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 priority to U.S. Provisional Patent Application No. 62 / 863,871, entitled "EYEPIECES FOR AUGMENTED REALITY DISPLAY SYSTEM," filed June 20, 2019, and U.S. Provisional Patent Application No. 63 / 024,343, entitled "EYEPIECES FOR AUGMENTED REALITY DISPLAY SYSTEM," filed May 13, 2020. Each of these applications, and any other applications identified in the Application Data Sheet with which a foreign or domestic priority claim is filed herewith, is hereby incorporated by reference under 37 CFR 1.57.

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

[0003] Modern computing and display technology has facilitated the development of virtual reality, augmented reality, and mixed reality systems. Virtual reality, or "VR," systems create 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, rather than also including actual real-world image data.

[0004] Augmented reality systems generally supplement real-world environments with simulated elements. For example, an augmented reality, or "AR," system may provide a user with a view of the surrounding real-world environment via a head-mounted display. However, computer-generated image data may also be presented on the display to enhance the real-world environment. This computer-generated image data may include elements that are contextually related to the real-world environment. Such elements may include simulated text, images, objects, etc. Mixed reality, or "MR," systems are a type of AR system that also introduces simulated objects into the real-world environment, but these objects typically feature an additional degree of interactivity. The simulated elements can often be interactive in real time.

[0005] 1 depicts an exemplary AR scene 1, in which a user sees a real-world park setting 6 featuring people, trees, a building 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 may include, for example, a robotic figure 10 standing on the real-world platform 20 and a flying, cartoon-like avatar character 2 that appears to be an anthropomorphic bumblebee, although these elements 2, 10 do not actually exist in the real-world environment. Summary of the Invention [Means for solving the problem]

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

[0007] In some embodiments, an augmented reality display system includes a first eyepiece waveguide comprising 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 configured to receive a set of input beams of light, the input beams associated with a set of k-vectors in k-space corresponding to an input image, and to translate the set of k-vectors to locations in k-space such that a first subset of the k-vectors are within a first k-space annulus associated with the first eyepiece waveguide, the first k-space annulus corresponding to a region in k-space associated with guided propagation within the first eyepiece waveguide; and The optical system comprises a second eyepiece waveguide having a second optically transparent substrate; and a second input coupling grating (ICG) region formed on or within the second eyepiece waveguide, the second ICG region configured to receive at least a portion of the set of input beams of light and translate the set of k-vectors to a location in k-space so that a second subset of the k-vectors is within a second k-space annulus associated with the second eyepiece waveguide, the second k-space annulus corresponding to a region in k-space associated with guided propagation within the second eyepiece waveguide, the first and second subsets of k-vectors being at least partially different but both including a complete set of k-vectors corresponding to the input image. The present invention provides, for example, the following. (Item 1) 1. An augmented reality display system, comprising: a first ocular waveguide comprising a first optically transmissive substrate; a first input coupling grating (ICG) region formed on or within the first eyepiece waveguide, the first ICG region configured to receive a set of input beams of light corresponding to an input image having a corresponding field of view and to couple a first subset of the input beams into the substrate as a first set of guided beams, the first subset of input beams corresponding to a first sub-portion of the field of view of the input image; a second ocular waveguide comprising a second optically transmissive substrate; a second input coupling grating (ICG) region formed on or within the second eyepiece waveguide, the second ICG region configured to receive at least a second subset of the input beams of light corresponding to the input image and to couple the second subset of the input beams into the substrate as a second set of guided beams, the second subset of the input beams corresponding to a second sub-portion of a field of view of the input image; and Equipped with An augmented reality display system, wherein the first and second sub-portions of the field of view are at least partially different but together comprise a full field of view of the input image. (Item 2) Item 1, an augmented reality display system, wherein the field of view of the input image is greater in at least one dimension than the range of total internal reflection propagation angles in the thickness direction of the first and second eyepiece waveguides. (Item 3) a third ocular waveguide comprising a third optically transmissive substrate; a third input coupling grating (ICG) region formed on or within the third eyepiece waveguide, the third ICG region configured to receive at least a third subset of the input beams of light corresponding to the input image and to couple the third subset of the input beams into the substrate as a third set of guided beams, the third subset of the input beams corresponding to a third sub-portion of a field of view of the input image; 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. [[ID=)18](Item 5) Regarding 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, Regarding 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, Regarding 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, Regarding 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, Regarding 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, Regarding 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 augmented reality display system further includes a projector system configured to project the set of input beams corresponding to the input image toward 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 beams for two or more of the color components into the third substrate, the third subset of input beams corresponding to a third sub-portion of a field of view of a color component 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 comprise the complete field of view of the color components of the input image; Item 3. The augmented reality display system of item 3. (Item 10) the first ICG region comprises a plurality of spatially separated subsections, each corresponding to one of the color components; the second ICG region comprises a plurality of spatially separated subsections, each corresponding to one of the color components; the third ICG region comprises a plurality of spatially separated subsections, each corresponding to one of the color components; Item 10. The augmented reality display system of item 9. (Item 11) 10. The augmented reality display system of item 9, wherein the third ICG region has a second-order diffraction efficiency of less than 10%. (Item 12) Item 10. The augmented reality display system of item 9, further comprising an optical filter positioned along the optical path of the input beam after the second eyepiece waveguide, the optical filter configured to selectively absorb the input beam for the color component having the shortest wavelength. (Item 13) Item 13. The augmented reality display system of item 12, wherein the optical filter is a yellow filter that absorbs at least 90% of blue light. (Item 14) Item 13. The augmented reality display system of item 12, wherein the optical filter is configured to selectively absorb input beams relating to the two color components having the two shortest wavelengths. (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 eyepiece waveguide and the third eyepiece waveguide. (Item 17) The augmented reality display system according to item 12, wherein the optical filter is a dye provided in the third eyepiece waveguide. (Item 18) The augmented reality display system according to item 1, wherein the first and second ICG regions have a primary 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 eyepiece 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 not more than 44.5°. [[ID=2,4]]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 not more than 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.° but not more than 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 not more than 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 not more than 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 eyepiece waveguide tubes have the same dimensions. (Item 23) The augmented reality display system according to item 1, wherein the first and second eyepiece waveguide tubes are aligned laterally and separated vertically 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 eyepiece waveguide tube, wherein the first OPE, MPE, or CPE region receives a first set of the guiding beams and is configured to replicate them over a spatially dispersed portion of the first eyepiece waveguide tube, the first OPE region, the first MPE region, or the first combined CPE region, and A second OPE region, or a second MPE region, or a second CPE region formed on or within the second eyepiece waveguide tube, wherein the second OPE, MPE, or CPE region receives a second set of the guiding beams and is configured to replicate them over a spatially dispersed portion of the second eyepiece waveguide tube, the second OPE region, the second MPE region, or the second combined CPE region The augmented reality display system according to item 1, further comprising. (Item 25) a first output-coupling grating area formed on or within the first eyepiece waveguide, the first output-coupling grating area configured to output the first set of guided beams from the first eyepiece waveguide as a first set of output beams; and a second output-coupling grating area formed on or within the second eyepiece waveguide, the second output-coupling grating area configured to output the second set of guided beams from the second eyepiece waveguide as a second set of output beams; Furthermore, Item 1. The augmented reality display system of item 1, wherein the first and second sets of output beams together comprise the full field of view of the input image. (Item 26) 1. An augmented reality display system, comprising: a first ocular waveguide comprising a first optically transmissive substrate; a first input coupling grating (ICG) region formed on or within the first eyepiece waveguide, the first ICG region configured to: receive a set of input beams of light, the set of input beams associated with a set of k-vectors in k-space corresponding to an input image; and translate the set of k-vectors to locations in k-space such that a first subset of the k-vectors are within a first k-space annulus associated with the first eyepiece waveguide, the first k-space annulus corresponding to a region in k-space associated with guided propagation within the first eyepiece waveguide; a second ocular waveguide comprising a second optically transmissive substrate; a second input coupling grating (ICG) region formed on or within the second eyepiece waveguide, the second ICG region configured to receive at least a portion of the set of input beams of light and translate a set of k-vectors to locations in k-space such that a second subset of the k-vectors are within a second k-space annulus associated with the second eyepiece waveguide, the second k-space annulus corresponding to a region in k-space associated with guided propagation within the second eyepiece waveguide; Equipped with An augmented reality display system, wherein the first and second subsets of k-vectors are at least partially different, but together comprise a complete set of the k-vectors corresponding to the input image. (Item 27) 27. The augmented reality display system of item 26, wherein the set of k-vectors corresponding to the input image has at least one dimension in k-space that is greater than the width of the first and second k-space annuli. (Item 28) a third ocular waveguide comprising a third optically transmissive substrate; a third input coupling grating (ICG) region formed on or within the third eyepiece waveguide, the third ICG region configured to receive at least a portion of the set of input beams of light and translate a set of k-vectors to locations in k-space such that a third subset of the k-vectors is within a third k-space annulus associated with the third eyepiece waveguide, the third k-space annulus corresponding to a region in k-space associated with guided propagation within the third eyepiece waveguide; Furthermore, Item 27. The augmented reality display system of item 26, wherein the first, second, and third subsets of k-vectors are at least partially different but together comprise the complete set of k-vectors corresponding to the input image. (Item 29) The display system is

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[0008] [Figure 1] FIG. 1 illustrates a user's view of an augmented reality (AR) scene through an AR device.

[0009] [Figure 2] FIG. 2 illustrates an example of a wearable display system.

[0010] [Figure 3] FIG. 3 illustrates a conventional display system for simulating three-dimensional image data for a user.

[0011] [Figure 4] FIG. 4 illustrates aspects of an approach for simulating three-dimensional image data using multiple depth planes.

[0012] [Figure 5] 5A-5C illustrate the relationship between the radius of curvature and the radius of focus.

[0013] [Figure 6] FIG. 6 illustrates an example of a waveguide stack for outputting image information to a user within an AR eyepiece.

[0014] [Figure 7] 7A-7B illustrate examples of output beams output by waveguides.

[0015] [Figure 8] FIG. 8 illustrates an example of a stacked waveguide assembly where each depth plane contains an image formed using multiple different primary colors.

[0016] [Figure 9A] FIG. 9A illustrates a cross-sectional side view of an example of a set of stacked waveguides, each including an internal coupling optical element.

[0017] [Figure 9B] FIG. 9B illustrates a perspective view of the multiple stacked waveguide embodiment of FIG. 9A.

[0018] [Figure 9C] FIG. 9C illustrates a top-down plan view of the multiple stacked waveguide embodiment of FIGS. 9A and 9B.

[0019] [Figure 10] FIG. 10 is a perspective view of an exemplary AR eyepiece waveguide stack.

[0020] [Figure 11] FIG. 11 is a cross-sectional view of a portion of an exemplary eyepiece waveguide stack, along with an edge seal structure for supporting the eyepiece waveguides in a stacked configuration.

[0021] [Figure 12A]12A and 12B illustrate a top view of the eyepiece waveguide in operation as it projects an image toward a user's eye. [Figure 12B] 12A and 12B illustrate a top view of the eyepiece waveguide in operation as it projects an image toward a user's eye.

[0022] [Figure 13A] FIG. 13A illustrates a k-vector, which can be used to represent the propagation direction of a ray or beam of light.

[0023] [Figure 13B] FIG. 13B illustrates light rays in a planar waveguide.

[0024] [Figure 13C] FIG. 13C illustrates the allowable k-vectors for light of a given angular frequency ω propagating in an unbounded homogeneous medium with refractive index n.

[0025] [Figure 13D] FIG. 13D illustrates the allowable k-vectors for light of a given angular frequency ω propagating in a homogeneous planar waveguide medium with refractive index n.

[0026] [Figure 13E] FIG. 13E illustrates rings in k-space corresponding to the k-vectors of light waves that may be guided in a waveguide having a refractive index n2.

[0027] [Figure 13F] FIG. 13F shows a k-space diagram and an eyepiece waveguide illustrating the relationship between a k-vector and the density of interactions between the guided beam corresponding to that k-vector and a diffraction grating formed on or within the waveguide.

[0028] [Figure 13G] FIG. 13G illustrates a top view of the grating and some of its associated k-space grating vectors (G-2, G-1, G1, G2).

[0029] [Figure 13H] FIG. 13H illustrates a side view of a diffraction grating and its effect in k-space on the k-vector corresponding to a normally incident ray or beam of light.

[0030] [Figure 13I] FIG. 13I illustrates a side view of the diffraction grating shown in FIG. 13G and its effect in k-space on the k-vector corresponding to an obliquely incident ray or beam of light.

[0031] [Figure 13J] FIG. 13J is a k-space diagram illustrating the field of view of an image projected into the AR eyepiece waveguide.

[0032] [Figure 13K] FIG. 13K is a k-space diagram showing the translational shift in k-space of the FOV rectangle caused by an input coupling grating (ICG) located at the entrance pupil of the eyepiece waveguide.

[0033] [Figure 14A] FIG. 14A illustrates an exemplary eyepiece waveguide with an ICG region, an orthogonal pupil expander (OPE) region, and an exit pupil expander (EPE) region.

[0034] [Figure 14B] FIG. 14B illustrates the k-space behavior of the eyepiece waveguide shown in FIG. 14A.

[0035] [Figure 14C] FIG. 14C illustrates the optical effect of the OPE region shown in FIGS. 14A and 14B.

[0036] [Figure 14D] FIG. 14D illustrates a technique for determining the size and shape of the OPE and EPE regions.

[0037] [Figure 15A] FIG. 15A illustrates an exemplary embodiment of a waveguide eyepiece in which the OPE region is tilted and positioned such that its lower boundary is parallel to the upper boundary of the EPE region.

[0038] [Figure 15B] FIG. 15B includes a k-space diagram illustrating the operation of the eyepiece waveguide shown in FIG. 15A.

[0039] [Figure 15C] FIG. 15C is another k-space diagram illustrating the operation of the eyepiece waveguide shown in FIG. 15A.

[0040] [Figure 15D] FIG. 15D is a schematic diagram of the first occurrence of an interaction between an input beam and the OPE region of the eyepiece waveguide embodiment shown in FIG. 15A.

[0041] [Figure 15E] FIG. 15E is a schematic diagram of a second occurrence of interaction between the input beam and the OPE region of the eyepiece waveguide embodiment shown in FIG. 15A.

[0042] [Figure 15F] FIG. 15F is a schematic diagram of a third occurrence of interaction between an input beam and the OPE region of the eyepiece waveguide embodiment shown in FIG. 15A.

[0043] [Figure 15G] FIG. 15G is a schematic diagram illustrating how a single input beam from the ICG region is replicated by the OPE region and redirected as multiple beams toward the EPE region.

[0044] [Figure 16A] FIG. 16A illustrates an exemplary eyepiece waveguide having a multidirectional pupil expander (MPE) region rather than an OPE region.

[0045] [Figure 16B] FIG. 16B illustrates a portion of an example 2D lattice, along with its associated lattice vectors, that may be used within the MPE region shown in FIG. 16A.

[0046] [Figure 16C] FIG. 16C is a k-space diagram illustrating the k-space effects of the MPE region of the eyepiece waveguide shown in FIG. 16A.

[0047] [Figure 16D] FIG. 16D is a k-space diagram further illustrating the k-space effects of the MPE region of the eyepiece waveguide shown in FIG. 16A.

[0048] [Figure 16E] FIG. 16E is a k-space diagram illustrating the k-space behavior of the eyepiece waveguide shown in FIG. 16A.

[0049] [Figure 16F] FIG. 16F is a schematic diagram of the first occurrence of interaction between an input beam and the MPE region of the eyepiece waveguide embodiment shown in FIG. 16A.

[0050] [Figure 16G] FIG. 16G is a schematic diagram of a second occurrence of interaction between an input beam and the MPE region of the eyepiece waveguide embodiment shown in FIG. 16A.

[0051] [Figure 16H] FIG. 16H is a schematic diagram of a third occurrence of interaction between an input beam and the MPE region of the eyepiece waveguide embodiment shown in FIG. 16A.

[0052] [Figure 16I] FIG. 16I is a schematic diagram of a fourth occurrence of interaction between an input beam and the MPE region of the eyepiece waveguide embodiment shown in FIG. 16A.

[0053] [Figure 16J]FIG. 16J is a diagram illustrating various paths a beam can follow through the MPE region and ultimately into the EPE region according to the eyepiece waveguide embodiment shown in FIG. 16A.

[0054] [Figure 16K] FIG. 16K is a schematic diagram illustrating how a single input beam from the ICG region is replicated by the MPE region and redirected as multiple beams toward the EPE region.

[0055] [Figure 16L] FIG. 16L is a side-by-side comparison illustrating the performance of an eyepiece waveguide with an OPE region versus an eyepiece waveguide with an MPE region.

[0056] [Figure 16M] FIG. 16M further illustrates the performance of an eyepiece waveguide with an MPE region versus an eyepiece waveguide with an OPE region.

[0057] [Figure 17A] FIG. 17A illustrates a portion of an example 2D grating, along with its associated grating vector, that may be used within the MPE region of the eyepiece waveguide.

[0058] [Figure 17B] FIG. 17B is a k-space diagram illustrating the k-space effects of the MPE region of the eyepiece waveguide.

[0059] [Figure 17C] FIG. 17C is a k-space diagram illustrating the k-space effect of the eyepiece waveguide with the MPE region.

[0060] [Figure 17D] FIG. 17D is a schematic diagram of the first occurrence of interaction between the input beam and the MPE region of the eyepiece waveguide.

[0061] [Figure 17E]FIG. 17E is a schematic diagram of a second occurrence of interaction between the input beam and the MPE region of the eyepiece waveguide.

[0062] [Figure 17F] FIG. 17F is a schematic diagram of a third occurrence of interaction between the input beam and the MPE region of the eyepiece waveguide.

[0063] [Figure 17G] FIG. 17G is a schematic diagram of a fourth occurrence of interaction between the input beam and the MPE region of the eyepiece waveguide.

[0064] [Figure 18A] FIG. 18A illustrates an exemplary eyepiece waveguide with an ICG region, two orthogonal pupil expander regions, and an exit pupil expander region.

[0065] [Figure 18B] 18B and 18C illustrate top views of the EPE region of the eyepiece waveguide shown in FIG. 18A. [Figure 18C] 18B and 18C illustrate top views of the EPE region of the eyepiece waveguide shown in FIG. 18A.

[0066] [Figure 19] FIG. 19 illustrates an embodiment of an eyepiece waveguide with an extended field of view.

[0067] [Figure 20A] FIG. 20A illustrates an embodiment of an extended FOV eyepiece waveguide with an MPE region overlapped by an EPE region.

[0068] [Figure 20B] FIG. 20B illustrates a portion of an example 2D grating, along with its associated grating vector, that may be used within the MPE region of the eyepiece waveguide in FIG. 20A.

[0069] [Figure 20C]FIG. 20C is a k-space diagram illustrating the k-space effect of the ICG region of the eyepiece waveguide in FIG. 20A.

[0070] [Figure 20D] FIG. 20D is a k-space diagram illustrating a portion of the k-space effect of the MPE region of the eyepiece waveguide in FIG. 20A.

[0071] [Figure 20E] FIG. 20E is a k-space diagram illustrating another portion of the k-space effect of the MPE region of the eyepiece waveguide in FIG. 20A.

[0072] [Figure 20F] FIG. 20F shows the k-space effect of the MPE region on the FOV rectangle from FIG. 20D, similar to FIG. 20E, but translated to the 9 o'clock position (instead of the 3 o'clock position as illustrated in FIG. 20E).

[0073] [Figure 20G] FIG. 20G is a k-space diagram illustrating the k-space effects of the EPE region within the eyepiece waveguide in FIG. 20A.

[0074] [Figure 20H] FIG. 20H is a k-space diagram summarizing the k-space behavior of the eyepiece waveguide in FIG. 20A.

[0075] [Figure 20I] FIG. 20I is a diagram illustrating how a beam of light spreads through the eyepiece waveguide shown in FIG. 20A.

[0076] [Figure 20J] FIG. 20J illustrates how the diffraction efficiency of the MPE region in the eyepiece waveguide in FIG. 20A can be spatially varied to improve brightness uniformity within the waveguide.

[0077] [Figure 20K]Figure 20K illustrates how the diffraction efficiency of the EPE region within the eyepiece waveguide in Figure 20A can be spatially varied to improve brightness uniformity within the waveguide.

[0078] [Figure 20L] FIG. 20L illustrates an embodiment of the eyepiece waveguide in FIG. 20A that includes one or more diffractive mirrors around the peripheral edge of the waveguide.

[0079] [Figure 20M] FIG. 20M illustrates an exemplary embodiment of eyeglasses incorporating one or more instances of the eyepiece waveguide in FIG. 20A.

[0080] [Figure 20N] FIG. 20N illustrates another exemplary embodiment of eyeglasses incorporating one or more instances of the eyepiece waveguide in FIG. 20A.

[0081] [Figure 21A] FIG. 21A illustrates another embodiment of an eyepiece waveguide with an MPE region overlapped by an EPE region.

[0082] [Figure 21B] FIG. 21B is a k-space diagram illustrating the k-space effect of the eyepiece waveguide in FIG. 20A on a first set of input beams corresponding to a first sub-portion of the FOV of the input image.

[0083] [Figure 21C] FIG. 21C is a k-space diagram illustrating the k-space effect of the eyepiece waveguide in FIG. 21A on a second set of input beams corresponding to a second sub-portion of the FOV of the input image.

[0084] [Figure 21D] FIG. 21D is a k-space diagram summarizing the k-space behavior of the eyepiece waveguide in FIG. 21A.

[0085] [Figure 21E] FIG. 21E illustrates an exemplary embodiment of eyeglasses incorporating one or more instances of the eyepiece waveguide in FIG. 21A.

[0086] [Figure 21F] FIG. 21F illustrates an example FOV corresponding to the glasses in FIG. 21E.

[0087] [Figure 21G] FIG. 21G illustrates the k-space behavior of another embodiment of the eyepiece waveguide shown in FIG. 21A.

[0088] [Figure 22A] FIG. 22A illustrates an embodiment of an eyepiece waveguide that can project an extended FOV in two directions.

[0089] [Figure 22B] FIG. 22B illustrates the opposite side of the eyepiece waveguide shown in FIG. 22A.

[0090] [Figure 22C] FIG. 22C illustrates the k-space effects of the ICG and OPE regions within the eyepiece waveguide embodiment in FIG. 22A.

[0091] [Figure 22D] FIG. 22D illustrates the k-space effects of the MPE region within the eyepiece waveguide embodiment in FIG. 22A.

[0092] [Figure 22E] FIG. 22E illustrates the k-space effects of the EPE region within the eyepiece waveguide embodiment in FIG. 22A.

[0093] [Figure 23] FIG. 23 illustrates an exemplary embodiment of an eyepiece waveguide designed to work with an angled projector.

[0094] [Figure 24A] FIG. 24A is an edge view of an exemplary eyepiece waveguide having multiple combined pupil expander-extractor (CPE) regions.

[0095] [Figure 24B] FIG. 24B illustrates the action of the first and second CPE regions in both physical space and k-space following the first type of primary path of light through the eyepiece waveguide.

[0096] [Figure 24C] FIG. 24C illustrates the behavior of the first and second CPE regions in both physical space and k-space following the second type of primary path of light through the eyepiece waveguide.

[0097] [Figure 24D] FIG. 24D illustrates the action of the first and second CPE regions in both physical space and k-space following the primary paths of both the first and second types of light through the eyepiece waveguide.

[0098] [Figure 24E] FIG. 24E is a schematic diagram of the first occurrence of an interaction between an input beam and the CPE region of the eyepiece waveguide embodiment shown in FIG. 24A.

[0099] [Figure 24F] FIG. 24F is a schematic diagram of a second occurrence of interaction between the input beam and the CPE region of the eyepiece waveguide embodiment shown in FIG. 24A.

[0100] [Figure 24G] FIG. 24G is a schematic diagram of a third occurrence of interaction between an input beam and the CPE region of the eyepiece waveguide embodiment shown in FIG. 24A.

[0101] [Figure 24H]FIG. 24H is a schematic diagram of a fourth occurrence of interaction between an input beam and the CPE region of the eyepiece waveguide embodiment shown in FIG. 24A.

[0102] [Figure 24I] FIG. 24I is a schematic diagram of a fifth occurrence of interaction between an input beam and the CPE region of the eyepiece waveguide embodiment shown in FIG. 24A.

[0103] [Figure 24J] FIG. 24J illustrates the higher order paths of light through the eyepiece waveguide shown in FIG. 24A in k-space.

[0104] [Figure 24K] FIG. 24K is a diagram illustrating how a beam of light spreads through the eyepiece waveguide shown in FIG. 24A.

[0105] [Figure 25A] FIG. 25A is an edge view of an exemplary eyepiece waveguide having a single 2D combined pupil expander-extractor (CPE) grating region.

[0106] [Figure 25B] FIG. 25B illustrates the operation of the 2D CPE region in both physical space and k-space.

[0107] [Figure 26A] FIG. 26A is an edge view of an exemplary eyepiece waveguide having 2D combined pupil expander-extractor (CPE) grating regions on each of its sides.

[0108] [Figure 26B] FIG. 26B illustrates the so-called "screen door effect," an image artifact related to the density of the output beam from the eyepiece waveguide.

[0109] [Figure 26C]FIG. 26C illustrates input coupling grating rebounce, an effect that can disadvantageously cause light to be lost from the eyepiece waveguide.

[0110] [Figure 26D] FIG. 26D illustrates how the double-sided 2D CPE grating in FIG. 26A increases the density of the output beam from the eyepiece waveguide.

[0111] [Figure 26E] FIG. 26E illustrates the output beam density for the eyepiece waveguides shown in FIG. 24A (double-sided 1D CPE grating), FIG. 25A (single-sided 2D CPE grating), and FIG. 26A (double-sided 2D CPE grating).

[0112] [Figure 26F] Figure 26F shows exemplary simulated images produced by an eyepiece waveguide with a 2D CPE grating, with images shown for both the single-sided embodiment of Figure 25A and the double-sided embodiment of Figure 26A.

[0113] [Figure 27A] FIG. 27A illustrates an exemplary embodiment of an eyepiece waveguide stack with an enhanced FOV.

[0114] [Figure 27B] FIG. 27B illustrates another exemplary embodiment of an eyepiece waveguide stack with an improved FOV.

[0115] [Figure 27-1] 27C-27E include k-space diagrams illustrating the k-space operation of the exemplary embodiment of the eyepiece waveguide stack shown in FIGS. 27A and 27B for three different refractive indices.

[0116] [Figure 27-2]Figures 27F-27H illustrate sub-portions of the FOV of each color component of an input image that can be internally coupled into each of the eyepiece waveguides in the stack shown in Figures 27A and 27B, according to one embodiment in which each color component is partially carried within two of the eyepiece waveguides.

[0117] [Figure 27-3] Figures 27I-27K are similar to Figures 27F-27H in that they illustrate sub-portions of the FOV of each color component of the input image that may be internally coupled into each of the eyepiece waveguides in the stack, but Figures 27I-27K illustrate an embodiment in which each color component is partially carried within three instead of two of the eyepiece waveguides.

[0118] [Figure 27-4] 27L-27N illustrate the sub-portions of the FOV for each color component of the input image that can be interconnected into the eyepiece waveguides of a single color component per layer.

[0119] [Figure 28A] FIG. 28A illustrates another exemplary embodiment of an eyepiece waveguide stack with an improved FOV and in-line pupil ICG configuration.

[0120] [Figure 28B] FIG. 28B illustrates another exemplary embodiment of an eyepiece waveguide stack with an improved FOV and split-pupil ICG configuration.

[0121] [Figure 29] FIG. 29 is a graph plotting the FOV values ​​in Table 1 as a function of refractive index.

[0122] [Figure 30] FIG. 30 illustrates an example of improved output image uniformity using the eyepiece waveguide stacks shown in FIGS. 27A-27B and 28A-28B. DETAILED DESCRIPTION OF THE INVENTION

[0123] Detailed Description overview This disclosure describes various eyepiece waveguides that can be used in AR display systems to project images into a user's eyes. The eyepiece waveguides are described in both physical terms and using k-space representations. Exemplary HMD Devices

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

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

[0126] Remote processing module 150 may include one or more processors for analyzing and processing data such as image and audio information. In some embodiments, remote data repository 160 may be a digital data storage facility, which may be available through the Internet or other networking configuration in a "cloud" resource configuration. In some embodiments, remote data repository 160 may include one or more remote servers that provide information (e.g., information for generating augmented reality content) to local processing and data module 140 and / or remote processing module 150. In other embodiments, all data is stored and all calculations are performed in the local processing and data module, allowing for fully autonomous use from the remote module.

[0127] The perception of an image as "three-dimensional" or "3-D" can be achieved by providing a slightly different presentation of the image to each eye of a user. 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. The images 190, 200 are spaced from the eyes 210, 220 by a distance 230 along an optical axis, or z-axis, parallel to the user's line of sight. The images 190, 200 are flat, and the eyes 210, 220 can focus on the images by assuming a single accommodative state. Such a 3-D display system relies on the human visual system to combine the images 190, 200 and provide the perception of depth and / or scale of the combined image.

[0128] However, the human visual system is complex, making it 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 any sense of depth at all. Objects can be perceived as "three-dimensional" due to a combination of vergence and accommodation. Vergence movement of the two eyes relative to one another (e.g., pupil rotation so that the pupils move toward or away from one another, converging the eyes' individual lines of sight and fixating on an object) is closely linked to the focusing (or "accommodation") of the eye's lens. Under normal conditions, a change in the focus of the eye's lens or accommodation of the eye to change focus from one object to another at a different distance will automatically produce a coordinated change in vergence at the same distance, a relationship known as the "accommodation-vergence reflex" and pupil dilation or constriction. Similarly, under normal conditions, changes in vergence-divergence will induce matching changes in accommodation in lens shape and pupil size. As described herein, many stereoscopic or "3-D" display systems display a scene using a slightly different presentation (and therefore a slightly different image) to each eye so that a three-dimensional perspective is perceived by the human visual system. However, such systems can be uncomfortable for some users because they simply present image information in a single accommodated state and work against the "accommodation-vergence-divergence reflex." Display systems that provide a better match between accommodation and vergence-divergence may produce a more realistic and comfortable simulation of three-dimensional image data.

[0129] FIG. 4 illustrates aspects of an approach for simulating three-dimensional image data using multiple depth planes. Referring to FIG. 4 , the eyes 210, 220 assume different accommodated states and focus objects at various distances along the z-axis. Consequently, a particular accommodated state may be said to be associated with a particular one of the illustrated depth planes 240, having an associated focal length such that an object or portion of an object at that depth plane is in focus when the eye is in an accommodated state relative to that depth plane. In some embodiments, three-dimensional image data may be simulated by providing different representations of images for each eye 210, 220, and by providing different representations of images corresponding to multiple depth planes. While 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, while the depth plane is shown as flat for ease of illustration, it should be understood that the contours of the depth plane may be curved in physical space such that all features within the depth plane are in focus with the eye in a particular accommodated state.

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

[0131] A highly realistic simulation of perceived depth can be achieved by providing the eyes with different representations of an image corresponding to each of a limited number of depth planes. The different representations may be focused separately by the user's eyes, thereby serving to provide depth cues to the user based on the amount of ocular accommodation required to focus on different image features for a scene located on the different depth planes and / or based on the observation of different image features on different depth planes that are out of focus. 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 stacked waveguide assembly 260 that can be utilized to provide a three-dimensional perception to the eye / brain using multiple waveguides 270, 280, 290, 300, 310. In some embodiments, display system 250 is system 60 of FIG. 2 , and FIG. 6 diagrammatically illustrates some portions of system 60 in greater detail. For example, waveguide assembly 260 may be part of display 70 of FIG. 2 . It should be understood that display system 250 may, in some embodiments, be considered a light field display.

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

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

[0135] In some embodiments, the light injected into the waveguides 270, 280, 290, 300, 310 is provided by a light projector system 520, which includes a light module 530, which may include a light source or light emitter, such as a light emitting diode (LED). Light from the light module 530 may be directed and modulated by a light modulator 540 (e.g., a spatial light modulator) via a beam splitter (BS) 550. The light modulator 540 may spatially and / or temporally vary the perceived intensity of the light injected 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, light projector system 520 or one or more components thereof may be attached to frame 80 (FIG. 2). For example, light projector system 520 may be part of an temple portion (e.g., earpiece 82) of frame 80 or may be located on an edge of display 70. In some embodiments, light module 530 may be separate from BS 550 and / or light modulator 540.

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

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

[0139] Waveguides 270, 280, 290, 300, 310 may be configured to propagate light within each individual waveguide by total internal reflection (TIR). Waveguides 270, 280, 290, 300, 310 may each be planar or have another shape (e.g., curved) with major top and bottom surfaces and edges extending between the major top and bottom surfaces. In the illustrated configuration, waveguides 270, 280, 290, 300, 310 may each include outcoupling 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 outcoupled light, and the optical element that outcouples light may also be referred to as a light extraction optical element. The extracted beam of light may be output by the waveguide at a location where light propagating within the waveguide strikes the light extraction optical element. The outcoupling optical elements 570, 580, 590, 600, 610 may be diffractive optical features, including, for example, diffraction gratings, as discussed further herein. While the outcoupling optical elements 570, 580, 590, 600, 610 are illustrated disposed on the bottom major surfaces of the waveguides 270, 280, 290, 300, 310, in some embodiments, they may be disposed on the top and / or bottom major surfaces and / or directly within the volume of the waveguides 270, 280, 290, 300, 310, as discussed further herein. In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 may be formed within a layer of material that is attached to a transparent substrate and forms the waveguides 270, 280, 290, 300, 310. In some other embodiments, the waveguides 270, 280, 290, 300, 310 may be a monolithic piece of material, and the outcoupling optical elements 570, 580, 590, 600, 610 may be formed on and / or within that piece of material.

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

[0141] The other waveguide layers 300, 310 and lenses 330, 320 are similarly configured, with the highest waveguide 310 in the stack sending its output through all of the lenses between it and the eye for a collective focal power representing the focal plane closest to the person. To compensate for the stack of lenses 320, 330, 340, 350 when viewing / interpreting light originating from the world 510 on the other side of the stacked waveguide assembly 260, a compensatory lens layer 620 may be placed on top of the stack to compensate for the collective refractive power of the lower lens stacks 320, 330, 340, 350. Such a configuration provides as many perceived focal planes as there are available waveguide / lens pairs. Both the waveguide outcoupling optical elements and the focusing sides of the lenses may be static (i.e., not dynamic or electro-active). In some alternative embodiments, one or both may be dynamic using electro-active features.

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

[0143] The outcoupling optical elements 570, 580, 590, 600, 610 may be configured to redirect light from their respective waveguides and output the light with an appropriate amount of divergence or collimation for the particular depth plane associated with the waveguide. As a result, waveguides with different associated depth planes may have differently configured outcoupling optical elements 570, 580, 590, 600, 610 that output light with different amounts of divergence depending on the associated depth plane. In some embodiments, the light extraction optical elements 570, 580, 590, 600, 610 may be volume or surface features that may be configured to output light at specific angles. For example, the light 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 (eg, cladding layers and / or structures to form an air gap).

[0144] In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 are diffractive features with sufficiently low diffraction efficiency so that only a portion of the optical power of the light in the beam is redirected toward the eye 210 with each interaction, while the remainder continues traveling through the waveguide via TIR. Thus, the exit pupil of the optical module 530 is replicated across the waveguide, creating multiple output beams carrying image information from the light source 530 and effectively expanding the number of locations where the eye 210 can see the replicated light source exit pupil. These diffractive features may also have variable diffraction efficiency across their geometry, improving the uniformity of the light output by the waveguide.

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

[0146] In some embodiments, a camera assembly 630 (e.g., a digital camera, including a visible light and IR light camera) is provided to capture images of the eye 210, a portion of the eye 210, or at least a portion of the tissue surrounding the eye 210, and may, for example, detect user input, extract biometric information from the eye, estimate and track the eye's gaze direction, monitor the user's physiological condition, etc. 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. In some embodiments, the camera assembly 630 may be mounted on the frame 80 ( FIG. 2 ) and may be in electrical communication with a processing module 140 or 150, which may process image information from the camera assembly 630 and make various determinations, for example, regarding the user's physiological condition, the wearer's gaze direction, iris identification, etc. In some embodiments, one camera assembly 630 may be utilized per eye to monitor each eye separately.

[0147] FIG. 7A illustrates an example of an output beam output by a waveguide. While one waveguide is shown (using a perspective view), other waveguides in waveguide assembly 260 ( FIG. 6 ) can function similarly. Light 640 is launched into waveguide 270 at input surface 460 of waveguide 270 and propagates within waveguide 270 via TIR. Through interaction with diffractive features, the light exits the waveguide as output beam 650. Output beam 650 replicates the exit pupil from a projector device that projects an image into the waveguide. Any one of output beams 650 contains a subportion of the total energy of input light 640. Furthermore, in a perfectly efficient system, the sum of the energies in all output beams 650 would be equal to the energy of input light 640. Although the exit beam 650 is shown in FIG. 7A as being approximately parallel, as discussed herein, a certain amount of optical power may be imparted depending on the depth plane associated with the waveguide 270. A parallel exit beam may refer to a waveguide with outcoupling optics that outcouples light and forms an image that appears to be set on a depth plane at a long distance (e.g., optical infinity) from the eye 210. Other sets of waveguides or other outcoupling optics may output a more divergent exit beam pattern, as shown in FIG. 7B, which would require the eye 210 to accommodate to a closer distance to focus on the retina 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 at each depth plane by overlaying an image in 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, with each depth plane including an image formed using multiple different primary colors. The illustrated embodiment shows depth planes 240a-240f, but more or fewer depths are also contemplated. Each depth plane may have three or more primary color images associated with it, including a first image in a first color G, a second image in a second color R, and a third image in a third color B. Different depth planes are indicated in the diagram by different diopter powers following the letters G, R, and B. The number following each of these letters indicates the diopter (1 / m), i.e., the inverse distance of the depth plane from the user, and each box in the diagram represents an individual primary color image. In some embodiments, the exact location of the depth planes for the different primary colors may vary to account for differences in the eye's focusing of different wavelengths of light. For example, different primary color images for a given depth plane may be placed on depth planes corresponding to different distances from the user. Such an arrangement may increase visual acuity and user comfort or reduce chromatic aberration.

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

[0150] 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 be used in addition to 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] References throughout this disclosure to a given color of light should be understood to encompass light of one or more wavelengths within the range of wavelengths of light that are perceived by a user as that given color. For example, red light may include one or more wavelengths of light that are within a range of approximately 620-780 nm, green light may include one or more wavelengths of light that are within a range of approximately 492-577 nm, and blue light may include one or more wavelengths of light that are within a range of approximately 435-493 nm.

[0152] In some embodiments, light source 530 (FIG. 6) may be configured to emit light at one or more wavelengths outside the user's visual perception range, e.g., IR and / or ultraviolet wavelengths. IR light may include light with wavelengths in the range of 700 nm to 10 μm. In some embodiments, IR light may include near-IR light with wavelengths in the range of 700 nm to 1.5 μm. Additionally, the waveguide in-coupling, out-coupling, and other light redirecting structures of display 250 may be configured to direct and emit this light from the display toward the user's eye 210, e.g., for imaging and / or user stimulation applications.

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

[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 the light 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 internal coupling optical elements 700, 710, 720 may be disposed on the bottom major surface of an individual waveguide 670, 680, 690 (particularly, one or more internal coupling optical elements are reflective optical elements). As shown, the internal coupling optical elements 700, 710, 720 may be disposed on the upper major surface of the respective waveguide 670, 680, 690 (or on top of the next lower waveguide), and in particular, the internal coupling optical elements are transmissive optical elements. In some embodiments, the internal coupling optical elements 700, 710, 720 may be disposed within the body of the respective waveguide 670, 680, 690. In some embodiments, as discussed herein, the internal coupling optical elements 700, 710, 720 are wavelength selective, such that they selectively redirect one or more wavelengths of light while transmitting other wavelengths of light. While illustrated on one side or corner of the respective waveguide 670, 680, 690, it should be understood that the internal coupling optical elements 700, 710, 720 may be disposed within other areas of the respective waveguide 670, 680, 690 in some embodiments.

[0155] As shown, the in-coupling optical elements 700, 710, 720 may be laterally offset from one another. In some embodiments, each in-coupling optical element may be offset to receive light without that light passing through another in-coupling optical element. For example, each in-coupling optical element 700, 710, 720 may be configured to receive light from a different image input device 360, 370, 380, 390, and 400, as shown in FIG. 6 , and may be separated (e.g., laterally spaced) from the other in-coupling optical elements 700, 710, 720 so as to receive substantially no light from others of the in-coupling optical elements 700, 710, 720.

[0156] Each waveguide also includes an associated optically dispersive element, for example, optically dispersive element 730 is disposed on a major surface (e.g., the top major surface) of waveguide 670, optically dispersive element 740 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and optically dispersive element 750 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some other embodiments, optically dispersive elements 730, 740, 750 may be disposed on the bottom major surfaces of associated waveguides 670, 680, 690, respectively. In some other embodiments, optically dispersive elements 730, 740, 750 may be disposed on both the top and bottom major surfaces of associated waveguides 670, 680, 690, respectively, or optically dispersive elements 730, 740, 750 may be disposed on different ones of the top and bottom major surfaces in different associated waveguides 670, 680, 690, respectively.

[0157] Waveguides 670, 680, 690 may be spaced apart and separated, for example, by gas, liquid, and / or solid layers of material. For example, as shown, layer 760a may separate waveguides 670 and 680, and layer 760b may separate waveguides 680 and 690. In some embodiments, layers 760a and 760b are formed from a low refractive index material (i.e., a material having a lower refractive index than the material forming the immediately adjacent ones of waveguides 670, 680, 690). Preferably, the refractive index of the material forming layers 760a, 760b is 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 to promote TIR of light through the waveguides 670, 680, 690 (e.g., TIR between the top and bottom major surfaces of each waveguide). In some embodiments, the layers 760a, 760b are formed from air. Although not shown, it should be understood that the top and bottom of the illustrated set of waveguides 660 may include immediate cladding layers.

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

[0159] 9A, light rays 770, 780, 790 enter the set of waveguides 660. Light rays 770, 780, 790 may be injected into the waveguides 670, 680, 690 by one or more image injection devices 360, 370, 380, 390, 400 (FIG. 6).

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

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

[0162] 9A , light rays 770, 780, 790 are redirected to propagate through corresponding waveguides 670, 680, 690. That is, the in-coupling optical element 700, 710, 720 of each waveguide redirects the light into its corresponding waveguide 670, 680, 690, in-coupling the light into the corresponding waveguide. Light rays 770, 780, 790 are redirected at an angle that causes the light to propagate through the respective waveguides 670, 680, 690 by TIR. Light rays 770, 780, 790 propagate through the respective waveguides 670, 680, 690 by TIR until they interact with the waveguide's corresponding optical dispersive element 730, 740, 750.

[0163] 9B, a perspective view of the multiple stacked waveguide embodiment of FIG. 9A is illustrated. As described above, light rays 770, 780, and 790 are in-coupled by in-coupling optical elements 700, 710, and 720, respectively, and then propagate by TIR within waveguides 670, 680, and 690, respectively. Light rays 770, 780, and 790 then interact with optically dispersive elements 730, 740, and 750, respectively. Optically dispersive elements 730, 740, and 750 redirect light rays 770, 780, and 790 to propagate toward out-coupling optical elements 800, 810, and 820, respectively.

[0164] In some embodiments, the optically dispersive elements 730, 740, 750 are orthogonal pupil expanders (OPEs). In some embodiments, the OPEs both redirect light to the out-coupling optical elements 800, 810, 820 and also expand the pupil associated with this light by sampling light rays 770, 780, 790 at many locations across the optically dispersive elements 730, 740, 750 as they propagate into the out-coupling optical elements. In some embodiments (e.g., if the exit pupil is already the desired size), the optically dispersive elements 730, 740, 750 may be omitted, and the in-coupling optical elements 700, 710, 720 may be configured to redirect light directly to the out-coupling optical elements 800, 810, 820. For example, with reference to FIG. 9A , the optically dispersive elements 730, 740, 750 may be replaced with the out-coupling optical elements 800, 810, 820, respectively. In some embodiments, the outcoupling optical element 800, 810, 820 is an exit pupil (EP) or exit pupil expander (EPE) that redirects light from the waveguide toward the user's eye 210 ( FIG. 7 ). The OPE may be configured to increase the dimension 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 perpendicular to) the axis of the OPE.

[0165] 9A and 9B, in some embodiments, a waveguide set 660 includes, for each primary color, waveguides 670, 680, 690, in-coupling optical elements 700, 710, 720, optically dispersive elements (e.g., OPEs) 730, 740, 750, and out-coupling optical elements (e.g., EPEs) 800, 810, 820. The waveguides 670, 680, 690 may be stacked with an air gap / cladding layer between each one. The in-coupling optical elements 700, 710, 720 direct incident light into the corresponding waveguide (with different in-coupling optical elements receiving light of different wavelengths). The light then propagates at angles that support TIR within the individual waveguides 670, 680, 690. Because TIR occurs only over a range of angles, the range of propagation angles of light rays 770, 780, and 790 is limited. The range of angles that support TIR can be considered the angular limits of the field of view that can be displayed by waveguides 670, 680, and 690 in such embodiments. In the illustrated embodiment, light ray 770 (e.g., blue light) is incoupled by first incoupling optical element 700 in the manner described above and then continues to reflect back and forth from the surfaces of the waveguide as it travels down the waveguide, with optical dispersive element (e.g., OPE) 730 progressively sampling it and creating additional replica light rays that are directed toward outcoupling optical element (e.g., EPE) 800. Light rays 780 and 790 (e.g., green and red light, respectively) pass through waveguide 670, with light ray 780 impinging on incoupling optical element 710 and thereby being incoupled. Light ray 780 would then propagate back down waveguide 680 via TIR to its light dispersive element (e.g., OPE) 740 and then to an outcoupling optical element (e.g., EPE) 810. Finally, light ray 790 (e.g., red light) passes through waveguides 670, 680 and impinges on light incoupling optical element 720 of waveguide 690. Light incoupling optical element 720 incouples light ray 790 such that the light ray propagates via TIR to a light dispersive element (e.g., OPE) 750 and then via TIR to an outcoupling optical element (e.g., EPE) 820. Outcoupling optical element 820 then finally outcouples light ray 790 to the user, who also receives outcoupled light from the other waveguides 670, 680.

[0166] FIG. 9C illustrates a top-down plan view of an example of the multiple stacked waveguides of FIGS. 9A and 9B. As shown, waveguides 670, 680, 690 may be vertically aligned, along with each waveguide's associated optically dispersive element 730, 740, 750 and associated out-coupling optical elements 800, 810, 820. However, as discussed herein, the in-coupling optical elements 700, 710, 720 are not vertically aligned. Rather, the in-coupling optical elements may be non-overlapping (e.g., laterally spaced apart, as seen in the top-down view). This non-overlapping spatial arrangement may facilitate the injection of light from different sources into different waveguides on a one-to-one basis, thereby allowing a specific light source to be uniquely optically coupled to a specific waveguide. In some embodiments, arrays including non-overlapping, spatially separated in-coupling optical elements may be referred to as shifted-pupil systems, and the in-coupling optical elements in these arrays may correspond to sub-pupils.

[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 to protect one or more eyepiece waveguides 1004 positioned between the cover windows. In other embodiments, one or both of the cover windows 1002, 1006 may be omitted. As previously discussed, the eyepiece waveguides 1004 may be arranged in a layered configuration. The eyepiece waveguides 1004 may be coupled together, for example, each individual eyepiece waveguide is coupled to one or more adjacent eyepiece waveguides. In some embodiments, the waveguides 1004 may be coupled with an edge seal (such as edge seal 1108 shown in FIG. 11 ) to prevent adjacent eyepiece waveguides 1004 from directly contacting each other.

[0168] Each eyepiece waveguide 1004 can be made from an at least partially transparent substrate material, such as glass, plastic, polycarbonate, sapphire, etc. The selected material may have a refractive index greater than 1.4, e.g., greater than 1.6 or 1.8, to facilitate light guidance. 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, light dispersion regions, image enhancement regions, and external coupling regions, which may consist of diffractive features formed on or within each waveguide substrate 902.

[0169] Although not shown in FIG. 10 , the eyepiece waveguide stack 1000 may include a physical support structure for supporting it in front of the user's eyes. 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 so that the external coupling region is directly in front of the user's eyes. It should be understood that FIG. 10 illustrates only a portion of the eyepiece waveguide stack 1000 that corresponds to one of the user's eyes. The completed eyepiece may include a mirror image of the same structure, possibly with the two halves separated by a nosepiece.

[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 in the eyepiece 1000 may correspond to a selected color component of the image data for the selected depth plane. For example, the eyepiece waveguide stack 1000 may include six eyepiece waveguides 1004 and thus 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 may include eyepiece waveguides 1004 for more or fewer color components and / or more or fewer depth planes.

[0171] FIG. 11 is a cross-sectional view of a portion of an exemplary eyepiece waveguide stack 1100 with an edge seal structure 1108 for supporting the eyepiece waveguides 1104 in a stacked configuration. The edge seal structure 1108 aligns the eyepiece waveguides 1104 and separates them from each other with an air space or another material disposed between them. Although not shown, the edge seal structure 1108 can extend around the entire circumference 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 waveguides 1104 designed to display red image data, one for the 3 m depth plane and the other for the 1 m depth plane. (Again, the divergence of the beam of light output by the eyepiece waveguides 1104 can make the image data appear to originate from a depth plane located at a particular distance.) Similarly, there are two eyepiece waveguides 1104 designed to display blue image data, one for the 3 m depth plane and the other for the 1 m depth plane, and two eyepiece waveguides 1104 designed to display green image data, one for the 3 m depth plane and the other for the 1 m depth plane. Each of these six eyepiece waveguides 1104 is illustrated as being 0.325 mm thick, although other thicknesses are also possible.

[0173] A world-side cover window 1102 and an eye-side cover window 1106 are also shown in Figure 11. These cover windows can be, for example, 0.330 mm thick. Considering the thickness of the six eyepiece waveguides 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] 12A and 12B illustrate a top view of the eyepiece waveguide 1200 in operation as it projects an image toward a user's eye 210. The image can initially be projected using a projection lens 1210 or some other projector device from an image plane 1207 toward the entrance pupil 1208 of the eyepiece waveguide 1200. Each image point (e.g., an image pixel or portion of an image pixel) has a corresponding input beam of light (e.g., 1202a, 1204a, 1206a) that propagates in a particular direction at the entrance pupil 1208 (e.g., at a particular angle relative to the optical axis of the projector lens 1210). While illustrated as rays of light, the input beams of light 1202a, 1204a, 1206a may be collimated beams, for example, with diameters of a few millimeters or less, as they enter the eyepiece waveguide 1200.

[0175] 12A and 12B, the central image point corresponds to input beam 1204a, which is illustrated using a solid line. The right image point corresponds to input beam 1202a, which is illustrated using a dashed line. The left image point corresponds to input beam 1206a, which is illustrated using a dotted line. 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 propagating over a range of angles in both the x- and y-directions, corresponding to different image points in the two-dimensional image plane.

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

[0177] 12A and 12B, an input beam of light 1204a, corresponding to a central image point in image plane 1207, is transformed into a set of replicated output beams 1204b, shown as solid lines, which are aligned with an optical axis perpendicular to the exit pupil 1210 of the eyepiece waveguide 1200. An input beam of light 1202a, corresponding to a right image point in image plane 1207, is transformed into a set of replicated output beams 1202b, shown as dashed lines, which exit the eyepiece waveguide 1200 at propagation angles such that they appear to originate from a location within the right portion of the user's field of view. Similarly, an input beam of light 1206a, corresponding to a left image point in image plane 1207, is transformed into a set of replicated output beams 1206b, shown as dashed lines, which exit the eyepiece waveguide 1200 at propagation angles such that they appear to originate from a location within the left portion of the user's field of view. The greater the range of input and / or output beam angles, 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 of the individual output beams (e.g., 1202b, 1204b, 1206b) can be collimated. The set of output beams corresponding to a given image point may consist of beams propagating along parallel paths (as shown in FIG. 12A) or diverging paths (as shown in FIG. 12B). In either case, the specific propagation angles of the sets of replicate output beams depend on the location of the corresponding image point in the image plane 1207. FIG. 12A illustrates the case where each set of output beams (e.g., 1202b, 1204b, 1206b) consists of beams propagating along parallel paths. This results in the image being projected so that it appears to originate from optical infinity. This is represented in Figure 12A by the thin lines extending from the peripheral output beams 1202b, 1204b, and 1206b toward optical infinity on the world side of the eyepiece waveguide 1200 (opposite where the user's eye 210 is located). Figure 12B illustrates the case where each set of output beams (e.g., 1202b, 1204b, and 1206b) consists of beams propagating along diverging paths. This results in images being projected that appear to originate from a virtual depth plane with a distance closer than optical infinity. This is represented in Figure 12B by the thin lines extending from the peripheral output beams 1202b, 1204b, and 1206b toward 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 that corresponds to a specific image point at image plane 1207. In the case of a set of replicated output beams propagating along parallel paths (see FIG. 12A), the propagation angles of all beams are identical. However, in the case of a set of replicated output beams propagating along diverging paths, the individual output beams may propagate at different angles, but those angles are related to each other in that they create an aggregate diverging wavefront and appear to originate from a common point along the axis of the set of beams (see FIG. 12B). This axis defines the angle of propagation for the set of diverging output beams, which corresponds to a specific image point at image plane 1207.

[0180] The various beams of light entering, propagating within, and exiting the eyepiece waveguide 1200 can all be described using one or more wave vectors, i.e., k-vectors, which describe the beam's propagation direction. 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 in turn can 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 sets of points (e.g., rectangles) in k-space. Diffraction features that change the propagation direction of a light beam as it travels through the eyepiece can be understood in k-space simply as translating the location of the set of k-space points that make up the image. This new translated k-space location corresponds to a new set of k-vectors, which in turn represent the new propagation angle of the beam or ray after interacting with the diffraction feature.

[0181] The operation of the eyepiece waveguide can be understood in terms of how it moves a set of points in k-space, such as points inside a k-space rectangle, corresponding to a projected image. This is in contrast to more complex ray trace diagrams, which may otherwise be used to illustrate beams and their propagation angles. K-space is therefore an effective tool for describing the design and operation of eyepiece waveguides. The following discussion describes k-space representations 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 beam of light. The particular illustrated k-vector 1302 represents a plane wave with a plane wavefront 1304. The k-vector 1302 points to the propagation direction of the ray or beam it represents. The magnitude, i.e., length, of the k-vector 1302 is defined by the wave number k. The dispersion equation ω = ck relates the angular frequency of light ω, the speed of light c, and the wave number k. (In a vacuum, the speed of light is equal to the speed of light constant c. However, within 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.) Note that by definition, k = 2π / λ and ω = 2πf, where f is the frequency of light (e.g., in Hertz). As is evident from this equation, a light beam with a higher angular frequency ω has a larger wave number and therefore a larger magnitude of the k-vector (assuming the same propagation medium). For example, a blue light beam has a larger magnitude of the k-vector than a red light beam, assuming the same propagation medium.

[0183] FIG. 13B illustrates a light 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 for an AR display system. The waveguide 1300 can guide a light ray having a k-vector via total internal reflection (TIR). For example, as shown in FIG. 13B, a light ray 1301 illustrated by a k-vector 1302 is directed toward the upper surface of the waveguide 1300 at an angle. If the angle is not too steep, as governed by Snell's Law, the light ray 1301 will reflect at the upper surface of the waveguide 1300 at an angle equal to the angle of incidence, then propagate downward toward the lower surface of the waveguide 1300, where it will again reflect back toward the upper surface. Light ray 1301 will propagate in a guided manner within waveguide 1300, continuing to reflect back and forth between its upper and lower surfaces.

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

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

[0186] Every point within the solid disk 1308 corresponds to a wave k-vector 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: one with a z-component that propagates into the page, and one with a z-component that propagates out of the page. Thus, the out-of-plane component k of the k-vector z is the equation [ka] The sign chosen determines whether the wave propagates into or out of the page. Because all light waves of a given angular frequency ω propagating in a homogeneous medium with refractive index n have the same magnitude k-vector, light waves with k-vectors whose x and y components are closer in size to the radius of the solid disk 1308 have smaller z-components of propagation (resulting in less steep propagation angles necessary for TIR, as discussed with respect to FIG. 13B ), while light waves with k-vectors whose x and y components lie closer to the center of the solid disk 1308 have larger z-components of propagation (resulting in steeper propagation angles that cannot be TIR). Thus, all references to k-space refer to projected k-space (unless otherwise clear from the context), in which the two-dimensional k-plane corresponds to the plane of the waveguide. That is, unless the direction of propagation between the surfaces of the waveguide is explicitly stated, the discussion and drawings generally consider only the direction parallel to the surfaces of the waveguide. Furthermore, when plotting k-space, it is typically most convenient to normalize the free-space disk radius to 1 so that the plot is effectively normalized to ω / c.

[0187] FIG. 13E illustrates a ring 1310 in k-space corresponding to the k-vector of a light wave that may be guided in 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 k-vectors corresponding to allowed waves in a planar waveguide medium in the xy plane are those k-vectors whose individual xy components lie within a solid circular plate 1308 in k-space. The radius of the solid circular plate 1308 is proportional to the refractive index of the waveguide medium. Therefore, referring back to FIG. 13E, the k-vectors corresponding to light waves that may propagate in a planar waveguide medium having a refractive index n2 = 1.5 are those whose individual xy components lie within the larger circular plate 1308a. On the other hand, k-vectors corresponding to light waves that can propagate in the surrounding medium with refractive index n1 = 1 are those whose individual x and y components lie within the smaller disk 1308b. All k-vectors whose individual x and y components lie inside the annulus 1310 correspond to light waves that can propagate in the waveguide medium but do not propagate in the surrounding medium (e.g., air). These are light waves that are guided within the waveguide medium via total internal reflection, as described with respect to FIG. 13B. Thus, light rays or beams can only undergo guided propagation within the waveguide of the AR eyepiece if they have a k-vector that lies within the k-space annulus 1310. Note that propagating light waves with a k-vector outside the larger disk 1308a are prohibited. That is, no propagating waves exist whose k-vectors lie within that region (waves within that region have evanescent decay amplitudes that are not constant along their propagation direction).

[0188] The various AR eyepiece waveguides described herein can use diffractive features, such as diffractive structures, to interconnect light and direct the k-vector of a light beam propagating in free space (n≈1) (e.g., from a projector) into the k-space annulus 1310 of the eyepiece waveguide. Any light wave whose k-vector is within the annulus 1310 can propagate in a guided manner within the eyepiece waveguide. The width of the annulus 1310 determines the range of k-vectors, and therefore the range of propagation angles, that can be guided within the eyepiece waveguide. Thus, the width of the k-space annulus 1310 is typically considered to determine the maximum field of view (FOV) that can be projected by the eyepiece waveguide. Because the width of the annulus 1310 depends on the radius of the larger disk 1308a, which itself depends in part 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, such as material cost, on the refractive index of the waveguide medium that can be used in an AR eyepiece. This, in turn, is believed to impose a practical limit on the FOV of the AR eyepiece. However, as described herein, there are techniques that can be used to overcome these limitations 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 therefore on the color of the light, but this does not imply that the FOV supported by the eyepiece waveguide is larger for light with higher angular frequencies, as any given angular range corresponding to the FOV similarly scales directly with angular frequency.

[0190] Figure 13F shows a k-space diagram similar to that depicted in Figure 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 an annulus 1310 between the outer boundaries of the smaller disk 1308a and the larger disk 1308b. All k-vectors within width 1342 of annulus 1310 correspond to guided propagation angles, although it is possible that fewer than all of the k-vectors within width 1342 of annulus 1310 may be sufficient for use in displaying an image.

[0191] FIG. 13F also shows a waveguide 1350 with two guided beams shown relative to one another. A first optical beam has a first k-vector 1344a near the outer edge of the annulus 1310. The first k-vector 1344a corresponds to a first TIR propagation path 1344b, shown in a cross-sectional view of the waveguide 1350 with refractive index n2 surrounded by air with refractive index n1. A second optical beam is also shown with a second k-vector 1346a closer to the center of the k-space annulus 1310. 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 the light beam encounters the surface of the waveguide 1350 with the diffraction grating 1352, an interaction occurs that can send a sample of the light beam energy out of the waveguide while the beam continues to TIR within the waveguide. The angle at which the light beam propagates in TIR through the waveguide determines the density of reflection events, i.e., the number of bounces, per unit length relative to the surface of the waveguide 1350 with the diffraction grating 1352. Returning to the example of light beam comparison, the first light beam in 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) across the length of the diffraction grating 1352, while the second light beam in the second TIR propagation path 1346b reflects ten times from the waveguide surface with the diffraction grating 1352 over the same or 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 constrain the output beam, i.e., the exit pupil spacing, to equal or within a preselected range to ensure that content projected to a user will be visible from any position within a predefined eyebox. Using this information, it is possible to limit the width 1342 of the annulus 1310 to the subset of k-vectors 1344 for which this constraint applies, eliminating angles with too much grazing incidence from being included in the design calculations. Angles greater or fewer than the subset 1344 may be acceptable, depending on the desired performance, the grating design, and other optimization factors. Similarly, in some embodiments, k-vectors corresponding to propagation angles that are too steep relative to the surface of the waveguide and provide too many interactions with the grating 1352 may also be excluded from use. In such embodiments, the width 1342 of the annulus 1310 can be reduced by effectively moving the boundary of usable angles radially outward from the boundary between the larger and smaller disks 1308a and 1308b. Any of the eyepiece waveguide designs disclosed herein can be adjusted by constraining the width 1310 of the k-space annulus in this way.

[0193] As described above, k-vectors within the annulus 1310 that correspond to suboptimal TIR propagation paths may be omitted from use in the eyepiece design calculations. Alternatively, k-vectors that correspond to TIR propagation paths with too large a grazing angle, and therefore too little density of reflection events on the surface of the waveguide with the diffraction grating, may be compensated for using various techniques described herein. One technique is to use an internal coupling grating to direct portions 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, the first and second sides of the k-space annulus 1310 being substantially opposite each other. For example, a first group of k-vectors may correspond to a k-vector FOV rectangle on the left side of the annulus 1310, and a second group of k-vectors may correspond to a k-vector FOV rectangle on the right side of the annulus 1310. The left FOV rectangle has its left edge near the outer edge of the larger disk 1308a and corresponds to a k-vector angle near the grazing incidence angle. Light at this 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 disk 1308a. Light at the same left edge of the right FOV rectangle will have a dense exit pupil. Thus, when the left and right FOV rectangles are recombined and exit the waveguide toward the user's eye to produce an image, a sufficient number of exit pupils are produced in all areas of the field of view.

[0194] Diffractive features, such as diffraction gratings, can be used to couple light into and out of the 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 component in the plane of the diffraction grating with a given grating vector. The magnitude and direction of the grating vector depend on the specific properties of the diffraction grating. Figures 13G, 13H, and 13I illustrate the effect of a diffraction grating on a k-vector in k-space.

[0195] FIG. 13G shows a top view of grating 1320 and some of its associated k-space grating vectors (G -2 , G -1 , G1, G2). The grating 1320 is oriented in the xy plane, and FIG. 13G shows a view of the grating from the perspective of a ray or beam incident on it from the z-direction. The grating 1320 is oriented in the same plane as the grating, with k-space grating vectors (e.g., G -2 , G -1 , G1, G2). -1 The grating vectors correspond to the ±1 diffraction orders, respectively, while G and G -2The grating vectors correspond to the ±2 diffraction orders, respectively. The grating vectors for the ±1 diffraction orders point in opposite directions (along the grating's periodicity axis) and have equal magnitudes that are inversely proportional to the period Λ of the diffraction grating 1320. Thus, a grating with a finer pitch has a larger grating vector. The grating vectors for the ±2 diffraction orders also point in opposite directions and have equal magnitudes that are twice as large as the grating vectors for the ±1 diffraction orders. Grating vectors for additional higher diffraction orders may also exist, but they are not shown. For example, the magnitude of the grating vector for the ±3 diffraction orders is three times that of the grating vector for the ±1 diffraction order, and so on. Note that the fundamental grating vector G1 is determined solely by the grating periodicity (orientation and pitch), while the grating composition (e.g., surface profile, material, layer structure) can affect other properties of the grating, such as diffraction efficiency and diffraction phase. The fundamental grating vectors (e.g., G -1 , G2, G -2 Since all harmonics of the grating (such as G, etc.) are simply integer multiples of the fundamental G, all diffraction directions of the grating are determined simply by the grating periodicity. The effect of the diffraction grating 1320 is to add the grating vector to the in-plane component of the k-vector corresponding to the incident ray or beam. This is shown in Figure 13H.

[0196] FIG. 13H illustrates a side view of a diffraction grating 1320 and its effect in k-space on a k-vector 1302 corresponding to a normally incident ray or beam of light. The diffraction grating 1320 diffracts the incident ray or beam of light into one or more diffraction orders. The new ray or beam of light in each of these diffraction orders is represented by a new k-vector (e.g., 1302a-e). These new k-vectors (e.g., 1302a-e) are then coupled to the grating vectors (e.g., G -2 , G -1, G1, G2). In the illustrated case of a normally incident ray or beam of light, the k-vector 1302 has no components in the xy plane of the diffraction grating. Thus, the effect of the diffraction grating 1320 is to create one or more new diffracted rays or beams of light whose k-vectors (e.g., 1302a-e) have xy components equal to the corresponding grating vector. For example, the xy components of the ±1 diffraction orders of the incident ray or beam of light are G1 and G -1 Meanwhile, the magnitude of the new k-vectors is constrained to 2π / ω, so that the new k-vectors (e.g., 1302a-e) all lie on a semicircle, as shown in FIG. 13H. While the in-plane component of the incident k-vector 1302 is added to a grating vector whose length is equal to the base increment, twice the base increment, etc., the magnitude of each resulting k-vector is constrained, 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 with increasing diffraction order.

[0197] In the case of a diffraction grating formed on or in a planar eyepiece waveguide, the in-plane components of the new k-vector (e.g., 1302a-e) may be of most interest because if they fall within the k-space annulus 1310 of the eyepiece waveguide, the diffracted ray or beam of light will undergo guided propagation through the eyepiece waveguide. However, if the in-plane components of the new k-vector (e.g., 1302a-e) fall within the central disk 1308b, the diffracted ray or beam of light will exit the eyepiece waveguide.

[0198] FIG. 13I illustrates a side view of a diffraction grating 1320 and its effect in k-space on a k-vector 1302 corresponding to an obliquely incident ray or beam of light. The effect is similar to that described with respect to FIG. 13H. Specifically, the k-vector of a diffracted ray or beam of light is proportional to the grating vector (G -2 , G-1 , G1, G2). For an oblique incidence k-vector 1302, the component of the k-vector in the xy plane of the diffraction grating 1320 is non-zero. This component is added to the grating vector to determine the in-plane component of the new k-vector for the diffracted ray or beam of light. The magnitude of the new k-vector is constrained to 2π / ω. Again, if the in-plane component of the k-vector of the diffracted ray or beam of light lies within the k-space annulus 1310 of the eyepiece waveguide, the diffracted ray or beam of light will undergo guided propagation through the eyepiece waveguide.

[0199] 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 may 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 may propagate within a medium, such as air, surrounding the eyepiece waveguide. Also, as previously discussed, k-space annulus 1310 defines the k-vectors of light beams or rays that may 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 Figures 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 angular spread in both the x- and y-directions. The angular spread in the x-direction may define a horizontal field of view, while the angular spread in the y-direction may define a vertical field of view. Additionally, for example, the angular spread of the input beams along a diagonal between the x- and y-directions may define a diagonal field of view.

[0201] In k-space, the field of view of the input image can be approximated by an FOV rectangle 1330. The FOV rectangle 1330 encompasses a set of k-vectors that correspond to a set of input light beams. x -axis, which corresponds to the angular spread of the input beam in the x-direction. Specifically, the horizontal width of the FOV rectangle 1330 is [ka] wherein θ x is the total horizontal FOV, and n is the refractive index of the incident medium. The FOV rectangle 1330 also includes k y -axis, which defines the angular spread of the input beam in the y-direction. Similarly, the vertical height of the FOV rectangle 1330 is [ka] wherein θ y is the total vertical FOV. Although a rectangle is shown to represent the set of input beams, in some embodiments, the set of input beams may be such that it would correspond to a different shape in k-space. However, k-space analysis herein generally shown using FOV rectangles or FOV squares can be equally applied to other shapes in k-space as well.

[0202] As shown in FIG. 13J , FOV rectangle 1330 is centered on and located entirely within smaller disk 1308b. This position of FOV rectangle 1330 corresponds to the k-vector of a set of input beams (e.g., in a configuration with on-axis, i.e., telecentric, projection from the image source) or a set of output beams propagating generally 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 relative to the ±z-directions). In other words, when FOV rectangle 1330 is within smaller disk 1308b in the k-space diagram, it can represent the input beams as they propagate from the image source, through free space, to the eyepiece waveguide, and the output beams as they propagate from the eyepiece waveguide to the user's eye. Each k-space point within FOV rectangle 1330 corresponds to a k-vector, which represents one of the input beam directions or one of the output beam directions. In order for the input beam represented by FOV rectangle 1330 to undergo guided propagation within the eyepiece waveguide, FOV rectangle 1330 must be translated to k-space annulus 1310. Conversely, in order for the output beam represented by FOV rectangle 1330 to exit the eyepiece waveguide, FOV rectangle 1330 must be translated back from k-space annulus 1310 to smaller disk 1308b. To avoid introducing geometric and chromatic dispersion from propagation through the waveguide, 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 equation describes the FOV that can be achieved in some eyepiece waveguides: [ka] FOV is θ x When horizontally aligned at .omega..times ... [ka] max(FOV x The only dependence of ) comes from the dependence of the waveguide refractive index on angular frequency, which may be an important detail in some applications, but in many cases has a relatively small effect.

[0204] 13K is a k-space diagram showing the translational shift in k-space of the FOV rectangle 1330 caused by an input coupling grating (ICG) located at the entrance pupil of the eyepiece waveguide. The ICG is connected to the associated grating vector (G -1 , G1). 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 determined by the G1 grating vector k x 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 −1 direction. -1 -k by lattice vector x The FOV rectangle 1330 is represented by a -direction displaced FOV rectangle 1330.

[0205] For 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 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 lie outside the larger disk 1308a will not be diffracted by the ICG at all, because those k-vectors are not allowed. (This would also prevent diffraction into ±2 and higher diffraction orders, since in this case the grating vectors associated with those orders would be longer and therefore translate the k-vectors further outside the larger disk 1308a.) On the other hand, if any portion of the translated FOV rectangle were to still be inside the smaller disk 1308b after translation by ICG, the light beams corresponding to those particular k-vectors would not TIR and would therefore exit the eyepiece waveguide by transmitting through that plane and would not undergo guided propagation through the waveguide.

[0206] One possible modification that can be made to support more of the input beam of light represented by the translated FOV rectangle 1330 in the guided mode would be to increase the difference between the refractive indices of the eyepiece waveguide and the surrounding medium. This would increase the size of the larger disk 1308a and / or decrease the size of the smaller disk 1308b (which 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 orthogonal pupil expander

[0207] Figure 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. Figure 14B includes a k-space diagram illustrating the effect of each 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 diffractive features that couple an input beam into the eyepiece waveguide, propagate through guided modes, replicate the beam at multiple dispersed locations in space, and cause the replicated beams to exit the eyepiece waveguide and be projected toward 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. The input device used to project the input beam can include, for example, a spatial light modulator projector (located in front of or behind the eyepiece waveguide 1400 relative 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 projected into the eyepiece waveguide 1400 at various propagation angles, generally in the illustrated -z-direction, and incident on the ICG region 1440 from outside the substrate of the eyepiece waveguide.

[0209] The ICG region 1440 includes diffractive features that redirect input beams so 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 extending vertically in the illustrated y-direction and periodically repeated horizontally in the illustrated x-direction. In some embodiments, the lines may be etched into the front or back surface of the eyepiece waveguide 1400 and / or they may be formed from material deposited on the front or back surface. The period, duty cycle, depth, profile, blaze angle, etc. of the lines can be selected based on the angular frequency ω of 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 to primarily couple input light into the +1 and −1 diffraction orders. (The diffraction grating can be designed to reduce or eliminate higher diffraction orders beyond the zeroth and first diffraction orders. This can be accomplished by appropriately shaping the profile of each line. However, in many practical ICGs in AR displays, all higher diffraction orders correspond to k-vectors beyond the k-space annulus. Therefore, 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 propagates generally in the -x-direction toward the OPE region 1450, while the diffracted beam in the other of the ±1 diffraction orders then propagates generally 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 each input beam of light at many new locations, generally in the -x-direction. Second, they can guide each replicated beam of light on a path generally toward 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, etc. of the lines can be selected based on the angular frequency ω of 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 divergence of the beam of light from the ICG region 1440 and the size and location of the EPE region 1460. This is discussed further with respect to FIG. 14D .

[0211] The diffraction grating of the OPE region 1450 can be designed with a relatively low and / or variable diffraction efficiency. These properties can allow the OPE region 1450 to replicate each beam of light arriving from the ICG region 1440 and / or distribute the light energy more uniformly in at least one dimension. Due to the relatively low diffraction efficiency, each interaction of a beam of light with the grating diffracts only a portion of the optical power in 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 a beam interacts with the diffraction grating in the OPE region 1450, a portion of its optical power will be diffracted toward the EPE region 1460, while the remaining portion may continue to transmit through the OPE region and again encounter the grating at a different spatial location, where another portion of the beam's optical power is diffracted toward the EPE region 1460, and so on. Because a portion of the refractive power of each light beam travels further through the OPE region 1450 than other portions before being diffracted toward the EPE region 1460, there are multiple copies of the incident beam traveling toward the EPE region from different locations in the -x-direction. The spatial extent of the replica beams in the direction of propagation of the original incident beam through the OPE region 1450 is therefore effectively increased, while the intensity of the incident beam is correspondingly decreased because the light that constitutes the input beam is now split into many replica beams.

[0212] The diffraction grating in the OPE region 1450 is oriented obliquely with respect to the beam arriving from the ICG region 1440 so as to diffract the beam generally toward the EPE region 1460. The specific angle of tilt of the diffraction grating in the OPE region 1450 may depend on the layout of the various regions of the eyepiece waveguide 1400 and may perhaps be seen more clearly in 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, to redirect light from the ICG region 1440 toward the EPE region 1460, the diffraction grating in the OPE region 1450 may be oriented at approximately 45° with respect to the illustrated x-axis.

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

[0214] When the input beam 1401 interacts with the diffraction grating formed in the OPE region 1450, a portion of its optical power is diffracted toward the EPE region, while another portion of its optical power continues through the OPE region 1450 along the same path. As previously mentioned, this is due, in part, to the relatively low diffraction efficiency of the grating. Furthermore, beams diffracted toward the EPE region may re-encounter the grating in the OPE region 1450 and diffract back toward the original propagation direction of the input beam 1401. The paths of some of these beams are indicated by arrows in FIG. 14C . The effect is to expand the spatial extent of the light as the input beam is replicated as it propagates through the OPE region 1450. This is evident from FIG. 14C , which shows that the input beam 1401 is replicated into many optical beams, ultimately traveling generally in the -y-direction toward the EPE region.

[0215] EPE region 1460 similarly includes diffractive features that can perform at least two functions. First, they can replicate beams along another direction (e.g., a direction substantially orthogonal to the direction in which the beam is replicated by OPE region 1450). Second, they can diffract each beam of light out of eyepiece waveguide 1400 toward the user's eye. EPE region 1460 can replicate light beams in the same manner as OPE region 1450. That is, as the beam propagates through EPE region 1460, it repeatedly interacts with the diffraction grating, diffracting a portion of its optical power into a first diffraction order, thereby being outcoupled toward the user's eye. The other portion of the beam's optical power diffracts to the zeroth order and continues to propagate in the same direction within EPE region 1460 until it again interacts with the grating. The diffractive optical features of EPE region 1460 can also impart a degree of optical power to the replicated output beams of light to make them appear as if they originated from a desired depth plane, as discussed elsewhere herein. This can be accomplished by using a lens function to impart curvature to the lines of the grating in the EPE region 1460 .

[0216] FIG. 14B illustrates the operation of the eyepiece waveguide 1400 in k-space. Specifically, FIG. 14B includes component-by-component k-space diagrams (KSDs) of the eyepiece waveguide 1400, illustrating the k-space effects of the components. The FOV rectangles in the k-space diagrams and the arrows indicating the corresponding propagation directions of light through the eyepiece waveguide have matching shading. The first k-space diagram, KSD1, shows the k-space representation of input beams incident on the ICG region 1440 from the input device. As previously discussed, the set of input beams are represented by their k-space representations. x and k y The k-space can be represented by a FOV rectangle 1430 whose dimensions correspond to the angular spread of the input beams 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 denotes the propagation angle of the input beam in the x-direction, and k y The component k denotes the propagation angle of the input beam in the y-direction. x =sin(θ x ) in which θ x is the angle formed by the input beam and the yz plane, and k y =sin(θ y ) in which θ y is the angle formed by the input beam and the xz plane. The FOV rectangle in KSD1 is z The fact that it is centered on the -z-axis means that the input light beams represented have propagation angles centered about the input beam propagating in the -z-direction, and therefore 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 FOVs that are off-axis relative to the ±z-directions.)

[0217] The second k-space diagram KSD2 shows the k-space behavior of the ICG region 1440. As previously discussed, the diffraction gratings are connected by associated grating vectors (e.g., G, G -1 ) KSD2 has the G1 lattice vector and G-1 indicates the grating 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 into ±1 diffraction orders. Also in k-space, this means that the ICG is divided into G and G -1 This means copying the FOV rectangle to two new locations by translating it using both of the lattice vectors. In the illustrated instance, the ICG uses the lattice vectors G1, G2, and G3. -1 The size of the diffracted input beam is designed with a period Λ based on the angular frequency ω of the input beam so that the copied FOV rectangle is placed completely within the k-space annulus of the waveguide. Therefore, all of the diffracted input beam enters a guided propagation mode.

[0218] -k x A copy of the FOV rectangle centered on a point on the -x axis (the 9 o'clock position in the k-space annulus) shows that the corresponding diffracted beams have propagation angles that center their propagation components in the plane of the eyepiece waveguide 1400 around the beam in the -x-direction. Thus, all of those beams propagate generally toward the OPE region 1450, bouncing back and forth between the front and back surfaces of the eyepiece waveguide 1400 via TIR. Meanwhile, the +k x A copy of the FOV rectangle centered at a point on the -axis (3 o'clock in the k-space annulus) shows that the corresponding diffracted beams have propagation angles that center their propagation components in the plane of the eyepiece waveguide 1400 around the beam in the +x-direction. Therefore, all of those beams propagate generally toward the right edge of the eyepiece waveguide 1400, reflecting back and forth between the front and back surfaces of the eyepiece waveguide 1400 via TIR. In this particular eyepiece waveguide 1400, those beams are generally lost and do not contribute meaningfully to the projection of the image toward the user's eye.

[0219] KSD2 is the linear lattice vector G1, G -1Higher order lattice vectors that are multiples of k are not shown. The ICG does not diffract the light beam into those diffraction orders because doing so would translate the k-vectors that make up the FOV rectangle beyond the periphery of the k-space disk that defines the allowed k-vectors in this instance. Therefore, higher diffraction orders do not occur in this embodiment.

[0220] The third k-space diagram KSD3 shows the k-space effect of the OPE region 1450. Again, the OPE region 1450 includes a diffraction grating, and therefore the associated grating vectors (e.g., G, G -1 ), which may be equal in magnitude and opposite in direction along the periodic axis of the OPE grating. In this case, the periodic axis of the grating is at a 45° angle to the x-axis. Therefore, the grating vectors (e.g., G, G) of the OPE grating -1 ) is k x -axis. As shown in KSD3, one of the grid vectors defines the FOV rectangle as -k y The FOV rectangle is translated to a new location centered on a point located on the -y-axis (the 6 o'clock position in the k-space annulus). This copy of the FOV rectangle shows that the corresponding diffracted beam has a propagation angle such that its propagation component in the plane of the eyepiece waveguide 1400 is centered around the beam in the -y-direction toward the EPE region 1460. Meanwhile, the other illustrated OPE grating vectors would place the FOV rectangle at a location outside the periphery of the k-space disk. However, k-vectors outside the disk are not allowed, and therefore the OPE grating will not diffract the beam into that diffraction order. The periodic axis of the grating in the OPE region 1450 does not necessarily have to be exactly 45°. For example, as can be seen by inspection of KSD3, the periodic axis can be somewhat 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 annulus. This means that the FOV rectangle does not necessarily have to be at the -k y This would place the FOV rectangle at the 6 o'clock position, not centered within the k-space annulus along the -axis.

[0221] In the illustrated instance, the OPE grating is defined by the grating vectors G, G -1 One of the OPE gratings is designed with a period Λ based on the angular frequency ω of the input beam to place a copied FOV rectangle at the 6 o'clock position, perfectly located within the k-space annulus of the waveguide. Therefore, all of the diffracted input beam remains in a guided propagation mode. Because the k-space distance from the 9 o'clock position to the 6 o'clock position in the k-space annulus, which is the translation performed by the OPE grating, exceeds the distance from the origin of the k-space diagram to the annulus, which is the translation performed by the ICG grating, the OPE grating vector must have a different magnitude than the ICG grating vector. In particular, the OPE grating vector is longer than the ICG grating vector, which means that the OPE grating therefore has a shorter period Λ than the ICG grating.

[0222] A fourth k-space diagram KSD4 shows the k-space effect of the EPE region 1460. Again, the EPE region 1460 includes a diffraction grating and therefore has associated grating vectors (e.g., G, G -1 ), which are equal in magnitude and opposite in direction along the periodic axis of the EPE grating. In this case, the periodic axis of the grating is along the y-axis of the eyepiece waveguide 1400. Therefore, the grating vectors (e.g., G, G) of the EPE grating -1 ) is ±k y-direction. As shown in KSD4, one of the grating vectors translates the FOV rectangle to a new location centered on the origin of the k-space diagram. This copy of the FOV rectangle indicates that the corresponding diffracted beam has a propagation angle whose propagation component in the plane of the eyepiece waveguide 1400 is centered around the beam in the +z-direction toward the user's eye. Meanwhile, the other first-order EPE grating vector places the FOV rectangle at a location outside the periphery of the k-space disk; therefore, the EPE grating will not diffract the beam into that diffraction order. However, one of the second-order EPE grating vectors will translate the FOV rectangle to the 12 o'clock location in the k-space annulus. Thus, the EPE grating may diffract a portion of the light into one of the second diffraction orders. The second-order diffraction direction may correspond to a guided propagation direction along the +y-direction, which is typically an undesirable effect. For example, second-order diffraction can result in visual artifacts when the EPE grating is perturbed and introduces optical power, as discussed below, resulting in flare or smear effects in the image presented to the user.

[0223] In the illustrated instance, the EPE grating is defined by grating vectors G, G -1 One of the EPE gratings is designed with a period Λ based on the angular frequency ω of the input beam to place the copied FOV rectangle completely inside the k-space disk of the waveguide. Therefore, all beams diffracted by the EPE grating are no longer guided propagation modes and therefore exit the eyepiece waveguide 1400. Furthermore, because the EPE grating translates the FOV rectangle back to the origin of the k-space diagram (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 grating has the same period Λ as the ICG because both of these gratings translate the FOV rectangle by the same k-space distance. However, this is not a requirement. The k of the FOV rectangle y The dimension is the k of the k-space ring at the 6 o'clock position. y If the FOV rectangle is less than the size of the ring, the different k yThere can be a range of possible six o'clock locations, and therefore there can be numerous engineering options for the EPE grid vector, and therefore the OPE vector, to place the FOV rectangle at a location within the k-space annulus and / or near the origin of the k-space diagram.

[0224] In some embodiments, the lines of the EPE grating may be slightly curved to impart optical power to the output beam exiting the EPE region 1460. For example, the lines of the grating in the EPE region 1460 can be bent in the plane of the waveguide toward the OPE region to impart negative optical power. This can be used to make the output beam follow a diverging path, as shown in FIG. 12B , for example. This causes the projected image to appear at a depth plane closer to 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 grating vectors pointing in slightly different directions, depending on the curvature of the grating lines in 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, causes the sets of output beams corresponding to each translated FOV rectangle to be centered around different propagation angles, which in turn creates the 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 as 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 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 incident on the ICG at the most oblique angles from the corners of the image in the input plane (see FIGS. 12A and 12B). Because the propagation angles of these input beams are the most extreme of all in 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 defining four diffracted beams from the ICG region 1440, corresponding to the four corners of the input image. In particular, rays near the top of the OPE region 1450 define a diffracted beam (i.e., a k-vector located at the upper right corner of the FOV rectangle) corresponding to the input beam incident on the ICG region 1440 at the steepest propagation angle, pointing upward and away from the OPE region. Also, rays near the bottom of the OPE region 1450 define a diffracted beam (i.e., a k-vector located at the lower right corner of the FOV rectangle) corresponding to the input beam incident on the ICG region 1450 at the steepest propagation angle, pointing downward and away from the OPE region. These two beams define the spread of diffracted beams from the ICG region 1440. To create and project replicated instances of these two beams and all others between them toward the user's eyes, the top and bottom 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-vector of the beam diffracting from the ICG region 1440 towards the OPE region 1450. The arrow in KSD2 indicates the propagation angle of the beam, which corresponds to the k-vector located in 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 evident from the k-vectors in the third k-space diagram KSD3. As evident from KSD3, the left and right corner k-vectors of the FOV rectangle define the extent of the propagation path the beam follows while propagating from the OPE region 1450 toward the EPE region 1460. Using these propagation angles, by tracing backward from the portion of the EPE region 1460 located farthest from the OPE region 1450 (i.e., the lower corner of the EPE region), the origins 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 right corner k-vectors can be determined. These origins of those rays can be used to determine the remaining boundaries of the OPE region 1450. For example, to direct a 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. Therefore, the propagation path with that angle can be used to define the left boundary of the OPE region 1450. Similarly, to direct a 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. Therefore, 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 , for the illustrated eyepiece waveguide 1400, the EPE region 1460 is located in the −x and −y directions from the ICG region 1440. Also, some of the diffracted beams diverge from the ICG region 1440 along paths in those same directions. To prevent these diffracted beams from initially entering the EPE region before propagating through the OPE region 1450, the ICG region 1440 may be located far enough away from the EPE region in the +y direction so that the divergence of the diffracted beams does not intersect with the EPE region 1460. This results in a large gap between the lower boundary of the OPE region 1450 and the upper boundary of the EPE region 1460. In some embodiments, it may be desirable to reduce the size of the eyepiece waveguide by eliminating or reducing this gap. FIG. 15A illustrates an example embodiment that accomplishes these goals.

[0230] 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 is parallel to the upper boundary of the EPE region 1560. In fact, the OPE region 1550 and the EPE region 1560 may actually share a boundary. 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 in the eyepiece waveguide embodiment shown in FIG. 14A.

[0231] To accommodate the tilted orientation of the OPE region 1550, the ICG region 1540 can be modified so 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 so 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 can be positioned near the shared boundary of the OPE region 1550 and the EPE region 1560, but such that no portion of the ICG region extends beyond that shared boundary in the -y-direction. The effect of the ICG region 1540 can be seen in the k-space diagram shown in FIG. 15B.

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

[0233] The second k-space diagram KSD2 shows the effect 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 grating vector associated with the ICG region 1540. In this embodiment, the grating lines in the ICG region 1540 are oriented with a periodicity axis that has a component in the +y-direction. This means that the grating vector associated with the ICG 1540 is also oriented in the +k y +k means that it has a component in the - direction. y The magnitude of this component in the - direction is k yThe width of the FOV rectangle in the -k direction may be greater than or equal to half the width of the FOV rectangle in the -k 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 will be in the -k direction. y -direction. Therefore, none of the diffracted beams will travel downward from the ICG region 1540 toward the EPE region 1560. Also, therefore, none of the diffracted beams will be incident on the EPE region 1560 prior to passing through the OPE region 1550.

[0234] A third k-space diagram, KSD3, shows the effect of OPE region 1550 on the diffracted beam from ICG region 1540. As shown, the diffraction grating of OPE region 1550 can be oriented to redirect the beam of light at an angle corresponding to a translated FOV rectangle to a position slightly displaced from the 6 o'clock position in the k-space ring. For example, the translated FOV rectangle in KSD3 can be displaced from the 6 o'clock position in the k-space ring by the same angle as the translated FOV rectangle in KSD2 is displaced from the 9 o'clock position. In other words, the translated FOV rectangle in KSD3 can be separated by 90° from the translated FOV rectangle in KSD2. 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 one another.

[0235] The translated FOV rectangle in KSD3 is -k xBecause the OPE region 1550 is centered around a k-vector having a component in the -x-direction, the beam of light from the OPE region 1550 generally travels toward 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 portion of the light beam from the tip portion 1555 of the OPE region 1550 will not intersect with the EPE region 1560. Because the tip portion 1555 of the OPE region 1550 may contribute a relatively small portion of the light to the EPE region 1560, the size advantage of eliminating the upper tip 1555 may outweigh any optical disadvantages. In some embodiments, the waveguide eyepiece 1500 can therefore be made even more compact by eliminating 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. Because 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 in the EPE region 1560 is also somewhat different. For example, the orientation of the grating lines of the diffraction grating in the EPE region 1560 is such that the associated grating vector is +k x -direction, and can be tilted so that the OPE region 1550 does not need to extend beyond the left edge of the EPE region 1560 (see the discussion of 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 in 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 toward the user's eye using the same propagation angle as its corresponding input beam, as previously described herein (i.e., the FOV rectangle representing the output beam is co-located in the k-space diagram with the FOV rectangle representing the input beam).

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

[0238] Figure 15D is a schematic diagram of a first occurrence of interaction between an input beam and the OPE region 1550 of the eyepiece waveguide embodiment shown in Figure 15A. The OPE region 1550 of the eyepiece waveguide 1500 includes a diffraction grating, consisting of parallel grating lines repeated in a direction of periodicity. The direction of periodicity determines the direction of the grating vector associated with the diffraction grating. In this instance, the grating vector with the double arrow in Figure 15C illustrates the effect of the OPE region 1550 and points along the direction of periodicity of the grating lines shown in Figures 15D-15F.

[0239] FIG. 15D shows an input beam entering the OPE region 1550 from the ICG region 1540. The input beam is shown propagating in a direction corresponding to the center point of the FOV rectangle, i.e., the k-vector, located near the 9 o'clock position of the k-space ring in FIG. 15C. As shown, the first occurrence of interaction between the input beam and the OPE region 1550 results in two diffracted output beams. That is, a portion of the input beam's optical power simply reflects off the top or bottom surface of the eyepiece waveguide 1500 as output 1 and continues in the same xy direction as the input beam (i.e., zeroth-order diffraction), and a portion of the input beam's optical power diffracts downward to the first order (e.g., by the first-order grating vector G1 of the OPE region) as output 2. The output 2 beam is shown propagating in a direction corresponding to the center point of the FOV rectangle, i.e., the k-vector, located near the 6 o'clock position of the k-space ring in FIG. 15C. After this first occurrence of interaction, the Output 1 and Output 2 beams have different propagation angles, but they both still propagate within the OPE region 1550 and may therefore have additional interactions with the OPE region, as shown in Figures 15E and 15F. Although not shown, other input beams entering the OPE region 1550 with different propagation angles will behave similarly, but with slightly different input and output angles.

[0240] Figure 15E is a schematic diagram of a second occurrence of interaction between the input beam and the OPE region 1550 of the eyepiece waveguide embodiment shown in Figure 15A. The beams associated with the first occurrence of interaction are shown using dashed lines, while the beams associated with the second occurrence of interaction are shown using solid lines. As shown in Figure 15E, the output beams from the first occurrence of interaction, i.e., Output 1 and Output 2, respectively, may now undergo interactions with the OPE region 1550 similar to those that occurred in the first occurrence. That is, a portion of the optical power from the Output 1 beam from Figure 15D simply continues in the same xy direction (i.e., zeroth order diffraction), while another portion of the optical power of that beam interacts with the grating and is redirected downward (e.g., by the first order grating vector G1 of the OPE region). Similarly, a portion of the optical power from the Output 2 beam from FIG. 15D simply continues downward toward the EPE region 1560 (i.e., 0th order diffraction), while another portion of the optical power of that beam interacts with the grating and is generally diffracted in the −x-direction (e.g., the negative first order grating vector G of the OPE region). -1 ), continues propagating further into the OPE region 1550 in the same direction as the initial input beam.

[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 intersect. The optical paths followed by each of these beams to arrive at the interference node 1556 are substantially the same length. Therefore, beams exiting the interference node 1556 propagating in the same direction may have the same or similar phase and may therefore undergo constructive or destructive wave interference with each other. This may result in image artifacts, which are discussed below.

[0242] FIG. 15F is a schematic diagram of a third occurrence of interaction between the input beams and the OPE region 1550 of the eyepiece waveguide embodiment shown in FIG. 15A. The beams associated with the first and second occurrences of interaction are shown using dashed lines, while the beams associated with the third occurrence of interaction are shown using solid lines. As shown in FIG. 15F, the output beams resulting from the second occurrence of interaction may again each undergo an interaction with the OPE region 1550 similar to that which occurred in the previous occurrence. Some of the optical power of those beams continues in the same direction (i.e., zeroth order diffraction), while other portions of the optical power of those beams diverge, some generally in the -x-direction and some generally in the -y-direction (i.e., relative to the first order grating vectors G and G of the OPE region). -1 ) and are redirected. Generally, all beams propagating in the -x-direction are in a state represented by the FOV rectangle located near the 9 o'clock position in the k-space annulus of the k-space diagram in FIG. 15C, while all 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 FIG. 15C, for an OPE region 1550 consisting of a 1D periodic grating, for any given input beam, replica beams of light corresponding to that input beam travel in only two directions within the OPE region (although the two directions will be different for different input beams entering the OPE region at different propagation angles).

[0243] A third occurrence of interaction with the OPE region results in the creation of additional interference nodes 1556, where beams with the same or similar optical path lengths intersect with each other, potentially resulting in constructive or destructive wave interference. Each node 1556 acts as a light source emitted toward the EPE region 1560. In the case of an OPE region consisting of a diffraction grating with 1D periodicity, the layout of these nodes 1556 forms a uniform checkerboard pattern, which may therefore result in image artifacts, as shown in FIG. 15G.

[0244] FIG. 15G is a schematic diagram illustrating how a single input beam 1545 from the ICG region 1540 is replicated by the OPE region 1550 and redirected as multiple beams 1565 toward the EPE region 1560. Each of the replicate beams 1565, shown propagating toward or within the EPE region 1560, originates from one of the interference nodes 1556. These interference nodes have an ordered distribution and act as a sparsely spaced, periodic array of sources. Due to the ordered distribution of the interference nodes 1556, the replicate beams 1565 illuminating the EPE region are all separated by the same spacing, but the beams may have non-monotonic varying intensities. As a result, the replicate light beams 1565 from the OPE region 1550 may illuminate the EPE region 1560 with a relatively sparsely spaced, non-uniform distribution. In some embodiments, it may be advantageous if the replicate light beams illuminating the EPE region of the eyepiece waveguide could be more uniformly distributed. FIG. 16 illustrates such an embodiment. Exemplary AR Eyepiece Waveguide with Multidirectional Pupil Expander

[0245] FIG. 16A illustrates an example eyepiece waveguide 1600 that has a multidirectional 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. Diffracted beams from the ICG region 1640 propagate toward and through the MPE region 1650, which replaces the OPE region. Finally, the MPE region 1650 diffracts the beams of light toward the EPE region 1660, where they are outcoupled toward 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 in the eyepiece waveguide 1500 described with reference to FIGS. 15A-15G. However, MPE region 1650 differs significantly from OPE region 1550 in that it diffracts light in more directions. This feature advantageously reduces the periodic uniformity in the distribution of the light beam within EPE region 1660, which in turn allows the EPE region to be more uniformly illuminated.

[0246] The MPE region 1650 is composed of diffractive features that exhibit periodicity in multiple directions. The MPE region 1650 may also be composed of an array of scattering features arranged in a 2D grid pattern. Individual scattering features can be, for example, depressions or protrusions of any shape. The 2D array of scattering features has an associated grating vector derived from the reciprocal grating pattern of the 2D grid pattern. As an example, the MPE region 1650 can be a 2D periodic diffraction grating composed of intersecting gratings with grating lines that repeat along two or more distinct directions of periodicity. This can be accomplished by superimposing two 1D gratings with different directions of periodicity.

[0247] Figure 16B illustrates a portion of an example 2D periodic grating, along with its associated grating vectors, that may be used within the MPE region 1650 shown in Figure 16A. The 2D periodic grating 1650 can be a spatial checkerboard of diffractive features whose direction of periodicity is illustrated by the vectors u and v. Such a 2D periodic grating is associated with a grating vector. Two primitive grating vectors, G and H, corresponding to the directions of periodicity, u and v, are mathematically defined by: [ka] Mathematically, vectors u and v define a spatial lattice, and G and H correspond to the elementary dual, or reciprocal, lattice vectors. Note that G is orthogonal to u and H is orthogonal to v. However, u is not necessarily parallel to H, and v is not necessarily parallel to G.

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

[0249] Any 2D periodic array of diffractive features will have associated grating vectors that correspond to the overall reciprocal grating pattern and point in directions determined by integer linear combinations (superpositions) of the elementary grating vectors G and H. In the illustrated embodiment, these superpositions result in additional grating 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. Although FIG. 16B illustrates only the first-order grating vectors and their superpositions associated with a 2D diffraction grating, higher-order grating vectors may also exist.

[0250] As already discussed elsewhere herein, the k-space effect of a grating on the set of light beams that make up an image is to translate the FOV rectangle corresponding to the image using a grating vector associated with the grating. This is illustrated in Figures 16C and 16D for the exemplary 2DMPE grating shown in Figure 16B.

[0251] FIG. 16C is a k-space diagram illustrating the k-space effect 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 annulus. This is the location of the FOV rectangle after the ICG region 1640 couples the input beams into the eyepiece waveguide 1600 and redirects them toward the MPE region 1650. FIG. 16C shows how the 2D grid in the MPE region 1650 translates the FOV rectangle using the grid vectors shown in FIG. 16B. Because there are eight grid vectors (G, H, -G, -H, H+G, HG, GH, 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 perimeter of the k-space diagram. These are illustrated using unshaded FOV rectangles. Because k-vectors outside the boundaries 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 a new position within the boundaries of the k-space diagram. One of these locations is near the 6 o'clock position in the k-space ring, and the other is near the 2 o'clock position. Because the k-vectors at these locations are allowed and result in guided propagation modes, the FOV rectangles at these locations are shaded to indicate that the beam of light is diffracted into those two states. Therefore, the refractive power of a beam of light entering the MPE region 1650 with a propagation angle indicated by the FOV rectangle located near the 9 o'clock position on 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 effect of the MPE region 1650 of the eyepiece waveguide 1600 shown in FIG. 16A. This particular k-space diagram illustrates the effect of the MPE region 1650 on beams of light whose propagation states are illustrated by the FOV rectangle located near the 2 o'clock position on the k-space ring. Again, the 2D diffraction grating within the MPE region 1650 attempts to diffract these beams of light into diffraction orders defined by its eight associated grating vectors. As shown, six of the grating vectors would translate the FOV rectangle to positions outside the boundaries of the k-space diagram. Therefore, those diffraction orders do not occur. These positions are illustrated using unshaded FOV rectangles. However, two of the grating vectors (i.e., H and HG) translate the FOV rectangle to positions within the boundaries of the k-space diagram. These are illustrated by the shaded FOV rectangles located near the 9 o'clock and 6 o'clock positions on the k-space ring. Thus, the 2D diffraction grating in MPE region 1650 partially diffracts the refractive power of a beam propagating in the direction indicated by the FOV rectangle located near the 2 o'clock position of the k-space annulus into both of the states indicated 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 effect of MPE region 1650 on a beam of light traveling with a propagation angle indicated by the FOV rectangle located near the 6 o'clock position on the k-space ring. The k-space diagram would show that the 2D periodic grating within MPE region 1650 partially diffracts the refractive power of those beams both to the states indicated by the two shaded FOV rectangles located near the 9 o'clock and 2 o'clock positions on the k-space ring.

[0254] Figure 16E is a k-space diagram illustrating the k-space behavior of the eyepiece waveguide 1600 shown in Figure 16A. As previously mentioned, the eyepiece waveguide 1600 can receive input beams of light that propagate generally in the -z-direction and that are incident on the ICG region 1640 of the waveguide 1600 from an external source. These input beams are located at the k-space origin at the origin of the k-space diagram. z The ICG region 1640 then diffracts the input beams such that they have propagation angles centered around the propagation direction corresponding to the center point of the FOV rectangle, which is located near the 9 o'clock position of the k-space annulus.

[0255] The guided beams enter MPE region 1650, where they can have multiple interactions. During each interaction, a portion of the beam's respective optical power can undergo zero-order diffraction and continue to propagate in the same direction through MPE region 1650. In the first interaction, for example, this zero-order diffraction corresponds to that portion of the beam's optical power that remains as indicated by the FOV rectangle located near the 9 o'clock position of the k-space ring. Another portion of the beam's optical power can be diffracted in a new direction. Again, in the first interaction, this creates individual diffracted beams with propagation angles centered around a 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 may undergo additional interactions, resulting in portions of the beam's optical power being diffracted to zero orders, continuing in the same direction, or being diffracted in new directions, respectively. This results in a set of spatially dispersed diffracted beams with propagation angles centered around each of the propagation directions indicated by the center points of the FOV rectangles in the k-space annulus shown in FIG. 16E. This behavior is represented by the double-headed arrows between each pair of FOV rectangles in the k-space annulus.

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

[0258] There are advantages associated with MPE region 1650 having three allowable propagation directions per input beam, as opposed to the two allowable propagation directions of OPE region 1550. These advantages are discussed further below, but suffice it to say for now that the increased number of propagation directions within MPE region 1650 may result in a more complex distribution of interference nodes within MPE region 1650, which in turn may improve the uniformity of illumination within EPE region 1660.

[0259] It should be understood that FIG. 16E illustrates the k-space behavior of one exemplary embodiment of the MPE region 1650. In other embodiments, the MPE region 1650 can be designed so that each input beam of light can be diffracted in more than three directions within the MPE region. For example, in some embodiments, the MPE region 1650 may be designed to allow diffraction of each input beam of light in four, five, six, seven, eight, etc. directions. As previously discussed, the diffractive features within the MPE region 1650 can be designed to provide grating vectors that copy the FOV rectangle to locations within the k-space annulus corresponding to the selected diffraction direction. Additionally, the diffractive features within the MPE region 1650 can be designed with a period corresponding to the magnitude of the grating vector, which results in these copies of the FOV rectangle being entirely within the k-space annulus (and other attempted copies of the FOV rectangle being entirely outside the periphery 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, diffractive features within the MPE region 1650 will need to be designed to provide grating vectors for making those angular transitions within the k-space annulus. Such grating vectors will be relatively short compared to the size of the k-space annulus due to the smaller angular separation. This may make it more likely that the superposition of elementary MPE grating vectors will create copies of the FOV rectangle that are only partially within the k-space annulus, which may result in a loss of image information (unless done carefully, as discussed further herein). In addition, if the angular separation between any pair of allowed propagation directions within the MPE region 1650 becomes too small, the resulting relatively short grating vectors may also make it more likely that the grating vector superposition will create copies of the FOV rectangle that are partially inside the central disk of the k-space diagram. This may be undesirable as it may result in light being coupled out of the eyepiece waveguide 1600 towards the user's eye from locations outside the designated EPE area 1660.

[0261] Various design guidelines may be followed when determining the allowable propagation directions within the MPE region 1650. For example, an allowable propagation direction may be selected such that one corresponds to the direction from the ICG region 1640 to the MPE region 1650. Additionally, an allowable propagation direction may 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 with the EPE region 1660. This ensures that a duplicate beam of light corresponding to each input beam enters the EPE region 1660 with the same propagation angle. Additionally, the allowable propagation directions inside the MPE region 1650 may be selected such that the FOV rectangles do not overlap. Overlapping FOV rectangles may result in a blending of image information from different image points, which may cause an afterimage image.

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

[0263] The MPE region 1650 can contain many sub-1 μm features. Furthermore, upon each interaction with the MPE region, an input approximately 1 mm diameter beam will be split in the TIR into three beams (of the same diameter but with a fraction of the original optical power of the input beam) propagating in three different directions. One direction corresponds to the zeroth diffraction order 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 interaction between the input beam and the MPE region 1650 results in three beams. That is, a portion of the optical power of the input beam simply reflects off the top or bottom surface of eyepiece waveguide 1600 as output 1 and continues in the same x and y direction as the input beam (i.e., zeroth order diffraction), a portion of the optical power of the input beam interacts with the 2D grating in MPE region 1650 and is diffracted downward as output 2, and a portion of the optical power of the input beam interacts with the grating and is diffracted upward and to the right as output 3. The output 2 beam is shown propagating in a direction corresponding to the center point, i.e., k-vector, of the FOV rectangle located near the 6 o'clock position of the k-space annulus in FIG. 16E, while the output 3 beam is shown propagating in a direction corresponding to the center point, i.e., k-vector, of the FOV rectangle located near the 2 o'clock position. After this first occurrence of interaction, the Output 1, Output 2, and Output 3 beams have different propagation angles, as shown in Figures 16G-16I, but they all still propagate within MPE region 1650 and may therefore have additional interactions with the MPE region. Although not shown, other input beams entering MPE region 1650 with different propagation angles will behave similarly, but with slightly different input and output angles.

[0264] FIG. 16G is a schematic diagram of a second occurrence of interaction between an input beam and the MPE region 1650 of the eyepiece waveguide embodiment shown in FIG. 16A. The beams associated with the first occurrence of interaction are shown using dashed lines, while the beams associated with the second occurrence of interaction are shown using solid lines. As shown in FIG. 16G, the output beams, Output 1, Output 2, and Output 3, from the first occurrence of interaction may now each undergo an interaction with the MPE region 1650 similar to that which occurred in the previous occurrence. That is, a portion of the optical power of the Output 1 beam from FIG. 16F simply continues in the same x and y directions, while another portion of that beam's optical power 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 that beam's optical power 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 optical power of the Output 2 beam from FIG. 16F simply continues toward EPE region 1660, while another portion of that beam's optical power interacts with the grating and is diffracted in the direction indicated by the FOV rectangle located near the 9 o'clock position, and another portion of that beam's optical power interacts with the grating and is diffracted in the direction corresponding to the FOV rectangle located near the 2 o'clock position. Furthermore, a portion of the optical power of the Output 3 beam from FIG. 16F simply continues in the direction indicated by the FOV rectangle located near the 2 o'clock position, while another portion of that beam's optical power interacts with the grating and is diffracted in the direction indicated by the FOV rectangle located near the 9 o'clock position, and another portion of that beam's optical power interacts with the grating and is diffracted in the 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 interaction between an 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 interaction are shown using dashed lines, while the beams associated with the third occurrence of interaction are shown using solid lines. As shown in Figure 16H, the output beams resulting from the second occurrence of interaction may again each undergo an interaction with the MPE region 1650 similar to that which occurred in the previous occurrence.

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

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

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

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

[0270] Figure 16L shows an eyepiece waveguide 1600 on the right that includes an MPE region 1650 with a 2D periodic diffraction grating. As can be seen, the MPE region 1650 provides more uniform illumination to the EPE region 1660. 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 eyepiece waveguide 1500 on the left. From the simulated image on the right, it is clear that the eyepiece waveguide 1600 using the MPE region 1650 achieves smoother and more uniformly distributed output light. In contrast, the image on the left, which is the simulated output of the eyepiece waveguide 1500 with the OPE region 1550, has visible high-spatial frequency striations that result from a sparsely spaced, ordered set of replicated light beams illuminating 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 top row of graphs in Figure 16M illustrates the performance of the eyepiece waveguide 1500 shown in Figure 15A. A graph of a horizontal cross-section of an image projected from this eyepiece waveguide shows relatively high spatial frequency variations, which are visible as striations in the simulated output image shown in Figure 16L. Figure 16M also shows that the eyepiece waveguide 1500 has an eyebox 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 dot. This shows that the eyepiece waveguide 1500 is very sharp, with only 2.5 to 5 arcmin of blur.

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

[0273] The bottom row of Figure 16M illustrates the performance of the eyepiece waveguide 1600 with the MPE region 1650. The cross section of the projected image for this waveguide shows much less high-spatial frequency variation. While low-frequency spatial variation is still present, this can be much easier to correct via software than high-spatial frequency variation. The eyebox efficiency of this eyepiece waveguide is slightly lower at 0.9%. 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 in the annulus of the k-space diagram shown in Figure 16E. Due to the macroscopic layout of the eyepiece waveguide 1600, light exiting the MPE region 1650 with this propagation direction never enters the EPE region and is therefore not projected toward the user's eye. Instead, it is lost from the edges of the waveguide 1600. However, this light loss results in only a relatively small reduction in eyebox efficiency. On the other hand, the point spread function for the eyepiece waveguide 1600 shows that it is very sharp, with only 2.5 to 5 arc minutes of blur.

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

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

[0276] FIG. 17B is a k-space diagram illustrating the k-space effect 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 annulus. This is the location of the FOV rectangle after the ICG region 1740 couples the input beams into the eyepiece waveguide 1700 and redirects them toward the MPE region 1750. FIG. 17B shows how the 2D grid in the MPE region 1750 translates the FOV rectangle using the grid vectors shown in FIG. 17A. Because there are eight grid 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 perimeter of the k-space diagram. These locations are illustrated using the unshaded FOV rectangle. Because k-vectors outside the perimeter of the k-space diagram are not allowed, none of these five lattice vectors result in diffraction. However, there are three lattice vectors (i.e., -H, -G, and -(H+G)) that result in the translation of the FOV rectangle to a new location within the boundary of the k-space diagram. One of these locations is near the 6 o'clock position in the k-space annulus, another is near the 12 o'clock position, and the last is near the 3 o'clock position. Because the k-vectors at these locations are allowed and result in guided propagation modes, the FOV rectangle at these locations is shaded to indicate that the beam of light is diffracted into these three states. Thus, a beam of light entering MPE region 1750 with a propagation angle indicated by the FOV rectangle located near the 9 o'clock position of the k-space ring will be 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 effect of MPE region 1750 on beams of light traveling with propagation angles indicated by the FOV rectangles located near the 12 o'clock, 3 o'clock, and 6 o'clock positions on the k-space ring. These k-space diagrams would show that the 2D diffraction grating within 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] 17C is a k-space diagram illustrating the k-space behavior of the eyepiece waveguide 1700. The eyepiece waveguide 1700 can receive input beams of light that propagate generally in the -z-direction and that are incident on the ICG region 1740 of the waveguide 1700 from an external source. These input beams are reflected by the k-space at the origin of the k-space diagram. z The ICG region 1740 then diffracts the input beams such that they have propagation angles centered around the propagation direction, corresponding to the center point of the FOV rectangle, which is located near the 9 o'clock position of the k-space annulus.

[0279] The diffracted beams enter MPE region 1750, where they may have multiple interactions. During each interaction, a portion of the beams' respective optical power continues to propagate in the same direction through MPE region 1750. In the first interaction, for example, this would correspond to that portion of the beams' optical power that remains as indicated by the FOV rectangle located near the 9 o'clock position. Other portions of the beams' optical power can be diffracted in new directions. Again, in the first interaction, this creates individual diffracted beams with propagation angles centered around the propagation direction corresponding to the center points of the FOV rectangles located near the 12 o'clock position, the 3 o'clock position, and the 6 o'clock position on the k-space annulus.

[0280] After each interaction, the diffracted beam, still remaining within the MPE region 1750, may undergo additional interactions. Each of these additional interactions results in a portion of the beam's refractive power being diffracted in a new direction while a portion of the beam's refractive power is diffracted in a zeroth order and continues in the same direction. This results in a set of spatially dispersed diffracted beams with propagation angles centered around each of the propagation directions indicated by the center points of the FOV rectangles in the k-space annulus shown in FIG. 17C . This is represented by the double-headed arrow between each pair of FOV rectangles in the k-space annulus. 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 in the k-space annulus to any other of these propagation states.

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

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

[0283] The MPE region 1750 can contain many sub-1 μm features. Also, upon each interaction with the MPE region, an approximately 1 mm diameter beam will be split into four beams (of the same diameter but with a fraction of the original optical power of the input beam) propagating in four different directions in the TIR. One direction corresponds to the zeroth diffraction order and is the original angle in the plane of the waveguide. The other three directions depend on the grating vectors G and H of the MPE region 1750. As shown, the first occurrence of an interaction between the input beam and the MPE region 1750 results in four beams. That is, a portion of the optical power of the input beam simply reflects off the top or bottom surface of the eyepiece waveguide 1700 and continues in the same x and y direction as the input beam (i.e., zeroth order diffraction) as output 1, a portion of the optical power of the input beam interacts with the grating and is diffracted downward as output 2, a portion of the optical power of the input beam interacts with the grating and is diffracted upward as output 3, and a portion of the optical power of the input beam interacts with the grating and is diffracted to the right as output 4. The output 2 beam is shown propagating in a direction corresponding to the center point of the FOV rectangle located near the 6 o'clock position of the k-space annulus in FIG. 17C , i.e., the k-vector, while the output 3 beam is shown propagating in a direction corresponding to the center point of the FOV rectangle located near the 12 o'clock position, i.e., the k-vector, and the output 4 beam is shown propagating in a direction corresponding to the center point of the FOV rectangle located near the 3 o'clock position, i.e., the k-vector. After this first occurrence of interaction, the Output 1, Output 2, Output 3, and Output 4 beams have different propagation angles, as shown in Figures 17E-17G, but they all still propagate within MPE region 1750 and may therefore have additional interactions with the MPE region. Although not shown, other input beams entering 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 interaction between the input beam and the MPE region 1750 of the eyepiece waveguide 1700. The beams associated with the first occurrence of interaction are shown using dashed lines, while the beams associated with the second occurrence of interaction are shown using solid lines. As shown in FIG. 17D, the output beams from the first occurrence of interaction, i.e., Output 1, Output 2, Output 3, and Output 4, each now undergo interactions with the MPE region 1750 similar to those that occurred in the previous occurrences. That is, a portion of the optical power of the Output 1 beam from FIG. 17D simply continues in the same x and y directions, while another portion of that beam's optical power interacts with the grating and is diffracted in directions corresponding to the FOV rectangles located near the 12 o'clock position, the 3 o'clock position, and the 6 o'clock position. Similarly, a portion of the optical power of the Output 2 beam from FIG. 17D simply continues toward the EPE region 1760, while another portion of that beam's optical power interacts with the grating and is diffracted in the directions indicated by the FOV rectangles located near the 9 o'clock position, the 12 o'clock position, and the 3 o'clock position. Furthermore, a portion of the optical 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 that beam's optical power interacts with the grating and is diffracted in the directions indicated by the FOV rectangles located near the 3 o'clock position, the 6 o'clock position, and the 9 o'clock position. Finally, a portion of the optical 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 that beam's optical power interacts with the grating and is diffracted in the directions indicated by the FOV rectangles located near the 6 o'clock position, the 9 o'clock position, and the 12 o'clock position.

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

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

[0287] In summary, the MPE regions described herein are capable of some or all of the following advantages: They can expand the image pupil in multiple directions at once. They can create a dense, non-periodic array of output pupils. They can reduce interference effects between light paths through the waveguide. MPE-based eyepiece waveguides can achieve improved brightness uniformity with reduced high-frequency striations and high image clarity. 1. Exemplary AR Eyepiece Waveguide with Multiple Distinct Regions for Replicating Input Beams

[0288] FIG. 18A illustrates an exemplary eyepiece waveguide 1800 with an ICG region 1840, two orthogonal pupil expander (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, the OPE regions 1850a, 1850b, and the EPE region 1860 of the eyepiece waveguide 1800 include various diffractive features that couple an input beam into the eyepiece waveguide 1800, propagate through guided modes, replicate the beam in a spatially dispersed manner, and cause the replicated beam to exit the eyepiece waveguide and project toward the user's eye. In particular, the eyepiece waveguide 1800 includes multiple distinct and / or non-contiguous regions for replicating the input beam. The replica beams from these distinct regions can be recombined in a common exit pupil region.

[0289] The eyepiece waveguide 1800 shown in FIG. 18A is similar to the eyepiece waveguide 1400 shown in FIG. 14A , but includes two OPE regions 1850 a, 1850 b instead of one. Recall that the ICG region 1440 in the eyepiece waveguide 1400 diffracted the input beam into +1 and −1 diffraction orders, but the beam in one of these diffraction orders propagated away from the OPE region 1450 and was ultimately lost from the eyepiece waveguide. Thus, some of the light from the input beam was lost. The eyepiece waveguide 1800 shown in FIG. 18A corrects for this by including two OPE regions 1850 a, 1850 b, 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 ICG region 1840 is similar to that described with respect to ICG region 1440 in Figures 14A and 14B. The same k-space diagram KSD1 shown in Figure 14B is also an illustration of the FOV rectangle corresponding to the set of input beams incident on ICG region 1840 in Figure 18A. That is, before the input beams are incident on ICG region 1840, the FOV rectangle is centered at the origin of the k-space diagram.

[0291] The k-space diagram KSD2 in Figure 18A illustrates the effect in k-space of the ICG region 1840. That is, as discussed with respect to the corresponding k-space diagram in Figure 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 in the k-space annulus, respectively. The translated FOV rectangle located at the 3 o'clock position represents the diffracted beam propagating toward the right OPE region 1850b, while the translated FOV rectangle located at the 9 o'clock position represents the diffracted beam propagating toward the left OPE region 1850a.

[0292] The effect of the left OPE region 1850a is also similar to that described for the OPE region 1450 in Figures 14A and 14B. k-space diagram KSD3a illustrates the k-space effect 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 in the k-space annulus. The FOV rectangle located at the 6 o'clock position represents the diffracted beam propagating in the -y-direction toward the EPE region 1860.

[0293] The operation of the right OPE region 1850b is similar to that of the left OPE region 1850a, except that its associated grating vector is mirrored about a vertical line relative to that of the left OPE region 1850a. This is due to the fact that the lines of the grating in the right OPE region 1850b are mirrored about a vertical line relative to those of the grating in the left OPE region 1850a. As a result of this orientation of the grating lines in the right OPE region 1850b, the effect of this grating in k-space is to translate the FOV rectangle from the 3 o'clock position to the 6 o'clock position in the k-space annulus, as shown in k-space diagram KSD3b. The translated FOVs in KSD3a and KSD3b are co-located at the 6 o'clock position of the k-space annulus. Thus, the refractive power of each input beam is split by ICG region 1840 into +1 and -1 diffraction orders, and although these distinct diffraction orders travel different paths through eyepiece waveguide 1800, they nevertheless arrive at EPE region 1860 with the same propagation angle. This means that the separate diffraction orders of each input beam that follow different propagation paths through eyepiece waveguide 1800 ultimately exit EPE region 1860 with the same angle and therefore represent the same point in the projected image.

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

[0295] Figures 18B and 18C illustrate top views of the EPE region 1860 of the eyepiece waveguide 1800 shown in Figure 18A. The EPE region 1860 is supported directly in front of the user's eye 210. As discussed elsewhere herein (see Figures 12A and 12B), the EPE region 1860 projects a set of replicated output beams, each of which 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 beams 1861 emerging from the EPE region 1860 travel from left to right. In other words, the replicated output beams 1861 have a propagation direction with a component in the +x-direction. The propagation angles of the replicated output beams 1861 result in some of them being more likely to intersect the user's eye 210 than others. In particular, the replicated output beams 1861 emerging from the left portion of the EPE region 1860 are more likely to intersect the user's eye 210 due to the central location of the eye 210 and the left / right propagation of the light beams. These light beams are illustrated using solid lines. On the other hand, the replicated output beams 1861 emerging from the right portion of the EPE region 1860 are more likely to miss the eye 210. These light beams are illustrated using dashed lines.

[0297] 18B also includes a k-space diagram KSD5 illustrating the state of the output beam in k-space after the EPE region has translated the FOV rectangle back to the origin of the diagram. The FOV rectangle is illustrated using two halves, each representing one half of the horizontal field of view of the eyepiece waveguide 1800. The shaded right half 1832 of the FOV rectangle is the +k x 18B. While only one set of replicated output beams 1861 is shown exiting the EPE region 1860, all output beams whose k-vectors fall within the shaded right half 1832 of the FOV rectangle will similarly exit the EPE region with a left / right propagation direction. Therefore, it is true that for all output beams whose k-vectors fall within the shaded right half 1832 of the FOV rectangle, those beams exiting from the left side of the EPE region 1860 will be more likely to intersect with the eye 210 than those beams exiting from the right side of the EPE region.

[0298] FIG. 18C illustrates another set of replicated light beams 1862 emerging from the EPE region 1860 of the eyepiece waveguide 1800. However, in this case, the replicated output beams 1862 emerging from 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. This propagation angle of the replicated output beams 1862 leads to the opposite observation to that derived from FIG. 18B. That is, for right / left propagating output beams 1862, beams emerging from the right portion of the EPE region 1860 (illustrated using solid lines) are more likely to intersect with the eye 210, while those light beams emerging from the left portion of the EPE region (illustrated using dashed lines) are more likely to miss the eye.

[0299] Referring to k-space diagram KSD5 included with Figure 18C, output beams whose k-vectors are within the shaded left half 1831 of the FOV rectangle are those that emerge from the EPE region 1860 with the right / left propagation type shown in Figure 18C. Although the output beams whose k-vectors are within the shaded left half 1831 of the FOV rectangle will all have different propagation angles, they all share the property that beams emerging from the right side of the EPE region 1860 will be more likely to intersect with the eye 210 than output beams emerging from the left side of the EPE region.

[0300] A conclusion that can be drawn from Figures 18B and 18C is that, based on the light beam actually incident on the user's eye 210, one half of the EPE region 1860 primarily contributes to one-half of the horizontal field of view, while the other half of the EPE region primarily contributes to the remaining half of the horizontal field of view. Based on this observation, the field of view that can be projected by the eyepiece waveguide can be extended in at least one dimension beyond the range of propagation angles supported by the eyepiece in guidance mode, since it is not necessary to project the entire FOV rectangle from all portions of the EPE region 1960. This is illustrated in Figure 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 a 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 diffractive 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 rectangles in the k-space diagram in FIG. 18A were constrained to have no dimensions greater than the width of the k-space annulus. This constraint ensured that those FOV rectangles could fit entirely within the k-space annulus at any position around the annulus, and thus all of the beams represented by k-vectors within the FOV rectangle could 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 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 annulus.

[0303] For the particular embodiment illustrated in the k-space diagram of Figure 19, the horizontal dimension of the FOV rectangle is wider than the k-space annulus. The horizontal dimension of the FOV rectangle corresponds to the horizontal spread in propagation angles of the input beam projected into the eyepiece waveguide. Thus, eyepiece waveguide 1900 is illustrated as being compatible with an FOV rectangle having a larger horizontal dimension, which means that the horizontal field of view of the eyepiece waveguide is increased. For an eyepiece waveguide (surrounded by air) with a refractive index of 1.8, the eyepiece waveguide 1800 shown in FIG. 18A can generally achieve an FOV of 45° x 45°, while the eyepiece waveguide 1900 shown in FIG. 19 can achieve an FOV of up to 90° x 45°, although some embodiments of the eyepiece waveguide may be designed for a smaller FOV of approximately 60° x 45° to meet typical design constraints of eyebox volume (it may be advantageous to route a portion of the FOV to both sides of the eyepiece waveguide to provide a properly sized eyebox) and avoid screen-door artifacts resulting from sparsely spaced output beams. While the techniques for extending the field of view of the eyepiece waveguide 1900 are described in the context of an extended horizontal field of view, the same techniques can also be used to extend the vertical field of view of the eyepiece waveguide 1900. Furthermore, in a later embodiment, a similar technique is shown to extend both the horizontal and vertical fields of view of the eyepiece waveguide.

[0304] 19, it can be seen that the illustrated FOV rectangles may not fit entirely within the k-space annulus when positioned at certain locations around the annulus, but may still fit entirely within the annulus when positioned at other locations. For example, if one dimension of the FOV rectangle is greater than the width of the k-space annulus, the FOV rectangle may not fit entirely within the annulus when the FOV rectangle is positioned at or near the axis of the expanded dimension. x The FOV rectangle whose dimensions are greater than the width of the k-space annulus is x -axis (i.e., at or near the 3 o'clock and 9 o'clock positions), it cannot fit entirely within the ring.y The FOV rectangle whose dimensions are greater than the width of the k-space annulus is y When positioned on or near the k-axis (i.e., at or near the 12 o'clock and 6 o'clock positions), such an FOV rectangle may not fit entirely within the k-space annulus. However, when positioned on or near the opposite axis, such an FOV rectangle may still fit entirely within the k-space annulus. x An FOV rectangle whose dimension is greater than the width of the k-space annulus is still considered to be a FOV rectangle whose dimension is greater than the width of the k-space annulus. y -axis (i.e., at or near the 12 o'clock and 6 o'clock positions), it can fit entirely within the ring. y The FOV rectangle whose dimensions are greater than the width of the k-space annulus is x -axis (i.e., at or near the 3 and 9 o'clock positions), it can still fit entirely within the annulus because there is an area within the k-space annulus to accommodate a larger FOV rectangle in the azimuth direction than in the radial direction.

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

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

[0307] Using these observations, the FOV of the eyepiece waveguide can be increased by dividing the FOV rectangle into multiple subportions, using diffractive features to replicate the beams belonging to the multiple subportions of the FOV in a spatially distributed manner, and using diffractive features to reassemble the multiple subportions of the FOV at the exit pupil of the eyepiece waveguide so that the beams corresponding to each subportion of the FOV have the correct propagation angle and recreate the original image. For example, diffractive features can be used to translate each subportion of the FOV rectangle to one or more locations in k-space so that they ultimately have the same relative position with respect to the other subportions of the FOV rectangle as they were in the original image.

[0308] In some embodiments, multiple sub-portions of the FOV may partially overlap each other (e.g., different pairs of FOV sub-portions may contain portions of the same input beam), as this may help to relax constraints on reassembling the entire FOV at the exit pupil of the waveguide and may help to ensure that all of the beams are 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 effect of an ICG region 1940 on an input beam projected into the eyepiece waveguide 1900. As discussed elsewhere herein, the input beam projected into the eyepiece waveguide 1900 may 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 grid vector. In the case of the ICG region 1840 illustrated in FIG. 18A, the ICG region 1940 translates the location of this FOV rectangle based on its associated grid vectors G1, G -1 was designed to have a dimension equal to the distance from the origin of the k-space diagram to the midpoint of the k-space annulus. This centered the FOV rectangle within the k-space annulus. However, the ICG region 1940 illustrated in FIG. 19 can be designed to have a larger grating vector. Also, as previously discussed, the set of input beams projected into the eyepiece waveguide 1900 can have at least one dimension in k-space that is larger than the width of the k-space annulus.

[0310] In some embodiments, the ICG region 1940 is -1 However, the expanded FOV rectangle can be designed to be translated far enough away from the origin of the k-space diagram so that no part of the expanded FOV rectangle is inside the inner disk of the k-space diagram. For an FOV rectangle whose horizontal dimension is twice as large as the width of the k-space annulus, the ICG1940 grid vectors G1, G2, and G3 can be used to achieve this goal.-1 The size of would need to be approximately equal to the radius of the outer disk of the k-space diagram. On the other hand, for a rectangular FOV whose horizontal dimension is simply slightly larger than the width of the k-space annulus, the grid vectors G, G of the ICG region 1940 would need to be approximately equal to the radius of the outer disk of the k-space diagram. -1 The magnitude of would need to exceed the distance from the origin of the k-space diagram to the midpoint of the k-space annulus. Mathematically, this means: [ka] This gives the following: [ka] (Note: this equation can also be applied to other eyepiece waveguide embodiments described herein, such as those shown in Figures 20-22 and described below.)

[0311] In other words, the present technique for expanding the field of view of the eyepiece waveguide 1900 involves adjusting the grating vectors G, G of the ICG region 1940. -1 means that the field of view is designed to be longer than the embodiment constrained in all dimensions by the range of propagation angles that can fit within the radial dimensions of the k-space annulus of a given eyepiece waveguide. -1 Since the length of ω is increased by decreasing the grating period Λ, this means that the ICG region 1940 has a finer pitch than would conventionally be used for light of a given angular frequency ω, ensuring that the input beam can all 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 grid vectors G1, G -1causes a portion of the translated FOV rectangle to extend beyond the periphery of a larger disk in the k-space diagram after diffraction by ICG region 1940. Because k-vectors outside this disk are not allowed, input beams corresponding to those k-vectors are not diffracted by ICG region 1940. Instead, only input beams corresponding to k-vectors within the shaded portion of the translated FOV rectangle in KSD2 enter guided propagation modes within eyepiece waveguide 1900. Input beams that would diffract into the +1 order with k-vectors that would fall outside the outer disk of the k-space diagram are not allowed to diffract and are therefore lost. Similarly, input beams that would diffract into the -1 order with k-vectors that would fall outside the outer disk of the k-space diagram are not allowed to diffract and are therefore lost. Fortunately, the beams lost from each of these diffraction orders are not identical. This allows the full field of view to be restored in EPE region 1960. Even if neither the truncated FOV rectangle located at the 3 o'clock position nor the truncated FOV rectangle located at the 9 o'clock position of the k-space diagram KSD2 contains the complete set of input beams, when these truncated FOV rectangles are appropriately recombined in the EPE region 1960, the complete set of input beams can be restored.

[0313] K-space diagrams KSD3a and KSD3b illustrate the k-space effects of gratings in left OPE region 1950a and right OPE region 1950b, respectively. As discussed with respect to FIG. 18A, these OPE regions may include gratings 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 gratings in OPE regions 1950a, 1950b may need to be adjusted to accomplish this goal. Specifically, the grating vectors G1, G2 associated with ICG region 1940 -1 can no longer terminate at the midpoints of the k-space annulus at the 3 o'clock and 9 o'clock positions, the magnitude and direction of the grid vectors associated with the OPE region must be such that the FOV rectangle is at some location at the 6 o'clock position (e.g., k yThe OPE regions 1950a, 1950b may need to be adjusted to translate the OPE regions 1950a, 1950b to their original positions (i.e., centered within the k-space annulus in the -direction). These adjustments can be accomplished by modifying the orientation of the grating lines in the OPE regions 1950a, 1950b and / or by changing their grating period Λ compared to the OPE regions in embodiments without the extended FOV.

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

[0315] 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 beams corresponding to the shaded right region of the FOV rectangle are present. 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, k-space diagram KSD4 shows that when two truncated FOV rectangles are superimposed at the 6 o'clock position of the k-space annulus, the unshaded portion of the FOV rectangle is filled, meaning that all of the beams making up the complete FOV of the input image are now present and can be projected out of the eyepiece waveguide 1900 toward the user's eye by the diffraction grating in EPE region 1960. As with the embodiment in FIG. 18A, EPE region 1960 translates the FOV rectangle back to the origin in 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 a manner that maintains the relative positions of the shaded regions in the original FOV rectangle. This ensures that the beams of light in each sub-portion of the FOV have the correct propagation angles to recreate the original image.

[0316] What this means in physical terms is that the eyepiece waveguide 1900 divides the image field into multiple portions. Light beams corresponding to each of these portions of the image field propagate along different paths through the eyepiece waveguide 1900, where they can be replicated by different OPE regions 1950 a, 1950 b in a spatially distributed manner. And finally, the separate portions of the image field are recombined in the EPE region 1960 and projected toward the user's eye.

[0317] In some embodiments, the various gratings of the eyepiece 1900 can be designed so that there is overlap between the subsets of beams provided by the individual OPE regions 1950 a, 1950 b to the EPE region 1960. In other embodiments, however, the gratings can be designed so that each OPE region 1950 a, 1950 b provides a unique subset of beams required to completely recreate the input image. Exemplary AR Eyepiece Waveguide with Extended Field of View and Overlapping MPE and EPE Regions

[0318] While Figure 19 illustrates an embodiment of an eyepiece waveguide with an extended FOV that uses an OPE region to replicate the input beam, other embodiments can advantageously use an MPE region. Figures 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 overlapped by an EPE region 2060. The eyepiece waveguide 2000 can achieve an extended field of view that may be greater than the range of propagation angles that can be supported by guided propagation modes in the thickness direction of the waveguide. The eyepiece waveguide 2000 has a first surface 2000a and a second surface 2000b. As discussed further below, different diffractive features can be formed on or within the opposing surfaces 2000a, 2000b of the eyepiece waveguide 2000. The two surfaces 2000a, 2000b of the eyepiece waveguide 2000 are illustrated in FIG. 20A as displaced relative to one another in the xy plane. However, this is for illustrative purposes only, and it is possible to show different diffractive features formed on or within each surface. It should be understood that first surface 2000a and second surface 2000b are aligned with one another in the xy plane. Additionally, while MPE regions 2050 and EPE regions 2060 are illustrated as being the same size and precisely aligned in the xy plane, in other embodiments they may have somewhat different sizes or may be partially misaligned. In some embodiments, MPE regions 2050 and EPE regions 2060 overlap one another by at least 70%, at least 80%, at least 90%, or at least 95%.

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

[0321] The MPE region 2050 can include multiple diffractive features that exhibit periodicity along multiple axes. The MPE region 2050 may consist of an array of scattering features arranged in a 2D grid pattern. Individual scattering features can be, for example, depressions or protrusions of any shape. The 2D array of scattering features has an associated lattice vector derived from the reciprocal grid pattern of the 2D grid pattern. As one example, the MPE region 2050 can be a 2D diffraction grating consisting of a crossed grid with grating lines that repeat along two or more directions of periodicity. The diffractive features that make up the MPE region 2050 can have relatively low diffraction efficiencies (e.g., 10% or less). As discussed herein, this allows beams of light to be replicated in multiple directions in a spatially dispersed manner as they propagate through the MPE region 2050.

[0322] FIG. 20B illustrates a portion of an example 2D grating, along with its associated grating vector, that may be used within the MPE region 2050 of the eyepiece waveguide 2000. While a crossed grating is illustrated, a 2D periodic grating could instead consist of individual scattering features located, for example, at the intersections of the illustrated grating lines. The 2D grating has a first set of grating lines 2056 that are repeated along a first direction of periodicity. These grating lines 2056 point along the direction of periodicity of the first set of grating lines 2056 and have an associated fundamental grating vector G that has a magnitude equal to 2π / a (where a is the period of the first set of grating lines 2056). The 2D grating shown in FIG. 20B is also associated with harmonics of the first fundamental grating vector G. These include -G and higher harmonics such as 2G, -2G, etc. The 2D grating in the MPE region 2050 also has a second set of grating 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 grating lines 2057 point along the direction of periodicity of the second set of grating lines and have an associated primitive grating vector H with a magnitude equal to 2π / b, where b is the period of the second set of grating lines 2057. The 2D grating shown in FIG. 20B is also associated with harmonics of the second primitive grating vector H. These include -H and higher harmonics such as 2H, -2H, etc. Finally, any 2D array of diffractive features will also have associated grating vectors that point in directions determined by integer linear combinations (superpositions) of the primitive grating vectors G and H. In the illustrated embodiment, these superpositions result in additional grating vectors, which are also shown in FIG. 20B. These include, for example, -G, -H, H+G, H-G, G-H, and -(H+G). Although Figure 20B illustrates only the first-order grating vectors and their superpositions associated with a 2D diffraction grating, higher-order grating vectors may also be present.

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

[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 Figure 20A, the diffraction grating in the ICG region 2040 can be designed to diffract the input beam in that direction. Thus, KSD1 in Figure 20C indicates that the ICG region 2040 diffracts the FOV rectangle from the origin of the k-space diagram to the -k o'clock position in the k-space annulus. y 2000. The image shows a translation to a location on the -y-axis. In this particular position, the wider dimension of the FOV rectangle is oriented azimuthally in the k-space annulus, so that the FOV rectangle fits entirely within the annulus. This means that the beams represented by the FOV rectangle all enter guided propagation modes within the eyepiece waveguide 2000 and propagate generally in the -y-direction toward the MPE region 2050.

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

[0326] FIG. 20D is a k-space diagram KSD2 illustrating a portion of the k-space effect 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 annulus. This is the location of the FOV rectangle after the ICG region 2040 couples the input beams into the eyepiece waveguide 2000 and diffracts them toward the MPE region 2050. FIG. 20D shows how the 2D grating in the MPE region 2050 translates the FOV rectangle using the grating vectors shown in FIG. 20B. Because there are eight grating vectors, the MPE region 2050 attempts to translate the FOV rectangle from the 6 o'clock position in the k-space annulus to eight possible new locations in the k-space diagram. Of these eight possible locations, five are completely outside the perimeter of the k-space diagram. These locations are illustrated using unshaded FOV rectangles. Because k-vectors outside the perimeter of the k-space diagram are disallowed, none of these five lattice vectors result in diffraction. However, there are three lattice vectors (i.e., G, -H, and GH) that result in the translation of the FOV rectangle to a new position, at least partially within the boundaries of the k-space diagram. One of these locations is at the 9 o'clock position in the k-space annulus, another at the 12 o'clock position, and the last at the 3 o'clock position. Because the k-vectors at these locations are allowed and result in guided propagation modes, the FOV rectangle at these locations is shaded to indicate that the beam of light is diffracted into these three states.

[0327] For the 9 o'clock and 3 o'clock positions in the k-space annulus, the translated FOV rectangle is xBecause their dimensions are larger than the width of the annulus, they do not fit completely within the annulus. Therefore, the translated FOV rectangle at these locations is truncated, meaning that beams whose k-vectors are outside the perimeter of the k-space diagram are not steered. This is represented in KSD2 by the unshaded portions of the translated FOV rectangle at the 9 o'clock and 3 o'clock positions. This means that the sets of beams diverging through MPE region 2050 in the +x and -x directions, respectively, do not each contain all of the original set of input beams. The set of beams propagating through MPE region 2050 in the +x direction misses the beams corresponding to the right side of the FOV rectangle, while the set of beams propagating in the -x direction misses the beams corresponding to the left side of the FOV rectangle. However, collectively, all of the beams that make up the FOV are still present.

[0328] The shaded right portion of the translated FOV rectangle at the 9 o'clock position represents a first sub-portion of the FOV, while the shaded left portion of the FOV rectangle at the 3 o'clock position represents a 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 mentioned, in some embodiments, the first and second periodicity axes in the 2D lattice of the MPE region 2050 are not orthogonal. This, in turn, means that the primitive lattice vectors G and H are also not orthogonal. This can allow the 2D lattice in the MPE region 2050 to translate the FOV rectangles at the 3 o'clock and 9 o'clock positions so that their centers lie beyond the midpoint of the k-space annulus, 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 annulus. 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 subportions. This is noteworthy in the illustrated embodiment because dividing the FOV into first and second subportions is part of the process for increasing the FOV of the eyepiece waveguide 2000.

[0330] FIG. 20E is a k-space diagram KSD3 illustrating another portion of the k-space operation 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 annulus. This is the location of one of the translated FOV rectangles after the first interaction within the MPE region 2050. FIG. 20E shows how, during subsequent interactions, the 2D grid within the MPE region 2050 translates this FOV rectangle using the grid vectors shown in FIG. 20B. Again, because there are eight grid vectors, the MPE region 2050 attempts to translate the FOV rectangle from the 3 o'clock position in the k-space annulus to eight possible new locations within the k-space diagram. Of these eight possible locations, five are again outside the perimeter of the k-space diagram. These locations are illustrated using unshaded FOV rectangles. Because k-vectors outside the perimeter of the k-space diagram are not allowed, none of these five lattice vectors result in diffraction. However, there are three lattice vectors (i.e., G, H, and H+G) that result in the translation of the FOV rectangle to a new position, at least partially within the boundaries of the k-space diagram. One of these locations is at the 9 o'clock position in the k-space ring, another at the 12 o'clock position, and the last back to the 6 o'clock position. Because the k-vectors at these locations are allowed and result in guided propagation modes, the FOV rectangles at these locations are shaded to indicate that the beam of light is diffracted into those three states (or the zero-order diffracted beam can remain in the propagation state represented by the FOV rectangle at the 3 o'clock position).

[0331] As shown in Figure 20E, the translated FOV rectangle at the 3 o'clock position of the k-space annulus is already truncated as a result of the first diffraction interaction within MPE region 2050 shown in Figure 20D. Therefore, only the truncated FOV rectangle is translated to the 9 o'clock, 12 o'clock, and 6 o'clock positions of the k-space annulus. In the 9 o'clock position, the FOV rectangle is further truncated, meaning that only the beam corresponding to the central 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 a mirror image (k y -axis).

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

[0334] As shown by the k-space diagrams in Figures 20D-20F, when the diffracted light beam from the ICG region 2040 arrives at the MPE region 2050, many replica beams are formed in a spatially dispersed manner. These replica beams all propagate in one of the directions indicated by the FOV rectangles at the 3, 6, 9, and 12 o'clock positions in the k-space annulus. Propagating through the MPE region 2050, the light beam may undergo any number of interactions with the diffractive features of the MPE region, resulting in any number of changes in propagation direction. In this way, the light beam is replicated along both the x- and y-directions throughout the MPE region 2050. This is represented by the arrows in the MPE region 2050 of the eyepiece waveguide 2000 in Figure 20A.

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

[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 constitutes 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. It is advantageous for the grating lines in the EPE region 2060 to be oriented perpendicular to the grating lines in the ICG region 2040, as this helps ensure that the light beam will interact with the MPE region 2050 before being 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 effect of EPE region 2060 within eyepiece waveguide 2000 shown in FIG. 20A. As previously discussed, a beam of light propagates through MPE region 2050 in all of the directions indicated by the FOV rectangles located at the 12, 3, 6, and 9 o'clock positions of the k-space annulus. Also, because EPE region 2060 physically overlaps MPE region 2050, the beam of light in all of these propagation states contacts the diffraction grating within the EPE region as it diffuses through the MPE region.

[0338] The periodic axes of the grating in the EPE region 2060 are ±k x - direction, the lattice vectors associated with the EPE region likewise point in the same direction. Figure 20G shows how the EPE region 2060 uses these lattice vectors to attempt to translate the FOV rectangle to the 12, 3, 6, and 9 o'clock positions. xDue to its orientation in the -direction, the lattice vector associated with EPE region 2060 can translate only the FOV rectangles located at the 3 o'clock and 6 o'clock positions of the k-space annulus back to the origin of the k-space diagram. Therefore, EPE region 2060 can only outcouple beams of light that are in one of those two propagation states. That is, the EPE region does not outcouple beams of light that are propagating in states corresponding to the FOV rectangles at the 12 o'clock and 6 o'clock positions of the k-space annulus.

[0339] If the periodicity axis for the grating lines in the EPE region 2060 is parallel to, rather than perpendicular to, the periodicity axis for the grating lines in the ICG region 2040, then the grating vector associated with the EPE region will be ±k y It is important to note that the input beam will point in the - direction. This, in turn, will allow light beams in propagation states corresponding to the FOV rectangles at the 12 o'clock and 6 o'clock positions of the k-space annulus to be outcoupled by the EPE region. Because the input beam arrives at the MPE / EPE region in a propagation state corresponding to the 6 o'clock position, this would mean that the light beam could be outcoupled by the EPE region 2060 before interacting with and being spread by the MPE region 2050, which would typically be undesirable. The fact that the periodicity axis for the grating lines in the EPE region 2060 is perpendicular to that of the ICG region 2040 means that the light beam will typically need to undergo at least one, and potentially more, direction change within the MPE region before being outcoupled. This allows for improved spreading of the light beam within the MPE region 2050.

[0340] FIG. 20H is a k-space diagram KSD6 summarizing the k-space behavior 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 an FOV rectangle with at least one dimension greater than the width of the k-space ring. In some embodiments, at least one dimension of the FOV rectangle can be up to about two times greater than the width of the k-space ring. In the illustrated embodiment, the horizontal dimension of the FOV rectangle is greater than the width of the k-space ring, but the same technique can also be used to extend the vertical field of view.

[0341] KSD6 includes an FOV rectangle centered at the origin of the diagram. Again, the location of the FOV rectangle may describe either an input beam being projected into the eyepiece waveguide 2000, or a replicated output beam being projected out of the waveguide toward 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 translates the FOV rectangle downward from the center of the k-space diagram to the 6 o'clock position. y The ICG region 2040 can be designed to be oriented in the -y-direction, which causes the diffracted beams to propagate in the -y-direction toward the MPE region 2050. Furthermore, the ICG region 2040 can be designed such that the magnitude of its grating vector causes the FOV rectangle to be copied to a position that fits perfectly within the k-space annulus 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 grating vector is equal to the distance from the origin of the k-space diagram to the midpoint of the k-space annulus. Because the FOV rectangle at the 6 o'clock position is completely within the k-space annulus, all of the diffracted beams enter a guided mode of propagation.

[0342] As previously discussed, the MPE region contains multiple diffractive features that exhibit periodicity along multiple different axes. This means that the MPE region has multiple associated grating vectors that can translate the FOV rectangle from the 6 o'clock position to any of the 9 o'clock, 12 o'clock, and 3 o'clock positions. During additional interactions 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-headed 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 annulus are truncated, meaning that not all of the beams of light associated with the complete FOV are present in each of those propagation states. However, when these subportions of the FOV are considered collectively, all of the beams of light that make up the complete FOV are present. Thus, when the FOV rectangle is translated back to the origin of the k-space diagram from the 3 o'clock or 6 o'clock position to ultimately out-couple the beam of light towards the user's eye, all of the beams required to make up the full FOV of the input image are present and projected from the eyepiece waveguide 2000.

[0343] Figure 20I is a schematic diagram illustrating how a beam of light spreads through the eyepiece waveguide 2000 shown in Figure 20A. The stimulated beam entering the MPE region 2050 and propagating from the ICG region 2040 in the -y-direction is replicated into many beams in a spatially dispersed manner, some traveling in the ±y-directions (corresponding to the FOV rectangles at the 6 o'clock and 12 o'clock positions in the k-space annulus) and some traveling in the ±x-directions (corresponding to the FOV rectangles at the 3 o'clock and 9 o'clock positions in the k-space annulus). In this way, the light beam spreads laterally throughout the eyepiece waveguide 2000.

[0344] 20J illustrates how the diffraction efficiency of the MPE region 2050 in the eyepiece waveguide 2000 can be spatially varied to improve brightness uniformity within the waveguide. In the figure, darker shading in the MPE region 2050 represents higher diffraction efficiency, while lighter shading represents lower diffraction efficiency. Spatial variation in the diffraction efficiency of the MPE region 2050 can be achieved by introducing spatial variations in grating characteristics such as grating depth, duty cycle, blaze angle, tilt angle, etc.

[0345] As can be seen in FIG. 20J, the brightness uniformity 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. Because this is where the light beam enters the MPE region 2050 from the ICG region 2040, more light is present in this area, and therefore the diffraction efficiency can be higher to more effectively diffuse 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 to input light to more locations, thereby improving the brightness uniformity within the waveguide.

[0346] Brightness uniformity can also be improved by designing the central portion of MPE region 2050 to have a higher diffraction efficiency along the direction in which the beam propagates from ICG region 2040 into MPE region 2050. Again, because ICG region 2040 is located along the axis that inputs the light, more light is present within this area of ​​MPE region 2050. Because more light is present within this area, the diffraction efficiency can be higher to more effectively diffuse the light to other portions of MPE region 2050.

[0347] FIG. 20K illustrates how the diffraction efficiency of the EPE region 2060 in the eyepiece waveguide 2000 can be spatially varied to improve brightness uniformity within the waveguide. Darker shading within the EPE region 2060 again represents higher diffraction efficiency, while lighter shading represents lower diffraction efficiency. The EPE region 2060 can be designed to have higher diffraction efficiency within the peripheral area. Higher diffraction efficiency within the peripheral area of ​​the EPE region 2060 helps to outcouple light into the user's eye before it is lost out the edge of the waveguide.

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

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

[0350] FIG. 20L illustrates the k-space behavior 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 that of the grating in the ICG region 2040. This finer period results in the bottom diffraction mirror having an associated grating vector that is twice as long as 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 in the k-space annulus. Although illustrated with respect to the eyepiece waveguide 2000, the same techniques (i.e., spatial variation of the diffraction efficiency of the OPE, MPE, EPE regions, etc., and the use of a diffraction mirror along the peripheral edge) can also be used with any of the other embodiments described herein.

[0351] 20M illustrates an exemplary embodiment of eyeglasses 70 incorporating one or more instances of eyepiece waveguide 2000. A first instance of eyepiece waveguide 2000 is integrated into the left viewing portion of eyeglasses 70, while a second instance of eyepiece waveguide 2000 is integrated into the right viewing portion. In the illustrated embodiment, waveguides 2000 each measure approximately 50 x 30 mm. 2Although many different sizes can be used. Each waveguide 2000 can be associated with a separate projector 2020 that projects an image into the corresponding waveguide. Assuming the eyepiece waveguide is made from a material with a refractive index of 1.8, some embodiments of eyepiece waveguide 2000 are capable of achieving an FOV as large as 90° x 45°, although some embodiments of eyepiece waveguide may be designed for a smaller FOV of about 60° x 45° to meet typical design constraints of eyebox volume (it may be advantageous to send a portion of the FOV to either side of the eyepiece waveguide to provide a properly sized eyebox) and avoid screen door artifacts resulting from sparsely spaced output beams.

[0352] FIG. 20N illustrates another exemplary embodiment of glasses 70 incorporating one or more instances of eyepiece waveguide 2000. This embodiment of glasses 70 is similar to that shown in FIG. 20M, except that the orientation of waveguide 2000 and accompanying projector 2020 is rotated 90 degrees toward the temples of glasses 70. In this configuration, some embodiments of eyepiece waveguide 2000 are capable of achieving an FOV as large as 45° by 90°, assuming the eyepiece waveguide is made from a material with a refractive index of 1.8, although some embodiments may be designed for a smaller FOV of approximately 45° by 60° to meet other design constraints.

[0353] FIG. 21A illustrates another embodiment of an eyepiece waveguide 2100 with an MPE region 2150 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 extended field of view, which may be greater than the range of propagation angles that can be supported for guided propagation modes in the thickness direction of the waveguide. The eyepiece waveguide 2100 has a first surface 2100a and a second surface 2100b. As discussed further below, different diffractive 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 illustrated in FIG. 21A as displaced relative to each other in the xy plane. However, this is for illustrative purposes only and may indicate different diffractive 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 xy plane. Additionally, while the MPE regions 2150 and the EPE regions 2160 are illustrated as being the same size and precisely aligned in the xy plane, in other embodiments they may have somewhat different sizes or may be partially misaligned. In some embodiments, the MPE regions 2150 and the EPE regions 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. Unlike the eyepiece waveguide 2000 shown in FIG. 20A , the eyepiece waveguide 2100 shown in FIG. 21A includes two ICG regions 2140 a, 2140 b, located on opposite sides of the MPE / EPE region, rather than a single ICG region. Each ICG region 2140 a, 2140 b can have its own associated projector. Each of the two projectors can input a subportion of the full input image FOV into the eyepiece waveguide 2100. Thus, each ICG region 2140 a, 2140 b can similarly be used to internally combine input beams corresponding to subportions of the FOV. These 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 subportion 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 subportion of the FOV from a second projector device. The first and second subportions of the FOV may be unique, or they may partially overlap. The first set of input beams may be projected toward the left ICG region 2140a generally along the -z-direction but centered around input beams having a component propagating in the -x-direction, while the second set of input beams may be projected toward the right ICG region 2140b generally along the -z-direction but centered around input beams having a component propagating in the +x-direction. The left ICG region 2140a diffracts a first set of input beams so that at least a portion of them enter guided modes propagating in the +x-direction, and the right ICG region 2140b diffracts a second set of input beams so that at least a portion of them enter guided modes propagating in the -x-direction. In this manner, 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 so that they propagate toward 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 a first side 2100 a of the waveguide and an overlapping EPE region 2160 formed on or within a second side 2100 b of the waveguide. The MPE region 2150 in the eyepiece waveguide 2100 shown in FIG. 21A can be similar to the MPE region 2050 in the eyepiece waveguide 2000 shown in FIG. 20A . That is, the MPE region 2150 can include multiple diffractive features exhibiting periodicity along multiple axes. Similarly, the EPE region 2160 in the eyepiece waveguide 2100 shown in FIG. 21A can be similar to the EPE region 2060 in the eyepiece waveguide 2000 shown in FIG. 20A . That is, EPE region 2160 can include a diffraction grating whose periodic axis is orthogonal to that of the two ICG regions 2140a, 2140b. The behavior of MPE region 2150 and EPE region 2160 in Figure 21A can also be similar to that of MPE region 2050 and EPE region 2060 in Figure 20A, as shown in Figures 21B-21D.

[0357] FIG. 21B is a k-space diagram KSD1 illustrating the k-space effect of the eyepiece waveguide 2100 on a first set of input beams corresponding to a first sub-portion of the input image FOV. The FOV rectangle centered at the origin of KSD1 represents the beams of light corresponding to the full input image FOV to be projected by the eyepiece waveguide 2100 toward the user's eye. The size of the overall FOV rectangle has a dimension up to approximately two times larger than the width of the k-space annulus. Thus, the eyepiece waveguide 2100 shown in FIG. 21A is designed to have an enhanced FOV similar to the embodiments shown in FIGS. 19 and 20A. However, the first set of input beams, projected toward the left ICG region 2140a, correspond to only 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 portion of the FOV rectangle. The center of the shaded portion of the FOV rectangle is at -k x-direction from the origin of the k-space diagram, the first set of input beams from the first projector are not centered on a beam propagating exactly in the -z-direction (as would be the case if the shaded portion of the FOV rectangle were centered on the origin of the k-space diagram), but rather on an oblique beam with a propagating component in the -x-direction.

[0358] The left ICG region 2140a has lattice vectors of ±k x The effect of the left ICG region 2140a in k-space is to translate the shaded left portion of the FOV rectangle from the center of the k-space diagram to the 3 o'clock position in the k-space annulus. This will cause the diffracted beam to propagate generally in the x-direction toward the MPE region 2150. In some embodiments, the shaded left portion 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 midpoint of the k-space annulus to the outer boundary of the annulus. Furthermore, the left ICG region 2140a can be designed such that the magnitude of its lattice vector copies the FOV rectangle to a position where the shaded portion fits perfectly within the k-space annulus at the 3 o'clock position. This can be accomplished, for example, by setting the magnitude of the ICG lattice vector to be greater than the distance from the origin of the k-space diagram to the midpoint of the k-space annulus. The shaded portion of the FOV rectangle at the 3 o'clock position is entirely within the k-space annulus, so that the first set of input beams corresponding to the first sub-portion of the FOV all enter a guided mode of propagation. Although the FOV rectangle at the 3 o'clock position of the k-space annulus has a right-hand portion that extends outside the annulus, this portion of the FOV rectangle corresponds to input beams that are not necessarily part of the first sub-portion of the FOV provided to the left ICG region 2140a by its associated projector.

[0359] The left ICG region 2140a may also diffract some of the first set of input beams in the opposite direction (i.e., translating the FOV rectangle to the 9 o'clock position on the k-space annulus), but in the illustrated embodiment of the eyepiece waveguide 2100, those particular diffracted beams would simply exit from the edge of the waveguide.

[0360] The MPE region 2150 includes multiple diffractive features with multiple periodicity axes. In some embodiments, the MPE region 2150 can be similar to the MPE region 2050 illustrated and discussed with respect to Figures 20A-20M. For example, the MPE region 2150 can have multiple associated grating 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 on the k-space annulus. As shown in Figure 21B, the shaded portion of the FOV rectangle at the 9 o'clock position on the k-space annulus is truncated, meaning that not all of the beams of light associated with the first subportion of the FOV are necessarily 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-headed arrows between their propagation states in KSD1. In this manner, the first set of input beams can be replicated throughout the MPE region 2150 by undergoing multiple interactions with its diffractive features, as described herein. This is indicated by the arrows in the OPE region 2150 of the eyepiece waveguide 2100 in FIG. 21A.

[0362] Because the EPE region 2160 overlaps the MPE region 2150 in the xy plane of the eyepiece waveguide 2100, the replicated light beams also interact with the EPE region 2160 as they diffuse 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 outcoupled toward 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, EPE region 2160 includes a diffraction grating whose lines are oriented perpendicular to the lines of the diffraction gratings that make up ICG regions 2140a, 2140b. In this particular example, ICG regions 2140a, 2140b have grating lines that extend in the y-direction and repeat periodically in the x-direction, and thus EPE region 2160 has grating lines that extend in the x-direction and repeat periodically in the y-direction. Again, it is advantageous for the grating lines in EPE region 2160 to be oriented perpendicular to the grating lines in ICG regions 2140a, 2140b, as this helps ensure that the light beam will interact with MPE region 2150 before being coupled out of eyepiece waveguide 2100 by EPE region 2160.

[0364] FIG. 21B also illustrates the k-space effect of EPE region 2160 on a first set of beams corresponding to a first sub-portion of the FOV. As previously discussed, beams of light can propagate through 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 annulus. Also, because EPE region 2160 overlaps MPE region 2150, beams of light in any of these propagation states can interact with the EPE region and be outcoupled from eyepiece waveguide 2100. The periodicity axes of the grating within EPE region 2160 are ±k y- direction, the lattice vectors associated with the EPE region likewise point in the same direction. FIG. 21B shows how the EPE region 2160 thus translates the FOV rectangles located at the 12 o'clock and 6 o'clock positions of the k-space annulus back to the origin of the k-space diagram. Thus, the EPE region 2160 can only outcouple beams of light in one of those two propagation states. As shown in FIG. 21B, when the FOV rectangle is finally translated back to the center of the k-space diagram KSD1, all of the first set of beams, comprising the first subportion of the FOV, are present and projected toward the user's eye.

[0365] FIG. 21C is a k-space diagram KSD2 illustrating the k-space effect of the eyepiece waveguide 2100 on a second set of input beams corresponding to a second sub-portion of the FOV of the input image. Again, the FOV rectangle centered at the origin of KSD2 represents the beams of light corresponding to the complete input image to be projected by the eyepiece waveguide 2100 toward the user's eye. However, the second set of input beams, projected toward the right ICG region 2140b, corresponds to only the shaded sub-portion 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 portion of the FOV rectangle. The center of the shaded portion of the FOV rectangle is +k from the origin of the k-space diagram. x Because they are offset in the - direction, the second set of input beams from the second projector are not centered on a beam propagating exactly in the -z-direction (as would be the case if the shaded portion of the FOV rectangle were centered on the origin of the k-space diagram), but rather on an oblique beam with a component propagating in the +x-direction.

[0366] In the illustrated embodiment, the effect 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 its lattice vectors aligned with ±k xThe right ICG region 2140b can be designed to be oriented in the -x-direction. This will cause a portion of the diffracted beams to propagate in the -x-direction toward 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 annulus to the outer boundary of the annulus. Furthermore, 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 perfectly within the k-space annulus 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 annulus. Because the shaded portion of the FOV rectangle at the 9 o'clock position is completely within the k-space annulus, the second set of input beams corresponding to the second sub-portion of the FOV all enter a guided mode of propagation. The FOV rectangle at the 9 o'clock position of the k-space annulus has a left portion that extends outside the annulus, but this portion of the FOV rectangle corresponds to the input beam, which 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 may also diffract some of the second set of input beams in the opposite direction (i.e., translating the FOV rectangle to the 3 o'clock position on the k-space annulus), but in the illustrated embodiment of the eyepiece waveguide 2100, those particular diffracted beams would simply exit from the edge of the waveguide.

[0368] As previously discussed, the MPE region 2150 can have multiple associated grating vectors that can translate the FOV rectangle from the 9 o'clock position to any of the 6 o'clock, 3 o'clock, and 12 o'clock positions of the k-space annulus. As shown in FIG. 21C, the shaded portion of the FOV rectangle at the 3 o'clock position of the k-space annulus is truncated, meaning that the beams of light associated with the second sub-portion of the FOV are not necessarily all in a particular propagation state.

[0369] 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-headed arrows between their propagation states in KSD2. In this manner, the second set of input beams can be replicated throughout the MPE region 2150 by undergoing multiple interactions with its diffractive features, as described herein. Again, this is indicated by the arrows in the OPE region 2150 of the eyepiece waveguide 2100 in FIG. 21A.

[0370] FIG. 21C also illustrates the k-space effect of EPE region 2160 on the second set of beams corresponding to the second subportion of the FOV. As previously discussed, EPE region 2160 translates the FOV rectangle located at the 12 o'clock and 6 o'clock positions of the k-space annulus back to the origin of the k-space diagram. Thus, EPE region 2160 can outcouple only beams of light in either of their two propagation states. As shown in FIG. 21C, when the FOV rectangle is finally translated back to the center of k-space diagram KSD2, all of the second set of beams comprising the second subportion of the FOV are present and projected toward the user's eyes.

[0371] FIG. 21D is a k-space diagram KSD3 summarizing the k-space behavior of the eyepiece waveguide 2100 shown in FIG. 21A. This is essentially a superposition of the k-space diagrams shown in FIGS. 21B and 21C. Again, the k-space diagram in FIG. 21D shows an FOV rectangle with at least one dimension greater than the width of the k-space ring. In some embodiments, at least one dimension of the FOV rectangle can be up to about two times greater than the width of the k-space ring. In the illustrated embodiment, the horizontal dimension of the FOV rectangle is greater than the width of the k-space ring. While the eyepiece waveguide 2100 is illustrated as providing an extended horizontal field of view, the same technique can also be used to extend the vertical field of view.

[0372] As shown in Figure 21D, using separate projectors and ICG regions 2140a, 2140b, the first and second sets of input beams are projected separately into the eyepiece waveguide 2100, but once the various FOV rectangles from the 12, 3, 6, and 9 o'clock positions of the k-space annulus are translated back to the origin of the k-space diagram and thus outcombined towards the user's eye, all of the beams required to make up the full image FOV are present, and the first and second sub-portions of the FOV are aligned in k-space with the same relative positions to each other as in the full input FOV.

[0373] FIG. 21E illustrates an exemplary embodiment of eyeglasses 70 incorporating one or more instances of eyepiece waveguide 2100. FIG. 21F illustrates an exemplary FOV corresponding to eyeglasses 70 in FIG. 21E. A first instance of eyepiece waveguide 2100 is integrated into the left viewing portion of eyeglasses 70, while a second instance of eyepiece waveguide 2100 is integrated into the right viewing portion. In the illustrated embodiment, eyepiece waveguides 2100 each measure approximately 50 x 30 mm. 2However, many different sizes can be used. Each eyepiece waveguide 2100 can be associated with two separate projectors 2120a, 2120b, each projecting a sub-portion of the FOV into the corresponding waveguide, as just discussed. In some embodiments, the first projector 2120a per waveguide 2100 can input light into the temple side of the eyepiece waveguide 2100, while the second projector 2120b can input light into the nose side of the eyepiece waveguide. For eyepiece waveguides made from a material with a refractive index of n=1.8, the projectors 2120a, 2120b can each input a sub-portion of the FOV as large as 50° x 60° or larger, depending on the eyebox size and other design constraints such as screen door artifacts. The complete FOV can also be as large as 100° x 60° or larger. This is shown as the monocular eyepiece FOV configuration illustrated in Figure 21F. As illustrated by the matching shading, in this configuration, a first projector 2120a (temporal) can be used to project the nasal side of the full FOV, and a second projector 2120b (nasal) can be used to project the temple side of the full FOV. Note that the crosshairs indicate one possible pupil alignment, but others can also be used.

[0374] Alternatively, two instances of the eyepiece waveguide 2100 and the glasses 70 can be used together to provide a binocular FOV. For example, each eyepiece waveguide 2100 can project an FOV, as shown in the monocular eyepiece configuration. However, the FOVs projected by the two eyepiece waveguides 2100 can at least partially overlap. FIG. 21F illustrates a case where the FOVs projected by the two eyepiece waveguides 2100 overlap horizontally by 50°, providing an overall binocular FOV of 150° by 60°. The binocular FOV can be even larger if less overlap is provided between the FOVs of the two eyepiece waveguides 2100. As illustrated by the matching shading, in a binocular FOV configuration, the first projector 2120a (temporal side) can be used to project the central portion of the binocular FOV, and the second projector 2120b (nasal side) can be used to project the sides of the binocular FOV.

[0375] Figure 21G illustrates the k-space behavior of another embodiment of the eyepiece waveguide 2100 shown in Figure 21A. In this embodiment, the size of the FOV rectangle is k x and k yThe left and right ICG regions 2140a, 2140b can be designed using lattice vectors to shift the FOV rectangle to the 3 o'clock and 9 o'clock positions, as previously discussed. The magnitude of the lattice vectors of the ICG regions can be such that the center of the full FOV rectangle is shifted to any radial position between the midpoint of the k-space ring and the outer periphery of the ring, for example. The MPE regions can also be designed using lattice vectors to shift the full FOV rectangle to the 3 o'clock, 6 o'clock, 9 o'clock, and 12 o'clock positions, as previously discussed. However, the magnitude of the lattice vectors of the MPE regions 2150 can also be designed such that the center of the full FOV rectangle is shifted to any radial position between the midpoint of the k-space ring and the outer periphery of the ring, for example. Thus, even at the 12 o'clock and 6 o'clock positions, which lie along the axis of the shorter dimension of the FOV rectangle, portions of the FOV rectangle may extend beyond the periphery of the k-space annulus such that portions of the rectangle are truncated.

[0376] Although the guided beams corresponding to the truncated portion of the FOV rectangle may be lost, all of the beams necessary to constitute the complete FOV are still present within the waveguide, considering all propagation conditions represented by the 3, 6, 9, and 12 o'clock positions. The left FOV (lighter shaded rectangle) is completely preserved at the 9 o'clock position, while the bottom portion is preserved at the 12 o'clock position and the top portion is preserved at the 6 o'clock position. Similarly, the right FOV (darker shaded rectangle) is completely preserved at the 3 o'clock position, while the bottom portion is preserved at the 12 o'clock position and the top portion is preserved at the 6 o'clock position. Thus, when the FOV rectangle is translated back to the origin of the k-space diagram and outcombined toward the user's eye, all of the beams necessary to constitute the complete FOV are present, and the complete FOV can be reconstructed. Extending the FOV rectangle in multiple directions is furth...

Claims

1. An eyepiece waveguide, comprising: an optically transparent substrate; an input coupling grid (ICG) region formed on or within the substrate, the ICG region configured to receive an input beam of light corresponding to an input image having a corresponding field of view, and to couple the input beam into the substrate as a guide beam; a multidirectional pupil expander (MPE) region arranged on or within a first surface of the substrate to receive at least a portion of the stimulating beam propagating within the substrate, the MPE region comprising scattering features configured to replicate the stimulating beam in at least two directions as the stimulating beam propagates through the MPE region; an exit pupil expander (EPE) region arranged on or within a second surface of the substrate opposite the first surface, the EPE region configured to further replicate and couple out of the substrate at least a portion of the guided beam propagating within the substrate; An eyepiece waveguide comprising:

2. An eyepiece waveguide as described in claim 1, wherein the MPE region and the EPE region overlap each other by at least 70%, at least 80%, at least 90%, or at least 95%.

3. An eyepiece waveguide as described in claim 1, wherein the scattering features contained within the MPE region are configured to have a diffraction efficiency of 10% or less.

4. An eyepiece waveguide as described in claim 1, wherein the scattering features of the MPE region are arranged in a two-dimensional array.

5. An eyepiece waveguide as described in claim 1, wherein the scattering features of the MPE region are arranged in a crossed grid with grid lines repeated along two or more periodic directions.

6. An eyepiece waveguide as described in claim 1, wherein the EPE region includes grating lines that are substantially perpendicular to the grating lines contained within the ICG region.

7. An eyepiece waveguide as described in claim 1, wherein the MPE region and the EPE region have substantially the same shape.

8. An eyepiece waveguide as described in claim 1, wherein the ICG region is arranged on or within the first surface of the substrate.

9. An augmented reality display system, comprising: A wearable display including the eyepiece waveguide of claim 1; a projection system including at least one projector arranged to emit the input beam of light towards the ICG region; Equipped with An augmented reality display system, wherein the eyepiece waveguide is arranged such that the EPE region of the eyepiece waveguide couples at least a portion of the guided beam out from the substrate toward the eye of a user of the wearable display.

10. An eyepiece waveguide as described in claim 1, wherein the ICE region is a first ICG region, the eyepiece waveguide includes a second ICG region arranged on or within the substrate, the second ICG region configured to receive an input beam of light corresponding to the input image and to couple the input beam into the substrate as a guide beam, and the first ICG region and the second ICG region are arranged on opposite sides of the MPE region and the EPE region.

11. An eyepiece waveguide as described in claim 10, wherein the first ICG region is configured to receive a first subset of the input beam of light corresponding to a first subportion of the field of view, and the second ICG region is configured to receive a second subset of the input beam of light corresponding to a second subportion of the field of view.

12. An eyepiece waveguide as described in claim 11, wherein the first and second sub-portions of the field of view are at least partially different and together include the complete field of view of the input image.

13. An eyepiece waveguide as described in claim 10, wherein the first ICG region and the second ICG region are arranged on or within the first surface of the substrate.

14. A first top orthogonal pupil expander (OPE) region and a first bottom OPE region arranged on or within the substrate on opposite sides of the first ICG region; a second top OPE region and a second bottom OPE region arranged on or within the substrate on opposite sides of the second ICG region; Furthermore, the first top OPE region and the first bottom OPE region are arranged to receive, replicate, and direct the stimulating beam coupled into the substrate through the first ICG region toward the MPE region and the EPE region; The eyepiece waveguide of claim 10, wherein the second top OPE region and the second bottom OPE region are arranged to receive, replicate, and direct the guiding beam coupled into the substrate through the second ICG region toward the MPE region and the EPE region.

15. An eyepiece waveguide as described in claim 10, wherein the EPE region includes a diffraction grating having a periodic axis substantially perpendicular to the periodic axis of each of the first and second ICG regions.

16. An augmented reality display system, comprising: A wearable display including the eyepiece waveguide of claim 10; a projection system including at least a first projector and a second projector; Equipped with the first projector is arranged to emit a first subset of the input beam of light towards the first ICG region; the second projector is arranged to emit a second subset of the input beam of light towards the second ICG region; An augmented reality display system, wherein the eyepiece waveguide is arranged such that the EPE region of the eyepiece waveguide couples at least a portion of the guided beam out from the substrate toward the eye of a user of the wearable display.

Images