plane components of the k-vector corresponding to the incident light ray or beam. This is shown in FIG. 13H.

[0196] FIG. 13H illustrates the cross-sectional view of the diffraction grating 1320 and its effect in k-space on the k-vector 1302 corresponding to a normally incident light ray or beam of light. The diffraction grating 1320 diffracts the incident light ray or beam of light into one or more diffraction orders. The new light rays or beams of light at each of these diffraction orders are represented by new k-vectors (e.g., 1302a-e). These new k-vectors (e.g., 1302a-e) are the lattice vectors (e.g., G -2 , G -1It is determined by the vector addition of the in-plane components of the k-vector 1302 associated with each of (, G1, G2). In the case of a normally incident light ray or beam of light as illustrated, the k-vector 1302 has no components in the x-y plane of the diffraction grating. Thus, the effect of the diffraction grating 1320 is to create one or more new diffracted light rays or beams of light whose k-vectors (e.g., 1302a-e) have x-y components equal to the corresponding lattice vectors. For example, the x-y components of the ±1 diffraction orders of the incident light ray or beam of light are G1 and G, respectively. -1 respectively. On the other hand, the magnitude of the new k-vector is restricted to 2π / ω, and thus all the new k-vectors (e.g., 1302a-e) lie on a semi-circle as shown in FIG. 13H. While the in-plane components of the incident k-vector 1302 are added to lattice vectors whose lengths are equal to the basic increment or twice the basic increment, etc., the magnitudes of the resulting k-vectors are restricted, so the angles between the k-vectors (e.g., 1302a-e) for the various diffraction orders are not equal. Rather, the k-vectors (e.g., 1302a-e) become more angularly spaced as the diffraction order increases.

[0197] In the case of a diffraction grating formed on or within a planar eyepiece waveguide, the in-plane components of the new k-vectors (e.g., 1302a-e) are most notable when they are within the k-space ring 1310 of the eyepiece waveguide because the diffracted light rays or beams of light will undergo guided propagation through the eyepiece waveguide. However, when the in-plane components of the new k-vectors (e.g., 1302a-e) are within the central disk 1308b, the diffracted light rays or beams of light will exit the eyepiece waveguide.

[0198] FIG. 13I illustrates the cross-sectional view of the diffraction grating 1320 and its effect in k-space on the k-vector 1302 corresponding to an obliquely incident light ray or beam of light. The effect is similar to that described with respect to FIG. 13H. Specifically, the k-vectors of the diffracted light rays or beams of light are lattice vectors (G -2 , G-1 Determined by adding vectors of the in-plane components of the incident k-vector with (G1, G2). For the obliquely incident k-vector 1302, the components of the k-vector in the x-y plane of the diffraction grating 1320 are non-zero. This component is added to the lattice vector to determine the in-plane components of the new k-vector for the diffracted ray or beam of light. The magnitude of the new k-vector is constrained by 2π / ω. Also, again, if the in-plane components of the k-vector of the diffracted ray or beam of light are within the k-space ring 1310 of the eyepiece waveguide, the diffracted ray or beam of light will undergo guided propagation through the eyepiece waveguide.

[0199] FIG. 13J is a k-space diagram illustrating the field of view (FOV) of an image projected into an AR eyepiece waveguide (e.g., 1200, 1300). The k-space diagram includes a larger disk 1308a that defines the k-vectors of light beams or rays that can propagate within the eyepiece waveguide. The k-space diagram also includes a smaller disk 1308b that defines the k-vectors of light beams or rays that can propagate within a medium such as air surrounding the eyepiece waveguide. Also, as already discussed, the k-space ring 1310 defines the k-vectors of light beams or rays that can undergo guided propagation within the eyepiece waveguide.

[0200] Input beams (e.g., 1202a, 1204a, 1206a) projected into the entrance pupil of the eyepiece waveguide are shown in FIGS. 12A and 12B. Each input beam has a propagation angle that is uniquely defined by the spatial location of the corresponding image point in the image plane. The set of input beams has an angular spread in both the x-direction and the y-direction. The angular spread in the x-direction can define the horizontal field of view, while the angular spread in the y-direction can define the vertical field of view. Additionally, for example, the angular spread of the input beams along a diagonal between the x-direction and the y-direction can define the diagonal field of view.

[0201] In k-space, the field of view of the input image can be approximated by the FOV rectangle 1330. The FOV rectangle 1330 encloses a set of k-vectors corresponding to a set of input light beams. The FOV rectangle 1330 has a dimension along the k x -axis, which corresponds to the angular spread of the input beams in the x-direction. Specifically, the horizontal width of the FOV rectangle 1330 is

Chem.

Chem.

[0202] As shown in FIG. 13J, the FOV rectangle 1330 is centered on and completely located within the smaller disc 1308b. The native position of the FOV rectangle 1330 corresponds to the k-vectors of a set of input beams (e.g., in a configuration with an on-axis, i.e., telecentric projection, from an image source), or generally, a set of output beams propagating in the ±z-directions (where the set of beams is centered on the z-axis and all beams, except those normal to the entrance or exit pupil, have some amount of angular deviation with respect to the ±z-directions). In other words, the FOV rectangle 1330 can represent the input beams as they propagate from the image source through free space to the eyepiece waveguide when they are within the smaller disc 1308b in the k-space diagram. Also, it can represent the output beams as they propagate from the eyepiece waveguide to the user's eye. Each k-space point within the FOV rectangle 1330 corresponds to a k-vector representing one of the input beam directions or one of the output beam directions. For the input beam represented by the FOV rectangle 1330 to undergo guided propagation within the eyepiece waveguide, the FOV rectangle 1330 must be translated parallel to the k-space annulus 1310. Conversely, for the output beam represented by the FOV rectangle 1330 to exit the eyepiece waveguide, the FOV rectangle 1330 must be translated anti-parallel from the k-space annulus 1310 to the smaller disc 1308b. To introduce no geometric and chromatic dispersion from propagation through the waveguide, the FOV rectangle 1330 of the input beam can coincide with the FOV rectangle of the output beam. That is, in this configuration, the eyepiece waveguide preserves the beam angle from input to output.

[0203] The following equations describe the FOV that can be achieved within some eyepiece waveguides.

Chemical formula

Chemical formula

[0204] FIG. 13K is a k-space diagram showing the translational shift in the k-space of the FOV rectangle 1330 caused by the input coupling grating (ICG) located at the entrance pupil of the eyepiece waveguide. The ICG has the associated diffraction grating vectors (G -1 , G1) as just discussed with respect to FIGS. 13G-13I. The ICG diffracts each of the input beams represented by the FOV rectangle 1330 into +1 and -1 diffraction orders. In k-space, the diffraction of the input beam into the +1 diffraction order is represented by the FOV rectangle 1330 displaced in the k x -direction by the G1 grating vector. Similarly, in k-space, the diffraction of the input beam into the -1 diffraction order is represented by the FOV rectangle 1330 displaced in the -k -1 -direction by the G x grating vector.

[0205] With respect to the particular embodiment shown in FIG. 13K, the translated FOV rectangle is too large to fit entirely within the k-space annulus 1310. This means that the eyepiece waveguide cannot support all of the input beams within the FOV in the guided propagation mode, regardless of whether they are in positive or negative diffraction orders, because the angular spread between them is too large. K-vectors corresponding to points within the translated FOV rectangle that are outside the larger disk 1308a will not be diffracted at all by the ICG because their k-vectors are not allowed. (This will also prevent diffraction into the ±2 and higher diffraction orders because the lattice vectors associated with those orders will be longer and will thus translate the k-vectors further outside the larger disk 1308a.) On the other hand, if any part of the translated FOV rectangle remains inside the smaller disk 1308b after translation by the ICG, the optical beams corresponding to their particular k-vectors will not undergo TIR and will thus exit the eyepiece waveguide by passing through that plane and will not undergo guided propagation through the waveguide.

[0206] One possible modification that could be made to support more of the input beams of light represented by the translated FOV rectangle 1330 in the guided mode is to increase the difference between the refractive indices of the eyepiece waveguide and the surrounding medium. This could increase the size of the larger disk 1308a and / or decrease the size of the smaller disk 1308b (decreasing the size of the smaller disk 1308b is possible if the waveguide is not surrounded by air), thereby increasing the size of the k-space annulus 1310. Exemplary AR eyepiece waveguide with an orthogonal pupil expander

[0207] FIG. 14A illustrates an exemplary eyepiece waveguide 1400 with an ICG region 1440, an orthogonal pupil expander (OPE) region 1450, and an exit pupil expander (EPE) region 1460. FIG. 14B includes a k-space diagram illustrating the respective effects of these components of the eyepiece waveguide 1400 in k-space. The ICG region 1440, the OPE region 1450, and the EPE region 1460 of the eyepiece waveguide 1400 include various diffraction features that couple an input beam into the eyepiece waveguide, propagate it through guided modes, replicate the beam at multiple dispersed locations in space, exit the replicated beam from the eyepiece waveguide, and project it towards the user's eye.

[0208] An input beam corresponding to an input image can be projected into the eyepiece waveguide 1400 from one or more input devices. The input beam can be incident on the ICG region 1440, which can coincide with the entrance pupil of the eyepiece waveguide 1400. Input devices used to project the input beam can include, for example, a spatial light modulator projector (positioned in front of or behind the eyepiece waveguide 1400 with respect to the user's face). In some embodiments, the input device may use a liquid crystal display (LCD), liquid crystal on silicon (LCoS), fiber scanning display (FSD) technology, or a scanning microelectromechanical system (MEMS) mirror display, although others can also be used. The input beam from the input device is generally projected into the eyepiece waveguide 1400 at various propagation angles in the illustrated -z - direction and is incident on the ICG region 1440 from outside the substrate of the eyepiece waveguide.

[0209] The ICG region 1440 includes diffractive features that redirect the input beam such that they propagate inside the eyepiece waveguide 1400 via total internal reflection. In some embodiments, the diffractive features of the ICG region 1440 may form a one-dimensional periodic (1D) diffraction grating consisting of many lines that extend perpendicular to the illustrated y-direction and are periodically repeated horizontally in the illustrated x-direction. In some embodiments, the lines may be etched into the front or back of the eyepiece waveguide 1400 and / or they may be formed from materials deposited on the front or back. The period, duty cycle, depth, profile, blaze angle, etc. of the lines can be selected based on the angular frequency ω of the light for which the eyepiece waveguide 1400 is designed, the desired diffraction efficiency of the grating, and other factors. In some embodiments, the ICG region 1440 is designed primarily to couple the input light to the +1 and -1 diffraction orders. (The diffraction grating can be designed to reduce or eliminate higher diffraction orders beyond the 0th and 1st diffraction orders. This can be accomplished by appropriately shaping the profile of each line. However, in many practical ICGs within an AR display, all higher diffraction orders correspond to k-vectors that exceed the k-space ring. Thus, those higher diffraction orders will be prohibited regardless of non-k-space attributes such as grating duty cycle, depth, and profile.) The diffracted beam in one of the ±1 diffraction orders from the ICG region 1440 then generally propagates in the -x-direction towards the OPE region 1450, while the diffracted beam in the other of the ±1 diffraction orders then generally propagates in the +x-direction and exits the eyepiece waveguide 1400.

[0210] The OPE region 1450 includes diffractive features that can perform at least two functions. First, they can perform pupil expansion by spatially replicating the input beam of each light at many new locations in the generally -x - direction. Second, they can direct each replicated light beam generally along a path towards the EPE region 1460. In some embodiments, these diffractive features are lines formed on or within the substrate of the eyepiece waveguide 1400. The period, duty cycle, depth, profile, blaze angle of the lines, etc. can be selected based on the angular frequency ω of the light for which the eyepiece waveguide 1400 is designed, the desired diffraction efficiency of the grating, and other factors. The specific shape of the OPE region 1450 can vary but may generally be determined based on the spread of the light beam from the ICG region 1440 and the size and location of the EPE region 1460. This is further discussed with respect to FIG. 14D.

[0211] The diffraction grating in the OPE region 1450 can be designed using a relatively low and / or variable diffraction efficiency. These properties can enable the OPE region 1450 to replicate each light beam arriving from the ICG region 1440 and / or to more uniformly disperse the light energy in at least one dimension. Due to the relatively low diffraction efficiency, each interaction of the light beam with the grating diffracts only a portion of the refractive force within the light beam, while the remaining portion continues to propagate in the same direction. (Some parameters that can be used to affect the diffraction efficiency of the grating are the height and width of the line feature or the magnitude of the refractive index difference between the line feature and the background medium.) That is, when the beam interacts with the diffraction grating within the OPE region 1450, a portion of its refractive force will be diffracted towards the EPE region 1460, while the remaining portion continues to pass through the OPE region and again encounters the grating at different spatial locations, where another portion of the refractive force of the beam can be diffracted towards the EPE region 1460 and so on. Since a portion of the refractive force of each light beam travels further through the OPE region 1450 than other portions before being diffracted towards the EPE region 1460, there are multiple copies of the incident beam traveling towards the EPE region from different locations in the -x- direction. The spatial extent of the replicated beams in the propagation direction of the original incident beam through the OPE region 1450 thus effectively increases, while the intensity of the incident beam correspondingly decreases as the light constituting the input beam is here split into many replicated beams.

[0212] The diffraction grating within the OPE region 1450 is oriented obliquely with respect to the beam arriving from the ICG region 1440 such that the beam is generally diffracted toward the EPE region 1460. The specific angle of inclination of the diffraction grating within the OPE region 1450 may depend on the layout of the various regions of the eyepiece waveguide 1400 and may perhaps be more clearly seen within the k-space diagram, found and discussed later in FIG. 14B. Within the eyepiece waveguide 1400, the ICG region 1440 is located to the right of the OPE region 1450 while the EPE region 1460 is located below the OPE region. Thus, for redirecting light from the ICG region 1440 toward the EPE region 1460, the diffraction grating of the OPE region 1450 may be oriented at approximately 45° with respect to the illustrated x-axis.

[0213] FIG. 14C is a three-dimensional illustration of the optical action of the OPE region 1450 shown in FIGS. 14A and 14B. FIG. 14C shows the ICG region 1440 and the OPE region 1450, both on the side of the waveguide closer to the viewer. The grating lines cannot be seen as they are microscopic. In this case, a single input beam 1401 is shown, but the image would consist of many such input beams propagating in slightly different directions through the eyepiece waveguide 1400. The input beam 1401 is incident from the ICG region 1440 on the OPE region 1450. The input beam 1401 then continues to propagate through the eyepiece waveguide 1400 via total internal reflection, reflecting back and forth repeatedly between its surfaces. This is represented in FIG. 14C by the zigzags within the illustrated propagation of each beam.

[0214] When the input beam 1401 interacts with the diffraction grating formed within the OPE region 1450, a portion of its refractive force is diffracted towards the EPE region, while another portion of its refractive force continues along the same path through the OPE region 1450. As already described, this is due, in part, to the relatively low diffraction efficiency of the grating. Further, the beam diffracted towards the EPE region can re-encounter the grating of the OPE region 1450 and be diffracted back towards the original propagation direction of the input beam 1401. The paths of some of these beams are indicated by the arrows in FIG. 14C. The effect is replicated as the input beam propagates through the OPE region 1450, so that the spatial extent of the light is expanded. This is evident from FIG. 14C, which shows that the input beam 1401 is replicated into multiple light beams and ultimately propagates generally in the -y- direction towards the EPE region.

[0215] The EPE region 1460 likewise includes diffraction features that can perform at least two functions. First, they can replicate the beam along another direction (e.g., a direction substantially orthogonal to the direction in which the beam is replicated by the OPE region 1450). Second, they can diffract each light beam out of the eyepiece waveguide 1400 towards the user's eye. The EPE region 1460 can replicate the light beam in the same manner as the OPE region 1450. That is, as the beam propagates through the EPE region 1460, it repeatedly interacts with the diffraction grating, diffracting a portion of its refractive force to a first diffraction order, thereby being externally coupled towards the user's eye. The other portion of the refractive force of the beam is diffracted to the zero order and continues to propagate in the same direction within the EPE region 1460 until it interacts with the grating again. The diffractive optical features of the EPE region 1460 can also impart a refractive force to the replicated output beam of light to an extent such that they appear as if they originated from the desired depth plane, as discussed anywhere in this specification. This can be accomplished by using a lens function to impart curvature to the lines of the diffraction grating within the EPE region 1460.

[0216] Figure 14B illustrates the operation of the eyepiece waveguide 1400 in k-space. Specifically, Figure 14B includes a k-space diagram (KSD) for each component of the eyepiece waveguide 1400, illustrating the k-space effect of that component. The FOV rectangle within the k-space diagram and the arrow indicating the corresponding propagation direction of light through the eyepiece waveguide have matching shading. The first k-space diagram KSD1 shows the k-space representation of the input beam incident on the ICG region 1440 from the input device. As already discussed, the set of input beams can be represented in k-space by the FOV rectangle 1430, where its k x and k y dimensions correspond to the angular spread of the input beam in the x- and y-directions. Each specific point within the FOV rectangle in KSD1 corresponds to a k-vector associated with one of the input beams, and the k x component indicates the propagation angle of the input beam in the x-direction, and the k y component indicates the propagation angle of the input beam in the y-direction. More precisely, k x = sin(θ x ), where θ x is the angle formed by the input beam and the y-z plane, and k y = sin(θ y ), where θ y is the angle formed by the input beam and the x-z plane. The fact that the FOV rectangle in KSD1 is centered on the approximate k z -axis means that the input light beams represented have propagation angles centered on the input beam propagating in the -z-direction, and thus all input beams generally propagate in the -z-direction. (Although not shown here, any of the waveguide displays described herein can also be designed for an off-axis FOV with respect to the ±z-directions.)

[0217] The second k-space diagram KSD2 shows the k-space operation of the ICG region 1440. As already discussed, the diffraction grating has associated lattice vectors (e.g., G1, G -1 ). KSD2 shows the G1 lattice vector and G-1 shows the lattice vectors, which are equal in magnitude and opposite in direction along the periodic axis of the ICG. The ICG region 1440 diffracts the input beam to ±1 diffraction order. Also, in k-space, this means that the ICG uses both the G1 and G -1 lattice vectors and translates it to copy the FOV rectangle to two new locations. In the illustrated instance, the ICG uses the lattice vectors G1, G -1 is designed using a period Λ based on the angular frequency ω of the input beam such that the size of the copied FOV rectangle fits completely within the k-space ring of the waveguide. Thus, all diffracted input beams enter the guided propagation mode.

[0218] -k x A copy of the FOV rectangle centered at a point on the -k-axis (9 o'clock position within the k-space ring) indicates that the corresponding diffracted beam has a propagation angle such that its propagation component in the plane of the eyepiece waveguide 1400 is around a beam with an -x-direction. Thus, all those beams generally propagate towards the OPE region 1450 while reflecting back and forth between the front and back of the eyepiece waveguide 1400 via TIR. On the other hand, +k x A copy of the FOV rectangle centered at a point on the +k-axis (3 o'clock position within the k-space ring) indicates that the corresponding diffracted beam has a propagation angle such that its propagation component in the plane of the eyepiece waveguide 1400 is around a beam with a +x-direction. Thus, all those beams generally propagate towards the right edge of the eyepiece waveguide 1400 while reflecting back and forth between the front and back of the eyepiece waveguide 1400 via TIR. In this particular eyepiece waveguide 1400, those beams are generally lost and do not significantly contribute to the projection of the image towards the user's eye.

[0219] KSD2 is the primary lattice vectors G1, G shown in the illustration -1Higher-order lattice vectors that are multiples of are not shown. Since ICG would translate the k-vectors in such a way that in this instance it would form an FOV rectangle that extends beyond the outer perimeter of the k-space disk that defines the allowed k-vectors, the light beam is not diffracted to those diffraction orders. Thus, higher diffraction orders do not occur in this embodiment.

[0220] The third k-space diagram KSD3 shows the k-space action of the OPE region 1450. Again, since the OPE region 1450 contains a diffraction grating, it has associated lattice vectors (e.g., G1, G -1 ), which can be equal in magnitude and opposite in direction along the periodicity axis of the OPE grating. In this case, the periodicity axis of the diffraction grating is at a 45° angle with respect to the x-axis. Thus, the lattice vectors of the OPE diffraction grating (e.g., G1, G -1 ) point at a 45° angle with respect to the k x -axis. As shown in KSD3, one of the lattice vectors translates the FOV rectangle to a new location centered at a point located on the -k y -axis (6 o'clock position within the k-space ring). This copy of the FOV rectangle indicates that the corresponding diffracted beam has a propagation angle such that its propagation component in the plane of the eyepiece waveguide 1400 is in the -y-direction towards the EPE region 1460. On the other hand, the other illustrated OPE lattice vectors would place the FOV rectangle at locations outside the outer perimeter of the k-space disk. However, k-vectors outside the disk are not allowed, and thus the OPE diffraction grating does not diffract the beam to its diffraction orders. The periodicity axis of the diffraction grating within the OPE region 1450 does not necessarily have to be exactly 45°. For example, as can be seen by examining KSD3, the periodicity axis can still be at an angle slightly greater or less than 45° while still translating the FOV rectangle to the 6 o'clock position where the FOV rectangle can fit entirely within the k-space ring. This means that the FOV rectangle will not necessarily be centered within the k-space ring along the -k y -axis and will place the FOV rectangle at the 6 o'clock position.

[0221] In the illustrated instance, the OPE diffraction grating has lattice vectors G1, G -1 wherein one of them is designed using a period Λ based on the angular frequency ω of the input beam such that a copied FOV rectangle that is entirely within the k-space loop of the waveguide is placed at the 6 o'clock position. Thus, all of the diffracted input beams remain in the guided propagation mode. The k-space distance from the 9 o'clock position to the 6 o'clock position within the k-space loop, which is the translation performed by the OPE grating, exceeds the distance from the origin of the k-space diagram to the loop, which is the translation performed by the ICG. Therefore, the OPE grating vector must be different in magnitude from the ICG grating vector. In particular, the OPE grating vector is longer than the ICG grating vector, which means that the OPE grating has a shorter period Λ than the ICG grating.

[0222] The fourth k-space diagram KSD4 shows the k-space action of the EPE region 1460. Again, since the EPE region 1460 includes a diffraction grating, it has associated lattice vectors (e.g., G1, G -1 ), which are equal in magnitude and opposite in direction along the periodicity axis of the EPE grating. In this case, the periodicity axis of the diffraction grating is along the y-axis of the eyepiece waveguide 1400. Thus, the lattice vectors of the EPE diffraction grating (e.g., G1, G -1 ) are ±k y- direction. As shown in KSD4, one of the lattice vectors translates the FOV rectangle to a new location centered at the origin of the k - space diagram, parallelly. This copy of the FOV rectangle indicates that the corresponding diffracted beam has a propagation angle such that its propagation component in the plane of the eyepiece waveguide 1400 is in the +z - direction towards the user's eye. On the other hand, the other primary EPE lattice vector places the FOV rectangle at a location outside the outer perimeter of the k - space disk, and thus the EPE diffraction grating will not diffract the beam to its diffraction order. However, one of the secondary EPE lattice vectors will translate the FOV rectangle to the 12 o'clock position within the k - space annulus. Thus, the EPE grating can diffract a portion of the light to one of the second diffraction orders. The secondary diffraction direction may correspond to the guided propagation direction along the +y - direction and is typically an undesirable effect. For example, secondary diffraction can introduce visual artifacts and bring about flare or smear effects into the image presented to the user when the EPE grating is perturbed and refractive forces are introduced, as discussed below.

[0223] In the illustrated instance, the EPE diffraction grating is designed using a period Λ based on the angular frequency ω of the input beam such that one of the lattice vectors G1, G -1 is placed so that the copied FOV rectangle is completely inside the k - space disk of the waveguide. Thus, all the beams diffracted by the EPE diffraction grating are no longer in the guided propagation mode and thus exit the eyepiece waveguide 1400. Further, since the EPE diffraction grating translates the FOV rectangle back to the origin of the k - space diagram (the location where the FOV rectangle corresponding to the input beam was located), the output beam has the same propagation angle as its corresponding input beam. In the illustrated embodiment, the EPE diffraction grating has the same period Λ as the ICG since both of these diffraction gratings translate the FOV rectangle by the same k - space distance. However, this is not a requirement. If the k y dimension of the FOV rectangle is less than the k y dimension of the k - space annulus at the 6 o'clock position, the FOV rectangle is at a different k yIt can have a range of 6 o'clock positions that can be considered as possibilities at the location. Thus, there can be numerous engineering options for placing the EPE lattice vectors and, consequently, the OPE vectors in the vicinity of the location within the k-space ring and / or the origin of the k-space diagram for the FOV rectangle.

[0224] In some embodiments, the lines of the EPE diffraction grating may be slightly curved so as to impart a refractive power to the output beam emerging from the EPE region 1460. For example, the lines of the diffraction grating within the EPE region 1460 can be bent towards the OPE region in the plane of the waveguide to impart a negative refractive power. This can be used, for example, to cause the output beam to follow a divergent path, as shown in FIG. 12B. This causes the projected image to appear on a depth plane closer than optical infinity. The specific curvature can be determined by the lens function. In k-space, this means that different spatial regions within the EPE region 1460 will have lattice vectors pointing in slightly different directions depending on the curvature of the lattice lines within that specific region. In these embodiments, this translates the FOV rectangle to various different locations centered around the origin of the k-space diagram. This, in turn, centers the set of output beams corresponding to each of the translated FOV rectangles around different propagation angles, which, in turn, creates an illusion of depth.

[0225] FIG. 14D illustrates a technique for determining the size and shape of the OPE region 1450 and the EPE region 1460. FIG. 14D illustrates the same eyepiece waveguide 1400 shown in FIGS. 14A and 14B, including the ICG region 1440, the OPE region 1450, and the EPE region 1460. FIG. 14D also includes simplified versions of the k-space diagrams KSD1, KSD2, and KSD3. Referring to the first k-space diagram KSD1, the four corner k-vectors of the FOV rectangle correspond to the input beams that are incident on the ICG at the most oblique angles from the corners of the image in the input plane (see FIGS. 12A and 12B). Since the propagation angles of these input beams are the most extreme of all those within the field of view, their k-vectors are located at the four corners of the FOV rectangle in k-space.

[0226] FIG. 14D shows rays that define four diffracted beams from the ICG region 1440 corresponding to the four corners of the input image. In particular, the rays near the top of the OPE region 1450 define a diffracted beam (i.e., the k-vector located at the upper right corner of the FOV rectangle) corresponding to an input beam that is incident on the ICG region 1440 at the steepest propagation angle in the upward direction and away from the OPE region. Also, the rays near the bottom of the OPE region 1450 define a diffracted beam (i.e., the k-vector located at the lower right corner of the FOV rectangle) corresponding to an input beam that is incident on the ICG region 1450 at the steepest propagation angle in the downward direction and away from the OPE region. These two beams define the spread of the diffracted beams from the ICG region 1440. To create these two beams and all other replicated instances therebetween and project them towards the user's eye, the upper and lower boundaries of the OPE region should encompass the propagation paths of these two beams. The specific propagation paths can be determined with reference to the second k-space diagram KSD2.

[0227] KSD2 shows the resulting k-vectors of the beams diffracting from the ICG region 1440 towards the OPE region 1450. The arrows in KSD2 indicate the propagation angles of the beams corresponding to the k-vector located at the upper right corner of the FOV rectangle.

[0228] The size, shape, and location of the EPE region 1460 can be determined by performing a backward ray trace using the propagation angles that are apparent from the k-vectors within the third k-space diagram KSD3. As is apparent from KSD3, the left and upper right corner k-vectors of the FOV rectangle define the spread of the propagation path that the beam follows while propagating in the direction from the OPE region 1450 to the EPE region 1460. Using these propagation angles, the origin within the OPE region of those rays that will arrive at the lower corner of the EPE region with the propagation angles defined by the left and upper right corner k-vectors can be determined by tracing backward from the portion of the EPE region 1460 that is located farthest from the OPE region 1450 (i.e., the lower corner of the EPE region). These origins of those rays can be used to determine the remaining boundaries of the OPE region 1450. For example, to direct the beam from the OPE region 1450 to the lower left corner of the EPE region 1460, the worst-case propagation angle is that indicated by the upper right corner k-vector of the FOV rectangle. Thus, the propagation path with that angle can be used to define the left boundary of the OPE region 1450. Similarly, to direct the beam from the OPE region 1450 to the lower right corner of the EPE region, the worst-case propagation angle is that indicated by the upper left corner k-vector of the FOV rectangle. Thus, the propagation path with that angle can be used to define the right boundary of the OPE region 1450.

[0229] As shown in FIG. 14D, in the case of the illustrated eyepiece waveguide 1400, the EPE region 1460 is located from the ICG region 1440 in the -x and -y directions. Also, a portion of the diffracted beam spreads from the ICG region 1440 along a path in those same directions. Initially, in order to avoid these diffracted beams from entering the EPE region before propagating through the OPE region 1450, the ICG region 1440 can be positioned sufficiently far from the EPE region in the +y direction so that the spread of the diffracted beam does not intersect the EPE region 1460. This results in a large gap between the lower boundary line of the OPE region 1450 and the upper boundary line of the EPE region 1460. In some embodiments, it may be desirable to reduce the size of the eyepiece waveguide by removing or reducing this gap. FIG. 15A illustrates an exemplary embodiment that accomplishes these goals.

[0230] FIG. 15A illustrates an exemplary embodiment of a waveguide eyepiece 1500 in which the OPE region 1550 is tilted and positioned such that its lower boundary line is parallel to the upper boundary line of the EPE region 1560. In fact, the OPE region 1550 and the EPE region 1560 may actually share a boundary line. According to this embodiment, the size of the waveguide eyepiece 1500 can be made more compact by reducing or eliminating the gap between the OPE region and the EPE region within the eyepiece waveguide embodiment shown in FIG. 14A.

[0231] To adapt to the tilted orientation of the OPE region 1550, the ICG region 1540 can be modified such that the spread of the diffracted beam from the ICG region is tilted to match the tilted orientation of the OPE region 1550. For example, the grating lines of the ICG region 1540 can be oriented such that the diffracted beam does not exit the ICG region in a propagation direction having a component in the -y- direction. Additionally, the ICG region 1540 is located near the shared boundary line of the OPE region 1550 and the EPE region 1560, but can be positioned such that no portion of the ICG region extends in the -y- direction beyond that shared boundary line. The operation of the ICG region 1540 can be seen in the k-space diagram shown in FIG. 15B.

[0232] FIG. 15B includes a k-space diagram illustrating the operation of the eyepiece waveguide 1500 shown in FIG. 15A. The first k-space diagram KSD1 shows a FOV rectangle corresponding to an input beam projected from a projector located outside the eyepiece waveguide 1500 towards the ICG region 1540. In the illustrated embodiment, these input beams have propagation angles centered about the -z- direction. Thus, in k-space, they can be represented by a FOV rectangle centered on the k z -axis at the origin of KSD1.

[0233] The second k-space diagram KSD2 shows the operation of the ICG region 1540 on the input beams. The ICG region 1540 diffracts the input beams and redirects them towards the OPE region 1550. In k-space, this corresponds to translating the FOV rectangle using the lattice vectors associated with the ICG region 1540. In this embodiment, the grating lines within the ICG region 1540 are oriented with a periodic axis having a component in the +y- direction. This means that the lattice vectors associated with ICG1540 also have a component in the +k y -direction. The magnitude of this component in the +k y -direction is k yIt can be greater than or equal to 1 / 2 of the width of the FOV rectangle in the - direction. This means that no part of the FOV rectangle extends below the horizontal axis of the k - space diagram KSD2 after being translated by the ICG region 1540. This, in turn, means that none of the diffracted beams from the ICG region 1540 have a propagation angle with a component in the - k y - direction. Thus, none of the diffracted beams travel downward from the ICG region 1540 towards the EPE region 1560. Also, therefore, none of the diffracted beams will enter the EPE region 1560 prior to passing through the OPE region 1550.

[0234] The third k - space diagram KSD3 shows the effect of the OPE region 1550 on the diffracted beams from the ICG region 1540. As shown, the diffraction grating of the OPE region 1550 can be oriented to redirect the beam of light at an angle corresponding to the FOV rectangle translated to a position slightly displaced from the 6 o'clock position within the k - space ring. For example, the translated FOV rectangle within KSD3 can be displaced from the 6 o'clock position within the k - space ring by the same angle as the translated FOV rectangle within KSD2 is displaced from the 9 o'clock position. In other words, the translated FOV rectangle within KSD3 can be separated from the translated FOV rectangle within KSD2 by 90°. However, this specific angular separation is not required. That is, the specific location of each FOV rectangle can depend on the layout of the various regions of the eyepiece waveguide relative to each other.

[0235] The translated FOV rectangle within KSD3 is in the - k xSince the beam of light from the OPE region 1550 is centered around the k-vector having a component in the - direction, it generally travels towards the EPE region 1560 at an angle having a component in the -x- direction. From FIG. 15A, it can be seen that due to this angle, a part of the light beam from the tip portion 1555 of the OPE region 1550 will not intersect the EPE region 1560. Since the tip portion 1555 of the OPE region 1550 can contribute to a relatively small portion of the light to the EPE region 1560, the size advantage of excluding the upper tip 1555 can outweigh any optical disadvantage. In some embodiments, the waveguide eyepiece 1500 can thus be made even more compact by excluding the upper tip 1555 of the OPE region 1550.

[0236] Finally, the fourth k-space diagram KSD4 shows that the EPE region 1560 has a diffraction grating designed to translate the FOV rectangle back to the origin of the k-space diagram. Since the starting location of the FOV rectangle in KSD4 for the eyepiece waveguide embodiment shown in FIG. 15A is slightly different from the starting location of the FOV rectangle in KSD4 for the eyepiece waveguide embodiment shown in FIG. 14A, the design of the diffraction grating within the EPE region 1560 is also somewhat different. For example, the orientation of the grating lines of the diffraction grating within the EPE region 1560 is such that the associated grating vector has a component in the +k x - direction and the OPE region 1550 can be tilted so that it does not need to extend beyond the left edge of the EPE region 1560 (see the discussion in FIG. 14D and compare the location of the upper right corner k-vector in KSD3 in FIG. 14D with the location of the corresponding k-vector in KSD3 in FIG. 15B). This results in the FOV rectangle in KSD4 of FIG. 15B being translated back to the origin of the k-space diagram, which means that the beam of light represented by the translated FOV rectangle is coupled out of the eyepiece waveguide 1500 towards the user's eye at the same propagation angle as its corresponding input beam, as already explained herein (i.e., the FOV rectangle representing the output beam is in the same location in the k-space diagram as the FOV rectangle representing the input beam).

[0237] FIG. 15C is another k-space diagram illustrating the operation of the eyepiece waveguide 1500 shown in FIG. 15A. The k-space diagram in FIG. 15C is a superposition of all the k-space diagrams shown in FIG. 15B. Also, the optical beam propagating through the OPE region 1550 generally has a propagation angle in the -k x - direction (as represented by the FOV rectangle located near the 9 o'clock position of the k-space ring) and generally a propagation angle in the -k y - direction (as represented by the FOV rectangle located near the 6 o'clock position of the k-space ring), and it is also illustrated that it can reciprocally switch between them. This is indicated by the lattice vectors with double arrows between the FOV rectangle near the 9 o'clock position and the FOV rectangle near the 6 o'clock position of the k-space ring. FIGS. 15D - 15F illustrate this behavior in more detail.

[0238] FIG. 15D is a schematic diagram of the first occurrence of the interaction between the input beam and the OPE region 1550 of the eyepiece waveguide embodiment shown in FIG. 15A. The OPE region 1550 of the eyepiece waveguide 1500 includes a diffraction grating composed of parallel grating lines repeated in the periodic direction. The periodic direction determines the direction of the lattice vector associated with the diffraction grating. In this instance, the lattice vectors with double arrows in FIG. 15C illustrate the operation of the OPE region 1550 and point along the periodic direction of the grating lines shown in FIGS. 15D - 15F.

[0239] FIG. 15D shows an input beam incident from the ICG region 1540 into the OPE region 1550. The input beam is shown to propagate in a direction corresponding to the k-vector, at the center point of the FOV rectangle located near the 9 o'clock position of the k-space ring in FIG. 15C. As shown, the first occurrence of the interaction between the input beam and the OPE region 1550 results in two diffracted output beams. That is, a part of the refractive force of the input beam simply reflects from the upper or bottom surface of the eyepiece waveguide 1500 as output 1 and continues in the same x-y direction as the input beam (i.e., zero-order diffraction), and a part of the refractive force of the input beam diffracts downward as output 2 at the first order (e.g., by the first lattice vector G1 of the OPE region). The output 2 beam is shown to propagate in a direction corresponding to the k-vector, at the center point of the FOV rectangle located near the 6 o'clock position of the k-space ring in FIG. 15C. After this first occurrence of the interaction, the output 1 beam and the output 2 beam have different propagation angles, but they both still propagate within the OPE region 1550 and thus may have additional interactions with the OPE region as shown in FIGS. 15E and 15F. Although not shown, other input beams incident on the OPE region 1550 using different propagation angles will behave similarly but with slightly different input and output angles.

[0240] FIG. 15E is a schematic diagram of a second occurrence of the interaction between the input beam and the OPE region 1550 of the eyepiece waveguide embodiment shown in FIG. 15A. The beam associated with the first occurrence of the interaction is shown using a dashed line, while the beam associated with the second occurrence of the interaction is shown using a solid line. As shown in FIG. 15E, the output beams from the first occurrence of the interaction, i.e., output 1 and output 2, can each undergo an interaction with an OPE region 1550 that is similar to what occurred in the first occurrence. That is, a portion of the refractive force from the output 1 beam from FIG. 15D simply continues in the same x-y direction (i.e., zero-order diffraction), while another portion of the refractive force of that beam interacts with the grating and is redirected downward (e.g., by the primary grating vector G1 of the OPE region). Similarly, a portion of the refractive force from the output 2 beam from FIG. 15D simply continues downward (i.e., zero-order diffraction) toward the EPE region 1560, while another portion of the refractive force of that beam interacts with the grating and is generally diffracted in the -x-direction (e.g., by the negative primary grating vector G -1 of the OPE region 1550) and continues to propagate further in the same direction as the initial input beam within the OPE region 1550.

[0241] After the second occurrence of the interaction occurs within the OPE region 1550, there is an interference node 1556 where two of the resulting beams cross. The optical paths followed by each of these beams to reach the interference node 1556 are substantially the same length. Thus, the beams emerging from the interference node 1556 that propagate in the same direction can have the same or similar phases and can thus undergo constructive or destructive wave interference with each other. This can result in image artifacts, as discussed below.

[0242] Figure 15F is a schematic diagram of a third occurrence of the interaction between the input beam and the OPE region 1550 in the eyepiece waveguide embodiment shown in Figure 15A. The beams associated with the first and second occurrences of the interaction are shown using dashed lines, while the beams associated with the third occurrence of the interaction are shown using solid lines. As shown in Figure 15F, the output beams resulting from the second occurrence of the interaction can each again experience an interaction with the OPE region 1550 similar to that which occurred in the previous occurrence. A portion of the refractive power of those beams continues in the same direction (i.e., zero-order diffraction), while another portion of the refractive power of those beams is redirected, some generally in the -x-direction and some generally in the -y-direction (i.e., by the primary lattice vectors G1 and G of the OPE region). Generally, all of the beams propagating in the -x-direction are in a state represented by the FOV rectangle located near the 9 o'clock position within the k-space loop of the k-space diagram in Figure 15C, while all of the beams propagating in the -y-direction are in a state represented by the FOV rectangle located near the 6 o'clock position. As can be seen from Figure 15C, in the case of the OPE region 1550 consisting of a 1D periodic diffraction grating, for any given input beam, the replicated beams of light corresponding to that input beam travel in only two directions within the OPE region (where the two directions will be different for different input beams incident on the OPE region at different propagation angles). -1 For the beams propagating generally in the -x-direction, all are in a state represented by the FOV rectangle located near the 9 o'clock position within the k-space loop of the k-space diagram in Figure 15C, while for the beams propagating generally in the -y-direction, all are in a state represented by the FOV rectangle located near the 6 o'clock position. As can be seen from Figure 15C, in the case of the OPE region 1550 consisting of a 1D periodic diffraction grating, for any given input beam, the replicated beams of light corresponding to that input beam travel in only two directions within the OPE region (where the two directions will be different for different input beams incident on the OPE region at different propagation angles).

[0243] The third occurrence of the interaction with the OPE region results in the creation of additional interference nodes 1556 where beams with the same or similar optical path lengths cross each other, potentially resulting in constructive or destructive wave interference. Each of the nodes 1556 serves as a light source that emits towards the EPE region 1560. In the case of the OPE region consisting of a diffraction grating with 1D periodicity, the layout of these nodes 1556 forms a uniform lattice pattern, and thus, as shown in Figure 15G, can result in image artifacts.

[0244] FIG. 15G is a schematic diagram illustrating a method in which a single input beam 1545 from the ICG region 1540 is replicated by the OPE region 1550 and redirected as a plurality of beams 1565 towards the EPE region 1560. The replicated beams 1565, shown as propagating towards or within the EPE region 1560, each originate from one of the interference nodes 1556. These interference nodes have an ordered distribution and serve as a spatially separated periodic array of sources. Due to the ordered distribution of the interference nodes 1556, all of the replicated beams 1565 illuminating the EPE region are separated by the same interval, although the beams may have non-monotonically varying intensities. As a result, the replicated optical beams 1565 from the OPE region 1550 can illuminate the EPE region 1560 with a relatively sparse non-uniform distribution. In some embodiments, it may be advantageous if the replicated optical beams illuminating the EPE region of the eyepiece waveguide can be more uniformly distributed. FIG. 16 illustrates such an embodiment. Exemplary AR Eyepiece Waveguide with Multi-Directional Pupil Expander

[0245] FIG. 16A illustrates an exemplary eyepiece waveguide 1600 having a multi-directional pupil expander (MPE) region 1650 rather than an OPE region. At a macroscopic level, the illustrated embodiment of the eyepiece waveguide 1600 is similar to the eyepiece waveguide 1500 shown in FIG. 15A. An input beam is coupled into the eyepiece waveguide 1600 by the ICG region 1640. The diffracted beam from the ICG region 1640 propagates towards and through the MPE region 1650, which replaces the OPE region. Finally, the MPE region 1650 diffracts the light beam towards the EPE region 1660, where they are externally coupled towards the user's eye. The ICG region 1640 and the EPE region 1660 may be designed to function in the same manner as the corresponding regions within the eyepiece waveguide 1500 described with respect to FIGS. 15A - 15G. However, the MPE region 1650 is distinct from the OPE region 1550 in that it diffracts light in more directions. This feature advantageously reduces the periodic uniformity in the distribution of the light beams within the EPE region 1660, which in turn allows the EPE region to be illuminated more uniformly.

[0246] The MPE region 1650 consists of diffraction features that exhibit periodicity in multiple directions. The MPE region 1650 may consist of an array of scattering features arranged in a 2D lattice pattern. The individual scattering features can be, for example, indentations or protrusions of any shape. The 2D array of scattering features has associated lattice vectors derived from the reciprocal lattice pattern of its 2D lattice pattern. As an example, the MPE region 1650 can be a 2D periodic diffraction grating consisting of an intersecting grating with grating lines repeated along two or more clearly different periodic directions. This can be accomplished by superimposing two 1D gratings with different directions of periodicity.

[0247] FIG. 16B illustrates a portion of an exemplary 2D periodic lattice that can be used within the MPE region 1650 shown in FIG. 16A, along with its associated lattice vectors. The 2D periodic lattice 1650 can be a spatial lattice pattern of diffraction features, the directions of whose periodicity are illustrated by vectors u and v. Such a 2D periodic lattice is associated with lattice vectors. Two basic lattice vectors G and H corresponding to the directions of periodicity u and v are mathematically defined as follows.

Chem.

[0248] As an example, the 2D periodic lattice can be designed or formed by superimposing two sets of 1D periodic lattice lines, as shown in FIG. 16B (however, the 2D periodic lattice can alternatively consist of individual scattering features, for example, located at the intersections of the lattice lines shown in FIG. 16B). The first set of lattice lines 1656 can be repeated along the direction of the basic lattice vector G. The basic lattice vector G can have a magnitude equal to 2π / a, where a is the period of the first set of lattice lines 1656. The 2D lattice shown in FIG. 16B is also associated with the harmonics of the first basic lattice vector G. These include higher-order harmonics such as -G and 2G, -2G, etc. The second set of lattice lines 1657 can be repeated along the direction of the basic lattice vector H. The basic lattice vector H can have a magnitude equal to 2π / b, where b is the period of the second set of lattice lines 1657. The 2D lattice shown in FIG. 16B is also associated with the harmonics of the second basic lattice vector H. These include higher-order harmonics such as -H and 2H, -2H, etc.

[0249] Any 2D periodic array of diffraction features will correspond to an entire reciprocal lattice pattern and will have associated lattice vectors that point in directions determined by integer linear combinations (superpositions) of the fundamental lattice vectors G and H. In the illustrated embodiment, these superpositions result in additional lattice vectors, which are also shown in FIG. 16B. These include, for example, -G, -H, H+G, H-G, G-H, and -(H+G). Typically, these vectors are described using two indices such as (±1,0), (0,±1), (±1,±1), (±2,0), etc. FIG. 16B illustrates only the primary lattice vectors and their superpositions associated with the 2D diffraction grating, but higher order lattice vectors may also be present.

[0250] As already discussed elsewhere in this specification, the k-space action of the grating on the set of light beams that make up the image is to translate the FOV rectangle corresponding to the image using the lattice vectors associated with the grating. This is shown in FIGS. 16C and 16D with respect to the exemplary 2DMPE diffraction grating shown in FIG. 16B.

[0251] FIG. 16C is a k-space diagram illustrating the k-space operation of the MPE region 1650 of the eyepiece waveguide 1600 shown in FIG. 16A. The k-space diagram includes a shaded FOV rectangle located near the 9 o'clock position of the k-space ring. This is the location of the FOV rectangle after the ICG region 1640 has coupled the input beams into the eyepiece waveguide 1600 and redirected them towards the MPE region 1650. FIG. 16C shows how the 2D lattice within the MPE region 1650 uses the lattice vectors shown in FIG. 16B to translate the FOV rectangle. Since there are eight lattice vectors (G, H, -G, -H, H+G, H-G, G-H, and -(H+G)), the MPE region 1650 attempts to translate the FOV rectangle to eight possible new k-space locations. Of these eight possible k-space locations, six are outside the outer perimeter of the k-space diagram. These are illustrated using non-shaded FOV rectangles. Since k-vectors outside the boundary of the k-space diagram are not allowed, none of the six lattice vectors result in diffraction. However, there are two lattice vectors (i.e., -G and -(H+G)) that result in translation of the FOV rectangle to new positions within the boundary of the k-space diagram. One of these locations is near the 6 o'clock position within the k-space ring and the other is near the 2 o'clock position. The k-vectors at these locations are allowed and result in guided propagation modes, so the FOV rectangles at these locations are shaded, indicating that the light beam is diffracted into those two states. Thus, the refractive power of the light beam incident on the MPE region 1650 with the propagation angle indicated by the FOV rectangle located near the 9 o'clock position of the k-space ring is partially diffracted into both of the states indicated by the other two shaded FOV rectangles (i.e., the FOV rectangle near the 2 o'clock position and the FOV rectangle near the 6 o'clock position).

[0252] FIG. 16D is a k-space diagram further illustrating the k-space action of the MPE region 1650 of the eyepiece waveguide 1600 shown in FIG. 16A. This particular k-space diagram illustrates the action of the MPE region 1650 on a beam of light in a propagation state illustrated by a FOV rectangle located near the 2 o'clock position of the k-space ring. Again, the 2D diffraction grating within the MPE region 1650 attempts to diffract these light beams into diffraction orders defined by its eight associated lattice vectors. As shown, six of the lattice vectors will translate the FOV rectangle to positions outside the boundary of the k-space diagram. Thus, those diffraction orders will not occur. These positions are illustrated using the non-shaded FOV rectangle. However, two of the lattice vectors (i.e., H and H-G) translate the FOV rectangle to positions within the boundary of the k-space diagram. These are illustrated by the shaded FOV rectangles located near the 9 o'clock position and the 6 o'clock position of the k-space ring. Thus, the 2D diffraction grating within the MPE region 1650 diffracts, in part, the refractive power of the beam propagating in the direction illustrated by the FOV rectangle located near the 2 o'clock position of the k-space ring into both states illustrated by the other two shaded FOV rectangles (i.e., the FOV rectangle near the 9 o'clock position and the FOV rectangle near the 6 o'clock position).

[0253] Although not shown, a similar k-space diagram can be derived to illustrate the k-space action of the MPE region 1650 on a beam of light traveling with a propagation angle illustrated by a FOV rectangle located near the 6 o'clock position of the k-space ring. That k-space diagram will show that the 2D periodic diffraction grating within the MPE region 1650 diffracts, in part, the refractive power of those beams into both states illustrated by the two shaded FOV rectangles located near the 9 o'clock position and the 2 o'clock position of the k-space ring.

[0254] FIG. 16E is a k-space diagram illustrating the k-space operation of the eyepiece waveguide 1600 shown in FIG. 16A. As already described, the eyepiece waveguide 1600 can generally receive an input beam of light that propagates in the -z- direction and is incident on the ICG region 1640 of the waveguide 1600 from an external source. Those input beams are centered on the k z -axis at the origin of the k-space diagram and are represented by the FOV rectangle. The ICG region 1640 then diffracts the input beams so that they have a propagation angle that is centered around the propagation direction corresponding to the center point of the FOV rectangle located near the 9 o'clock position of the k-space ring.

[0255] The induced beams are incident on the MPE region 1650, where they can have multiple interactions. During each occurrence of an interaction, a portion of the refractive force of each beam can be zero-order diffracted and continue to propagate in the same direction through the MPE region 1650. In the first occurrence of an interaction, for example, this zero-order diffraction corresponds to that portion of the refractive force of those beams that remains in the state shown by the FOV rectangle located near the 9 o'clock position of the k-space ring. The other portion of the refractive force of the beam can be diffracted in a new direction. Again, in the first occurrence of an interaction, this creates individual diffracted beams having a propagation angle centered around the propagation direction corresponding to the center point of the FOV rectangle located near the 2 o'clock position of the k-space ring and a propagation direction corresponding to the center point of the FOV rectangle located near the 6 o'clock position.

[0256] As long as the beams remain within the MPE region 1650, they can undergo additional interactions, each resulting in a portion of the refractive force of the beam that is zero-order diffracted and continues in the same direction or is diffracted in a new direction. This results in a set of spatially dispersed diffracted beams having a propagation angle centered around each of the propagation directions shown by the center points of the FOV rectangles within the k-space ring shown in FIG. 16E. This behavior is represented by the double arrows between each pair of FOV rectangles within the k-space ring.

[0257] As any given optical input beam propagates within the MPE region 1650, it is split into a number of diffracted beams that can travel only in three allowed directions, each direction being defined by a corresponding k-vector within the FOV rectangle inside the loop of the k-space diagram in FIG. 16E, i.e., by a point. (This applies to any optical input beam propagating within the MPE region 1650. However, the three allowed directions will be slightly different depending on the propagation angle at which each initial input beam impinges on the MPE region 1650.) Also, since a portion of the refractive power of any given optical input beam is diffracted into one of the same three propagation directions after any number of interactions with the MPE region 1650, the image information is preserved throughout these interactions.

[0258] In contrast to the two allowed propagation directions of the OPE region 1550, there are advantages associated with the MPE region 1650 that has three allowed propagation directions per input beam. These advantages are further discussed below, but here it suffices to say that the increased number of propagation directions within the MPE region 1650 can result in a more complex distribution of interference nodes within the MPE region 1650, which in turn can improve the uniformity of illumination within the EPE region 1660.

[0259] It should be understood that FIG. 16E illustrates the k-space operation of an exemplary embodiment of the MPE region 1650. In other embodiments, the MPE region 1650 can be designed such that each input beam of light can diffract in more than three directions within the MPE region. For example, in some embodiments, the MPE region 1650 may be designed to enable diffraction of each input beam of light in four, five, six, seven, eight, etc. directions. As already discussed, the diffraction features within the MPE region 1650 can be designed to provide lattice vectors that copy the FOV rectangle to locations within the k-space ring corresponding to the selected diffraction directions. Additionally, the diffraction features within the MPE region 1650 can be designed using a period corresponding to the magnitude of the lattice vectors, which results in these copies of the FOV rectangle being entirely within the k-space ring (and other attempted copies of the FOV rectangle being entirely outside the outer perimeter of the k-space diagram).

[0260] In some embodiments, the angular separation between each of the allowed propagation directions for a given beam of light inside the MPE region 1650 is at least 45 degrees. If the angular separation between any pair of selected directions is less than this amount, the diffractive features within the MPE region 1650 would need to be designed to provide lattice vectors for performing those angular transitions within the k-space ring. Such lattice vectors would be relatively short compared to the size of the k-space ring due to the smaller angular separation. This could increase the likelihood that the superposition of the fundamental MPE lattice vectors would only partially create a copy of the FOV rectangle that is within the k-space ring, which could result in a loss of image information (if not done carefully, as further discussed herein). Additionally, if the angular separation between any pair of allowed propagation directions within the MPE region 1650 becomes too small, the resulting relatively short lattice vectors could also increase the likelihood that the lattice vector superposition would create a copy of the FOV rectangle that is partially inside the central disk of the k-space diagram. This could be undesirable as it could result in light being externally coupled from outside the designated EPE region 1660 from a location outside the MPE region 1650 towards the user's eye as the light travels from the eyepiece waveguide 1600.

[0261] When determining the allowable propagation directions within the MPE region 1650, various design guidelines can be emulated. For example, the allowable propagation directions can be selected such that one corresponds to the direction from the ICG region 1640 to the MPE region 1650. Additionally, the allowable propagation directions can be selected such that only one will cause a beam of light propagating in that direction from a location inside the MPE region 1650 to intersect the EPE region 1660. This ensures that the replicated beams of light corresponding to each input beam will enter the EPE region 1660 with the same propagation angle. Additionally, the allowable propagation directions inside the MPE region 1650 can be selected such that the FOV rectangles do not overlap. Overlap of the FOV rectangles can result in the mixing of image information from different image points and can cause ghost images.

[0262] FIG. 16F is a schematic diagram of a first occurrence of the interaction between the input beam and the MPE region 1650 of the embodiment of the eyepiece waveguide shown in FIG. 16A. FIG. 16F shows the input beam incident from the ICG region 1640 into the MPE region 1650. The input beam is shown to propagate in a direction corresponding to the center point of the FOV rectangle located near the 9 o'clock position of the k-space ring in FIG. 16E, i.e., the k-vector.

[0263] The MPE region 1650 can include many features less than 1 μm. Also, for each interaction with the MPE region, the approximately 1 mm diameter input beam will be split into three beams (of the same diameter but with a fraction of the original refractive power of the input beam) that propagate in three different directions in TIR. One direction corresponds to zero-order diffraction and is the original propagation angle in the plane of the waveguide. The other two directions depend on the lattice vectors G and H of the MPE region 1650. As shown, the first occurrence of the interaction between the input beam and the MPE region 1650 results in three beams. That is, a portion of the refractive power of the input beam simply reflects as output 1 from the upper or lower surface of the eyepiece waveguide 1600 and continues in the same x-y direction as the input beam (i.e., zero-order diffraction), a portion of the refractive power of the input beam interacts with the 2D lattice within the MPE region 1650 and is diffracted downward as output 2, and a portion of the refractive power of the input beam interacts with the lattice and is diffracted upward and to the right as output 3. The output 2 beam is shown to propagate in a direction corresponding to the center point of the FOV rectangle located near the 6 o'clock position of the k-space ring in FIG. 16E, i.e., the k-vector, while the output 3 beam is shown to propagate in a direction corresponding to the center point of the FOV rectangle located near the 2 o'clock position, i.e., the k-vector. After the first occurrence of this interaction, the output 1 beam, output 2 beam, and output 3 beam have different propagation angles as shown in FIGS. 16G-16I, but they all still propagate within the MPE region 1650 and thus can have additional interactions with the MPE region. Although not shown, other input beams incident on the MPE region 1650 with different propagation angles will behave similarly but with slightly different input and output angles.

[0264] Figure 16G is a schematic diagram of a second occurrence of the interaction between the input beam and the MPE region 1650 of the eyepiece waveguide embodiment shown in Figure 16A. The beam associated with the first occurrence of the interaction is shown using a dashed line, while the beam associated with the second occurrence of the interaction is shown using a solid line. As shown in Figure 16G, the output beams, output 1, output 2, and output 3 from the first occurrence of the interaction can each undergo an interaction with an MPE region 1650 similar to that which occurred in the previous occurrence. That is, a portion of the refractive power of the output 1 beam from Figure 16F simply continues in the same x-y direction, while another portion of the refractive power of that beam interacts with the grating and is diffracted in a direction corresponding to the FOV rectangle located near the 6 o'clock position, and yet another portion of the refractive power of that beam interacts with the grating and is diffracted in a direction corresponding to the FOV rectangle located near the 2 o'clock position. Similarly, a portion of the refractive power of the output 2 beam from Figure 16F simply continues toward the EPE region 1660, while another portion of the refractive power of that beam interacts with the grating and is diffracted in the direction indicated by the FOV rectangle located near the 9 o'clock position, and yet another portion of the refractive power of that beam interacts with the grating and is diffracted in a direction corresponding to the FOV rectangle located near the 2 o'clock position. Further, a portion of the refractive power of the output 3 beam from Figure 16F simply continues in the direction indicated by the FOV rectangle located near the 2 o'clock position, while another portion of the refractive power of that beam interacts with the grating and is diffracted in the direction indicated by the FOV rectangle located near the 9 o'clock position, and yet another portion of the refractive power of that beam interacts with the grating and is diffracted in a direction corresponding to the FOV rectangle located near the 6 o'clock position.

[0265] Figure 16H is a schematic diagram of a third occurrence of the interaction between the input beam and the MPE region 1650 of the eyepiece waveguide embodiment shown in Figure 16A. The beams associated with the first and second occurrences of the interaction are shown using dashed lines, while the beam associated with the third occurrence of the interaction is shown using solid lines. As shown in Figure 16H, the output beams resulting from the second occurrence of the interaction can each again experience an interaction with an MPE region 1650 similar to that which occurred in the previous occurrence.

[0266] Figure 16I is a schematic diagram of a fourth occurrence of the interaction between the input beam and the MPE region 1650 of the eyepiece waveguide embodiment shown in Figure 16A. The beams associated with the first, second, and third occurrences of the interaction are shown using dashed lines, while the beam associated with the fourth occurrence of the interaction is shown using solid lines. After all of these interactions, all of the resulting beams propagate in one of three directions, which are allowed inside the MPE region 1650 for any given input beam, namely, the direction corresponding to the FOV rectangle located near the 9 o'clock position of the k-space ring, the direction corresponding to the FOV rectangle located near the 2 o'clock position, or the direction corresponding to the FOV rectangle located near the 6 o'clock position. While there are nodes where some of these beams can cross each other while propagating through the MPE region 1650, the locations of those nodes have a more complex distribution than in the case of the OPE region 1550 as illustrated in Figures 15D - 15G. Furthermore, the beams can arrive at each of these nodes via different paths and thus will not necessarily be in phase with each other. Therefore, image artifacts that could result from an ordered distribution of interference nodes can be reduced within the eyepiece waveguide embodiment 1600 that uses the MPE region 1650 instead of an OPE region (e.g., 1550). This can be seen in Figures 16J and 16K.

[0267] FIG. 16J is a schematic diagram illustrating various paths by which a beam can ultimately follow the EPE region 1660 through the MPE region 1650. There are several paths, some including only a single direction change and others including multiple direction changes (although some of the longer and more complex paths will necessarily carry less refractive power). Due to the complexity introduced by the presence of another diffraction angle within the MPE region 1650, there are many different spacings between the light beams 1665 that ultimately illuminate the EPE region 1660. Also, in fact, any possible spacing between the light beams 1665 can be achieved through a sufficient number of interactions within the MPE region 1650. As shown in FIG. 16K, this can result in a more uniform illumination of the EPE region 1660.

[0268] FIG. 16K is a schematic diagram illustrating how a single input beam 1645 from the ICG region 1640 is replicated by the MPE region 1650 and redirected as multiple beams 1665 towards the EPE region 1660. These beams 1665 each originate from a dense grid of nodes. Still, there may be gaps between some of these replicated beams 1665, but they are generally smaller and less regular than the gaps between the replicated beams output from the OPE region (e.g., 1550 as shown in FIG. 15G). Because there are so many paths towards the EPE region 1660 at all different positions, the MPE region 1650 provides a complex exit pupil pattern, which can illuminate the EPE region 1560 more uniformly.

[0269] Figure 16L is a comparative comparison showing the performance of an eyepiece waveguide with an OPE region versus an eyepiece waveguide with an MPE region. On the left, an eyepiece waveguide 1500 is shown that includes an OPE region 1550 with a 1D periodic diffraction grating. As already discussed, the OPE region 1550 illuminates the EPE region 1560 using a set of spaced-apart replicated optical beams that are periodically spaced. Below the eyepiece waveguide 1500 is a simulated output image. This is a simulated output image that would be projected from the EPE region 1560 of the eyepiece waveguide 1500 in response to an input image consisting of pixels all having the same color and brightness.

[0270] Figure 16L shows, on the right, an eyepiece waveguide 1600 that includes an MPE region 1650 with a 2D periodic diffraction grating. As can be seen from the figure, the MPE region 1650 illuminates the EPE region 1660 more uniformly. Below the eyepiece waveguide 1600 is a simulated output image that is the result of the same input image used in the simulation for the left eyepiece waveguide 1500. From the simulated image on the right, it is clear that the eyepiece waveguide 1600 using the MPE region 1650 achieves a smoother and more uniformly distributed output light. In contrast, the left image, which is the simulated output of the eyepiece waveguide 1500 with the OPE region 1550, has visible high spatial frequency stripes that result from the set of spaced-apart and ordered replicated optical beams that illuminate its EPE region 1560.

[0271] Figure 16M further illustrates the performance of an eyepiece waveguide with an MPE region versus an eyepiece waveguide with an OPE region. The upward trace of the graph in Figure 16M illustrates the performance of the eyepiece waveguide 1500 shown in Figure 15A. The graph of the horizontal cross-section of the image projected from this eyepiece waveguide shows relatively high spatial frequency variations, which were visible as streaks in the simulated output image shown in Figure 16L. Figure 16M shows that the eyepiece waveguide 1500 has an eye box efficiency of 1.2%. It also shows the point spread function associated with this eyepiece waveguide. The point spread function illustrates the output image obtained from the eyepiece waveguide in response to an input image of a single bright point. This shows that the eyepiece waveguide 1500 is very sharp because it has only 2.5 to 5 arc minutes of blur.

[0272] One approach to overcoming the high spatial frequency variations in the output image from the eyepiece waveguide 1500 is to introduce some amount of dithering into the OPE region 1550. For example, small variations can be introduced into the orientation angle and / or the grating period of the OPE region 1550. This is done in an attempt to disrupt the ordered nature of the interference nodes that may exist within the OPE region 1550. The second and third traces in Figure 16M illustrate the performance of the eyepiece waveguide 1500 with two different types of dithering. As can be seen from the horizontal cross-section of the image projected for these waveguides, high spatial frequency variations still exist. Furthermore, the point spread functions for these dithered embodiments show, in some cases, as much as 45 arc minutes of additional blur.

[0273] The downward travel of FIG. 16M illustrates the performance of the eyepiece waveguide 1600 with the MPE region 1650. The cross-section of the projected image regarding this waveguide shows much less high spatial frequency variation. Still, there are low frequency spatial variations, which can be corrected much more easily via software than high spatial frequency variations. The eyebox efficiency of this eyepiece waveguide is 0.9%, which is slightly lower than others. This may be due to the fact that the MPE region 1650 redirects a portion of the input light in a general direction corresponding to the FOV rectangle located near the 2 o'clock position within the loop of the k-space diagram shown in FIG. 16E. Due to the macroscopic layout of the eyepiece waveguide 1600, the light emitted from the MPE region 1650 with this propagation direction never enters the EPE region and thus is not projected towards the user's eye. Instead, it is lost from the edge of the waveguide 1600. However, this light loss only results in a relatively small decrease in the eyebox efficiency. On the other hand, the point spread function regarding the eyepiece waveguide 1600 shows that it is very sharp with only a blur of 2.5 to 5 arc minutes.

[0274] Figures 16A - 16M illustrate the eyepiece waveguide 1600 with the MPE region 1650, which has three allowable propagation directions for each input beam. However, other embodiments of the MPE region can be designed to allow even more propagation directions for each input beam. One such example is illustrated in FIGS. 17A - 17G. These figures illustrate the eyepiece waveguide 1700, which is the same as the eyepiece waveguide 1600 in its macroscopic design. That is, the eyepiece waveguide 1700 includes the ICG region 1740, the MPE region 1750, and the EPE region 1760, all of which are arranged in the same way as the corresponding regions within the eyepiece waveguide 1600 shown in FIG. 16A. However, the eyepiece waveguide 1700 differs in the microscopic design of its MPE region 1750.

[0275] FIG. 17A illustrates a portion of an exemplary 2D lattice that can be used within the MPE region 1750 of the eyepiece waveguide 1700, along with its associated lattice vectors. The 2D periodic lattice 1750 can be a spatial lattice pattern of diffraction features, the directions of whose periodicity are u and v. As already discussed, such a 2D periodic lattice is associated with the base lattice vectors G and H. As an example, the 2D periodic lattice 1750 can be designed or formed by superimposing two sets of 1D periodic lattice lines (however, the 2D periodic lattice can alternatively consist of, for example, individual scattering features located at the intersections of the lattice lines shown in FIG. 17A). The first set of lattice lines 1756 can be repeated along the direction of the base lattice vector G. The base lattice vector G can have a magnitude equal to 2π / a, where a is the period of the first set of lattice lines 1756. The 2D lattice shown in FIG. 17B is also associated with the harmonics of the first base lattice vector G. These include higher order harmonics such as -G and 2G, -2G, etc. The second set of lattice lines 1757 can be repeated along the direction of the base lattice vector H. The base lattice vector H can have a magnitude equal to 2π / b, where b is the period of the second set of lattice lines 1657. The 2D lattice shown in FIG. 17B is also associated with the harmonics of the second base lattice vector H. These include higher order harmonics such as -H and 2H, -2H, etc. Also, as already discussed, any 2D periodic array of diffraction features will have associated lattice vectors that point in directions determined by integer linear combinations (superpositions) of the base lattice vectors. In this case, these superpositions result in additional lattice vectors. These include, for example, -G, -H, H+G, H-G, G-H, and -(H+G). FIG. 17A illustrates only the primary lattice vectors and their superpositions associated with the 2D diffraction lattice, but higher order lattice vectors may also exist.

[0276] Figure 17B is a k-space diagram illustrating the k-space operation of the MPE region 1750 of the eyepiece waveguide 1700. The k-space diagram includes a shaded FOV rectangle located near the 9 o'clock position of the k-space ring. This is the location of the FOV rectangle after the ICG region 1740 has coupled the input beams into the eyepiece waveguide 1700 and redirected them towards the MPE region 1750. Figure 17B shows how the 2D lattice within the MPE region 1750 uses the lattice vectors shown in Figure 17A to translate the FOV rectangle. Since there are eight lattice vectors, the MPE region 1750 attempts to translate the FOV rectangle to eight possible new locations within the k-space diagram. Of these eight possible locations, five are outside the outer perimeter of the k-space diagram. These locations are illustrated using non-shaded FOV rectangles. Since the k-vectors outside the outer perimeter of the k-space diagram are not allowed, none of those five lattice vectors result in diffraction. However, there are three lattice vectors (i.e., -H, -G, and -(H + G)) that result in translation of the FOV rectangle to new positions within the boundaries of the k-space diagram. One of these locations is near the 6 o'clock position within the k-space ring, another is near the 12 o'clock position, and the last is near the 3 o'clock position. The k-vectors at these locations are allowed and result in guided propagation modes, so the FOV rectangles at these locations are shaded to indicate that the light beam is diffracted into those three states. Thus, a light beam incident on the MPE region 1750 with a propagation angle indicated by the FOV rectangle located near the 9 o'clock position of the k-space ring is diffracted into all of the states indicated by the other three shaded FOV rectangles (i.e., the FOV rectangle near the 12 o'clock position, the FOV rectangle near the 3 o'clock position, and the FOV rectangle near the 6 o'clock position).

[0277] Although not shown, similar k-space diagrams can be derived to illustrate the k-space action of the MPE region 1750 on beams of light traveling with propagation angles indicated by FOV rectangles located near the 12 o'clock position, near the 3 o'clock position, and near the 6 o'clock position of the k-space ring. Those k-space diagrams will show that the 2D diffraction grating within the MPE region 1750 diffracts those beams into all of the remaining states indicated by the shaded FOV rectangles within the ring of the k-space diagram in FIG. 17B.

[0278] FIG. 17C is a k-space diagram illustrating the k-space action of the eyepiece waveguide 1700. The eyepiece waveguide 1700 can generally receive an input beam of light that propagates in the -z-direction and is incident on the ICG region 1740 of the waveguide 1700 from an external source. Those input beams are represented by FOV rectangles centered on the k z -axis at the origin of the k-space diagram. The ICG region 1740 then diffracts the input beams so that they have propagation angles centered around the propagation direction corresponding to the center points of FOV rectangles located near the 9 o'clock position of the k-space ring.

[0279] The diffracted beams are incident on the MPE region 1750 where they can have multiple interactions. During each occurrence of an interaction, a portion of the refractive force of each beam continues to propagate in the same direction through the MPE region 1750. For the first occurrence of an interaction, for example, this would correspond to that portion of the refractive force of those beams that remains in the state indicated by the FOV rectangle located near the 9 o'clock position. The other portion of the refractive force of the beam can be diffracted into a new direction. Again, for the first occurrence of an interaction, this creates individual diffracted beams having propagation angles centered around the propagation direction corresponding to the center point of the FOV rectangle located near the 12 o'clock position of the k-space ring, the center point of the FOV rectangle located near the 3 o'clock position, and the center point of the FOV rectangle located near the 6 o'clock position.

[0280] After each interaction, the diffracted beam that still remains within the MPE region 1750 can undergo additional interactions. Each of these additional interactions results in a situation where a portion of the beam's refractive power is diffracted in the zero order and continues in the same direction, while a portion of the beam's refractive power is diffracted in a new direction. This results in a set of spatially dispersed diffracted beams having propagation angles that are centered around each of the propagation directions indicated by the center points of the FOV rectangles within the k - space ring shown in FIG. 17C. This is represented by the double arrows between each pair of FOV rectangles within the k - space ring. In other words, a beam of light propagating within the MPE region 1750 can transition from any propagation state represented by one of the FOV rectangles within the k - space ring to any other of these propagation states.

[0281] As any given input beam of light propagates through the MPE region 1750, it splits into multiple diffracted beams, which can only travel in four possible directions. Each direction is defined by the corresponding k - vector within the FOV rectangle within the ring of the k - space diagram in FIG. 17C, i.e., by a point. (This applies to any input beam of light propagating through the MPE region 1750. However, the four possible directions will be slightly different depending on the propagation angle at which each initial input beam enters the MPE region 1750.) Also, since a portion of the refractive power of any given input beam of light is diffracted in the same four propagation directions after any number of interactions with the MPE region 1750, the image information is preserved throughout these interactions. Compared to the MPE region 1650 described with respect to FIGS. 16A - 16M, the additional allowed propagation directions within the MPE region 1750 can result in a further improvement in the uniformity of illumination within the EPE region 1760. This can be seen in the schematic diagrams shown in FIGS. 17D - 17G.

[0282] FIG. 17D is a schematic diagram of a first occurrence of an interaction between an input beam and the MPE region 1750 of the eyepiece waveguide 1700. FIG. 17D shows an input beam incident from the ICG region 1740 into the MPE region 1750. The input beam is shown to propagate in a direction corresponding to the center point of the FOV rectangle located near the 9 o'clock position of the k-space ring in FIG. 17C, i.e., corresponding to the k-vector.

[0283] The MPE region 1750 can contain many features below 1 μm. Also, for each interaction with the MPE region, a beam of approximately 1 mm diameter will be split in TIR into four beams (of the same diameter but with a certain fraction of the original refractive power of the input beam) that propagate in four different directions. One direction corresponds to zero-order diffraction and is the original angle in the plane of the waveguide. The other three directions depend on the lattice vectors G and H of the MPE region 1750. As shown, the first occurrence of the interaction between the input beam and the MPE region 1750 results in four beams. That is, a fraction of the refractive power of the input beam simply reflects from the top or bottom surface of the eyepiece waveguide 1700 as output 1 and continues in the same x-y direction as the input beam (i.e., zero-order diffraction), a fraction of the refractive power of the input beam interacts with the grating and is diffracted downward as output 2, a fraction of the refractive power of the input beam interacts with the grating and is diffracted upward as output 3, and a fraction of the refractive power of the input beam interacts with the grating and is diffracted to the right as output 4. The output 2 beam is shown to propagate in the direction corresponding to the center point of the FOV rectangle near the 6 o'clock position of the k-space ring in FIG. 17C, i.e., the k-vector, while the output 3 beam is shown to propagate in the direction corresponding to the center point of the FOV rectangle near the 12 o'clock position, i.e., the k-vector, and the output 4 beam is shown to propagate in the direction corresponding to the center point of the FOV rectangle near the 3 o'clock position, i.e., the k-vector. After the first occurrence of this interaction, the output 1 beam, output 2 beam, output 3 beam, and output 4 beam have different propagation angles as shown in FIGS. 17E - 17G, but they all still propagate within the MPE region 1750 and thus can have additional interactions with the MPE region. Although not shown, other input beams incident on the MPE region 1750 with different propagation angles will behave similarly but with slightly different input and output angles.

[0284] FIG. 17E is a schematic diagram of a second occurrence of an interaction between an input beam and the MPE region 1750 of the eyepiece waveguide 1700. The beam associated with the first occurrence of the interaction is shown using a dashed line, while the beam associated with the second occurrence of the interaction is shown using a solid line. As shown in FIG. 17D, the output beams from the first occurrence of the interaction, i.e., output 1, output 2, output 3, and output 4, respectively, can each undergo an interaction with an MPE region 1750 similar to that which occurred in the previous occurrence. That is, a portion of the refractive power of the output 1 beam from FIG. 17D simply continues in the same x-y direction, while another portion of the refractive power of that beam interacts with the grating and is diffracted in a direction corresponding to the FOV rectangles located near the 12 o'clock position, near the 3 o'clock position, and near the 6 o'clock position. Similarly, a portion of the refractive power of the output 2 beam from FIG. 17D simply continues towards the EPE region 1760, while another portion of the refractive power of that beam interacts with the grating and is diffracted in a direction indicated by the FOV rectangles located near the 9 o'clock position, near the 12 o'clock position, and near the 3 o'clock position. Further, a portion of the refractive power of the output 3 beam from FIG. 17D simply continues in the direction indicated by the FOV rectangle located near the 12 o'clock position, while another portion of the refractive power of that beam interacts with the grating and is diffracted in a direction indicated by the FOV rectangles located near the 3 o'clock position, near the 6 o'clock position, and near the 9 o'clock position. Finally, a portion of the refractive power of the output 4 beam from FIG. 17D simply continues in the direction indicated by the FOV rectangle located near the 3 o'clock position, while another portion of the refractive power of that beam interacts with the grating and is diffracted in a direction indicated by the FOV rectangles located near the 6 o'clock position, near the 9 o'clock position, and near the 12 o'clock position.

[0285] Figure 17F is a schematic diagram of a third occurrence of interaction between the input beam and the MPE region 1750 of the eyepiece waveguide embodiment 1700. The beams associated with the first and second occurrences of the interaction are shown using dashed lines, while the beam associated with the third occurrence of the interaction is shown using solid lines. As shown in Figure 17F, each of the output beams resulting from the second occurrence of the interaction can again experience interaction with an MPE region 1750 similar to that which occurred in the previous occurrence.

[0286] Figure 17G is a schematic diagram of a fourth occurrence of interaction between the input beam and the MPE region 1750 of the eyepiece waveguide embodiment 1700. The beams associated with the first, second, and third occurrences of the interaction are shown using dashed lines, while the beam associated with the fourth occurrence of the interaction is shown using solid lines. After all of these interactions, all of the resulting beams are propagating in one of four allowed propagation directions with respect to the MPE region 1750 for any given input beam, namely, the direction corresponding to the FOV rectangle located near the 9 o'clock position of the k-space ring, the direction corresponding to the FOV rectangle located near the 12 o'clock position, the direction corresponding to the FOV rectangle located near the 3 o'clock position, or the direction corresponding to the FOV rectangle located near the 6 o'clock position. Although there are nodes where some of these beams can cross each other while propagating through the MPE region 1750, the locations of those nodes have a more complex distribution than in the case of the MPE region 1650 as illustrated in Figures 16A - 16M. Furthermore, these nodes are even less likely to cause interference between two in-phase beams. Thus, this MPE region 1750 can provide even more uniform illumination of the EPE region 1760.

[0287] As a summary, the MPE region described in this specification enables some or all of the following advantages. That is, the MPE region can expand the image pupil in multiple directions at once. The MPE region can create a dense aperiodic array of output pupils. The MPE region can reduce the interference effect between optical paths through the waveguide. The MPE-based eyepiece waveguide can achieve improved luminance uniformity with reduced high-frequency striations and high image sharpness. Exemplary AR eyepiece waveguide with multiple distinct regions for replicating an input beam

[0288] FIG. 18A illustrates an exemplary eyepiece waveguide 1800 with an ICG region 1840, two orthogonal pupil expanders (OPE) regions 1850a, 1850b, and an exit pupil expander (EPE) region 1860. FIG. 18A also includes a k-space diagram illustrating the effect of each of these components of the eyepiece waveguide 1800 in k-space. The ICG region 1840, OPE regions 1850a, 1850b, and EPE region 1860 of the eyepiece waveguide 1800 couple an input beam into the eyepiece waveguide 1800, propagate it through guided modes, replicate the beam in a spatially dispersed manner, and emit the replicated beam from the eyepiece waveguide and project it towards the user's eye, including various diffraction features. In particular, the eyepiece waveguide 1800 includes multiple distinct and / or discontinuous regions for replicating the input beam. The replicated beams from these distinct regions can be recombined within a common exit pupil region.

[0289] The eyepiece waveguide 1800 illustrated in FIG. 18A is similar to the eyepiece waveguide 1400 illustrated in FIG. 14A, but instead of one, it includes two OPE regions 1850a, 1850b. The ICG region 1440 in the eyepiece waveguide 1400 diffracted the input beam into +1 and -1 diffraction orders, but recall that the beam at one of these diffraction orders propagated away from the OPE region 1450 and was ultimately lost from the eyepiece waveguide. Thus, a portion of the light from the input beam was lost. The eyepiece waveguide 1800 shown in FIG. 18A corrects this by including two OPE regions 1850a, 1850b, one on each side of the ICG region 1840. In this way, the eyepiece waveguide 1800 can utilize both the +1 and -1 diffraction orders of the ICG 1840.

[0290] The operation of the ICG region 1840 is similar to that described for the ICG region 1440 in FIGS. 14A and 14B. The same k-space diagram KSD1 shown in FIG. 14B is also an illustration of the FOV rectangle corresponding to the set of input beams incident on the ICG region 1840 in FIG. 18A. That is, before the input beam is incident on the ICG region 1840, the FOV rectangle is centered at the origin of the k-space diagram.

[0291] The k-space diagram KSD2 in FIG. 18A illustrates the action in the k-space of the ICG region 1840. That is, as discussed with respect to the corresponding k-space diagram in FIG. 14B, the ICG region 1840 is associated with two lattice vectors that translate the FOV rectangle to the 3 o'clock and 9 o'clock positions within the k-space ring, respectively. The translated FOV rectangle located at the 3 o'clock position represents the diffracted beam propagating towards the right OPE region 1850b, while the translated FOV rectangle located at the 9 o'clock position represents the diffracted beam propagating towards the left OPE region 1850a.

[0292] The operation of the left OPE region 1850a is also similar to that described for the OPE region 1450 in FIGS. 14A and 14B. The k-space diagram KSD3a illustrates the k-space operation of the left OPE region 1850a, showing that its diffraction grating translates the FOV rectangle from the 9 o'clock position to the 6 o'clock position within the k-space ring. The FOV rectangle located at the 6 o'clock position represents the diffracted beam propagating in the -y-direction towards the EPE region 1860.

[0293] The operation of the right OPE region 1850b is similar to that of the left OPE region 1850a, but its associated lattice vectors are mirrored about a perpendicular line with respect to those of the left OPE region 1850a. This is due to the fact that the lines of the diffraction grating within the right OPE region 1850b are mirrored about a perpendicular line with respect to those of the diffraction grating within the left OPE region 1850a. As a result of the true orientation of the lines of the diffraction grating within the right OPE region 1850b, the effect of the grating in k-space is to translate the FOV rectangle from the 3 o'clock position to the 6 o'clock position within the k-space ring, as shown in the k-space diagram KSD3b. The translated FOVs in KSD3a and KSD3b are in the same place at the 6 o'clock position of the k-space ring. Thus, the refractive power of each input beam is split by the ICG region 1840 into +1 and -1 diffraction orders, and their distinctly different diffraction orders travel different paths through the eyepiece waveguide 1800, but they nevertheless arrive at the EPE region 1860 with the same propagation angle. This means that the separate diffraction orders of each input beam following different propagation paths through the eyepiece waveguide 1800 ultimately exit the EPE region 1860 with the same angle and thus represent the same point within the projected image.

[0294] Finally, the operation of the EPE region 1860 is also similar to that described for the EPE region 1460 in FIGS. 14A and 14B. The k-space diagram KSD4 illustrates the k-space operation of the EPE region 1860, and its diffraction grating translates the FOV rectangle (consisting of light beams from both the OPE regions 1850a and 1850b) located at the 6 o'clock position of the k-space ring back to the center of the k-space diagram. As already discussed elsewhere, this represents that the EPE region 1860 externally couples the light beam generally in the z-direction towards the user's eye.

[0295] FIGS. 18B and 18C illustrate top views of the EPE region 1860 of the eyepiece waveguide 1800 shown in FIG. 18A. The EPE region 1860 is supported directly in front of the user's eye 210. As discussed anywhere herein (see FIGS. 12A and 12B), the EPE region 1860 projects a set of replicated output beams, and each set of replicated output beams has a propagation angle corresponding to one of the input beams projected into the eyepiece waveguide.

[0296] FIG. 18B illustrates one of these sets of replicated output beams. In this particular case, the replicated output beam 1861 exiting the EPE region 1860 travels from left to right. In other words, the replicated output beam 1861 has a propagation direction with a component in the +x-direction. The actual propagation angles of the replicated output beams 1861 result in some of them tending to intersect the user's eye 210 more strongly than others. In particular, the replicated output beam 1861 exiting from the left side portion of the EPE region 1860 tends to intersect the user's eye 210 strongly due to the central position of the eye 210 and the left / right propagation of the light beam. These light beams are illustrated using solid lines. On the other hand, the replicated output beam 1861 exiting from the right side portion of the EPE region 1860 tends to miss the eye 210. These light beams are illustrated using dashed lines.

[0297] FIG. 18B also includes a k-space diagram KSD5 that illustrates the state of the output beam in k-space after the EPE region has been translated so that the FOV rectangle returns to the origin of the sketch. The FOV rectangle is illustrated using two halves. Each half represents half of the horizontal field of view of the eyepiece waveguide 1800. The shaded right half 1832 of the FOV rectangle contains k-vectors with components in the +k x - direction. These are the k-vectors corresponding to the output beam 1861 that exits the EPE region 1860 with the type of left / right propagation illustrated in FIG. 18B. Only one set of replicated output beams 1861 is illustrated as exiting the EPE region 1860, but all output beams whose k-vectors are within the shaded right half 1832 of the FOV rectangle will similarly exit the EPE region with a left / right propagation direction. Thus, for all output beams whose k-vectors are within the shaded right half 1832 of the FOV rectangle, it follows that those beams exiting from the left side of the EPE region 1860 will tend to intersect the eye 210 more strongly than those output beams exiting from the right side of the EPE region.

[0298] FIG. 18C illustrates another set of replicated light beams 1862 that exit the EPE region 1860 of the eyepiece waveguide 1800. However, in this case, the replicated output beams 1862 that exit the EPE region 1860 travel from right to left. In other words, the replicated output beams 1862 have a propagation direction with a component in the -x- direction. The principal propagation angle of the replicated output beams 1862 leads to an opposite observation derived from FIG. 18B. That is, for the output beams 1862 propagating right / left, the beams (illustrated using solid lines) exiting from the right side portion of the EPE region 1860 tend to intersect the eye 210 more strongly, while those light beams (illustrated using dashed lines) exiting from the left side portion of the EPE region tend to miss the eye more strongly.

[0299] Referring to the k-space diagram KSD5 included with FIG. 18C, the output beams whose k-vectors are within the shaded left half 1831 of the FOV rectangle exit from the EPE region 1860 with the type of right / left propagation shown in FIG. 18C. All of the output beams whose k-vectors are within the shaded left half 1831 of the FOV rectangle will have different propagation angles, but they all share the property that the beams exiting from the right side of the EPE region 1860 will tend to intersect the eye 210 more strongly than the output beams exiting from the left side of the EPE region.

[0300] The conclusion that can be drawn from FIGS. 18B and 18C is that based on the light beams actually incident on the user's eye 210, one half of the EPE region 1860 mainly contributes to one half of the horizontal field of view, while the other half of the EPE region mainly contributes to the remaining half of the horizontal field of view. Based on this observation, since it is not necessary to project the entire FOV rectangle from all parts of the EPE region 1960, the field of view that can be projected by the eyepiece waveguide can be extended beyond the range of propagation angles supported by the eyepiece in the guided mode in at least one dimension. This is illustrated in FIG. 19. Exemplary AR Eyepiece Waveguide with Extended Field of View

[0301] FIG. 19 illustrates an embodiment of an eyepiece waveguide 1900 with an extended field of view. The eyepiece waveguide 1900 includes an ICG region 1940, a left OPE region 1950a, a right OPE region 1950b, and an EPE region 1960. At the macroscopic level, the eyepiece waveguide 1900 shown in FIG. 19 can be the same as the eyepiece waveguide 1800 shown in FIG. 18A. However, some of the diffraction features within the eyepiece waveguide 1900 can be designed with properties that enable an increased field of view in at least one dimension. These features can be clearly understood based on the k-space behavior of the eyepiece waveguide 1900 illustrated by the k-space diagram shown in FIG. 19.

[0302] The k-space diagram shown in FIG. 19 has a larger FOV rectangle than that shown in FIG. 18A. This is because the FOV rectangle in the k-space diagram in FIG. 18A was constrained to not have any dimension larger than the width of the k-space ring. This constraint ensures that those FOV rectangles can fit entirely within the k-space ring at any position around the ring, and thus that all beams represented by k-vectors within the FOV rectangle can undergo guided propagation within the eyepiece waveguide 1800 while propagating in any direction in the plane of the eyepiece. However, in the exemplary embodiment of FIG. 19, the FOV rectangle has at least one dimension (e.g., k x dimension) that is larger than the width of the k-space ring. In some embodiments, one or more dimensions of the FOV rectangle can be up to 20%, up to 40%, up to 60%, up to 80%, or up to 100% larger than the width of the k-space ring.

[0303] With respect to a particular embodiment illustrated in the k-space diagram of FIG. 19, the horizontal dimension of the FOV rectangle is wider than the k-space ring. The horizontal dimension of the FOV rectangle corresponds to the horizontal spread within the propagation angle of the input beam that is projected into the eyepiece waveguide. Thus, the eyepiece waveguide 1900 is illustrated to be capable of being used in combination with an FOV rectangle having a larger horizontal dimension, which means that the horizontal field of view of the eyepiece waveguide is increased. In the case of an eyepiece waveguide (surrounded by air) with a refractive index of 1.8, the eyepiece waveguide 1800 shown in FIG. 18A is generally capable of achieving a 45°×45° FOV, while the eyepiece waveguide 1900 shown in FIG. 19 is capable of achieving a maximum 90°×45° FOV. However, some embodiments of the eyepiece waveguide satisfy the typical design constraints of the eyebox volume (it may be advantageous to send a portion of the FOV to both sides of the eyepiece waveguide and provide a properly sized eyebox) and may be designed for a smaller FOV of about 60°×45° to avoid the grating artifacts resulting from the sparsely spaced output beams. The techniques for expanding the field of view of the eyepiece waveguide 1900 are described in the context of an expanded horizontal field of view, but the same techniques can also be used to expand the vertical field of view of the eyepiece waveguide 1900. Further, in later embodiments, similar techniques are shown for expanding both the horizontal and vertical fields of view of the eyepiece waveguide.

[0304] Upon examination of the k-space diagram in FIG. 19, it can be seen that the FOV rectangles shown may not fit entirely within the k-space ring when located at certain positions around the ring, but they can still fit entirely within the ring when located at other positions. For example, if one dimension of the FOV rectangle is larger than the width of the k-space ring, the FOV rectangle may not fit entirely within the ring when the FOV rectangle is located along or near the axis of the enlarged dimension. x An FOV rectangle with a dimension larger than the width of the k-space ring, the FOV rectangle x may not fit entirely within the ring when the FOV rectangle is located along or near they A FOV rectangle with dimensions larger than the width of the k-space ring may not fit entirely within the ring when the FOV rectangle is located on or near the k y -axis or its vicinity (i.e., at or near the 12 o'clock and 6 o'clock positions). However, such a FOV rectangle can still fit entirely within the k-space ring when it is located on or near the opposite axis. k x A FOV rectangle with dimensions larger than the width of the k-space ring can still fit entirely within the ring when the FOV rectangle is located on or near the k y -axis or its vicinity (i.e., at or near the 12 o'clock and 6 o'clock positions). Similarly, a k y A FOV rectangle with dimensions larger than the width of the k-space ring can still fit entirely within the ring when the FOV rectangle is located on or near the k x -axis or its vicinity (i.e., at or near the 3 o'clock and 9 o'clock positions). This is because there is an area within the k-space ring to accommodate a FOV rectangle that is larger in the azimuthal direction than in the radial direction.

[0305] The radial size of the k-space ring corresponds to the range of propagation angles in the direction normal (i.e., the thickness direction) to the plane of the waveguide that supports the inductive propagation mode. This range of propagation angles is constrained by the requirements that must be satisfied for Snell's law and TIR to occur. In contrast, the spread of the k-vector in the azimuthal dimension of the k-space ring corresponds to various propagation angles in the in-plane direction of the planar waveguide. Since the spread of propagation angles in the plane of the planar waveguide is not limited by the same constraints as those in the thickness direction, a wider range of beam propagation angles can be supported.

[0306] Furthermore, it is possible to convert various propagation angles in the thickness direction of the eyepiece waveguide into various propagation angles in the in-plane direction, and vice versa. When a diffraction grating (or a group of other diffraction features) causes the set of beams represented by the FOV rectangle to then propagate in a new direction by translating the FOV rectangle from one position to another within the k-space ring, this also diffuses a portion of the beam that was previously diffused in the thickness direction of the planar waveguide, instead, in the in-plane direction, and vice versa. This can be seen, for example, when the diffraction grating translates the FOV rectangle from the 9 o'clock position to the 6 o'clock position within the k-space ring. While at the 9 o'clock position, the spread of the beam in the k x direction is, at that location, the k x direction corresponding to the radial direction of the k-space ring, corresponding to the physical spread in the thickness direction of the waveguide. However, at the 6 o'clock position, the spread of the beam in the k x direction is, at that location, the k x direction corresponding to the azimuthal direction of the k-space ring, corresponding to the physical spread in the in-plane direction of the waveguide.

[0307] Using these observations, the FOV of the eyepiece waveguide can be increased by dividing the FOV rectangle into a plurality of sub-parts, using diffraction features to replicate the beams belonging to the plurality of sub-parts of the FOV in a spatially dispersed pattern, and using diffraction features to reassemble the plurality of sub-parts of the FOV at the exit pupil of the eyepiece waveguide such that the beams corresponding to each sub-part of the FOV have the correct propagation angles and recreate the original image. For example, the diffraction features can be used to translate each sub-part of the FOV rectangle to one or more locations within the k-space such that they ultimately have the same relative position as in the original image with respect to other sub-parts of the FOV rectangle.

[0308] In some embodiments, multiple sub - portions of the FOV can partially overlap with each other (e.g., different pairs of FOV sub - portions can include a part of the same input beam) because this can help relax the constraints for reassembling the entire FOV at the exit pupil of the waveguide and can help ensure that all of the beam is present. For example, in some embodiments, a pair of sub - portions of the input image FOV may overlap by 10% or less, 20% or less, 30% or less, 40% or less, 50% or less, or more.

[0309] The k - space diagram KSD2 in FIG. 19 illustrates the k - space action of the ICG region 1940 on the input beam projected into the eyepiece waveguide 1900. As discussed anywhere herein, the input beam projected into the eyepiece waveguide 1900 can be represented by an FOV rectangle centered at the origin of the k - space diagram KSD2. The ICG region 1940 translates the location of this FOV rectangle in k - space based on its associated lattice vectors. In the case of the ICG region 1840 illustrated in FIG. 18A, the ICG region has a size equal to the distance from the origin of the k - space diagram to the mid - point of the k - space ring. This centers the FOV rectangle within the k - space ring. However, the ICG region 1940 illustrated in FIG. 19 can be designed to have larger lattice vectors. Also, as already discussed, the set of input beams projected into the eyepiece waveguide 1900 can have at least one dimension in k - space larger than the width of the k - space ring. -1 is designed to have a size equal to the distance from the origin of the k - space diagram to the mid - point of the k - space ring. This centers the FOV rectangle within the k - space ring. However, the ICG region 1940 illustrated in FIG. 19 can be designed to have larger lattice vectors. Also, as already discussed, the set of input beams projected into the eyepiece waveguide 1900 can have at least one dimension in k - space larger than the width of the k - space ring.

[0310] In some embodiments, the ICG region 1940 has its lattice vectors G1, G -1 designed to translate the enlarged FOV rectangle far enough from the origin of the k - space diagram so that no part of the enlarged FOV rectangle is inside the inner disk of the k - space diagram. For a case where the horizontal dimension of the FOV rectangle is twice the width of the k - space ring, to achieve this goal, the lattice vectors G1, G of ICG1940-1 Its size would need to be approximately equal to the radius of the outer disc of the k-space diagram. On the other hand, in the case of the FOV rectangle where its horizontal dimension is simply slightly larger than the width of the k-space ring, in order to achieve this goal, for the lattice vectors G1, G of the ICG region 1940 -1 Its size would need to exceed the distance from the origin of the k-space diagram to the midpoint of the k-space ring. Mathematically, this means the following.

Chemical formula

Chemical formula

[0311] In other words, the technique for expanding the field of view of the eyepiece waveguide 1900 means that the lattice vectors G1, G of the ICG region 1940 -1 are designed to be longer than in embodiments where the field of view is constrained in all dimensions by the range of propagation angles such that the field of view can fit within the radial dimension of the k-space ring of a given eyepiece waveguide. Since the lengths of the lattice vectors G1, G -1 are increased by reducing the lattice period Λ, this means that the ICG region 1940 has a finer pitch than what would conventionally be used for light of a given angular frequency ω, ensuring that all input beams can be diffracted into guided modes.

[0312] Of course, according to the embodiment illustrated in FIG. 19, the larger size of the FOV rectangle and the longer lattice vectors G1, G -1A part of the translated FOV rectangle extends beyond the outer periphery of a larger disc in the k-space diagram after diffraction by the ICG region 1940. Since the k-vectors outside this disc are not allowed, the input beams corresponding to those k-vectors are not diffracted by the ICG region 1940. Instead, only the input beams corresponding to the k-vectors within the shaded portion of the translated FOV rectangle in KSD2 enter the guided propagation mode within the eyepiece waveguide 1900. Input beams that would diffract in the +1 order with k-vectors that would be outside the outer disc of the k-space diagram are not allowed to diffract and are thus lost. Similarly, input beams that would diffract in the -1 order with k-vectors that would be outside the outer disc of the k-space diagram are not allowed to diffract and are thus lost. Fortunately, the beams lost from each of these diffraction orders are not the same. This allows the full field of view to be restored in the EPE region 1960. Even if either the clipped FOV rectangle located at the 3 o'clock position of the k-space diagram KSD2 or the clipped FOV rectangle located at the 9 o'clock position does not contain the full set of input beams, when these clipped FOV rectangles are properly recombined in the EPE region 1960, the full set of input beams can be restored.

[0313] The k-space diagrams KSD3a and KSD3b respectively illustrate the k-space action of the diffraction gratings within the left OPE region 1950a and the right OPE region 1950b. As discussed with respect to FIG. 18A, these OPE regions can include diffraction gratings that are oriented to translate the FOV rectangles located at the 3 o'clock and 9 o'clock positions to the 6 o'clock position. However, in the embodiment illustrated in FIG. 19, the orientation of the diffraction gratings within the OPE regions 1950a, 1950b may need to be adjusted to accomplish this purpose. Specifically, the lattice vectors G1, G associated with the ICG region 1940 -1 Since it can no longer terminate at the midpoint of the k-space ring at the 3 o'clock and 9 o'clock positions, the magnitude and direction of the lattice vectors associated with the OPE region are such that the FOV rectangle is located at a certain place at the 6 o'clock position (e.g., k yIt may be necessary to adjust to translate it in the direction parallel to the one centered within the k-space ring in the -direction. These adjustments can be accomplished by modifying the orientation of the grating lines within the OPE regions 1950a, 1950b and / or by changing its grating period Λ as compared to the OPE regions in embodiments without an extended FOV.

[0314] The shaded right portion of the FOV rectangle within KSD3a represents the first sub-portion of the FOV, while the shaded left portion of the FOV rectangle within KSD3b represents the second sub-portion of the FOV. In the illustrated embodiment, these FOV sub-portions overlap within the central region of the FOV rectangle.

[0315] The k-space diagram KSD3a illustrates that when the FOV rectangle located at the 9 o'clock position is translated to the 6 o'clock position, only the beams corresponding to the shaded right region of the FOV rectangle are present. The k-space diagram KSD3b shows the same phenomenon, but the absent beams are those whose k-vectors are located on the opposite side of the FOV rectangle. Finally, the k-space diagram KSD4 shows that when two truncated FOV rectangles are superimposed at the 6 o'clock position of the k-space ring, the non-shaded portions of the FOV rectangle are filled, meaning that all the beams that make up the full FOV of the input image are present here and can be projected out of the eyepiece waveguide 1900 towards the user's eye by the diffraction grating within the EPE region 1960. Similar to the embodiment in FIG. 18A, the EPE region 1960 translates the FOV rectangle back to the origin within the k-space diagram KSD4. Importantly, the two truncated FOV rectangles from the 9 o'clock and 3 o'clock positions should be translated to the 6 o'clock position in such a way as to maintain the relative positions of the shaded regions within the original FOV rectangle. This ensures that the beams of light within each sub-portion of the FOV have the correct propagation angles to recreate the original image.

[0316] What this means from a physical perspective is that the eyepiece waveguide 1900 divides the image field of view into a plurality of portions. The light beams corresponding to each of these portions of the image field of view propagate along different paths through the eyepiece waveguide 1900, where they can be replicated by different OPE regions 1950a, 1950b in a spatially dispersed manner. Also, ultimately, the separate portions of the image field of view are recombined within the EPE region 1960 and projected towards the user's eye.

[0317] In some embodiments, the various diffraction gratings of the eyepiece 1900 can be designed such that there is an overlap between subsets of the beams supplied to the EPE region 1960 by the individual OPE regions 1950a, 1950b. In other embodiments, however, the diffraction gratings can be designed such that each OPE region 1950a, 1950b supplies a unique subset of the beams required to fully recreate the input image. Exemplary AR eyepiece waveguide with extended field of view and overlapping MPE and EPE regions

[0318] FIG. 19 illustrates an embodiment of an eyepiece waveguide with an extended FOV that uses OPE regions to replicate an input beam, although other embodiments can advantageously use MPE regions. FIGS. 20A - 20L illustrate one such exemplary embodiment.

[0319] FIG. 20A illustrates an embodiment of an extended FOV eyepiece waveguide 2000 with an MPE region 2050 that is overlapped by an EPE region 2060. The eyepiece waveguide 2000 can achieve an extended field of view that can be greater than the range of propagation angles that can be supported in an inductive propagation mode in the thickness direction of the waveguide. The eyepiece waveguide 2000 has a first surface 2000a and a second surface 2000b. As further discussed below, different diffractive features can be formed on or within opposite surfaces 2000a, 2000b of the eyepiece waveguide 2000. The two surfaces 2000a, 2000b of the eyepiece waveguide 2000 are shown in FIG. 20A as being displaced relative to each other in the x-y plane. However, this is for illustrative purposes only and is capable of showing different diffractive features formed on or within each surface. It should be understood that the first surface 2000a and the second surface 2000b are aligned with each other in the x-y plane. In addition, although the MPE region 2050 and the EPE region 2060 are shown as being of the same size and being exactly aligned in the x-y plane, in other embodiments, they may have somewhat different sizes and may be partially misaligned. In some embodiments, the MPE region 2050 and the EPE region 2060 overlap each other by at least 70%, at least 80%, at least 90%, or at least 95%.

[0320] The eyepiece waveguide 2000 includes an ICG region 2040, an MPE region 2050, and an EPE region 2060. The ICG region 2040 receives a set of input beams from a projector device. As described anywhere in the specification, the input beams can generally propagate in the z-direction through free space from the projector device until they are incident on the ICG region 2040. The ICG region 2040 diffracts those input beams such that all or at least a portion of them enter an inductive propagation mode within the eyepiece waveguide 2000. The grating lines of the ICG region 2040 can be oriented to direct the diffracted beams in the -y- direction towards the MPE region 2050.

[0321] The MPE region 2050 can include a plurality of diffraction features that exhibit periodicity along a plurality of axes. The MPE region 2050 may consist of an array of scattering features that are arranged in a 2D lattice pattern. The individual scattering features can be, for example, indentations or protrusions of any shape. The 2D array of scattering features has associated lattice vectors that are derived from the reciprocal lattice pattern of its 2D lattice pattern. As one example, the MPE region 2050 can be a 2D diffraction grating consisting of an intersecting grating with grating lines that repeat along two or more directions of periodicity. The diffraction features that make up the MPE region 2050 can have a relatively low diffraction efficiency (e.g., 10% or less). As discussed herein, this enables a beam of light to be replicated in a plurality of directions in a spatially dispersed manner as it propagates through the MPE region 2050.

[0322] FIG. 20B illustrates a portion of an exemplary 2D lattice that can be used within the MPE region 2050 of the eyepiece waveguide 2000, along with its associated lattice vectors. Intersecting gratings are illustrated, although the 2D periodic lattice can alternatively consist of individual scattering features located, for example, at the intersections of the illustrated lattice lines. The 2D lattice has a first set of lattice lines 2056 that are repeated along a first direction of periodicity. These lattice lines 2056 point along the direction of periodicity of the first set of lattice lines 2056 and have an associated primitive lattice vector G with a magnitude equal to 2π / a, where a is the period of the first set of lattice lines 2056. The 2D lattice shown in FIG. 20B is also associated with harmonics of the first primitive lattice vector G. These include higher order harmonics such as -G and 2G, -2G, etc. The 2D lattice within the MPE region 2050 also has a second set of lattice lines 2057 that are repeated along a second direction of periodicity. In some embodiments, the first and second directions of periodicity are not perpendicular. The second set of lattice lines 2057 point along the direction of periodicity of the second set of lattice lines and have an associated primitive lattice vector H with a magnitude equal to 2π / b, where b is the period of the second set of lattice lines 2057. The 2D lattice shown in FIG. 20B is also associated with harmonics of the second primitive lattice vector H. These include higher order harmonics such as -H and 2H, -2H, etc. Finally, any 2D array of diffraction features will also have an associated lattice vector that points in a direction determined by an integer linear combination (superposition) of the primitive lattice vectors G and H. In the illustrated embodiment, these superpositions result in additional lattice vectors, which are also shown in FIG. 20B. These include, for example, -G, -H, H+G, H-G, G-H, and -(H+G). FIG. 20B illustrates only the primary lattice vectors and their superpositions associated with the 2D diffraction grating, although higher order lattice vectors may also be present.

[0323] FIG. 20C is a k-space diagram KSD1 illustrating the k-space operation of the ICG region 2040 of the eyepiece waveguide 2000. The FOV rectangle centered at the origin of KSD1 represents a set of input beams projected towards the ICG region 2040 by a projector device. The dimension of the FOV rectangle in the k x -direction represents the FOV of the input beam in the x-direction, while the dimension of the FOV rectangle in the k y -direction represents the FOV of the input beam in the y-direction. As shown, in this particular embodiment, the dimension of the FOV rectangle in the k x is larger than the width of the k-space ring.

[0324] Since the MPE region 2050 is located in the -y-direction from the ICG region 2040 according to the physical layout of the eyepiece waveguide 2000 shown in FIG. 20A, the diffraction grating in the ICG region 2040 can be designed to diffract the input beam in that direction. Thus, KSD1 in FIG. 20C shows that the ICG region 2040 translates the FOV rectangle from the origin of the k-space diagram to a location on the -k y axis at the 6 o'clock position within the k-space ring. At this particular position, the wider dimension of the FOV rectangle is oriented in the azimuthal direction of the k-space ring, and thus the FOV rectangle fits entirely within the ring. This means that all the beams represented by the FOV rectangle enter the guided propagation mode within the eyepiece waveguide 2000 and generally propagate in the -y-direction towards the MPE region 2050.

[0325] As in the other MPE regions (e.g., 1650, 1750) discussed herein, the MPE region 2050 expands the image pupil in multiple directions by replicating the input beams in a spatially dispersed manner as they propagate through it. FIGS. 20D - 20F and 20H illustrate this behavior of the MPE region 2050 in k-space.

[0326] FIG. 20D is a k-space diagram KSD2 that illustrates a portion of the k-space operation of the MPE region 2050 of the eyepiece waveguide 2000. The k-space diagram includes a shaded FOV rectangle located at the 6 o'clock position of the k-space ring. This is the location of the FOV rectangle after the ICG region 2040 has coupled the input beams into the eyepiece waveguide 2000 and diffracted them towards the MPE region 2050. FIG. 20D shows how the 2D lattice within the MPE region 2050 uses the lattice vectors shown in FIG. 20B to translate the FOV rectangle. Since there are eight lattice vectors, the MPE region 2050 attempts to translate the FOV rectangle from the 6 o'clock position within the k-space ring to eight possible new locations within the k-space diagram. Of these eight possible locations, five are completely outside the outer perimeter of the k-space diagram. These locations are illustrated using non-shaded FOV rectangles. Since k-vectors outside the outer perimeter of the k-space diagram are not allowed, none of those five lattice vectors result in diffraction. However, there are three lattice vectors (i.e., G, -H, and G-H) that result in at least a partial translation of the FOV rectangle to a new position within the boundaries of the k-space diagram. One of these locations is at the 9 o'clock position within the k-space ring, another is at the 12 o'clock position, and the last is at the 3 o'clock position. The k-vectors at these locations are allowed and result in guided propagation modes, so the FOV rectangles at these locations are shaded to indicate that the light beams are diffracted into those three states.

[0327] For the 9 o'clock and 3 o'clock positions within the k-space ring, the translated FOV rectangle has its k xSince the dimensions are larger than the width of the ring, they do not fit perfectly within the ring. Thus, the translated FOV rectangles at these locations are truncated, meaning that the beams whose k-vectors are outside the outer perimeter of the k-space diagram are not induced. This is represented in KSD2 by the non-shadowed portions of the translated FOV rectangles at the 9 o'clock and 3 o'clock positions. This means that the sets of beams that propagate through the MPE region 2050 in the +x and -x directions, respectively, do not include all of the original set of input beams. The set of beams propagating in the +x direction through the MPE region 2050 is missing the beams corresponding to the right side of the FOV rectangle, while the set of beams propagating in the -x direction is missing the beams corresponding to the left side of the FOV rectangle. However, collectively, all of the beams that make up the FOV still exist.

[0328] The shadowed right portion of the translated FOV rectangle at the 9 o'clock position represents the first sub-portion of the FOV, while the shadowed left portion of the FOV rectangle at the 3 o'clock position represents the second sub-portion of the FOV. In the illustrated embodiment, these FOV sub-portions overlap in the central region of the FOV rectangle (although overlap is not necessarily required).

[0329] As already described, in some embodiments, the first and second periodic axes within the 2D lattice of the MPE region 2050 are not orthogonal. This, in turn, means that the fundamental lattice vectors G and H are also not orthogonal. This allows the 2D lattice within the MPE region 2050 to translate the FOV rectangles at the 3 o'clock and 9 o'clock positions such that the centers of those rectangles are beyond the midpoint of the k-space ring, while the centers of the FOV rectangles at the 6 o'clock and 12 o'clock positions can be located at or closer to the midpoint of the ring. As a result, the translated FOV rectangles at the 3 o'clock and 9 o'clock positions are truncated, which results in the FOV being divided into first and second sub-portions. Since dividing the FOV into first and second sub-portions is part of the process for increasing the FOV of the eyepiece waveguide 2000, this is worthy of note in the illustrated embodiment.

[0330] Figure 20E is k-space diagram KSD3, which illustrates another part of the k-space action of the MPE region 2050 of the eyepiece waveguide 2000. KSD3 includes a partially shaded FOV rectangle located at the 3 o'clock position of the k-space ring. This is the location of one of the translated FOV rectangles after the first interaction within the MPE region 2050. Figure 20E shows how the 2D lattice within the MPE region 2050 translates this FOV rectangle using the lattice vectors shown in Figure 20B. Again, since there are eight lattice vectors, the MPE region 2050 attempts to translate the FOV rectangle from the 3 o'clock position within the k-space ring to eight possible new locations within the k-space diagram. Of these eight possible locations, five are again outside the outer perimeter of the k-space diagram. These locations are illustrated using non-shaded FOV rectangles. Since k-vectors outside the outer perimeter of the k-space diagram are not allowed, none of those five lattice vectors result in diffraction. However, there are three lattice vectors (i.e., G, H, and H+G) that result in translation of the FOV rectangle to a new position at least partially within the boundary of the k-space diagram. One of these locations is at the 9 o'clock position within the k-space ring, another is at the 12 o'clock position, and the last one returns to the 6 o'clock position. The k-vectors at these locations are allowed and result in guided propagation modes, so the FOV rectangles at these locations are shaded (or the zero-order diffracted beam can remain in the propagation state represented by the FOV rectangle at the 3 o'clock position) to indicate that the light beam is diffracted into those three states.

[0331] As shown in FIG. 20E, the translated FOV rectangle at the 3 o'clock position of the k-space ring has already been clipped as a result of the first diffraction interaction within the MPE region 2050 shown in FIG. 20D. Thus, only the clipped FOV rectangles are translated to the 9 o'clock, 12 o'clock, and 6 o'clock positions of the k-space ring. In the case of the 9 o'clock position, the FOV rectangle is further clipped, meaning that only the beam corresponding to the centered shaded portion of that particular translated FOV rectangle is actually diffracted into this state.

[0332] FIG. 20F is similar to FIG. 20E, but shows the k-space effect of the MPE region 2050 on the FOV rectangle from FIG. 20D translated to the 9 o'clock position (instead of the 3 o'clock position as shown in FIG. 20E). The effect of the MPE region 2050 on the beam in this state is the mirror image (about the k y -axis) of that shown in FIG. 20E.

[0333] Although not shown, a similar k-space diagram can be derived to illustrate the k-space effect of the MPE region 2050 on a beam of light traveling with the propagation angle represented by the FOV rectangle located at the 12 o'clock position of the k-space ring. That k-space diagram would show that the 2D diffraction gratings within the MPE region 2050 would diffract those beams into the states represented by the FOV rectangles at the 3 o'clock, 6 o'clock, and 9 o'clock positions within the ring of the k-space diagrams in FIGS. 20D, 20E, and 20F.

[0334] As shown by the k-space diagrams in FIGS. 20D-20F, when the diffracted light beam from the ICG region 2040 arrives at the MPE region 2050, many replicated beams are formed in a spatially dispersed manner. Also, all of these replicated beams propagate in one of the directions indicated by the FOV rectangles at the 3 o'clock, 6 o'clock, 9 o'clock, and 12 o'clock positions within the k-space ring. The light beam propagating through the MPE region 2050 can undergo any number of interactions with the diffraction features of the MPE region, resulting in any number of changes in the propagation direction. Thus, the light beam is replicated along both the x- and y-directions throughout the MPE region 2050. This is represented by the arrows within the MPE region 2050 of the eyepiece waveguide 2000 in FIG. 20A.

[0335] Since the EPE region 2060 overlaps the MPE region 2050 in the x-y plane of the eyepiece waveguide 2000, the replicated light beams also interact with the EPE region 2060 as they spread through the waveguide and reflect back and forth between the first surface 2000a and the second surface 2000b via total internal reflection. When one of the light beams interacts with the EPE region 2060, a portion of its refractive power is diffracted, as indicated by the arrows within the EPE region 2060 of the eyepiece waveguide 2000 in FIG. 20A, and exits the eyepiece waveguide towards the user's eye.

[0336] In some embodiments, the EPE region 2060 includes a diffraction grating whose lines are oriented perpendicular to the lines of the diffraction grating that make up the ICG region 2040. An example of this is shown in FIG. 20A, where the ICG region 2040 has grating lines that extend in the x-direction and are periodically repeated in the y-direction, while the EPE region 2060 has grating lines that extend in the y-direction and are periodically repeated in the x-direction. The grating lines within the EPE region 2060 are advantageously oriented perpendicular to the grating lines within the ICG region 2040 to ensure that the light beam will interact with the MPE region 2050 before it is coupled out of the eyepiece waveguide 2000 by the EPE region 2060. This behavior is shown in k-space in FIG. 20G.

[0337] FIG. 20G is a k-space diagram KSD5 illustrating the k-space behavior of the EPE region 2060 within the eyepiece waveguide 2000 shown in FIG. 20A. As already discussed, the beam of light propagates through the MPE region 2050 in all directions indicated by the FOV rectangles located at the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positions of the k-space ring. Also, since the EPE region 2060 physically overlaps the MPE region 2050, the beam of light in all of these propagation states contacts the diffraction grating within the EPE region while diffusing through the MPE region.

[0338] The periodicity axis of the diffraction grating within the EPE region 2060 points in the ±k x -direction, and thus the lattice vectors associated with the EPE region likewise point in the same direction. FIG. 20G shows how the EPE region 2060 attempts to use these lattice vectors to translate the FOV rectangles to the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positions. ±k xDue to its orientation in the - direction, the lattice vectors associated with the EPE region 2060 can translate only the FOV rectangles located at the 3 o'clock and 6 o'clock positions of the k - space ring back to the origin of the k - space diagram. Thus, the EPE region 2060 can externally couple only the light beams that are in one of those two propagation states. That is, the EPE region does not externally couple the light beams propagating in the states corresponding to the FOV rectangles at the 12 o'clock and 6 o'clock positions of the k - space ring.

[0339] When the periodicity axes for the lattice lines within the EPE region 2060 are not perpendicular but parallel to the periodicity axes for the lattice lines within the ICG region 2040, the lattice vectors associated with the EPE region will point in the ±k y - direction. It is important to note that this will, in turn, enable the light beams in the propagation states corresponding to the FOV rectangles at the 12 o'clock and 6 o'clock positions of the k - space ring to be externally coupled by the EPE region. The input beam arrives at the MPE / EPE region in the propagation state corresponding to the 6 o'clock position, which means that the light beam can be externally coupled by the EPE region 2060 before it interacts with and is thereby spread by the MPE region 2050, which would typically be undesirable. The fact that the periodicity axes for the lattice lines within the EPE region 2060 are perpendicular to those of the ICG region 2040 means that the light beam will typically need to undergo a direction change, at least once and possibly more than once, within the MPE region before it is externally coupled. This enables an improved spread of the light beam within the MPE region 2050.

[0340] FIG. 20H is k-space diagram KSD6 that summarizes the k-space operation of the eyepiece waveguide 2000 shown in FIG. 20A. This is essentially a superposition of the k-space diagrams shown in FIGS. 20C-20G. Again, the k-space diagram in FIG. 20H shows a FOV rectangle having at least one dimension larger than the width of the k-space ring. In some embodiments, at least one dimension of the FOV rectangle can be up to approximately 2 times larger than the width of the k-space ring. In the illustrated embodiment, the horizontal dimension of the FOV rectangle is larger than the width of the k-space ring, but the same technique can also be used to expand the vertical field of view.

[0341] KSD6 includes a FOV rectangle centered at the origin of the schematic. Again, the home location of the FOV rectangle can explain either where the input beam is projected into the eyepiece waveguide 2000 or where the replicated output beam is projected out of the waveguide towards the user's eye. In the illustrated embodiment, the effect of the ICG region 2040 in k-space is to translate the FOV rectangle downward from the center of the k-space diagram to the 6 o'clock position. As shown, the ICG region 2040 can be designed such that one of its lattice vectors is oriented in the -k y -direction. This propagates the diffracted beam in the -y-direction towards the MPE region 2050. Further, the ICG region 2040 can be designed such that the magnitude of its lattice vectors copies the FOV rectangle to a position that completely fits within the k-space ring at the 6 o'clock position. This can be done, for example, by designing the ICG region 2040 with a pitch such that the magnitude of its primary lattice vector is equal to the distance from the origin of the k-space diagram to the midpoint of the k-space ring. Since the FOV rectangle at the 6 o'clock position is completely within the k-space ring, all diffracted beams enter the guided mode of propagation.

[0342] As already discussed, the MPE region includes multiple diffraction features that exhibit periodicity along multiple different axes. This means that the MPE region has multiple associated lattice vectors by which the FOV rectangle can be translated parallel to any of the 6 o'clock, 9 o'clock, 12 o'clock, and 3 o'clock positions. During additional interaction with the MPE region 2050, the FOV rectangle can be translated back and forth between any of the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positions. This is represented by the double arrows between their propagation states. As shown in FIG. 20H, the FOV rectangles at the 3 o'clock and 6 o'clock positions of the k-space ring are clipped, meaning that not all of the light beams associated with the full FOV are present in each of their propagation states. However, when those sub-portions of the FOV are considered collectively, all of the light beams that make up the full FOV are present. Thus, when the FOV rectangle is finally translated back to the origin of the k-space diagram from the 3 o'clock or 6 o'clock position so as to externally couple the light beams towards the user's eye, all of the beams required to constitute the full FOV of the input image are present and are projected from the eyepiece waveguide 2000.

[0343] FIG. 20I is a schematic diagram illustrating how light beams spread through the eyepiece waveguide 2000 shown in FIG. 20A. The guided beam that is incident on the MPE region 2050 and propagates from the ICG region 2040 in the -y-direction is replicated into multiple beams in a spatially dispersed manner, with some traveling in the ±y-directions (corresponding to the FOV rectangles at the 6 o'clock and 12 o'clock positions within the k-space ring) and some traveling in the ±x-directions (corresponding to the FOV rectangles at the 3 o'clock and 9 o'clock positions within the k-space ring). Thus, the light beams spread laterally throughout the eyepiece waveguide 2000.

[0344] FIG. 20J illustrates a way in which the diffraction efficiency of the MPE region 2050 within the eyepiece waveguide 2000 can be spatially varied so as to improve the uniformity of luminance within the waveguide. In the figure, darker shading within the MPE region 2050 represents higher diffraction efficiency, while lighter shading represents lower diffraction efficiency. The spatial variation in the diffraction efficiency of the MPE region 2050 can be accomplished by introducing spatial variations in grating characteristics such as grating depth, duty cycle, blaze angle, tilt angle, and the like.

[0345] As seen in FIG. 20J, the uniformity of luminance within the waveguide can be improved by designing the portion of the MPE region 2050 closer to the ICG region 2040 to have a higher diffraction efficiency. This is because more light is present within this area as the light beam is incident from the ICG region 2040 into the MPE region 2050, and thus the diffraction efficiency can be made higher to more effectively spread the light to other portions of the MPE region 2050 where less light is present. Additionally, or alternatively, multiple ICG regions can be provided at various angular locations around the periphery of the MPE region 2050 so as to input light at more locations and thereby improve the uniformity of luminance within the waveguide.

[0346] The uniformity of luminance can also be improved by designing the central portion of the MPE region 2050 to have a higher diffraction efficiency along the direction in which the beam propagates from the ICG region 2040 into the MPE region 2050. Again, since the ICG region 2040 is located along the axis where light is input, more light is present within the area of the MPE region 2050. Since more light is present within this area, the diffraction efficiency can be made higher to more effectively spread the light to other portions of the MPE region 2050.

[0347] FIG. 20K illustrates a way in which the diffraction efficiency of the EPE region 2060 within the eyepiece waveguide 2000 can be spatially varied so as to improve the uniformity of the luminance within the waveguide. The darker shading within the EPE region 2060 represents, again, a higher diffraction efficiency, while the lighter shading represents a lower diffraction efficiency. The EPE region 2060 can be designed to have a higher diffraction efficiency within the peripheral area. The higher diffraction efficiency within the peripheral area of the EPE region 2060 serves to externally couple light to the user's eye before the light is lost out of the edge of the waveguide.

[0348] FIG. 20L illustrates an embodiment of the eyepiece waveguide 2000 that includes one or more diffraction mirrors 2070 around the peripheral edge of the waveguide. The diffraction mirror 2070 can receive light that propagates through the MPE / EPE region and exits from the edge of the waveguide 2000. The diffraction mirror can then diffract that light so as to return it into the MPE / EPE region so that it can be used to contribute to the projection of an image from the eyepiece waveguide 2000. As already discussed, the MPE region 2050 permits the propagation of beams in four general directions, namely generally in the x-direction (i.e., as represented by the FOV rectangle at the 3 o'clock position of the k-space ring), generally in the -x-direction (i.e., as represented by the FOV rectangle at the 9 o'clock position), generally in the y-direction (i.e., as represented by the FOV rectangle at the 12 o'clock position), and generally in the -y-direction (i.e., as represented by the FOV rectangle at the 6 o'clock position). The diffraction mirror 2070 can be designed to diffract the beam into one of these same propagation states.

[0349] For example, the diffraction mirror 2070 on the left side of the eyepiece waveguide 2000 can generally diffract the beams incident from the -x- direction so that they generally travel back through the OPE region 2050 in the x- direction, and can be diffracted into the propagation state represented by the FOV rectangle at the 3 o'clock position. Similarly, the diffraction mirror 2070 at the bottom of the eyepiece waveguide 2010 can generally diffract the beams incident from the -y- direction so that they generally travel back through the OPE region 2050 in the y- direction, and can be diffracted into the propagation state represented by the FOV rectangle at the 12 o'clock position.

[0350] FIG. 20L illustrates the k- space action of the bottom diffraction mirror 2070. As shown in the k- space diagram, the bottom diffraction mirror 2070 can be designed with a period that is half of that of the lattice within the ICG region 2040. This finer period results in a bottom diffraction mirror having a lattice vector associated with a length that is twice that of the ICG region 2040. Thus, the bottom diffraction mirror can translate the FOV rectangle from the 6 o'clock position to the 12 o'clock position within the k- space ring. Although illustrated for the eyepiece waveguide 2000, the same techniques (i.e., spatial variations in diffraction efficiency in the OPE, MPE, EPE regions, etc., and the use of diffraction mirrors along the peripheral edges) can also be used in combination with any of the other embodiments described herein.

[0351] FIG. 20M illustrates an exemplary embodiment of the glasses 70 incorporating one or more instances of the eyepiece waveguide 2000. The first instance of the eyepiece waveguide 2000 is integrated into the left viewing portion of the glasses 70, while the second instance of the eyepiece waveguide 2000 is integrated into the right viewing portion. In the illustrated embodiment, the waveguides 2000 are each approximately 50×30 mm 2However, many different sizes can be used. Each waveguide 2000 can be accompanied by a separate projector 2020 that projects an image into the corresponding waveguide. Assuming that the eyepiece waveguide is made of a material with a refractive index of 1.8, some embodiments of the eyepiece waveguide 2000 can achieve a FOV of 90°×45° in size. However, some embodiments of the eyepiece waveguide may be designed for a smaller FOV of about 60°×45° to avoid the grating artifacts resulting from the sparsely spaced output beams, while satisfying the typical design constraints of the eyebox volume (it may be advantageous to send a portion of the FOV to both sides of the eyepiece waveguide and provide a properly sized eyebox).

[0352] FIG. 20N illustrates another exemplary embodiment of the glasses 70 incorporating one or more instances of the eyepiece waveguide 2000. This embodiment of the glasses 70 is similar to that shown in FIG. 20M, but the orientation of the waveguide 2000 and the accompanying projector 2020 is rotated 90° towards the temple of the glasses 70. In this configuration, some embodiments of the eyepiece waveguide 2000 can achieve a FOV of 45°×90° in size, assuming that the eyepiece waveguide is made of a material with a refractive index of 1.8. However, some embodiments may be designed for a smaller FOV of about 45°×60° to meet other design constraints.

[0353] FIG. 21A illustrates another embodiment of an eyepiece waveguide 2100 with an MPE region 2150 that is overlapped by an EPE region 2160. Similar to the eyepiece waveguide 2000 shown in FIG. 20A, the eyepiece waveguide 2100 shown in FIG. 21A can achieve an expanded field of view that can be larger than the range of propagation angles that can be supported in the inductive propagation mode in the thickness direction of the waveguide. The eyepiece waveguide 2100 has a first surface 2100a and a second surface 2100b. As further discussed below, different diffraction features can be formed on or within the opposing surfaces 2100a, 2100b of the eyepiece waveguide 2100. The two surfaces 2100a, 2100b of the eyepiece waveguide 2100 are shown in FIG. 21A as being displaced relative to each other in the x-y plane. However, this is for illustrative purposes only and it is possible to show different diffraction features formed on or within each surface. It should be understood that the first surface 2100a and the second surface 2100b are aligned with each other in the x-y plane. In addition, the MPE region 2150 and the EPE region 2160 are shown as being of the same size and being exactly aligned in the x-y plane, but in other embodiments they may have somewhat different sizes and may be partially misaligned. In some embodiments, the MPE region 2150 and the EPE region 2160 overlap each other by at least 70%, at least 80%, at least 90%, or at least 95%.

[0354] Like the eyepiece waveguide 2000 shown in FIG. 20A, the eyepiece waveguide 2100 shown in FIG. 21A includes an MPE region 2150 and an EPE region 2160. Different from the eyepiece waveguide 2000 shown in FIG. 20A, the eyepiece waveguide 2100 shown in FIG. 21A includes two ICG regions 2140a, 2140b that are located on the opposite side of the MPE / EPE region rather than a single ICG region. Each of the ICG regions 2140a, 2140b can have its own associated projector. Each of the two projectors can input a sub - portion of the full input image FOV into the eyepiece waveguide 2100. Thus, each of the ICG regions 2140a, 2140b can likewise be used to internally couple the input beam corresponding to the sub - portion of the FOV. Those sub - portions can then be combined at the exit pupil of the eyepiece waveguide 2100.

[0355] The left ICG region 2140a receives a first set of input beams corresponding to a first sub - portion of the FOV from a first projector device, while the right ICG region 2140b receives a second set of input beams corresponding to a second sub - portion of the FOV from a second projector device. The first and second sub - portions of the FOV may be unique, or they may partially overlap. The first set of input beams is projected generally along the - z - direction towards the left ICG region 2140a, but may be centered around input beams having a component of propagation in the - x - direction, while the second set of input beams is projected generally along the - z - direction towards the right ICG region 2140b, but may be centered around input beams having a component of propagation in the +x - direction. The left ICG region 2140a diffracts the first set of input beams so that at least a portion enters an induced mode propagating in the +x - direction, and the right ICG region 2140b diffracts the second set of input beams so that at least a portion enters an induced mode propagating in the - x - direction. Thus, both the first and second sets of input beams corresponding to the first and second sub - portions of the FOV are coupled into the eyepiece waveguide 2100 such that they propagate towards the MPE region 2150 located between the left and right ICG regions 2140a, 2140b.

[0356] Similar to the eyepiece waveguide 2000 shown in FIG. 20A, the eyepiece waveguide 2100 shown in FIG. 21A can also include an MPE region 2150 formed on or within the first side 2100a of the waveguide and an overlapping EPE region 2160 formed on or within the second side 2100b of the waveguide. The MPE region 2150 within the eyepiece waveguide 2100 shown in FIG. 21A can be similar to the MPE region 2050 within the eyepiece waveguide 2000 shown in FIG. 20A. That is, the MPE region 2150 can include a plurality of diffraction features that exhibit periodicity along a plurality of axes. Similarly, the EPE region 2160 within the eyepiece waveguide 2100 shown in FIG. 21A can be similar to the EPE region 2060 within the eyepiece waveguide 2000 shown in FIG. 20A. That is, the EPE region 2160 can include a diffraction grating whose periodic axis is orthogonal to those of the two ICG regions 2140a, 2140b. The operation of the MPE region 2150 and the EPE region 2160 in FIG. 21A can also be similar to that of the MPE region 2050 and the EPE region 2060 in FIG. 20A, as shown in FIGS. 21B - 21D.

[0357] FIG. 21B is a k - space diagram KSD1 illustrating the k - space action of the eyepiece waveguide 2100 on a first set of input beams corresponding to a first sub - portion of the FOV of the input image. The FOV rectangle centered at the origin of KSD1 represents a beam of light corresponding to the complete input image FOV to be projected towards the user's eye by the eyepiece waveguide 2100. The size of the overall FOV rectangle has a dimension that is at most approximately twice as large as the width of the k - space ring. Thus, the eyepiece waveguide 2100 shown in FIG. 21A is designed to have an improved FOV similar to the embodiments shown in FIGS. 19 and 20A. However, the first set of input beams projected towards the left ICG region 2140a corresponds only to the shaded sub - portion of the FOV rectangle. As shown in FIG. 21B, the shaded portion of the FOV rectangle corresponding to the first set of input beams is the left - hand portion of the FOV rectangle. The center of the shaded portion of the FOV rectangle is at - k xIn the - direction, since it is offset from the origin of the k - space diagram, the set of first input beams from the first projector is centered not on the beam propagating exactly in the - z - direction (which would be the case if the shaded part of the FOV rectangle were centered around the origin of the k - space diagram), but rather on the oblique beam with a propagation component in the - x - direction.

[0358] The left ICG region 2140a can be designed such that its lattice vectors are oriented in the ±k x - direction. The effect of the left ICG region 2140a in k - space is to translate the shaded left part of the FOV rectangle from the center of the k - space diagram to the 3 o'clock position within the k - space ring. This will generally cause the diffracted beams to propagate in the x - direction towards the MPE region 2150. In some embodiments, the shaded left part of the FOV rectangle can be configured to be half or more of the FOV rectangle. Also, in some embodiments, the left ICG region 2140a can be designed to translate the center of the FOV rectangle for any radial position from the mid - point of the k - space ring to the outer boundary of the ring. Further, the left ICG region 2140a can be designed such that the magnitude of its lattice vectors copies the FOV rectangle to a position where the shaded part fits exactly within the k - space ring at the 3 o'clock position. This can be accomplished, for example, by setting the magnitude of the ICG lattice vectors to be greater than the distance from the origin of the k - space diagram to the mid - point of the k - space ring. Since the shaded part of the FOV rectangle at the 3 o'clock position is entirely within the k - space ring, all of the set of first input beams corresponding to the first sub - part of the FOV enter the guided mode of propagation. The FOV rectangle at the 3 o'clock position of the k - space ring has a right - hand part that extends outside the ring, but this part of the FOV rectangle does not necessarily correspond to the input beams that are part of the first sub - part of the FOV provided to the left ICG region 2140a by its associated projector.

[0359] The left ICG region 2140a can also diffract a portion of the first set of input beams in the opposite direction (i.e., translate the FOV rectangle to the 9 o'clock position of the k-space ring), but in the illustrated embodiment of the eyepiece waveguide 2100, those particular diffracted beams will simply exit out of the edge of the waveguide.

[0360] The MPE region 2150 includes a plurality of diffraction features having a plurality of periodic axes. In some embodiments, the MPE region 2150 can be similar to the MPE region 2050 illustrated and discussed with respect to FIGS. 20A-20M. For example, the MPE region 2150 can have a plurality of associated lattice vectors that can translate the FOV rectangle from the 3 o'clock position to any of the 6 o'clock, 9 o'clock, and 12 o'clock positions of the k-space ring. As shown in FIG. 21B, the shaded portion of the FOV rectangle at the 9 o'clock position of the k-space ring is truncated, meaning that not all of the beams of light associated with the first sub-portion of the FOV necessarily exist in that particular propagation state.

[0361] During additional interactions with the MPE region 2150, the FOV rectangle can be translated back and forth between any of the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positions. This is represented by the double arrows between those propagation states within KSD1. Thus, the first set of input beams can be replicated throughout the MPE region 2150 by undergoing a plurality of interactions with its diffraction features, as described herein. This is shown by the arrows within the OPE region 2150 of the eyepiece waveguide 2100 in FIG. 21A.

[0362] Since the EPE region 2160 overlaps with the MPE region 2150 in the x-y plane of the eyepiece waveguide 2100, the replicated light beams also interact with the EPE region 2160 as they spread through the waveguide and reflect back and forth between the first surface 2100a and the second surface 2100b via total internal reflection. Each time one of the replicated light beams interacts with the EPE region 2160, a portion of its refractive power is diffracted and externally coupled towards the user's eye, as indicated by the arrows in the EPE region 2160 of the eyepiece waveguide 2100 in FIG. 21A.

[0363] In some embodiments, the EPE region 2160 includes a diffraction grating whose lines are oriented perpendicular to the lines of the diffraction grating that make up the ICG regions 2140a, 2140b. In this particular example, since the ICG regions 2140a, 2140b have grating lines that extend in the y-direction and are periodically repeated in the x-direction, the EPE region 2160 has grating lines that extend in the x-direction and are periodically repeated in the y-direction. Again, it is advantageous for the grating lines in the EPE region 2160 to be oriented perpendicular to the grating lines in the ICG regions 2140a, 2140b to ensure that the light beam will interact with the MPE region 2150 before it is coupled out of the eyepiece waveguide 2100 by the EPE region 2160.

[0364] FIG. 21B also illustrates the k-space action of the EPE region 2160 on the first set of beams corresponding to the first sub-part of the FOV. As already discussed, the light beam can propagate through the MPE region 2150 in any of the directions indicated by the FOV rectangles located at the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positions of the k-space ring. Also, since the EPE region 2160 overlaps with the MPE region 2150, the light beam in any of these propagation states can interact with the EPE region and be externally coupled out of the eyepiece waveguide 2100. The periodicity axis of the diffraction grating in the EPE region 2160 is ±k y- To indicate direction, the lattice vectors associated with the EPE region also point in the same direction. FIG. 21B shows how the EPE region 2160 translates the FOV rectangles located at the 12 o'clock and 6 o'clock positions of the k-space ring back to the origin of the k-space diagram. Thus, the EPE region 2160 can only externally couple the light beams in either of those two propagation states. As shown in FIG. 21B, when the FOV rectangles are finally translated back to the center of the k-space diagram KSD1, all of the first set of beams that make up the first subportion of the FOV are present and projected towards the user's eye.

[0365] FIG. 21C is a k-space diagram KSD2 that illustrates the k-space action of the eyepiece waveguide 2100 on the second set of input beams corresponding to the second subportion of the FOV of the input image. Again, the FOV rectangle centered at the origin of KSD2 represents the light beams corresponding to the full input image to be projected towards the user's eye by the eyepiece waveguide 2100. However, the second set of input beams projected towards the right ICG region 2140b only corresponds to the shaded subportion of the FOV rectangle. As shown in FIG. 21C, the shaded portion of the FOV rectangle corresponding to the second set of input beams is the right side portion of the FOV rectangle. The center of the shaded portion of the FOV rectangle is offset +k x - In the -direction, so the second set of input beams from the second projector is centered not on the beam propagating exactly in the -z-direction (which would be the case if the shaded portion of the FOV rectangle were centered at the origin of the k-space diagram), but rather on the skew beam with a propagation component in the +x-direction.

[0366] In the illustrated embodiment, the action of the right ICG region 2140b in k-space is to translate the right shaded portion of the FOV rectangle from the center of the k-space diagram to the 9 o'clock position. As shown, the right ICG region 2140b has lattice vectors of ±k x-direction, and can be designed to direct a portion of the diffracted beam to propagate in the -x- direction towards the MPE region 2150. In some embodiments, the shaded right portion of the FOV rectangle can be configured to be half or more of the FOV rectangle. Also, in some embodiments, the right ICG region 2140b can be designed to translate the center of the FOV rectangle for any radial position from the midpoint of the k-space ring to the outer boundary of the ring. Further, the right ICG region 2140b can be designed such that the magnitude of its lattice vector copies the FOV rectangle to a position where the shaded portion fits entirely within the k-space ring at the 9 o'clock position. This can be done, for example, by designing the ICG such that the magnitude of its lattice vector exceeds the distance from the origin of the k-space diagram to the midpoint of the k-space ring. Since the shaded portion of the FOV rectangle at the 9 o'clock position is entirely within the k-space ring, all of the second set of input beams corresponding to the second sub-portion of the FOV enter the guided propagation mode. The FOV rectangle at the 9 o'clock position of the k-space ring has a left portion that extends outside the ring, but this portion of the FOV rectangle corresponds to the input beam and is not necessarily part of the second sub-portion of the FOV projected into the right ICG region 2140b by its associated projector.

[0367] The right ICG region 2140b can also diffract a portion of the second set of input beams in the opposite direction (i.e., translate the FOV rectangle to the 3 o'clock position of the k-space ring), but in the ill...

Claims

1. An augmented reality display system, a first eyepiece waveguide having a first optically transparent substrate, a first input coupling grating (ICG) region formed on or within the first eyepiece waveguide, the first ICG region being configured to receive a set of input beams of light, the set of input beams being associated with a set of k-vectors in k-space corresponding to an input image, and to translate the set of k-vectors to a location in k-space such that a first subset of the k-vectors is inside a first k-space ring associated with the first eyepiece waveguide, the first k-space ring corresponding to a region in k-space associated with guided propagation within the first eyepiece waveguide, the first ICG region; a second eyepiece waveguide having a second optically transparent substrate, a second input coupling grating (ICG) region formed on or within the second eyepiece waveguide, the second ICG region being configured to receive at least a portion of the set of input beams of light, and to translate the set of k-vectors to a location in k-space such that a second subset of the k-vectors is inside a second k-space ring associated with the second eyepiece waveguide, the second k-space ring corresponding to a region in k-space associated with guided propagation within the second eyepiece waveguide, the second ICG region; comprising wherein the first and second subsets of the k-vectors are at least partially different but together include the complete set of k-vectors corresponding to the input image; and wherein the set of k-vectors corresponding to the input image has at least one dimension in k-space that is larger than the widths of the first and second k-space rings. An augmented reality display system.

2. The display system satisfies the equation 【Number 1】 where n is the refractive index of the first and second eyepiece waveguides, λBlue is the central wavelength of the blue input light, Λ2 is the period of the second ICG region, and kFoV is the k-space dimension of the input image in the direction of the ICG vector. The augmented reality display system according to claim 1.

3. The display system satisfies the equation 【Number 2】 where n is the refractive index of the first and second eyepiece waveguide, λGreen is the central wavelength of the green input light, Λ1 is the period of the first ICG region, and Λ2 is the period of the second ICG region, the augmented reality display system according to claim 1.

4. The display system satisfies the equation 【Mathematics 3】 where n is the refractive index of the first and second eyepiece waveguide, λRed is the central wavelength of the red input light, Λ1 is the period of the first ICG region, and Λ2 is the period of the second ICG region, the augmented reality display system according to claim 1.

5. The display system satisfies the equation 【Number 4】 where n is the refractive index of the first and second eyepiece waveguide, λBlue is the central wavelength of the blue input light, Λ1 is the period of the first ICG region, and kFoV is the k-space dimension of the input image in the direction of the ICG vector, the augmented reality display system according to claim 1.

6. The display system satisfies the equation 【Number 5】 where n is the refractive index of the first and second eyepiece waveguide, λBlue is the central wavelength of the blue input light, Λ2 is the period of the second ICG region, and kFoV is the k-space dimension of the input image in the direction of the ICG vector, the augmented reality display system according to claim 1.

7. The display system satisfies the equation 【Number 6】 where n is the refractive index of the first and second eyepiece waveguide, λGreen is the central wavelength of the green input light, Λ2 is the period of the second ICG region, and kFoV is the k-space dimension of the input image in the direction of the ICG vector, the augmented reality display system according to claim 1.

8. The first ICG region has a primary lattice vector with a first magnitude, the second ICG region has a primary lattice vector with a second magnitude, the first magnitude is greater than the second magnitude, the augmented reality display system according to claim 1. **Claim 9**: The projection system further configured to project the set of input beams toward the first and second ocular waveguide, wherein the first ocular waveguide is positioned in front of the second ocular waveguide along the optical path of the set of input beams. The augmented reality display system according to claim 8. **Claim 10**: The augmented reality display system according to claim 1, wherein the first and second subsets of k-vectors are partially overlapping. **Claim 11**: The augmented reality display system according to claim 1, wherein the first and second ICG regions are laterally aligned. **Claim 12**: The first and second ICG regions are configured to receive input beams of light for a plurality of color components of the input image, and the input beams for each color component are associated with a set of k-vectors in k-space. The first ICG region is configured to translate the set of k-vectors to a location in k-space such that a first subset of the k-vectors for two or more of the color components is inside the first k-space ring. The second ICG region is configured to translate the set of k-vectors to a location in k-space such that a second subset of the k-vectors for two or more of the color components is inside the second k-space ring. The first and second subsets of k-vectors for individual color components of the input image are at least partially different but together include the complete set of k-vectors for the color components of the input image. The augmented reality display system according to claim 1. **Claim 13**: The first ICG region comprises a plurality of spatially separated subsections, each corresponding to one of the color components. **Claim 14**: The second ICG region comprises a plurality of spatially separated subsections, each corresponding to one of the color components. The augmented reality display system according to claim 12. **Claim 14**: The augmented reality display system according to claim 12, further comprising an optical filter positioned after the second ocular waveguide along the optical path of the input beam, the optical filter being configured to selectively absorb the input beam for the color component having the shortest wavelength.

15. The extended reality display system according to claim 14, wherein the optical filter is a yellow filter that absorbs at least 90% of blue light.

16. The extended reality display system according to claim 14, wherein the optical filter is configured to selectively absorb an input beam with respect to two color components having two shortest wavelengths.

17. The extended reality display system according to claim 14, wherein the optical filter is a red filter that absorbs at least 90% of green and blue light.

18. The first and second ICG regions have a primary diffraction efficiency of 5 to 90%, The extended reality display system according to claim 1, wherein the first ICG region is configured such that a second subset of the k-vector passes through it without being diffracted.

19. The extended reality display system according to claim 1, wherein the first and second eyepiece waveguides have a refractive index of 1.5 to 2.1.

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