Eyepiece for augmented reality display systems

Abstract

Providing eyepiece waveguides for augmented reality display systems. [Solution] The eyepiece waveguide may include an optically transparent substrate with an input coupling grating (ICG) region. The ICG region can receive a beam of light and couple the beam into the substrate in the inductive propagation mode. The eyepiece waveguide may also include a combined pupil expander-extractor (CPE) grating region that receives a beam of light from the ICG region, modifies the direction of beam propagation using a first interaction, and externally couples the beam using a second interaction. The diffraction features of the CPE grating region may be arranged in alternating rows and columns of higher and lower quadrilateral surfaces, or the diffraction features may comprise rhombic raised ridges. The eyepiece waveguide may also include one or more recycler grating regions.

Description

[Technical Field]

[0001] (Incorporation by reference of priority application) This application claims priority to U.S. Provisional Patent Application No. 63 / 079,307, filed on September 16, 2020, and entitled “EYEPIECES FOR AUGMENTED REALITY DISPLAY SYSTEM,” and to U.S. Provisional Patent Application No. 63 / 079,938, filed on September 17, 2020, and entitled entitled “EYEPIECES FOR AUGMENTED REALITY DISPLAY SYSTEM.” These applications and any other applications identified in the application datasheets that claim foreign or domestic priority with respect to these applications are filed together with this application are incorporated herein by reference under 37 CFR 1.57.

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

[0003] Modern computing and display technologies are driving the development of virtual reality, augmented reality, and mixed reality systems. Virtual reality, or "VR," systems create simulated environments for users 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, immersing the user in the simulated environment. Virtual reality scenarios typically involve the presentation of computer-generated image data only, without also including actual real-world image data.

[0004] Augmented reality systems generally complement the real-world environment with simulated elements. For example, augmented reality, or "AR," systems can provide users with a view of their surrounding real-world environment via a head-mounted display. However, computer-generated image data can also be presented on the display to enhance the real-world environment. This computer-generated image data can include elements that are contextually relevant to the real-world environment. Such elements 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 are typically characterized by a greater degree of interaction. Simulated elements can often be interactive in real time.

[0005] Figure 1 depicts an exemplary AR scene 1, in which the user sees a real-world park setting 6 featuring people, trees, buildings in the background, and a concrete platform 20. In addition to these items, computer-generated image data is also presented to the user. The computer-generated image data may include, for example, a robot figure 10 standing on the real-world platform 20 and a flying cartoon-like avatar character 2 that looks like an anthropomorphic bumblebee, although these elements 2 and 10 do not actually exist in the real-world environment. [Overview of the project] [Means for solving the problem]

[0006] In some embodiments, an eyepiece waveguide for an augmented reality display system comprises an optically transparent substrate having a first surface and a second surface; an input coupling grid (ICG) region formed on or within one of the surfaces of the substrate, configured to receive a beam of light and, in an inductive propagation mode, couple the beam into the substrate; and a first combined pupil expander-extractor (CPE) grid region formed on or within the first surface of the substrate, positioned to receive a beam of light from the ICG region, configured to modify the propagation direction of the beam using a first interaction and to externally couple the beam out of the eyepiece waveguide using a second interaction, wherein the diffraction features are arranged in alternating rows and columns of higher and lower quadrilateral surfaces.

[0007] In some embodiments, an eyepiece waveguide for an augmented reality display system comprises an optically transparent substrate, an input coupling grid (ICG) region, and a first combined pupil expander-extractor (CPE) grid region formed on a first side of the substrate, wherein the ICG region is configured to receive a set of multiple input beams of light, the set of input beams being associated with a set of k-vectors that form a field of view (FOV) shape, located at the center of a k-space ring associated with the eyepiece waveguide, and the ICG region is configured to couple the input beams into the substrate as guided beams, and at least partially within the k-space ring, the FOV shape is first The first CPE lattice region is configured to diffract the guided beam so as to translate it to position 1, and using a first interaction, the first CPE lattice region is configured to diffract the guided beam so as to translate the FOV shape from position 1 to positions 2 and 3 within the k-space ring, at least partially, but not so as to translate the FOV shape directly back to the center of the k-space ring from position 1, with an efficiency of more than 1% of diffracting the FOV shape from position 1 to positions 2 and 3, and using a second interaction, the first CPE lattice region is configured to diffract the guided beam so as to translate the FOV shape from positions 2 and 3 to the center of the k-space ring.

[0008] In some embodiments, an eyepiece waveguide for an augmented reality display system comprises an optically transparent substrate having a first surface and a second surface; an input coupling grating (ICG) region formed on or within one of the surfaces of the substrate, configured to receive a beam of light and couple the beam into the substrate in an inductive propagation mode; and a first combined pupil expander-extractor (CPE) grating region formed on or within the first surface of the substrate, positioned to receive a beam of light from the ICG region, and configured to modify the direction of beam propagation using a first interaction and to couple the beam out of the eyepiece waveguide using a second interaction, comprising a plurality of diffraction features, the diffraction features comprising rhomboid raised ridges.

[0009] In some embodiments, the eyepiece waveguide for an augmented reality display system comprises an optically transparent substrate having a first surface and a second surface; an input coupling grating (ICG) region formed on or within one of the surfaces of the substrate, configured to receive an input beam of light and couple the input beam into the substrate as a guided beam; a first combined pupil expander-extractor (CPE) grating region formed on or within the first surface of the substrate, configured to receive the guided beam from the ICG region, create a first plurality of diffracted beams at a plurality of dispersion locations, and externally couple a first plurality of output beams; and a second CPE grating region formed on or within the second surface of the substrate. The system comprises: a second CPE grating region positioned to receive a guided beam from the ICG region, create a second plurality of diffracted beams at a plurality of dispersion locations, and externally couple a second plurality of output beams; a first recycler grating region adjacent to the first CPE grating region, positioned and configured to receive a portion of the first plurality of diffracted beams from the first CPE grating region and redirect them toward the first CPE region; and a second recycler grating region adjacent to the second CPE grating region, positioned and configured to receive a portion of the second plurality of diffracted beams from the second CPE grating region and redirect them toward the second CPE region.

[0010] In some embodiments, an eyepiece waveguide for an augmented reality display system comprises an optically transparent substrate, an input coupling grid (ICG) region, a first combined pupil expander-extractor (CPE) grid region, a second CPE grid region, a first recycler grid region, and a second recycler grid region, wherein the ICG region is configured to receive a set of multiple input beams of light, the set of input beams being associated with a set of k-vectors that form a field of view (FOV) shape, located at the center of a k-space ring associated with the eyepiece waveguide, the ICG region being configured to diffract the input beams as guided beams, so as to couple them into the substrate and at least partially so as to translate the FOV shape to a first position within the k-space ring, and the first CPE grid region is configured to diffract the guided beams at least partially within the k-space ring Within the first CPE grating region, the second CPE grating region is configured to diffract the guided beam so as to shift the FOV shape from a first position to a second position, at least partially within the k-space ring, the FOV shape shifts from a first position to a third position, the first CPE grating region is configured to diffract the guided beam so as to shift the FOV shape from a third position to the center of the k-space ring, the second CPE grating region is configured to diffract the guided beam so as to shift the FOV shape from a second position to the center of the k-space ring, the first recycler grating region is configured to diffract the guided beam so as to shift the FOV shape from a second position to a third position, and the second recycler grating region is configured to diffract the guided beam so as to shift the FOV shape from a third position to a second position. The present invention provides, for example, the following: (Item 1) An eyepiece waveguide for an augmented reality display system, wherein the eyepiece waveguide is An optically transparent substrate having a first surface and a second surface, An input coupling grid (ICG) region formed on or within one of the surfaces of the substrate, wherein the ICG region is configured to receive a beam of light and, in the inductive propagation mode, couple the beam into the substrate; A first combined pupil expander-extractor (CPE) grating region formed on or within the first surface of the substrate, wherein the first CPE grating region is positioned to receive a beam of light from the ICG region, and the first CPE grating region has a plurality of diffraction features configured to modify the propagation direction of the beam using a first interaction and to externally couple the beam from the eyepiece waveguide using a second interaction. Equipped with, The diffraction features are arranged in alternating rows and columns of higher and lower quadrilateral surfaces in an eyepiece waveguide. (Item 2) The alternating rows and columns of higher and lower quadrilateral surfaces form a checkerboard pattern in the eyepiece waveguide described in item 1. (Item 3) The aforementioned checkerboard pattern is an eyepiece waveguide as described in item 2, having a duty cycle of substantially 50%. (Item 4) The quadrilateral surface is rectangular, as described in item 1, for the eyepiece waveguide. (Item 5) The eyepiece waveguide according to item 4, wherein the rectangular surface has length and width dimensions such that the angle between its diagonals is substantially 60°. (Item 6) The higher and lower quadrilateral surfaces are equally sized and shaped, as described in item 1 of the eyepiece waveguide. (Item 7) The diffraction feature is an eyepiece waveguide as described in item 1, comprising a 2D grating with rhombic unit cells. (Item 8) The eyepiece waveguide according to item 7, wherein the rhombic unit cell comprises one of the higher quadrilateral surfaces inscribed therein such that the corner of the higher quadrilateral surface is located at the midpoint of the rhombic unit cell. (Item 9) The eyepiece waveguide according to item 8, wherein the 2D grid comprises a tiled pattern of the rhombic unit cells. (Item 10) The eyepiece waveguide according to item 1, wherein the CPE lattice region exhibits direct external coupling diffraction with an efficiency of less than 1% of diffusion diffraction. (Item 11) The eyepiece waveguide according to item 1, wherein the higher quadrilateral surface comprises columns with side walls perpendicular to the first surface of the substrate. (Item 12) The eyepiece waveguide according to item 1, wherein the higher quadrilateral surface comprises a column with side walls inclined with respect to the first surface of the substrate. (Item 13) The inclined sidewall is symmetrical, as described in item 12, for the eyepiece waveguide. (Item 14) The inclined sidewalls are asymmetric and form a blazed grid, as described in item 12, for the eyepiece waveguide. (Item 15) The height of the higher quadrilateral surface is spatially graded, as described in item 1, for the eyepiece waveguide. (Item 16) The eyepiece waveguide according to item 15, wherein the higher quadrilateral surface has a height that increases with increasing distance from the ICG region. (Item 17) An eyepiece waveguide according to item 1, wherein the coating is formed over the diffraction features. (Item 18) The eyepiece waveguide according to item 17, wherein the coating comprises a material having a higher refractive index than that of the diffractive features. (Item 19) The eyepiece waveguide according to item 18, wherein the refractive index of the coating is at least 2.0. (Item 20) The aforementioned coating is conformal, as described in item 18, for the eyepiece waveguide. (Item 21) The aforementioned coating is an eyepiece waveguide as described in item 18, with a thickness of 100 nm or less. (Item 22) The aforementioned coating is an eyepiece waveguide as described in item 21, with a thickness of 60 nm or less. (Item 23) The eyepiece waveguide according to item 1, wherein the plurality of diffraction features in the first CPE grating region exhibit periodicity in at least two directions. (Item 24) The eyepiece waveguide according to item 23, wherein the plurality of diffraction features of the first CPE grating region exhibit periodicity in first and second directions oriented at substantially 60° angles to each other. (Item 25) The eyepiece waveguide according to item 24, wherein the ICG region has a plurality of diffraction features that exhibit periodicity in a third direction oriented at a substantially 60° angle with respect to both the first and second directions. (Item 26) The eyepiece waveguide according to item 1, further comprising a second CPE grating region formed on or within the second surface of the substrate, wherein the second CPE grating region has a plurality of diffraction features configured to modify the propagation direction of the beam using a first interaction and to externally couple the beam from the eyepiece waveguide using a second interaction. (Item 27) The first and second CPE grating regions are the same as those in the eyepiece waveguide described in item 26. (Item 28) The eyepiece waveguide according to item 26, wherein the substrate has a thickness large enough to prevent the beam from interacting with the ICG region after it has been coupled into the inductive propagation mode. (Item 29) The beam is collimated and has a diameter of 5 mm or less, as described in item 1, through an eyepiece waveguide. (Item 30) The optically transparent substrate is planar, as described in item 1, for the eyepiece waveguide. (Item 31) The eyepiece waveguide described in item 1 is incorporated into an eyepiece for an augmented reality display system. (Item 32) The eyepiece waveguide according to item 31, wherein the eyepiece is configured to display a color image in multiple depth planes. (Item 33) An eyepiece waveguide for an augmented reality display system, wherein the eyepiece waveguide is An optically transparent substrate, The input coupled grid (ICG) region, A first combined pupil expander-extractor (CPE) grid region formed on the first side of the substrate and Equipped with, The ICG region is configured to receive a set of multiple input beams of light, and the set of input beams is associated with a set of k-vectors that form a field of view (FOV) shape located at the center of a k-space ring associated with the eyepiece waveguide. The ICG region is configured to diffract the input beam as a guided beam so as to couple them into the substrate, and at least partially so as to translate the FOV shape to a first position within the k-space ring. Using the first interaction, the first CPE lattice region is configured to diffract the guided beam such that it at least partially translates the FOV shape from the first position to the second and third positions within the k-space ring, but does not translate the FOV shape directly back to the center of the k-space ring with an efficiency greater than 1% of that of translating the FOV shape from the first position to the second and third positions. An eyepiece waveguide in which, using a second interaction, the first CPE grating region is configured to diffract the guided beam such that the FOV shape is translated parallel from the second and third positions to the center of the k-space ring. (Item 34) The center of the k-space ring, the first position, and the second position define a first equilateral triangle in k-space, as described in item 33, in the eyepiece waveguide. (Item 35) The center of the k-space ring, the first position, and the third position define a second equilateral triangle in k-space, as described in item 34, in the eyepiece waveguide. (Item 36) The first and second equilateral triangles in k-space share sides with the eyepiece waveguide described in item 35. (Item 37) The substrate further comprises a second CPE grid region formed on the second side of the substrate, Using the first interaction, the second CPE lattice region is configured to diffract the guided beam so as to at least partially translate the FOV shape from the first position to the second and third positions within the k-space ring. The eyepiece waveguide according to item 33, wherein, using a second interaction, the second CPE grating region is configured to diffract the guided beam such that the FOV shape is translated from the second and third positions to the center of the k-space ring. (Item 38) The eyepiece waveguide according to item 37, wherein the second CPE grating region increases the density of the output beam from the eyepiece waveguide. (Item 39) The eyepiece waveguide according to item 38, wherein the second CPE grating region increases the density of the output beam by at least four times. (Item 40) An eyepiece waveguide for an augmented reality display system, wherein the eyepiece waveguide is An optically transparent substrate having a first surface and a second surface, An input coupling grid (ICG) region formed on or within one of the surfaces of the substrate, wherein the ICG region is configured to receive a beam of light and, in the inductive propagation mode, couple the beam into the substrate; A first combined pupil expander-extractor (CPE) grating region formed on or within the first surface of the substrate, wherein the first CPE grating region is positioned to receive a beam of light from the ICG region, and the first CPE grating region has a plurality of diffraction features configured to modify the propagation direction of the beam using a first interaction and to externally couple the beam from the eyepiece waveguide using a second interaction. Equipped with, The diffraction feature is an eyepiece waveguide with a rhomboid-shaped raised ridge. (Item 41) The aforementioned rhomboid-shaped raised ridges intersect at substantially a 60° angle in the eyepiece waveguide described in item 40. (Item 42) The eyepiece waveguide described in item 40, wherein the rhomboid-shaped raised ridges form rhomboid-shaped gaps between them. (Item 43) The eyepiece waveguide described in item 42, wherein the rhomboid gap has dimensions "a" and "b" between opposing vertices, and the a / b ratio is 0.1 to 0.6. (Item 44) The a / b ratio is 0.2 to 0.5, as described in item 43, for the eyepiece waveguide. (Item 45) The eyepiece waveguide according to item 40, wherein the CPE lattice region exhibits direct external coupling diffraction with an efficiency of less than 1% of diffusion diffraction. (Item 46) An eyepiece waveguide according to item 40, wherein the coating is formed over the diffraction features. (Item 47) The eyepiece waveguide according to item 46, wherein the coating comprises a material having a higher refractive index than that of the diffraction features. (Item 48) The eyepiece waveguide according to item 47, wherein the refractive index of the coating is at least 2.0. (Item 49) The aforementioned coating is conformal, as described in item 47 for the eyepiece waveguide. (Item 50) The aforementioned coating is less than 100 nm thick, as described in item 47, for the eyepiece waveguide. (Item 51) The aforementioned coating is 60 nm or less in thickness, as described in item 50, for the eyepiece waveguide. (Item 52) The eyepiece waveguide according to item 40, wherein the plurality of diffraction features of the first CPE grating region exhibit periodicity in at least two directions. (Item 53) The eyepiece waveguide according to item 52, wherein the plurality of diffraction features of the first CPE grating region exhibit periodicity in first and second directions oriented at substantially 60° angles to each other. (Item 54) The eyepiece waveguide according to item 53, wherein the ICG region has a plurality of diffraction features that exhibit periodicity in a third direction oriented at a substantially 60° angle with respect to both the first and second directions. (Item 55) The eyepiece waveguide according to item 40, further comprising a second CPE grating region formed on or within the second surface of the substrate, wherein the second CPE grating region has a plurality of diffraction features configured to modify the propagation direction of the beam using a first interaction and to externally couple the beam from the eyepiece waveguide using a second interaction. (Item 56) The first and second CPE grating regions are the same as those in the eyepiece waveguide described in item 55. (Item 57) The eyepiece waveguide according to item 55, wherein the substrate has a thickness large enough to prevent the beam from interacting with the ICG region after it has been coupled into the inductive propagation mode. (Item 58) The beam is collimated and has a diameter of 5 mm or less, as described in item 40. (Item 59) The optically transparent substrate is planar, as described in item 40, for the eyepiece waveguide. (Item 60) The eyepiece waveguide described in item 40 is incorporated into an eyepiece for an augmented reality display system. (Item 61) The eyepiece waveguide according to item 60, wherein the eyepiece is configured to display a color image in multiple depth planes. (Item 62) An eyepiece waveguide for an augmented reality display system, wherein the eyepiece waveguide is An optically transparent substrate having a first surface and a second surface, An input coupling grid (ICG) region formed on or within one of the surfaces of the substrate, wherein the ICG region is configured to receive an input beam of light and couple the input beam into the substrate as a guided beam, A first combined pupil expander-extractor (CPE) grating region formed on or within the first surface of the substrate, wherein the first CPE grating region is positioned to receive the guided beam from the ICG region, create a first plurality of diffracted beams at a plurality of dispersion locations, and externally couple a first plurality of output beams, A second CPE grating region formed on or within the second surface of the substrate, wherein the second CPE grating region is positioned to receive the guided beam from the ICG region, create a plurality of second diffracted beams at a plurality of dispersion locations, and externally couple the plurality of second output beams, A first recycler lattice region adjacent to the first CPE lattice region, the first recycler lattice region being positioned and configured to receive a portion of the first plurality of diffraction beams from the first CPE lattice region and redirect them toward the first CPE region, A second recycler lattice region adjacent to the second CPE lattice region, the second recycler lattice region is positioned and configured to receive a portion of the second plurality of diffraction beams from the second CPE lattice region and redirect them toward the second CPE region. An eyepiece waveguide equipped with an eyepiece lens. (Item 63) The eyepiece waveguide according to item 62, wherein the first CPE grating region is configured to externally couple the second plurality of diffracted beams, and the second CPE grating region is configured to externally couple the first plurality of diffracted beams. (Item 64) The eyepiece waveguide described in item 63, wherein the first and second plurality of diffracted beams alternately interact with the first and second CPE grating regions. (Item 65) The eyepiece waveguide according to item 62, wherein both the first CPE grating region and the second CPE grating region comprise a plurality of periodically repeating diffraction lines, and the diffraction lines of the first CPE grating region are oriented at a substantially 60° angle with respect to the diffraction lines of the second CPE grating region. (Item 66) The diffraction lines of the first and second CPE grating regions have the same period, as described in item 65 of the eyepiece waveguide. (Item 67) The diffraction lines of the first and second CPE grating regions are formed using a common master template in the eyepiece waveguide described in item 65. (Item 68) The eyepiece waveguide according to item 65, wherein the ICG region comprises a plurality of periodically repeating diffraction lines, and the diffraction lines of the ICG region are oriented at a substantially 60° angle with respect to the diffraction lines of the first CPE grating region and the diffraction lines of the second CPE grating region. (Item 69) The eyepiece waveguide according to item 68, wherein the diffraction lines of the ICG region, the first CPE grating region, and the second CPE grating region have the same period. (Item 70) The eyepiece waveguide according to item 65, wherein the first and second recycler grating regions comprise a plurality of periodically repeating diffraction lines, and the diffraction lines of the first and second recycler grating regions are oriented at a substantially 30° angle with respect to the diffraction lines of the first CPE grating region and the diffraction lines of the second CPE grating region. (Item 71) The eyepiece waveguide according to item 62, wherein the first and second CPE grating regions overlap by at least 90%. (Item 72) The first and second CPE grating regions are of the same size, as described in item 62, for the eyepiece waveguide. (Item 73) The first and second CPE grating regions are matched to each other in the eyepiece waveguide described in item 72. (Item 74) The eyepiece waveguide according to item 62, wherein the first CPE grating region is configured to create the first plurality of diffracted beams by diffracting a portion of the refractive power of the guided beam from the ICG region in at least two directions. (Item 75) One of the two directions mentioned above corresponds to the zero-order diffracted beam, and is an eyepiece waveguide as described in item 74. (Item 76) The eyepiece waveguide according to item 62, wherein the second CPE grating region is configured to create the second plurality of diffracted beams by diffracting a portion of the refractive power of the guided beam from the ICG region in at least two directions. (Item 77) One of the two directions is the eyepiece waveguide described in item 76, corresponding to the zero-order diffracted beam. (Item 78) An eyepiece waveguide according to item 62, wherein the first plurality of diffracted beams propagate in a first direction, and the second plurality of diffracted beams propagate in a second direction at a substantially 60° angle with respect to the first direction. (Item 79) The input beam is collimated and has a diameter of 5 mm or less, as described in item 62, through an eyepiece waveguide. (Item 80) The optically transparent substrate is planar, as described in item 62, for the eyepiece waveguide. (Item 81) The eyepiece waveguide described in item 62 is incorporated into an eyepiece for an augmented reality display system. (Item 82) The eyepiece waveguide described in item 81 is configured to display a color image in multiple depth planes. (Item 83) The ICG region is configured to receive a set of multiple input beams of light, and the set of input beams is associated with a set of k-vectors that form a field of view (FOV) shape located at the center of a k-space ring associated with the eyepiece waveguide. The ICG region is configured to diffract the input beam as a guided beam so as to couple them into the substrate, and at least partially so as to translate the FOV shape to a first position within the k-space ring. The first CPE grating region is configured to diffract the guided beam so as to at least partially translate the FOV shape to a second position within the k-space ring. The eyepiece waveguide according to item 62, wherein the second CPE grating region is configured to diffract the guided beam such that it at least partially translates the FOV shape to a third position within the k-space ring. (Item 84) The center of the k-space ring, the first position, and the second position define a first equilateral triangle in k-space, as described in item 83, in the eyepiece waveguide. (Item 85) The center of the k-space ring, the first position, and the third position define a second equilateral triangle in k-space, as described in item 84, in the eyepiece waveguide. (Item 86) The first and second equilateral triangles in k-space share sides with the eyepiece waveguide described in item 85. (Item 87) An eyepiece waveguide for an augmented reality display system, wherein the eyepiece waveguide is An optically transparent substrate, The input coupled grid (ICG) region, The first combined pupil expander-extractor (CPE) grid region, The second CPE grid region, The first recycling lattice region, The second recycler lattice region and Equipped with, The ICG region is configured to receive a set of multiple input beams of light, and the set of input beams is associated with a set of k-vectors that form a field of view (FOV) shape located at the center of a k-space ring associated with the eyepiece waveguide. The ICG region is configured to diffract the input beam as a guided beam so as to couple them into the substrate, and at least partially so as to translate the FOV shape to a first position within the k-space ring. The first CPE grating region is configured to diffract the guided beam, at least partially, so as to shift the FOV shape from a first position to a second position within the k-space ring. The second CPE grating region is configured to diffract the guided beam, at least partially, so as to shift the FOV shape from the first position to the third position within the k-space ring. The first CPE grating region is configured to diffract the guided beam such that it shifts the FOV shape from the third position to the center of the k-space ring. The second CPE grating region is configured to diffract the guided beam such that it shifts the FOV shape from the second position to the center of the k-space ring. The first recycler grating region is configured to diffract the guided beam such that it shifts the FOV shape from the second position to the third position. An eyepiece waveguide, wherein the second recycler grating region is configured to diffract the guided beam such that the FOV shape is shifted in parallel from the third position to the second position. (Item 88) The center of the k-space ring, the first position, and the second position define a first equilateral triangle in k-space, as described in item 87, in the eyepiece waveguide. (Item 89) The center of the k-space ring, the first position, and the third position define a second equilateral triangle in k-space, as described in item 88, in the eyepiece waveguide. (Item 90) The first and second equilateral triangles in k-space share sides with the eyepiece waveguide described in item 89. (Item 91) The eyepiece waveguide according to item 87, wherein the first CPE grating region and the second CPE grating region are formed on or within the opposing side of the optically transparent substrate. (Item 92) The guiding beam alternately interacts with the first and second CPE grating regions in the eyepiece waveguide described in item 87. (Item 93) The eyepiece waveguide according to item 87, wherein the first-order lattice vector associated with the first CPE lattice region has the same magnitude as the first-order lattice vector associated with the second CPE lattice region. (Item 94) The eyepiece waveguide according to item 93, wherein the primary grid vector associated with the ICG region has the same magnitude as the primary grid vector associated with the first CPE grid region and the primary grid vector associated with the second CPE grid region. (Item 95) The eyepiece waveguide according to item 93, wherein the primary grid vector associated with the first or second recycler region is equal to ±(CPE1-CPE2), where CPE1 is the primary grid vector associated with the first CPE region and CPE2 is the primary grid vector associated with the second CPE region. (Item 96) The eyepiece waveguide described in item 87 is incorporated into an eyepiece for an augmented reality display system. (Item 97) The eyepiece waveguide according to item 96, wherein the eyepiece is configured to display a color image in multiple depth planes. [Brief explanation of the drawing]

[0011] [Figure 1] Figure 1 illustrates the user's view of augmented reality (AR) through an AR device.

[0012] [Figure 2] Figure 2 illustrates an embodiment of a wearable display system.

[0013] [Figure 3] Figure 3 illustrates a conventional display system for simulating three-dimensional image data for the user.

[0014] [Figure 4] Figure 4 illustrates aspects of an approach to simulating 3D image data using multiple depth planes.

[0015] [Figure 5]Figures 5A-5C illustrate the relationship between the radius of curvature and the radius of focus.

[0016] [Figure 6] Figure 6 illustrates an example of a waveguide stack for outputting image information to the user within an AR eyepiece.

[0017] [Figure 7] Figures 7A-7B illustrate an example of an output beam generated by a waveguide.

[0018] [Figure 8] Figure 8 illustrates an embodiment of a stacked waveguide assembly, where each depth plane includes an image formed using multiple different primary colors.

[0019] [Figure 9A] Figure 9A shows a cross-sectional side view of an embodiment of a stacked waveguide set, each including an internally coupled optical element.

[0020] [Figure 9B] Figure 9B shows a perspective view of an embodiment of the multiple stacked waveguides shown in Figure 9A.

[0021] [Figure 9C] Figure 9C shows top and bottom plan views of the embodiment of the multiple stacked waveguides shown in Figures 9A and 9B.

[0022] [Figure 10] Figure 10 is a perspective view of an exemplary AR eyepiece waveguide stack.

[0023] [Figure 11] Figure 11 is a cross-sectional view of a portion of an exemplary eyepiece waveguide stack, with an edge sealing structure for supporting the eyepiece waveguides in a stacked configuration.

[0024] [Figure 12A]Figures 12A and 12B illustrate the top view of the eyepiece waveguide during operation when projecting an image toward the user's eye. [Figure 12B] Figures 12A and 12B illustrate the top view of the eyepiece waveguide during operation when projecting an image toward the user's eye.

[0025] [Figure 13A] Figure 13A illustrates a k-vector, which can be used to represent the propagation direction of a ray or beam of light.

[0026] [Figure 13B] Figure 13B illustrates the light rays within a planar waveguide.

[0027] [Figure 13C] Figure 13C illustrates the acceptable k-vectors for light of a given angular frequency ω propagating through a non-boundary homogeneous medium with refractive index n.

[0028] [Figure 13D] Figure 13D illustrates the allowable k-vectors for light of a given angular frequency ω propagating through a homogeneous planar waveguide medium with refractive index n.

[0029] [Figure 13E] Figure 13E illustrates a ring in k-space corresponding to the k-vector of a light wave that can be induced in a waveguide with refractive index n2.

[0030] [Figure 13F] Figure 13F shows a k-space diagram and an eyepiece waveguide illustrating the relationship between the k-vector and the density of interaction between the k-vector and the corresponding guided beam and the diffraction grating formed on or inside the waveguide.

[0031] [Figure 13G] Figure 13G shows a top view of the diffraction grating and some of its associated k-space diffraction grating vectors (G-2, G-1, G1, G2).

[0032] [Figure 13H] Figure 13H illustrates a side view of the diffraction grating and its effect in k-space on the k-vector corresponding to the normal incident ray or beam of light.

[0033] [Figure 13I] Figure 13I illustrates a side view of the diffraction grating shown in Figure 13G and its effect in k-space on the k-vector corresponding to the obliquely incident light ray or beam of light.

[0034] [Figure 13J] Figure 13J is a k-space diagram illustrating the field of view of the image projected into the AR eyepiece waveguide.

[0035] [Figure 13K] Figure 13K is a k-space diagram showing the k-space translational shift of the FOV rectangle caused by the input coupling grating (ICG) located at the entrance pupil of the eyepiece waveguide.

[0036] [Figure 14A] Figure 14A illustrates an exemplary eyepiece waveguide with an ICG region, an orthogonal pupil expander (OPE) region, and an exit pupil expander (EPE) region.

[0037] [Figure 14B] Figure 14B illustrates the k-space action of the eyepiece waveguide shown in Figure 14A.

[0038] [Figure 14C] Figure 14C illustrates the optical effects of the OPE region shown in Figures 14A and 14B.

[0039] [Figure 14D] Figure 14D illustrates the techniques used to determine the size and shape of the OPE and EPE regions.

[0040] [Figure 15A] Figure 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.

[0041] [Figure 15B] Figure 15B includes a k-space diagram illustrating the operation of the eyepiece waveguide shown in Figure 15A.

[0042] [Figure 15C] Figure 15C is another k-space diagram illustrating the operation of the eyepiece waveguide shown in Figure 15A.

[0043] [Figure 15D] Figure 15D is a schematic diagram of the first occurrence of interaction between the input beam and the OPE region of the eyepiece waveguide embodiment shown in Figure 15A.

[0044] [Figure 15E] Figure 15E is a schematic diagram of the second occurrence of the interaction between the input beam and the OPE region of the eyepiece waveguide embodiment shown in Figure 15A.

[0045] [Figure 15F] Figure 15F is a schematic diagram of the third generation of interaction between the input beam and the OPE region of the eyepiece waveguide embodiment shown in Figure 15A.

[0046] [Figure 15G] Figure 15G is a schematic diagram illustrating how a single input beam from the ICG region is duplicated by the OPE region and redirected as multiple beams toward the EPE region.

[0047] [Figure 16A] Figure 16A illustrates an exemplary eyepiece waveguide that has a multidirectional pupil expander (MPE) region rather than an OPE region.

[0048] [Figure 16B] Figure 16B illustrates a portion of an exemplary 2D grid that may be used within the MPE region shown in Figure 16A, along with its associated grid vectors.

[0049] [Figure 16C] Figure 16C is a k-space diagram illustrating the k-space action in the MPE region of the eyepiece waveguide shown in Figure 16A.

[0050] [Figure 16D] Figure 16D is a k-space diagram that further illustrates the k-space action in the MPE region of the eyepiece waveguide shown in Figure 16A.

[0051] [Figure 16E] Figure 16E is a k-space diagram illustrating the k-space action of the eyepiece waveguide shown in Figure 16A.

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

[0053] [Figure 16G] Figure 16G is a schematic diagram of the second occurrence of the interaction between the input beam and the MPE region of the eyepiece waveguide embodiment shown in Figure 16A.

[0054] [Figure 16H] Figure 16H is a schematic diagram of the third occurrence of the interaction between the input beam and the MPE region of the eyepiece waveguide embodiment shown in Figure 16A.

[0055] [Figure 16I] Figure 16I is a schematic diagram of the fourth generation of interaction between the input beam and the MPE region of the eyepiece waveguide embodiment shown in Figure 16A.

[0056] [Figure 16J]Figure 16J is a schematic diagram illustrating various paths through which the beam can follow from the MPE region to the EPE region, ultimately, according to the eyepiece waveguide embodiment shown in Figure 16A.

[0057] [Figure 16K] Figure 16K is a schematic diagram illustrating how a single input beam from the ICG region is duplicated by the MPE region and redirected as multiple beams toward the EPE region.

[0058] [Figure 16L] Figure 16L is a comparative diagram illustrating the performance of an eyepiece waveguide with an OPE region versus an eyepiece waveguide with an MPE region.

[0059] [Figure 16M] Figure 16M further illustrates the performance of an eyepiece waveguide with an MPE region versus another with an OPE region.

[0060] [Figure 17A] Figure 17A illustrates a portion of an exemplary 2D grid that may be used within the MPE region of an eyepiece waveguide, along with its associated grid vector.

[0061] [Figure 17B] Figure 17B is a k-space diagram illustrating the k-space action in the MPE region of the eyepiece waveguide.

[0062] [Figure 17C] Figure 17C is a k-space diagram illustrating the k-space action of an eyepiece waveguide with an MPE region.

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

[0064] [Figure 17E]Figure 17E is a schematic diagram of the second generation of interaction between the input beam and the MPE region of the eyepiece waveguide.

[0065] [Figure 17F] Figure 17F is a schematic diagram of the third generation of interaction between the input beam and the MPE region of the eyepiece waveguide.

[0066] [Figure 17G] Figure 17G is a schematic diagram of the fourth generation of interaction between the input beam and the MPE region of the eyepiece waveguide.

[0067] [Figure 18A] Figure 18A illustrates an exemplary eyepiece waveguide with an ICG region, two orthogonal pupil expander regions, and an exit pupil expander region.

[0068] [Figure 18B] Figures 18B and 18C illustrate the top view of the EPE region of the eyepiece waveguide shown in Figure 18A. [Figure 18C] Figures 18B and 18C illustrate the top view of the EPE region of the eyepiece waveguide shown in Figure 18A.

[0069] [Figure 19] Figure 19 illustrates an embodiment of an eyepiece waveguide with an extended field of view.

[0070] [Figure 20A] Figure 20A illustrates an embodiment of an extended FOV eyepiece waveguide with an MPE region overlapping with the EPE region.

[0071] [Figure 20B] Figure 20B illustrates a portion of an exemplary 2D grid that may be used within the MPE region of the eyepiece waveguide in Figure 20A, along with its associated grid vector.

[0072] [Figure 20C]Figure 20C is a k-space diagram illustrating the k-space action of the ICG region of the eyepiece waveguide in Figure 20A.

[0073] [Figure 20D] Figure 20D is a k-space diagram illustrating a portion of the k-space action in the MPE region of the eyepiece waveguide shown in Figure 20A.

[0074] [Figure 20E] Figure 20E is a k-space diagram illustrating another portion of the k-space action in the MPE region of the eyepiece waveguide in Figure 20A.

[0075] [Figure 20F] Figure 20F is similar to Figure 20E, but shifted to the 9 o'clock position (instead of the 3 o'clock position as shown in Figure 20E), showing the k-space action of the MPE region on the FOV rectangle from Figure 20D.

[0076] [Figure 20G] Figure 20G is a k-space diagram illustrating the k-space action of the EPE region within the eyepiece waveguide in Figure 20A.

[0077] [Figure 20H] Figure 20H is a k-space diagram summarizing the k-space action of the eyepiece waveguide in Figure 20A.

[0078] [Figure 20I] Figure 20I is a schematic diagram illustrating how a beam of light diffuses through the eyepiece waveguide shown in Figure 20A.

[0079] [Figure 20J] Figure 20J illustrates a method by which the diffraction efficiency of the MPE region within the eyepiece waveguide in Figure 20A can be spatially varied to improve the uniformity of brightness within the waveguide.

[0080] [Figure 20K]Figure 20K illustrates a method by which the diffraction efficiency of the EPE region within the eyepiece waveguide in Figure 20A can be spatially varied to improve the uniformity of brightness within the waveguide.

[0081] [Figure 20L] Figure 20L illustrates an embodiment of the eyepiece waveguide in Figure 20A, which includes one or more diffraction mirrors around the peripheral edge of the waveguide.

[0082] [Figure 20M] Figure 20M illustrates an exemplary embodiment of eyeglasses that incorporates one or more instances of the eyepiece waveguide shown in Figure 20A.

[0083] [Figure 20N] Figure 20N illustrates another exemplary embodiment of eyeglasses that incorporates one or more instances of the eyepiece waveguide in Figure 20A.

[0084] [Figure 21A] Figure 21A illustrates another embodiment of an eyepiece waveguide, with an MPE region overlapping the EPE region.

[0085] [Figure 21B] Figure 21B is a k-space diagram illustrating the k-space action of the eyepiece waveguide in Figure 20A on a set of first input beams corresponding to a first sub-part of the FOV of the input image.

[0086] [Figure 21C] Figure 21C is a k-space diagram illustrating the k-space action of the eyepiece waveguide in Figure 21A on a second set of input beams corresponding to a second sub-part of the input image's FOV.

[0087] [Figure 21D] Figure 21D is a k-space diagram summarizing the k-space action of the eyepiece waveguide in Figure 21A.

[0088] [Figure 21E] Figure 21E illustrates an exemplary embodiment of eyeglasses that incorporates one or more instances of the eyepiece waveguide shown in Figure 21A.

[0089] [Figure 21F] Figure 21F illustrates an exemplary FOV corresponding to the eyeglasses in Figure 21E.

[0090] [Figure 21G] Figure 21G illustrates the k-space action of another embodiment of the eyepiece waveguide shown in Figure 21A.

[0091] [Figure 22A] Figure 22A illustrates an embodiment of an eyepiece waveguide capable of projecting an extended field of view in two directions.

[0092] [Figure 22B] Figure 22B shows the opposite side of the eyepiece waveguide shown in Figure 22A.

[0093] [Figure 22C] Figure 22C illustrates the k-space interaction of the ICG region and OPE region within the eyepiece waveguide embodiment shown in Figure 22A.

[0094] [Figure 22D] Figure 22D illustrates the k-space action of the MPE region within the eyepiece waveguide embodiment shown in Figure 22A.

[0095] [Figure 22E] Figure 22E illustrates the k-space action of the EPE region within the eyepiece waveguide embodiment shown in Figure 22A.

[0096] [Figure 23] Figure 23 illustrates an exemplary embodiment of an eyepiece waveguide designed to function with an angled projector.

[0097] [Figure 24A] Figure 24A is an edge view of an exemplary eyepiece waveguide having a plurality of combined pupil expander - extractor (CPE) regions.

[0098] [Figure 24B] Figure 24B illustrates the operation of the first and second CPE regions in both physical space and k - space following the first type of main path of light through the eyepiece waveguide.

[0099] [Figure 24C] Figure 24C illustrates the operation of the first and second CPE regions in both physical space and k - space following the second type of main path of light through the eyepiece waveguide.

[0100] [Figure 24D] Figure 24D illustrates the operation of the first and second CPE regions in both physical space and k - space following both the first and second types of main paths of light through the eyepiece waveguide.

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

[0102] [Figure 24F] [[ID={33}]]Figure 24F is a schematic diagram of the second occurrence of the interaction between the input beam and the CPE region of the eyepiece waveguide embodiment shown in Figure 24A.

[0103] [Figure 24G] Figure 24G is a schematic diagram of the third occurrence of the interaction between the input beam and the CPE region of the eyepiece waveguide embodiment shown in Figure 24A.

[0104] [Figure 24H]Figure 24H is a schematic diagram of a fourth occurrence of the interaction between the input beam and the CPE region of the eyepiece waveguide embodiment shown in Figure 24A.

[0105] [Figure 24I] Figure 24I is a schematic diagram of a fifth occurrence of the interaction between the input beam and the CPE region of the eyepiece waveguide embodiment shown in Figure 24A.

[0106] [Figure 24J] Figure 24J illustrates higher-order paths of light passing through the eyepiece waveguide shown in Figure 24A in k-space

[0107] [Figure 24K] Figure 24K is a schematic diagram illustrating a method by which a beam of light diffuses through the eyepiece waveguide shown in Figure 24A.

[0108] [Figure 24L] Figure 24L illustrates another exemplary embodiment of an eyepiece waveguide that is the same as that shown in Figure 24A, but rotated such that the ICG region is located on the sides of the first and second CPE regions rather than above them.

[0109] [Figure 24M] Figure 24M illustrates another exemplary embodiment of an eyepiece waveguide that is the same as that shown in Figure 24L, except that the eyepiece waveguide is modified to include a recycler diffraction grating.

[0110] [Figure 24N] Figure 24N is a k-space diagram KSD3 illustrating the k-space action of the eyepiece waveguide shown in Figure 24M, including the k-space action of the recycler region.

[0111] [Figure 25A] Figure 25A is an edge view of an exemplary eyepiece waveguide having a single 2D combined pupil expander-extractor (CPE) grating region.

[0112] [Figure 25B] Figure 25B illustrates the behavior of the 2D CPE region in both physical space and k-space.

[0113] [Figure 25C] Figure 25C illustrates an exemplary embodiment of a 2D lattice structure that, when used in the eyepiece waveguide of Figure 25A, can reduce direct external coupling of light from the CPE region.

[0114] [Figure 25D] Figure 25D illustrates several exemplary embodiments of a 2D lattice structure that, when used in the eyepiece waveguide of Figure 25A, can regenerate light as shown in Figures 24M-N and reduce direct external coupling of light from the CPE region as shown in Figure 25C.

[0115] [Figure 26A] Figure 26A is an edge view of an exemplary eyepiece waveguide, having 2D combined pupil expander-extractor (CPE) grating regions on each of its sides.

[0116] [Figure 26B] Figure 26B illustrates the so-called "screen effect," an image artifact related to the density of the output beam from the eyepiece waveguide.

[0117] [Figure 26C] Figure 26C illustrates input-coupled grating rebounce, an undesirable effect that can cause light loss from the eyepiece waveguide.

[0118] [Figure 26D] Figure 26D illustrates how the double-sided 2D CPE grating in Figure 26A increases the density of the output beam from the eyepiece waveguide.

[0119] [Figure 26E]Figure 26E illustrates the output beam density for the eyepiece waveguide shown in Figure 24A (double-sided 1D CPE grid), Figure 25A (single-sided 2D CPE grid), and Figure 26A (double-sided 2D CPE grid).

[0120] [Figure 26F] Figure 26F shows an exemplary simulated image produced by an eyepiece waveguide with a 2D CPE grating, with images for both the single-sided embodiment in Figure 25A and the double-sided embodiment in Figure 26A.

[0121] [Figure 27A] Figure 27A illustrates an exemplary embodiment of an eyepiece waveguide stack with an improved field of view (FOV).

[0122] [Figure 27B] Figure 27B illustrates another exemplary embodiment of an eyepiece waveguide stack with an improved field of view (FOV).

[0123] [Figure 27C] Figures 27C–27E include k-space diagrams illustrating the k-space action of exemplary embodiments of the eyepiece waveguide stack shown in Figures 27A and 27B for three different refractive indices. [Figure 27D] Figures 27C–27E include k-space diagrams illustrating the k-space action of exemplary embodiments of the eyepiece waveguide stack shown in Figures 27A and 27B for three different refractive indices. [Figure 27E] Figures 27C–27E include k-space diagrams illustrating the k-space action of exemplary embodiments of the eyepiece waveguide stack shown in Figures 27A and 27B for three different refractive indices.

[0124] [Figure 27F]Figures 27F-27H illustrate sub-portions of the FOV of each color component of the input image, which 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 transported within two of the eyepiece waveguides. [Figure 27G] Figures 27F-27H illustrate sub-portions of the FOV of each color component of the input image, which 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 transported within two of the eyepiece waveguides. [Figure 27H] Figures 27F-27H illustrate sub-portions of the FOV of each color component of the input image, which 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 transported within two of the eyepiece waveguides.

[0125] [Figure 27I] 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, which can be internally coupled into each of the eyepiece waveguides in the stack; however, Figures 27I-27K illustrate one embodiment in which each color component is partially carried in three eyepiece waveguides instead of two. [Figure 27J] 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, which can be internally coupled into each of the eyepiece waveguides in the stack; however, Figures 27I-27K illustrate one embodiment in which each color component is partially carried in three eyepiece waveguides instead of two. [Figure 27K] 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, which can be internally coupled into each of the eyepiece waveguides in the stack; however, Figures 27I-27K illustrate one embodiment in which each color component is partially carried in three eyepiece waveguides instead of two.

[0126] [Figure 27L] Figures 27L-27N illustrate sub-fields of the field of view (FOV) for each color component of the input image, which can be internally coupled within the eyepiece waveguide for each monochromatic component per layer. [Figure 27M] Figures 27L-27N illustrate sub-fields of the field of view (FOV) for each color component of the input image, which can be internally coupled within the eyepiece waveguide for each monochromatic component per layer. [Figure 27N] Figures 27L-27N illustrate sub-fields of the field of view (FOV) for each color component of the input image, which can be internally coupled within the eyepiece waveguide for each monochromatic component per layer.

[0127] [Figure 28A] Figure 28A illustrates another exemplary embodiment of an eyepiece waveguide stack with improved FOV and inline pupil ICG configuration.

[0128] [Figure 28B] Figure 28B illustrates another exemplary embodiment of an eyepiece waveguide stack with improved FOV and split pupil ICG configuration.

[0129] [Figure 29] Figure 29 is a graph plotting the FOV values ​​in Table 1 as a function of refractive index.

[0130] [Figure 30] Figure 30 illustrates an example of improved output image uniformity using the eyepiece waveguide stack shown in Figures 27A-27B and 28A-28B.

[0131] [Figure 31A] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31B]Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31C] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31D] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31E] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31F] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31G] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31H] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31I] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31J] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31K] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31L] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31M] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31N] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31O] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31P] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31Q] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31R] Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Figure 31S]Figures 31A-31S illustrate embodiments of diffraction gratings that may be used in an eyepiece waveguide, including diffraction gratings with high refractive index coatings, blazed diffraction gratings, and gradation diffraction gratings. [Modes for carrying out the invention]

[0132] Detailed explanation overview This disclosure describes various eyepiece waveguides that may be used in AR display systems to project images onto a user's eye. The eyepiece waveguides are described both in physical terms and using k-space representations. Exemplary HMD device

[0133] Figure 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 function of the display 70. The display 70 may be coupled to a frame 80, which is wearable by the display system user 90 and is configured to position the display 70 in front of the user 90's eyes. In some embodiments, the display 70 may be considered eyewear. In some embodiments, a speaker 100 is coupled to the frame 80 and positioned adjacent to the user 90's ear canal. The display system may also include one or more microphones 110 to detect sound. The microphones 110 can enable the user to provide input or commands to the system 60 (e.g., selection of voice menu commands, natural language questions, etc.) and / or enable audio communication with other persons (e.g., other users of a similar display system). The microphones 110 can also collect audio data (e.g., sounds from the user and / or the environment) from the user's surroundings. In some embodiments, the display system may also include a peripheral sensor 120a, which is separate from the frame 80 and may be mounted on the user 90's body (e.g., on the head, torso, limbs, etc.). In some embodiments, the peripheral sensor 120a may acquire data characterizing the user 90's physiological state.

[0134] The display 70 is operably coupled to the local data processing module 140 by a communication link 130, such as a wired connection or wireless connectivity, which may be mounted in various configurations, such as being fixedly attached to the frame 80, fixedly attached to a helmet or hat worn by the user, built into headphones, or detachably attached to the user 90 (e.g., in a backpack configuration or a belt-mounted configuration). Similarly, the sensor 120a may be operably coupled to the local processor and data module 140 by a communication link 120b (e.g., a wired connection 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 used to assist in data processing, caching, and storage. The data may include 1) data captured from sensors such as image acquisition devices (e.g., cameras), microphones, inertial measurement units, accelerometers, compasses, GPS units, wireless devices, gyroscopes, and / or other sensors disclosed herein (e.g., operably coupled to frame 80 or otherwise attached to user 90), and / or 2) possibly data obtained and / or processed using the remote processing module 150 and / or remote data repository 160 (including data related to virtual content) for passage to display 70 after processing or reading. The local processing and data module 140 may be operably coupled to the remote processing module 150 and the remote data repository 160 by communication links 170, 180 via wired or wireless communication links, etc., so that these remote modules 150, 160 are operably coupled to each other and available as resources for the local processing and data module 140.In some embodiments, the local processing and data module 140 may include one or more of the following: an image acquisition device, a microphone, an inertial measurement unit, an accelerometer, a compass, a GPS unit, a wireless device, and / or a gyroscope. In some other embodiments, one or more of these sensors may be mounted on the frame 80 or be a standalone device communicating with the local processing and data module 140 via a wired or wireless communication path.

[0135] The remote processing module 150 may include one or more processors for analyzing and processing data such as image and audio information. In some embodiments, the remote data repository 160 may be a digital data storage facility, which may be available through the internet or other networking configurations in a “cloud” resource configuration. In some embodiments, the remote data repository 160 may include one or more remote servers that provide information (e.g., information for generating augmented reality content) to the local processing and data module 140 and / or the remote processing module 150. In other embodiments, all data is stored, and all calculations are performed in the local processing and data module, enabling fully autonomous use from the remote module.

[0136] The perception of an image as "three-dimensional" or "3-D" can be achieved by providing slightly different presentations of the image to each of the user's eyes. Figure 3 illustrates a conventional display system for simulating three-dimensional image data relating to a user. Two distinctly different images 190, 200, one for each eye 210, 220, are output to the user. Images 190, 200 are spaced only 230 units apart from eyes 210, 220 along the optical or z-axis parallel to the user's line of sight. Images 190, 200 are flat, and eyes 210, 220 can focus on the image by taking a single, focused state. Such a 3-D display system relies on the human visual system, combines images 190, 200, and provides a perception of depth and / or scale of the combined image.

[0137] However, the human visual system is complex, and providing a realistic perception of depth is difficult. For example, many users of conventional "3-D" display systems find such systems unpleasant or perceive no sense of depth at all. Objects can be perceived as "three-dimensional" due to a combination of convergence-divergence movements and accommodation. The convergence-divergence movement of two eyes relative to each other (e.g., pupillary rotation such that the pupils move toward or away from each other, converging the individual lines of sight of the eyes and fixing on an object) is closely related to the focusing (or "accommodation") of the eye's lens. Under normal conditions, a change in the focus of the eye's lens or the eye's accommodation to change the focus from one object to another object at a different distance will automatically result in a consistent change in convergence-divergence movements at the same distance, under the relationship known as the "accommodation-convergence-divergence reflex" and pupillary dilation or miosis. Similarly, under normal conditions, changes in convergence and divergence movements will induce changes in the alignment of accommodative lens shape and pupil size. As described herein, many stereoscopic or "3-D" display systems display a scene using slightly different presentations (and therefore slightly different images) to each eye so that the three-dimensional viewpoint is perceived by the human visual system. However, such systems may be uncomfortable for some users because they simply provide image information in a single accommodative state and function against the "accommodative-convergence / divergence reflex." A display system that provides a better match between accommodation and convergence / divergence movements can form a more realistic and comfortable simulation of three-dimensional image data.

[0138] Figure 4 illustrates aspects of an approach for simulating three-dimensional image data using multiple depth planes. Referring to Figure 4, eyes 210, 220 take on different accommodated states, focusing objects at various distances along the z-axis. As a result, a particular accommodated state can be associated with one of the illustrated depth planes 240, each having an associated focal length such that an object or part of an object in a particular depth plane is in focus when the eye is accommodated to that depth plane. In some embodiments, the three-dimensional image data may be simulated by providing a different presentation of the image for each eye 210, 220, and by providing different presentations of the image corresponding to multiple depth planes. Although shown as separate for the sake of clarity in the illustration, the individual fields of view of eyes 210, 220 may overlap, for example, as the distance along the z-axis increases. In addition, while the depth plane is shown as flat for the sake of illustration, it should be understood that the contour of the depth plane can be curved in physical space so that all features within the depth plane are in focus with the eye in a particular state of focus adjustment.

[0139] The distance between an object and the eye 210 or 220 can also change the amount of light diverging from that object as visible to that eye. Figures 5A-5C illustrate the relationship between distance and ray divergence. The distance between the object and the eye 210 is expressed in the order of decreasing distances R1, R2, and R3. As shown in Figures 5A-5C, rays diverge more as the distance to the object decreases. As the distance increases, rays become more collimated. In other words, the light field produced by a point (object or part of an object) can be said to have a spherical wavefront curvature, which is a function of the distance the point is from the user's eye. The curvature increases with decreasing distance between the object and the eye 210. Consequently, in different depth planes, the ray divergence is also different, and the divergence increases with decreasing distance between the depth plane and the user's eye 210. Only a single eye 210 is illustrated in Figures 5A–5C and other figures herein for illustrative purposes, but it should be understood that the discussion relating to eye 210 may apply to both eyes 210 and 220 of the user.

[0140] A highly realistic simulation of perceived depth can be achieved by providing the eye with different presentations of images corresponding to each of a limited number of depth planes. These different presentations can be individually focused by the user's eye and thereby help provide the user with depth cues based on the amount of eye accommodation required to focus on different image features for scenes located on different depth planes, and / or on observations of different image features on different depth planes that are out of focus. (An example of a waveguide stack assembly for AR or MR eyepieces)

[0141] Figure 6 illustrates an embodiment of a waveguide stack for outputting image information to the user within an AR eyepiece. The display system 250 includes a waveguide stack or stacked waveguide assembly 260, which may be used to provide three-dimensional perception to the eye / brain using a plurality of waveguides 270, 280, 290, 300, 310. In some embodiments, the display system 250 is system 60 in Figure 2, and Figure 6 shows some parts of that system 60 in more detail. For example, the waveguide assembly 260 may be part of the display 70 in Figure 2. It should be understood that the display system 250 may be considered a light field display in some embodiments.

[0142] Waveguide assembly 260 may also include several features 320, 330, 340, 350 between the waveguides. In some embodiments, features 320, 330, 340, 350 may be one or more lenses. 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 varying levels of wavefront curvature or ray divergence. Each waveguide level may be associated with a specific depth plane and may be configured to output image information corresponding to that depth plane. Image input devices 360, 370, 380, 390, and 400 may function as light sources for the waveguides and may be used to input image information into the waveguides 270, 280, 290, 300, and 310, and each may be configured to disperse incident light across each individual waveguide for output toward the eye 210, as described herein. The light exits from the output surfaces 410, 420, 430, 440, and 450 of each individual image input device 360, 370, 380, 390, and 400 and is input into the corresponding input surfaces 460, 470, 480, 490, and 500 of the individual waveguides 270, 280, 290, 300, and 310. In some embodiments, the input surfaces 460, 470, 480, 490, and 500 may each be the edge of the corresponding waveguide or a portion of the main 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 injected into each waveguide, replicated by refraction within the waveguide, such as by sampling into a beamlet, and then directed toward the eye 210 with an amount of refractive force corresponding to the depth plane associated with that particular waveguide. In some embodiments, one of the image input devices 360, 370, 380, 390, and 400 may be associated with a plurality (e.g., three) of waveguides 270, 280, 290, 300, and 310, into which light may be injected.

[0143] In some embodiments, the image input devices 360, 370, 380, 390, and 400 are discrete displays, each producing image information for input into the corresponding waveguides 270, 280, 290, 300, and 310, respectively. In some other embodiments, the image input devices 360, 370, 380, 390, and 400 are output terminals of a single multiplexed display, which can send image information to each of the image input devices 360, 370, 380, 390, and 400 via one or more optical conduits (such as fiber optic cables). It should be understood that the image information provided by the image input devices 360, 370, 380, 390, and 400 may include light of different wavelengths or colors.

[0144] In some embodiments, the light introduced into waveguides 270, 280, 290, 300, and 310 is provided by an optical projector system 520, which includes an optical module 530, which may include a light source or optical emitter such as a light-emitting diode (LED). The light from the optical module 530 may be directed and modulated by an optical modulator 540 (e.g., a spatial light modulator) via a beam splitter (BS) 550. The optical modulator 540 may spatially and / or temporally vary the perceived intensity of the light introduced into waveguides 270, 280, 290, 300, and 310. Embodiments of the spatial light modulator include liquid crystal displays (LCDs) and digital light processing (DLP) displays, including liquid crystal displays on silicon (LCOS).

[0145] In some embodiments, the optical projector system 520 or one or more components thereof may be mounted on the frame 80 (Figure 2). For example, the optical projector system 520 may be part of the temple portion (e.g., the ear hook portion 82) of the frame 80, or positioned on the edge of the display 70. In some embodiments, the optical module 530 may be separate from the BS550 and / or the optical modulator 540.

[0146] 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 scanning, helical scanning, Lissajous patterns, etc.) into one or more waveguides 270, 280, 290, 300, 310, and ultimately into the user's eye 210. In some embodiments, the illustrated image input devices 360, 370, 380, 390, 400 may schematically represent a single scanning fiber or a bundle of scanning fibers configured to input light into one or more waveguides 270, 280, 290, 300, 310. In some other embodiments, the illustrated image input devices 360, 370, 380, 390, 400 may schematically represent a plurality of scanning fibers or a plurality of bundles of scanning fibers, each configured to input light into one of the associated waveguides 270, 280, 290, 300, 310. One or more optical fibers may transmit light from the optical module 530 to one or more waveguides 270, 280, 290, 300, and 310. In addition, one or more intervening optical structures may be provided between the scanning fiber or multiple fibers and one or more waveguides 270, 280, 290, 300, and 310 to, for example, redirect light emanating from the scanning fiber into one or more waveguides 270, 280, 290, 300, and 310.

[0147] The controller 560 controls the operation of the stacked waveguide assembly 260, including the operation of the image input devices 360, 370, 380, 390, 400, the light source 530, and the optical modulator 540. In some embodiments, the controller 560 is part of the local data processing module 140. The controller 560 includes programming (e.g., instructions in a non-transient medium) to coordinate the timing and delivery of image information to the waveguides 270, 280, 290, 300, 310. In some embodiments, the controller may be a single integrated device or a distributed system connected by wired or wireless communication channels. In some embodiments, the controller 560 may be part of the processing module 140 or 150 (Figure 2).

[0148] Waveguides 270, 280, 290, 300, and 310 may be configured to propagate light within each individual waveguide by total internal reflection (TIR). Waveguides 270, 280, 290, 300, and 310 may each be planar or have another shape (e.g., curved), with major upper and lower surfaces and edges extending between their major upper and lower surfaces. In the illustrated configuration, waveguides 270, 280, 290, 300, and 310 may each include external coupling optical elements 570, 580, 590, 600, and 610, respectively, configured to extract light from the waveguide by redirecting the light propagating within each individual waveguide outwards from the waveguide and outputting image information to the eye 210. The extracted light may also be referred to as externally coupled light, and the optical elements that externally couple the light may also be referred to as light extraction optical elements. The extracted beam of light can be output by a waveguide at the point where light propagating within the waveguide strikes the light extraction optical element. The external coupling optical elements 570, 580, 590, 600, 610 may be diffractive optical features, including, for example, a diffraction grating, as further discussed herein. The external coupling optical elements 570, 580, 590, 600, 610 are shown positioned on the bottom main surface of the waveguides 270, 280, 290, 300, 310, but in some embodiments they may be positioned on the top and / or bottom main surface, and / or directly within the volume of the waveguides 270, 280, 290, 300, 310, as further discussed herein. In some embodiments, the external coupling optical elements 570, 580, 590, 600, 610 may be mounted on a transparent substrate and formed within a layer of material that 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 external coupling optical elements 570, 580, 590, 600, 610 may be formed on and / or inside the material piece.

[0149] Each waveguide 270, 280, 290, 300, and 310 may output light and form an image corresponding to a specific depth plane. For example, waveguide 270, closest to the eye, may deliver a collimated beam of light to the eye 210. The collimated beam of light may represent the 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 some convex wavefront curvature to the collimated beam so that the eye / brain interprets the light emanating from its waveguide 280 as emanating from a first focal plane that is closer and inward from optical infinity toward the eye 210. Similarly, the third waveguide 290 passes its output light through both the first lens 350 and the second lens 340 before reaching the eye 210. The combined refractive power of the first lens 350 and the second lens 340 may have an additional gradually increasing wavefront curvature added so that the eye / brain interprets the light emanating from the third waveguide 290 as emanating from a second focal plane that is even closer inward from optical infinity than the light emanating from the second waveguide 280.

[0150] Other waveguide layers 300, 310 and lenses 330, 320 are configured similarly, with the highest waveguide 310 in the stack emitting its output through all the lenses between it and the eye for a concentrated focal force representing the focal plane closest to the person. When viewing / interpreting light originating from the other side world 510 of the stacked waveguide assembly 260, a compensating lens layer 620 may be positioned on top of the stack to compensate for the stack of lenses 320, 330, 340, 350 and to compensate for the concentrated refractive force of the lower lens stacks 320, 330, 340, 350. Such a configuration provides the same number of perceived focal planes as there are available waveguide / lens pairs. Both the external coupling optical elements of the waveguides and the focusing sides of the lenses may be static (i.e., not dynamic or electroactive). In some alternative embodiments, one or both may be dynamic using electroactive features.

[0151] In some embodiments, two or more of the waveguides 270, 280, 290, 300, and 310 may have the same associated depth plane. For example, multiple waveguides 270, 280, 290, 300, and 310 may output images set to the same depth plane, or multiple subsets of waveguides 270, 280, 290, 300, and 310 may output images set to the same multiple depth planes, with one set for each depth plane. This may offer the advantage of forming tiled images that provide an extended field of view in those depth planes.

[0152] External coupling optical elements 570, 580, 590, 600, 610 may be configured to redirect light from their individual waveguides for specific depth planes associated with the waveguides and to output the light with an appropriate amount of divergence or collimation. As a result, waveguides having different associated depth planes may have external coupling optical elements 570, 580, 590, 600, 610 with different configurations, outputting light with different amounts of divergence depending on the associated depth plane. In some embodiments, the light extraction optical elements 570, 580, 590, 600, 610 may be three-dimensional or surface features that can be configured to output light at specific angles. For example, the light extraction optical elements 570, 580, 590, 600, 610 may be three-dimensional holograms, surface holograms, and / or diffraction gratings. In some embodiments, features 320, 330, 340, 350 may not be lenses. Rather, they may simply be spacers (e.g., cladding layers and / or structures for forming voids).

[0153] In some embodiments, the external coupling optical elements 570, 580, 590, 600, and 610 are diffraction features with sufficiently low diffraction efficiency such that only a portion of the refractive power of the light in the beam is redirected toward the eye 210 with each interaction, while the remainder continues to travel through the waveguide via TIR. Thus, the exit pupil of the optical module 530 is replicated across the waveguide, creating multiple output beams that carry image information from the light source 530, effectively expanding the number of locations where the eye 210 can capture the replicated light source exit pupil. These diffraction features may also have variable diffraction efficiency across their geometry, improving the uniformity of the light output by the waveguide.

[0154] In some embodiments, one or more diffraction features may be switchable between an "on" state in which they actively diffract and an "off" state in which they do not significantly diffract. For example, a switchable diffraction feature may comprise a layer of polymer-dispersed liquid crystal in which microdroplets form a diffraction 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 refractive index of the microdroplets may be switched to one that does not match that of the host medium (in which case the pattern actively diffracts incident light).

[0155] 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 perform, for example, detecting user input, extracting biometric information from the eye, estimating and tracking the direction of the eye's gaze, monitoring the user's physiological state, etc. In some embodiments, the camera assembly 630 may include an image capturing device and a light source for projecting light (e.g., IR or near-IR light) onto the eye (which can then be reflected by the eye and detected by the image capturing 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 a frame 80 (Figure 2) and may communicate with a processing module 140 or 150, which can process image information from the camera assembly 630 and make various decisions, for example, regarding the user's physiological state, the wearer's gaze direction, iris identification, etc. In some embodiments, one camera assembly 630 may be used for each eye, monitoring each eye separately.

[0156] Figure 7A illustrates an embodiment of an output beam produced by a waveguide. One waveguide is shown (using a perspective view), but other waveguides in the waveguide assembly 260 (Figure 6) can function similarly. Light 640 is introduced into the waveguide 270 at the input surface 460 of the waveguide 270 and propagates through the waveguide 270 by TIR. Through interaction with diffraction features, the light exits the waveguide as an output beam 650. The output beam 650 replicates the exit pupil from a projector device that projects an image into the waveguide. Any one of the output beams 650 contains a sub-portion of the total energy of the input light 640. Also, in a perfectly efficient system, the sum of the energies in all the output beams 650 will be equal to the energy of the input light 640. The outgoing beam 650 is illustrated as substantially parallel in Figure 7A, but as discussed herein, a certain amount of refractive force may be imparted depending on the depth plane associated with the waveguide 270. A parallel outgoing beam may represent a waveguide with an externally coupled optical element that externally couples the light and forms an image that appears set on the depth plane at long distances from the eye 210 (e.g., optical infinity). Other waveguides or other sets of externally coupled optical elements may output a more divergent outgoing beam pattern, as shown in Figure 7B, which would require the eye 210 to adjust for closer distances and focus on the retina, and would be interpreted by the brain as light from a distance closer to the eye 210 than optical infinity.

[0157] In some embodiments, a full-color image may be formed in each depth plane by overlaying an image onto each of the primary colors (e.g., three or more primary colors such as red, green, and blue). Figure 8 illustrates an embodiment of a stacked waveguide assembly, where each depth plane includes an image formed using multiple different primary colors. The illustrated embodiment shows depth planes 240a–240f, but more or fewer depths are also considered. Each depth plane may have three or more associated primary color images, including a first image of a first color G, a second image of a second color R, and a third image of a third color B. Different depth planes are indicated in the figure by different diopter degrees following the letters G, R, and B. The numbers following each of these letters indicate the diopter (1 / m), i.e., the inverse distance of the depth plane from the user, and each box in the figure represents an individual primary color image. In some embodiments, the precise location of the depth plane for different primary colors may vary to account for differences in the focusing of light of different wavelengths in the eye. 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 arrangements may increase visual acuity and user comfort, or reduce chromatic aberration.

[0158] In some embodiments, each primary color light may be output by a single dedicated waveguide, and as a result, each depth plane may have multiple waveguides associated with it. In such embodiments, each box in the figure may be understood to represent an individual waveguide, and three waveguides may be provided for each depth plane to display three primary color images for each depth plane. The waveguides associated with each depth plane are shown adjacent to each other in this drawing for ease of illustration, but it should be understood that in a physical device, all waveguides may be arranged in a stack with one waveguide per level. In some other embodiments, multiple primary colors may be output by the same waveguide, for example, so that only a single waveguide may be provided for each depth plane.

[0159] Continuing with Figure 8, in some embodiments, G is green, R is red, and B is blue. In some other embodiments, other colors associated with other wavelengths of light, including yellow, magenta, and cyan, may also be used, 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 block or selectively pass light from the ambient environment to the user's eyes.

[0160] Throughout this disclosure, any reference to a given color of light should be understood as encompassing light of one or more wavelengths within the range of wavelengths of light that are perceived by the user as that given color. For example, red light may include light of one or more wavelengths within the range of approximately 620–780 nm, green light may include light of one or more wavelengths within the range of approximately 492–577 nm, and blue light may include light of one or more wavelengths within the range of approximately 435–493 nm.

[0161] In some embodiments, the light source 530 (Figure 6) may be configured to emit light of one or more wavelengths outside the user's visual perception range, such as IR and / or ultraviolet wavelengths. The IR light may include light with wavelengths in the range of 700 nm to 10 μm. In some embodiments, the IR light may include near-IR light with wavelengths in the range of 700 nm to 1.5 μm. In addition, internal coupling, external coupling, and other light redirection structures of the waveguide of the display 250 may be configured to direct and emit this light from the display toward the user's eye 210, for example, for imaging and / or user stimulation applications.

[0162] Referring here to Figure 9A, in some embodiments, light impacting a waveguide may need to be redirected to internally couple the light into the waveguide. Internal coupling optical elements may be used to redirect and internally couple the light into its corresponding waveguide. Figure 9A illustrates a cross-sectional side view of an embodiment of a set of stacked waveguides 660, each including an internal coupling optical element. Each waveguide may be configured to output light of one or more different wavelengths or one or more different wavelength ranges. Stack 660 may correspond to stack 260 (Figure 6), and the illustrated waveguides of stack 660 may correspond to some of a plurality of waveguides 270, 280, 290, 300, 310, but it should be understood that light from one or more of the image input devices 360, 370, 380, 390, 400 is input into the waveguide from a position or orientation that requires the light to be redirected for internal coupling.

[0163] The illustrated set of stacked waveguides 660 includes waveguides 670, 680, and 690. Each waveguide includes associated internal coupling optical elements (which may also be referred to as optical input areas on the waveguide), for example, internal coupling optical element 700 is located on the main surface of waveguide 670 (e.g., the upper main surface), internal coupling optical element 710 is located on the main surface of waveguide 680 (e.g., the upper main surface), and internal coupling optical element 720 is located on the main surface of waveguide 690 (e.g., the upper main surface). In some embodiments, one or more of the internal coupling optical elements 700, 710, and 720 may be located on the bottom main surfaces of the individual waveguides 670, 680, and 690 (in particular, one or more internal coupling optical elements are reflective optical elements). As illustrated, the internal coupling optical elements 700, 710, and 720 may be located on the upper main surface of their respective waveguides 670, 680, and 690 (or on the upper part of the following lower waveguide), and in particular, these internal coupling optical elements are transmissive optical elements. In some embodiments, the internal coupling optical elements 700, 710, and 720 may be located within the body of the respective waveguides 670, 680, and 690. In some embodiments, as discussed herein, the internal coupling optical elements 700, 710, and 720 are wavelength-selective, selectively redirecting one or more wavelengths of light while transmitting other wavelengths of light. Although illustrated on one side or corner of their respective waveguides 670, 680, and 690, it should be understood that in some embodiments, the internal coupling optical elements 700, 710, and 720 may be located within other areas of their respective waveguides 670, 680, and 690.

[0164] As illustrated, the internally coupled optical elements 700, 710, and 720 may be offset laterally from one another. In some embodiments, each internally coupled optical element may be offset so that its light does not pass through another internally coupled optical element before receiving light. For example, each internally coupled optical element 700, 710, and 720 may be configured to receive light from different image input devices 360, 370, 380, 390, and 400, as shown in Figure 6, and may be separated from the other internally coupled optical elements 700, 710, and 720 (e.g., separated laterally) so that it does not substantially receive light from the other internally coupled optical elements 700, 710, and 720.

[0165] Each waveguide also includes associated optical dispersion elements, for example, optical dispersion element 730 is located on the main surface (e.g., upper main surface) of waveguide 670, optical dispersion element 740 is located on the main surface (e.g., upper main surface) of waveguide 680, and optical dispersion element 750 is located on the main surface (e.g., upper main surface) of waveguide 690. In some other embodiments, optical dispersion elements 730, 740, and 750 may be located on the bottom main surfaces of the associated waveguides 670, 680, and 690, respectively. In some other embodiments, optical dispersion elements 730, 740, and 750 may be located on both the top and bottom main surfaces of the associated waveguides 670, 680, and 690, respectively, or optical dispersion elements 730, 740, and 750 may be located on different top and bottom main surfaces within different associated waveguides 670, 680, and 690, respectively.

[0166] Waveguides 670, 680, and 690 may be separated and isolated by, for example, gaseous, 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 immediate vicinity of waveguides 670, 680, and 690). Preferably, the refractive index of the material forming layers 760a and 760b is at least 0.05 or at least 0.10 lower than the refractive index of the material forming waveguides 670, 680, and 690. Advantageously, the lower refractive index layers 760a, 760b may function as cladding layers that facilitate the TIR of light through the waveguides 670, 680, 690 (e.g., the TIR between the upper and lower main surfaces of each waveguide). In some embodiments, layers 760a, 760b are formed from air. It should be understood that, although not shown, the upper and lower parts of the illustrated set of waveguides 660 may also include an immediate cladding layer.

[0167] Preferably, to facilitate manufacturing and other considerations, the materials forming waveguides 670, 680, and 690 are similar or identical, and the materials forming layers 760a and 760b are similar or identical. In other embodiments, the materials forming waveguides 670, 680, and 690 may differ between one or more waveguides, or the materials forming layers 760a and 760b may differ while still maintaining the various refractive index relationships described above.

[0168] Continuing to refer to Figure 9A, rays 770, 780, and 790 are incident on the set of waveguides 660. Rays 770, 780, and 790 may be injected into waveguides 670, 680, and 690 by one or more image input devices 360, 370, 380, 390, and 400 (Figure 6).

[0169] In some embodiments, the rays 770, 780, and 790 have different properties (e.g., different wavelengths or different wavelength ranges) that may correspond to different colors. The internally coupled optical elements 700, 710, and 720 each redirect the incident light so that it propagates through one of the waveguides 670, 680, and 690 by TIR.

[0170] For example, the internally coupled optical element 700 may be configured to selectively redirect a ray 770 having a first wavelength or wavelength range. Similarly, the transmitted ray 780 collides with the internally coupled optical element 710, which is configured to redirect light of a second wavelength or wavelength range, and is thereby redirected. Likewise, the ray 790 is redirected by the internally coupled optical element 720, which is configured to selectively redirect light of a third wavelength or wavelength range.

[0171] Continuing with Figure 9A, the rays 770, 780, and 790 are redirected to propagate through their corresponding waveguides 670, 680, and 690. That is, the internal coupling optical elements 700, 710, and 720 of each waveguide redirect the light into their corresponding waveguides 670, 680, and 690, and internally couple the light into their corresponding waveguides. The rays 770, 780, and 790 are redirected at an angle that causes the light to propagate through the individual waveguides 670, 680, and 690 by TIR. The rays 770, 780, and 790 propagate through the individual waveguides 670, 680, and 690 by TIR until they interact with the corresponding optical dispersion elements 730, 740, and 750 of the waveguides.

[0172] Referring now to Figure 9B, a perspective view of an embodiment of the multiple stacked waveguides shown in Figure 9A is illustrated. As described above, rays 770, 780, and 790 are internally coupled by internal coupling optical elements 700, 710, and 720, respectively, and then propagate by TIR within waveguides 670, 680, and 690, respectively. Rays 770, 780, and 790 then interact with optical dispersion elements 730, 740, and 750, respectively. Optical dispersion elements 730, 740, and 750 redirect rays 770, 780, and 790 to propagate toward external coupling optical elements 800, 810, and 820, respectively.

[0173] In some embodiments, the light-dispersing elements 730, 740, and 750 are orthogonal pupil expanders (OPEs). In some embodiments, the OPEs both redirect the light to the external coupling optical elements 800, 810, and 820, and expand the pupil associated with the light by sampling rays 770, 780, and 790 at many locations across the light-dispersing elements 730, 740, and 750 as they propagate to the external coupling optical elements. In some embodiments (for example, when the exit pupil is already of a desired size), the light-dispersing elements 730, 740, and 750 may be omitted, and the internal coupling optical elements 700, 710, and 720 may be configured to directly redirect the light to the external coupling optical elements 800, 810, and 820. For example, referring to Figure 9A, the light-dispersing elements 730, 740, and 750 may be replaced by the external coupling optical elements 800, 810, and 820, respectively. In some embodiments, the external coupling optical elements 800, 810, 820 are exit pupils (EPs) or exit pupil expanders (EPEs) that redirect light from the waveguide towards the user's eye 210 (Figure 7). The OPEs may be configured to increase the dimensions of the eyebox along at least one axis, and the EPEs may be configured to increase the eyebox along an axis intersecting (e.g., orthogonal to) the axis of the OPEs.

[0174] Therefore, referring to Figures 9A and 9B, in some embodiments, the set of waveguides 660 includes, for each primary color, waveguides 670, 680, 690, internal coupling optical elements 700, 710, 720, optical dispersion elements (e.g., OPE) 730, 740, 750, and external coupling optical elements (e.g., EP) 800, 810, 820. Waveguides 670, 680, 690 may be stacked with air gaps / cladding layers between each one. The internal coupling optical elements 700, 710, 720 direct incident light into the corresponding waveguide (using different internal coupling optical elements that receive light of different wavelengths). The light then propagates at angles that support TIR within the individual waveguides 670, 680, 690. Since TIR occurs only over a certain angular range, the range of propagation angles for rays 770, 780, and 790 is limited. The angular range supporting TIR can be considered the angular limit of the field of view, which can be represented by waveguides 670, 680, and 690 in such embodiments. In the embodiments shown, ray 770 (e.g., blue light) is internally coupled by the first internal coupling optical element 700 in the manner described above, and then continues to reflect back and forth from the surface of the waveguide as it propagates along the waveguide, and an optical dispersion element (e.g., OPE) 730 gradually samples it and directs it toward the external coupling optical element (e.g., EPE) 800, creating an additional duplicate ray. Rays 780 and 790 (e.g., green and red light, respectively) pass through waveguide 670, and ray 780 collides onto internal coupling optical element 710, thereby internally coupling. The ray 780 will then propagate along waveguide 680 via TIR, passing through its optical dispersion element (e.g., OPE) 740, and then to its external coupling optical element (e.g., EPE) 810. Finally, the ray 790 (e.g., red light) will pass through waveguides 670 and 680 and collide with the internal optical coupling optical element 720 of waveguide 690. The internal optical coupling optical element 720 internally couples the ray 790 so that the ray propagates via TIR to the optical dispersion element (e.g., OPE) 750, and then via TIR to the external coupling optical element (e.g., EPE) 820. The external coupling optical element 820 then finally externally couples the ray 790 to the user, and the viewer also receives externally coupled light from the other waveguides 670 and 680.

[0175] Figure 9C illustrates upper and lower plan views of embodiments of the multiple stacked waveguides shown in Figures 9A and 9B. As shown, waveguides 670, 680, and 690 may be vertically aligned with their associated optical dispersion elements 730, 740, and 750 and associated external coupling optical elements 800, 810, and 820. However, as discussed herein, the internal coupling optical elements 700, 710, and 720 are not vertically aligned. Rather, the internal coupling optical elements may be non-overlapping (e.g., laterally spaced, as seen in the upper and lower figures). This non-overlapping spatial arrangement can facilitate the ingress of light from different sources into different waveguides on a one-to-one basis, thereby enabling a specific light source to be uniquely optically coupled to a specific waveguide. In some embodiments, arrangements including non-overlapping, spatially separated internal coupling optical elements may be referred to as pupil-shifting systems, where the internal coupling optical elements in these arrangements may correspond to subpupils.

[0176] Figure 10 is a perspective view of an exemplary AR eyepiece waveguide stack 1000. The eyepiece waveguide stack 1000 includes a world-side cover window 1002 and an eye-side cover window 1006, which may 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 already 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 edge seals (such as the edge seal 1108 shown in Figure 11) so that adjacent eyepiece waveguides 1004 do not come into direct contact with each other.

[0177] Each eyepiece waveguide 1004 can be fabricated from a substrate material that is at least partially transparent, such as glass, plastic, polycarbonate, or sapphire. The selected material may have a refractive index greater than 1.4, for example, greater than 1.6 or greater than 1.8, to promote optical induction. The thickness of each eyepiece waveguide substrate may be, for example, 325 microns or less, but other thicknesses can also be used. Each eyepiece waveguide may include one or more internal coupling regions, optical dispersion regions, image expansion regions, and external coupling regions, which may consist of diffraction features formed on or within each waveguide substrate 902.

[0178] Although not shown in Figure 10, the eyepiece waveguide stack 1000 may include a physical support structure to support it in front of the user's eye. In some embodiments, the eyepiece waveguide stack 1000 is part of a head-mounted display system 60, as shown in Figure 2. Generally, the eyepiece waveguide stack 1000 is supported so that its external coupling region is directly in front of the user's eye. It should be understood that Figure 10 shows only a portion of the eyepiece waveguide stack 1000 corresponding to one of the user's eyes. The finished eyepiece may include mirror images of the same structure, possibly with two halves separated by a nose rest.

[0179] In some embodiments, the eyepiece waveguide stack 1000 can project color image data into the user's eye from multiple depth planes. The image data displayed by each individual eyepiece waveguide 1004 within the eyepiece 1000 may correspond to selected color components of the image data for a selected depth plane. For example, since the eyepiece waveguide stack 1000 includes six eyepiece waveguides 1004, it can project color image data (e.g., consisting of red, green, and blue components) corresponding to two different depth planes, i.e., one eyepiece waveguide 1004 per color component per depth plane. Other embodiments may include eyepiece waveguides 1004 for more or fewer color components and / or more or fewer depth planes.

[0180] Figure 11 is a partial cross-sectional view 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 using air space or another material placed between them. Although not shown, the edge seal structure 1108 can extend around the entire circumference of the stacked waveguide configuration. In Figure 11, the separation between each eyepiece waveguide is 0.027 mm, but other distances are also possible.

[0181] In the illustrated embodiment, there are two eyepiece waveguides 1104, one designed to display red image data, one for a 3m depth plane and the other for a 1m depth plane. (Again, the divergence of the light beam output by the eyepiece waveguides 1104 can be made to appear as if the image data originates from a depth plane located at a specific distance.) Similarly, there are two eyepiece waveguides 1104, one designed to display blue image data, one for a 3m depth plane and the other for a 1m depth plane, and two eyepiece waveguides 1104, one designed to display green image data, one for a 3m depth plane and the other for a 1m depth plane. Each of these six eyepiece waveguides 1104 is illustrated as being 0.325mm thick, but other thicknesses are also possible.

[0182] The world-side cover window 1102 and the 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 and 1106, and the edge seal 1108, the total thickness of the illustrated eyepiece waveguide stack 1100 is 2.8 mm. (k-space representation of AR eyepiece waveguide)

[0183] Figures 12A and 12B illustrate top views of the eyepiece waveguide 1200 in operation when projecting an image toward the user's eye 210. The image can first be projected from the image plane 1207 toward the entrance pupil 1208 of the eyepiece waveguide 1200 using the projection lens 1210 or some other projector device. Each image point (e.g., an image pixel or a portion of an image pixel) has a corresponding input beam of light (e.g., 1202a, 1204a, 1206a) which propagates in a specific direction at the entrance pupil 1208 (e.g., a specific angle with respect to the optical axis of the projector lens 1210). Although illustrated as rays, the input beams of light 1202a, 1204a, 1206a may be collimated beams, for example, with a diameter of a few millimeters or less when they enter the eyepiece waveguide 1200.

[0184] In Figures 12A and 12B, the central image point corresponds to input beam 1204a, which is illustrated with a solid line. The right image point corresponds to input beam 1202a, illustrated with a dashed line. The left image point corresponds to input beam 1206a, illustrated with a dashed line. To clarify the illustration, only three input beams 1202a, 1204a, and 1206a are shown in the entrance pupil 1208, but a typical input image would contain many input beams propagating within a certain angular range in both the x- and y-directions, corresponding to different image points in the two-dimensional image plane.

[0185] A unique correspondence exists between the various propagation angles of the input beam (e.g., 1202a, 1204a, 1206a) in the entrance pupil 1208 and the individual image points in the image plane 1207. The eyepiece waveguide 1200 can be designed to internally combine the input beams (e.g., 1202a, 1204a, 1206a), replicate them in a dispersed manner through space, guide them, and form an exit pupil 1210 larger than the entrance pupil 1208 and consisting of the replicated beams, all while substantially maintaining the correspondence between the image points and beam angles. The eyepiece waveguide 1200 can transform a given input beam of light (e.g., 1202a) which propagates into many replicated beams (e.g., 1202b) at a particular angle and is output across the exit pupil 1210 at an angle substantially uniquely correlated with that particular input beam and its corresponding image point. For example, a duplicate output beam corresponding to each input beam may be emitted from the eyepiece waveguide 1200 at substantially the same angle as its corresponding input beam.

[0186] As shown in Figures 12A and 12B, the input beam 1204a of light corresponds to the central image point in the image plane 1207 and is converted 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. The input beam 1202a of light corresponding to the right image point in the image plane 1207 is converted into a set of replicated output beams 1202b, shown as dashed lines, which exit the eyepiece waveguide 1200 at a propagation angle such that they appear to originate from a location within the right portion of the user's field of view. Similarly, the input beam 1206a of light corresponding to the left image point in the image plane 1207 is converted into a set of replicated output beams 1206b, shown as dashed lines, which exit the eyepiece waveguide 1200 at a propagation angle such that they appear to originate from a location within the left portion of the user's field of view. The larger the range of input beam angle and / or output beam angle, the larger the field of view (FOV) of the eyepiece waveguide 1200.

[0187] For each image, there is a set of duplicated output beams (e.g., 1202b, 1204b, 1206b), i.e., one set of duplicated beams per image point, which are output at different angles across the exit pupil 1210. Each individual output beam (e.g., 1202b, 1204b, 1206b) can be collimated. The set of output beams corresponding to a given image point may consist of beams propagating along parallel paths (as shown in Figure 12A) or divergent paths (as shown in Figure 12B). In either case, the specific propagation angle of the set of duplicated output beams depends on the location of the corresponding image point on the image plane 1207. Figure 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 to appear as if it originates from optical infinity. This is represented in Figure 12A by 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 the location of the user's eye 210). Figure 12B illustrates the case where each set of output beams (e.g., 1202b, 1204b, and 1206b) consists of beams propagating along divergent paths. This results in the image appearing to be projected as if it originates from a virtual depth plane with a distance closer than optical infinity. This is represented in Figure 12B by thin lines extending from the peripheral output beams 1202b, 1204b, and 1206b toward a point on the world side of the eyepiece waveguide 1200.

[0188] Again, each set of replicated power beams (e.g., 1202b, 1204b, 1206b) has a propagation angle corresponding to a specific image point in the image plane 1207. In the case of a set of replicated power beams propagating along parallel paths (see Figure 12A), the propagation angles of all beams are identical. However, in the case of a set of replicated power beams propagating along a divergent path, the individual power beams may propagate at different angles, but these angles are related in that they appear to form a convergent divergent wavefront, arising from a common point along the axis of the beam set (see Figure 12B). This axis defines the propagation angle for the set of divergent power beams and corresponds to a specific image point in the image plane 1207.

[0189] All various beams of light that enter the eyepiece waveguide 1200, propagate within the eyepiece waveguide, and exit the eyepiece waveguide can be described using one or more wave vectors, i.e., k-vectors, which describe the direction of beam propagation. k-space is an analytical framework that relates k-vectors to geometric points. In k-space, each point in space corresponds to a unique k-vector, which can in turn represent a beam or ray of light with a specific direction of propagation. This allows input and output beams with their corresponding propagation angles to be understood as a set of points in k-space (e.g., a rectangle). Diffraction features, which change the direction of propagation of a light beam as it travels through the eyepiece, can be understood in k-space simply as translating the locations 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.

[0190] The operation of an eyepiece waveguide can be understood by moving a set of points, such as points inside a k-space rectangle, in k-space, corresponding to the projected image. This is in contrast to more complex ray tracing diagrams, which can be used to illustrate a beam and its propagation angle. K-space is therefore an effective tool for describing the design and operation of eyepiece waveguides. The following discussion describes the k-space representation of the features and functions of various AR eyepiece waveguides.

[0191] Figure 13A illustrates a k-vector 1302, which can be used to represent the propagation direction of a ray or beam of light. A 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 constant c. However, in a medium, the speed of light is inversely proportional to the refractive index of the medium. Thus, in a medium, the equation becomes k=nω / c.) 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, light beams with higher angular frequencies ω have higher wavenumbers and, therefore, larger k-vectors (assuming the same propagation medium). For example, assuming the same propagation medium, a blue light beam has a larger k-vector than a red light beam.

[0192] Figure 13B illustrates a ray 1301 corresponding to a k-vector 1302 within a planar waveguide 1300. Waveguide 1300 may represent any of the waveguides described herein and may be part of an eyepiece for an AR display system. Waveguide 1300 can induce a ray having a certain k-vector via total internal reflection (TIR). For example, as shown in Figure 13B, a ray 1301 illustrated by k-vector 1302 is directed toward the upper surface of waveguide 1300 at a certain angle. If the angle is not too steep, as governed by Snell's law, the ray 1301 will reflect at the upper surface of waveguide 1300 at an angle equal to the angle of incidence, then propagate downward toward the lower surface of waveguide 1300, where it will reflect again toward the upper surface. The ray 1301 will propagate inductively within the waveguide 1300, continuously reflecting back and forth between its upper and lower surfaces.

[0193] Figure 13C illustrates the permissible k-vectors for light of a given angular frequency ω propagating in a non-boundary homogeneous medium with refractive index n. The length, i.e., magnitude k, of the illustrated k-vector 1302 is equal to the refractive index n of the medium × the angular frequency ω of the light, divided by the constant c of the speed of light. For a ray or beam of light of a given angular frequency ω propagating in a homogeneous medium with refractive index n, the magnitudes of all permissible k-vectors are identical. Furthermore, for uninductive propagation, all propagation directions are permissible. Therefore, the manifold in k-space that defines all permissible 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.

[0194] Figure 13D illustrates the permissible k-vectors for light of a given angular frequency ω propagating in a homogeneous planar waveguide medium with refractive index n. In a non-boundary medium, all permissible k-vectors lie on the hollow sphere 1306; however, to determine the permissible k-vectors in the planar waveguide, the sphere 1306 of permissible k-vectors on a plane (e.g., the xy-plane) can be projected. This results in a projected solid disk 1308 in k-space representing the k-vectors that can propagate in the planar waveguide. As shown in Figure 13D, all k-vectors that can 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 n of the medium × angular frequency ω of light, divided by the constant c of the speed of light.

[0195] Every point within the solid disk 1308 corresponds to a k-vector of a wave that can propagate within the waveguide (however, not all of these k-vectors result in induced propagation within the waveguide, as will be discussed below with respect to Figure 13E). At each point within the solid disk 1308, there are two possible waves: one with a z-component of propagation inward from the page, and the other with a z-component of propagation outward from the page. Thus, the out-of-plane component k of the k-vector z is, equation [ka] The sign obtained and selected using determines whether the wave propagates in and out of the page. All light waves of a given angular frequency ω propagating in a homogeneous medium with refractive index n have k-vectors of the same magnitude. Therefore, light waves with k-vectors whose xy components are closer in size to the radius of the solid disk 1308 have a smaller z-component of propagation (resulting in a less steep propagation angle necessary for TIR, as discussed with respect to Figure 13B), while light waves with k-vectors whose xy components are closer to the center of the solid disk 1308 have a larger z-component of propagation (resulting in a steeper propagation angle that cannot be TIR'd). Thus, all references to k-space refer to projected k-space, in which the 2-dimensional k-plane corresponds to the plane of the waveguide (unless otherwise evident from the context). In other words, unless explicitly stated, the propagation direction between waveguide surfaces is generally considered only in directions parallel to the waveguide surfaces. 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.

[0196] Figure 13E illustrates the ring 1310 in k-space, corresponding to the k-vector of a light wave, which can be induced in a waveguide having a refractive index n2 (e.g., n2 = 1.5). Waveguides have a lower refractive index n1 [ka] The k-vectors are physically surrounded by a medium (e.g., air) that has the following properties. As just discussed with respect to Figure 13D, all k-vectors corresponding to allowable waves in the plane waveguide medium in the xy plane are those k-vectors whose individual xy components lie within the solid disk 1308 in k-space. The radius of the solid disk 1308 is proportional to the refractive index of the waveguide medium. Therefore, referring back to Figure 13E, the k-vectors corresponding to light waves that can propagate in the plane waveguide medium with refractive index n2=1.5 are those whose individual xy components lie within the larger disk 1308a. On the other hand, the k-vectors corresponding to light waves that can propagate in the surrounding medium with refractive index n1=1 are those whose individual xy components lie within the smaller disk 1308b. All k-vectors whose individual xy components lie inside the ring 1310 correspond to light waves that can propagate in the waveguide medium but not in the surrounding medium (e.g., air). These are light waves induced within the waveguide medium via total internal reflection, as explained with respect to Figure 13B. Therefore, light rays or beams can only undergo induced propagation within the waveguide of the AR eyepiece if they have k-vectors within the k-space ring 1310. Note that propagating light waves with k-vectors outside the larger disk 1308a are prohibited; that is, no propagating wave exists whose k-vector lies within that region (waves within that region have an evanescent decay amplitude, not a constant amplitude along their propagation direction).

[0197] The various AR eyepiece waveguides described herein utilize diffraction features such as diffraction structures to internally couple light into free space (e.g., from a projector). [ka] The k-vector of a light beam propagating within the eyepiece waveguide can be directed into the k-space ring 1310 of the eyepiece waveguide. Any light wave whose k-vector is within the ring 1310 can propagate inductively within the eyepiece waveguide. The width of the ring 1310 determines the range of k-vectors that can be induced within the eyepiece waveguide, and therefore the range of propagation angles. Thus, the width of the k-space ring 1310 is typically considered to determine the maximum field of view (FOV) that can be projected by the eyepiece waveguide. Since the width of the ring 1310 depends on the radius of the larger disk 1308a, which itself partially depends on the refractive index n2 of the eyepiece waveguide medium, one technique to increase 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 limitations regarding the refractive index of waveguide mediums that can be used in AR eyepieces, such as material costs. This, in turn, is considered to impose practical limitations on the field of view (FOV) of AR eyepieces. However, as described herein, techniques exist that can be used to overcome these limitations in order to enable a larger FOV.

[0198] The radius of the larger disk 1308a in Figure 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. However, this does not imply that the FOV supported by the eyepiece waveguide is larger with respect to light with higher angular frequencies, since any given angular range corresponding to the FOV is scaled in line with the angular frequency, as well.

[0199] 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 the allowable k-vectors in a first medium with refractive index n1, a larger disk 1308a corresponding to the allowable k-vectors in a second medium with refractive index n2 (n2>n1), and a ring 1310 between the outer boundaries of the smaller disk 1308a and the larger disk 1308b. All k-vectors within the width 1342 of ring 1310 correspond to the induced propagation angles, but it is also possible that fewer than all k-vectors within the width 1342 of ring 1310 may be sufficient for use when displaying the image.

[0200] Figure 13F also shows waveguide 1350 with two guided beams shown for comparison with each other. The first light beam has a first k-vector 1344a near the outer edge of the ring 1310. The first k-vector 1344a corresponds to a first TIR propagation path 1344b shown in a cross-sectional view of waveguide 1350 having refractive index n2 surrounded by air of refractive index n1. A second light beam is also shown, having a second k-vector 1346a closer to the center of the k-space ring 1310. The second k-vector 1346a corresponds to a second TIR propagation path 1346b within waveguide 1350. Waveguide 1350 may include a diffraction grating 1352 on or within waveguide 1350. When the light beam encounters the surface of the waveguide 1350 with the diffraction grating 1352, an interaction occurs, which can send a sample of the light beam energy out of the waveguide while the beam continues to undergo TIR within the waveguide. The angle at which the light beam propagates through the waveguide with TIR determines the density of reflection events per unit length against the surface of the waveguide 1350 with the diffraction grating 1352, i.e., the number of bounces. Returning to the example of light beam comparison, the first light beam in the first TIR propagation path 1344b is reflected four times from the waveguide surface with the diffraction grating 1352, producing four exit pupils 1354 (illustrated with solid lines) along the length of the diffraction grating 1352, while the second light beam in the second TIR propagation path 1346b is reflected ten times from the waveguide surface with the diffraction grating 1352 over the same or similar distance, traversing the length of the diffraction grating 1352 and producing ten exit pupils 1356 (illustrated with dashed lines).

[0201] In practice, it may be desirable to ensure that the output beam, i.e., the exit pupil spacing, is equal to or constrained to a pre-selected range, so that the content projected to the user will be visible from any position within a predefined eye box. Using this information, it is possible to limit the width 1342 of the ring 1310 to a subset 1344 of k-vectors to which this constraint applies, and to exclude angles of excessively large glancing incidence angles from being included in the design calculations. Angles larger or smaller than the subset 1344 may also be acceptable depending on the desired performance, diffraction grating design, and other optimization factors. Similarly, in some embodiments, k-vectors corresponding to propagation angles that are too steep with respect to the waveguide surface and provide too much interaction with the diffraction grating 1352 may also be excluded from use. In such embodiments, the width 1342 of the ring 1310 can be reduced by effectively shifting the boundary of usable angles radially outward from the boundary between the larger disk 1308a and the smaller disk 1308b. Any design of the eyepiece waveguide disclosed herein can be adjusted by thus constraining the width of the k-space ring 1310.

[0202] As described above, k-vectors in the ring 1310 corresponding to suboptimal TIR propagation paths may be omitted from use in eyepiece design calculations. Alternatively, k-vectors corresponding to TIR propagation paths with excessively large grazing angles, and therefore excessively low density of reflection events on the surface of the waveguide with the diffraction grating, may be compensated using various techniques described herein. One technique is to use an internally coupled grating to direct a portion of the field of view (FOV) of the incident image to two different areas of the k-space ring 1310. In particular, it may be advantageous to direct the incident image to a first side of the k-space ring 1310 represented by a first group of k-vectors and to a second side of the k-space ring 1310 represented by a second group of k-vectors, where the first and second sides of the k-space ring 1310 are substantially opposite each other. For example, the first group of k-vectors may correspond to the FOV rectangle of the k-vectors on the left side of ring 1310, and the second group of k-vectors may correspond to the FOV rectangle of the k-vectors on the right side of ring 1310. The left FOV rectangle has its left edge near the outer edge of the larger disk 1308a and corresponds to a near-grazing incidence k-vector angle. Light at this edge will produce a sparsely spaced exit pupil. However, the same left edge of the right FOV rectangle, located on the right side of ring 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 densely spaced exit pupil. Therefore, when the left and right FOV rectangles are recombined and emitted from the waveguide toward the user's eye to produce an image, a sufficient number of exit pupils are produced across the entire area of ​​the field of view.

[0203] Diffraction features, such as those of a diffraction grating, can be used to couple light into and out of an eyepiece waveguide, and / or to change the direction of light propagation 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.

[0204] Figure 13G shows a top view of the diffraction grating 1320 and some of its associated k-space diffraction grating vectors (G -2 , G -1 Figure 13G shows the k-space diffraction grating vectors (e.g., G1, G2) oriented in the xy-plane. The diffraction grating 1320 is oriented in the xy-plane, and Figure 13G shows the grating from the viewpoint of a ray or beam incident on it from the z-direction. The diffraction grating 1320 is oriented in the same plane as the diffraction grating, and the k-space diffraction grating vectors (e.g., G1, G2) are shown. -2 , G -1 It has an associated set of G1 and G2. -1 The lattice vectors correspond to ±1 diffraction orders, respectively, while G2 and G -2The lattice vectors each correspond to ±2 diffraction orders. The lattice vectors for the ±1 diffraction orders point in opposite directions (along the periodic axes of the lattice) and have equal magnitudes that are inversely proportional to the period Λ of the diffraction grating 1320. Thus, a diffraction grating with a finer pitch has larger lattice vectors. The lattice vectors for the ±2 diffraction orders also point in opposite directions and have equal magnitudes that are twice those of the lattice vectors for the ±1 diffraction orders. Additional higher diffraction order lattice vectors may also exist, but they are not shown. For example, the magnitude of the lattice vectors for the ±3 diffraction orders is three times that of the lattice vectors for the ±1 diffraction orders, and so on. Note that the fundamental lattice vector G1 is simply determined by the periodicity (direction and pitch) of the lattice, while the composition of the lattice (e.g., surface profile, material, layer structure) can affect other properties of the lattice such as diffraction efficiency and diffraction phase. The fundamental lattice vectors (e.g., G -1 , G2, G -2 etc.) and all their harmonics are simply integer multiples of the fundamental G1, so all the diffraction directions of the lattice are simply determined by the periodicity of the lattice. The function of the diffraction grating 1320 is to add the lattice vectors to the in-plane components of the k-vector corresponding to the incident light ray or beam. This is shown in Fig. 13H.

[0205] Fig. 13H illustrates the cross-sectional view of the diffraction grating 1320 and its effect in k-space on the k-vector 1302 corresponding to a normally incident light ray or beam of light. The diffraction grating 1320 diffracts the incident light ray or beam of light into one or more diffraction orders. The new light rays or beams of light at each of these diffraction orders are represented by new k-vectors (e.g., 1302a-e). These new k-vectors (e.g., 1302a-e) are the lattice vectors (e.g., G -2 , G -1The in-plane components of the k-vector 1302 are determined by the vector additions of G1 and G2, respectively. When a normal incident ray or beam of light is illustrated, 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 in which its k-vectors (e.g., 1302a-e) have xy components equal to the corresponding grating vectors. For example, the xy components of ±1 diffraction orders of an incident ray or beam of light are G1 and G2, respectively. -1 This is the result. On the other hand, the magnitude of the new k-vectors is constrained to 2π / ω, and therefore all the new k-vectors (e.g., 1302a-e) lie on a semicircle, as shown in Figure 13H. The in-plane component of the incident k-vector 1302 is added to a lattice vector whose length is equal to or twice the basic increment, etc., while the magnitude of each resulting k-vector is constrained, so the angles between k-vectors (e.g., 1302a-e) with respect to various diffraction orders are not equal. Rather, the k-vectors (e.g., 1302a-e) become more angularly spaced as the diffraction order increases.

[0206] In the case of a diffraction grating formed on or within a plane-facing eyepiece waveguide, the in-plane components of new k-vectors (e.g., 1302a-e) are of most interest because, if they are within the k-space ring 1310 of the eyepiece waveguide, the diffracted rays or beams of light will undergo induced propagation through the eyepiece waveguide. However, if the in-plane components of new k-vectors (e.g., 1302a-e) are within the central disk 1308b, the diffracted rays or beams of light will exit the eyepiece waveguide.

[0207] Figure 13I illustrates a side view of the diffraction grating 1320 and its effect in k-space on the k-vector 1302 corresponding to the obliquely incident ray or beam of light. The effect is similar to that described with respect to Figure 13H. Specifically, the k-vector of the diffracted ray or beam of light is affected by the grating vector (G -2 , G-1 The in-plane component of the incident k-vector is determined by the addition of vectors (G1, G2) to the incident k-vector. With respect to the obliquely incident 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 and determines the in-plane component of the new k-vector with respect to 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 is within the k-space ring 1310 of the eyepiece waveguide, the diffracted ray or beam of light will undergo induced propagation through the eyepiece waveguide.

[0208] Figure 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 a light beam or ray that can propagate within the eyepiece waveguide. The k-space diagram also includes a smaller disk 1308b that defines the k-vectors of a light beam or ray that can propagate within a medium such as air surrounding the eyepiece waveguide. Furthermore, as previously discussed, the k-space ring 1310 defines the k-vectors of a light beam or ray that can undergo induced propagation within the eyepiece waveguide.

[0209] The 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, uniquely defined by the spatial location of the corresponding image point in the image plane. The set of input beams has angular spreads in both the x-direction and the y-direction. The angular spread in the x-direction may define the horizontal field of view, while the angular spread in the y-direction may define the vertical field of view. In addition, for example, the angular spread of the input beams along the diagonal between the x-direction and the y-direction may define the diagonal field of view.

[0210] In k-space, the field of view of the input image can be approximated by the FOV rectangle 1330. The FOV rectangle 1330 surrounds a set of k-vectors corresponding to the set of input light beams. The FOV rectangle 1330 is k x -It has dimensions along the axis, which correspond to the angular spread of the input beam in the x-direction. Specifically, the horizontal width of the FOV rectangle 1330 is, [ka] And in the formula, θ x is the total horizontal FOV, and n is the refractive index of the incident medium. The FOV rectangle 1330 is also k y -It has dimensions along the axis, which define the angular spread of the input beam in the y-direction. Similarly, the vertical height of the FOV rectangle 1330 is, [ka] And in the formula, θ y This is the total vertical FOV. The rectangle is shown to represent a set of input beams, although in some embodiments the set of input beams may correspond to different shapes in k-space. However, generally, the k-space analysis herein, shown using FOV rectangles or FOV squares, can be equally applied to other shapes in k-space as well.

[0211] As shown in Figure 13J, the FOV rectangle 1330 is centered on and entirely located within the smaller disk 1308b. The position of the FOV rectangle 1330 corresponds to the k-vectors of the set of input beams (e.g., on the axis from the image source, i.e., in a configuration with telecentric projection), or generally, the set of output beams propagating in the ±z-direction (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 degree of angular deviation in the ±z-direction). In other words, when the FOV rectangle 1330 is within the 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 it can also represent the output beams as they propagate from the eyepiece waveguide to the user's eye. Each k-space point within the FOV rectangle 1330 corresponds to a k-vector representing either one of the input beam directions or one of the output beam directions. For the input beam represented by the FOV rectangle 1330 to undergo induced propagation within the eyepiece waveguide, the FOV rectangle 1330 must be translated parallel to the k-space ring 1310. Conversely, for the output beam represented by the FOV rectangle 1330 to exit the eyepiece waveguide, the FOV rectangle 1330 must be de-translated parallel to the k-space ring 1310 to a smaller disk 1308b. To avoid introducing geometric and chromatic dispersion from propagation through the waveguide, the FOV rectangle 1330 of the input beam can coincide with the FOV rectangle of the output beam. That is, in this configuration, the eyepiece waveguide preserves the beam angle from input to output.

[0212] The following equation describes the field of view (FOV) that can be achieved in some eyepiece waveguides. [ka] FOV, θ x When aligned horizontally to =0, conventional eyepiece waveguides may have the following limitations: [ka] max(FOV) related to angular frequency x The only dependence of ) is from the dependence of the waveguide refractive index on angular frequency, which can be an important detail in some applications, but often has a relatively small effect.

[0213] Figure 13K is a k-space diagram showing the k-space translational shift of the FOV rectangle 1330 caused by the input coupled grating (ICG) located at the entrance pupil of the eyepiece waveguide. The ICG is associated with the diffraction grating vector (G), as discussed in relation to Figures 13G-13I. -1 The ICG has G1). The ICG diffracts each of the input beams, represented by the FOV rectangle 1330, to the +1 diffraction order and the -1 diffraction order. In k-space, the diffraction of the input beam to the +1 diffraction order is determined by the G1 lattice vector k x - Represented by an FOV rectangle 1330 displaced in the direction. Similarly, in k-space, the diffraction of the input beam to the -1 diffraction order is G -1 -k by lattice vector x - Represented by a FOV rectangle 1330 displaced in the direction.

[0214] In the particular embodiment shown in Figure 13K, the translated FOV rectangle is too large to fit entirely within the k-space ring 1310. This means that the eyepiece waveguides cannot support all of the input beam in the FOV in the induced propagation mode, whether in positive or negative diffraction order, because the angular spread between them is too large. k-vectors corresponding to points in the translated FOV rectangle that are outside the larger disk 1308a will not be diffracted at all by the ICG because those k-vectors are not allowed. (This also prevents diffraction to ±2 and higher diffraction orders, as the lattice vectors associated with those orders in this case will be longer and therefore translate the k-vectors further outward on the larger disk 1308a.) On the other hand, if any portion of the translated FOV rectangle is still inside the smaller disk 1308b after translation by the ICG, the light beams corresponding to those particular k-vectors will not undergo TIR and will exit the eyepiece waveguide by transmitting through its plane and will not undergo induced propagation through the waveguide.

[0215] One possible modification that could be made to support much of the input beam of light represented by the translated FOV rectangle 1330 in the induction mode might 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 (a decrease in the size of the smaller disk 1308b is possible if the waveguide is not surrounded by air), thereby increasing the size of the k-space ring 1310. (Exemplary AR eyepiece waveguide with orthogonal pupil expander)

[0216] 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, OPE region 1450, and EPE region 1460 of the eyepiece waveguide 1400 contain various diffraction features, which couple the input beam into the eyepiece waveguide, propagate it through inductive modes, replicate the beam at multiple dispersed locations in space, and cause the replicated beam to exit the eyepiece waveguide and project toward the user's eye.

[0217] An input beam corresponding to the 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 may coincide with the entrance pupil of the eyepiece waveguide 1400. The input device used to project the input beam may 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 be a liquid crystal display (LCD), liquid crystal on silicon (LCoS), fiber scanning display (FSD) technology, or scanning microelectromechanical system (MEMS) mirror display, but others may also be used. The input beam from the input device is generally projected into the eyepiece waveguide 1400 at various propagation angles in the illustrated -z-direction and incident on the ICG region 1440 from outside the substrate of the eyepiece waveguide.

[0218] The ICG region 1440 includes diffraction features that redirect the input beam so that they propagate inside the eyepiece waveguide 1400 via total internal reflection. In some embodiments, the diffraction features of the ICG region 1440 may form a one-dimensional periodic (1D) diffraction grating consisting of many lines that extend perpendicularly in the illustrated y-direction and periodically repeat horizontally in the illustrated x-direction. In some embodiments, the lines may be etched into the front or back of the eyepiece waveguide 1400, and / or they may be formed from a material deposited on the front or back. The period, duty cycle, depth, profile, blaze angle, etc., of the lines can be selected based on the angular frequency ω of the light for which the eyepiece waveguide 1400 is designed, the desired diffraction efficiency of the grating, and other factors. In some embodiments, the ICG region 1440 is primarily designed to couple the input light to +1 and -1 diffraction orders. (Diffraction gratings can be designed to reduce or eliminate higher diffraction orders above the 0th and 1st order. This can be accomplished by appropriately shaping the profile of each line. However, in many practical ICGs within AR displays, all higher diffraction orders correspond to k-vectors beyond the k-space ring. Therefore, those higher diffraction orders will be prohibited, regardless of non-k-space attributes such as grating duty cycle, depth, and profile.) A diffracted beam at one of the ±1 diffraction orders from ICG region 1440 then propagates generally in the -x- direction toward OPE region 1450, while a diffracted beam at the other of the ±1 diffraction orders then propagates generally in the +x- direction and exits from eyepiece waveguide 1400.

[0219] The OPE region 1450 includes diffraction features that can perform at least two functions. Firstly, they can perform pupil expansion by spatially replicating each light input beam at many new locations in the -x-direction. Secondly, they can guide each replicated light beam along a path toward the EPE region 1460. In some embodiments, these diffraction features are lines formed on or within the substrate of the eyepiece waveguide 1400. The period, duty cycle, depth, profile, blaze angle of the lines, etc., can be selected based on the angular frequency ω of the light for which the eyepiece waveguide 1400 is designed, the desired diffraction efficiency of the grating, and other factors. The specific shape of the OPE region 1450 may vary, but may generally be determined based on the beam spread from the ICG region 1440 and the size and location of the EPE region 1460. This will be discussed further with respect to Figure 14D.

[0220] The diffraction grating in the OPE region 1450 can be designed with relatively low and / or variable diffraction efficiencies. These properties 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 between the beam of light and the grating diffracts only a portion of the refractive power within the beam, while the rest continues to propagate in the same direction. (Several parameters that may 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 a diffraction grating in the OPE region 1450, a portion of its refractive power will be diffracted toward the EPE region 1460, while the rest continues to pass through the OPE region, again encountering the grating at a different spatial location, where another portion of the beam's refractive power is diffracted toward the EPE region 1460, and so on. Because a portion of the refractive power of each light beam propagates further through the OPE region 1450 than the rest before being diffracted toward the EPE region 1460, there are multiple copies of the incident beam propagating toward the EPE region from different locations in the -x-direction. The spatial range of the duplicate beams in the propagation direction of the original incident beam through the OPE region 1450 is therefore effectively increased, while the intensity of the incident beam decreases accordingly because the light constituting the input beam is split into many duplicate beams.

[0221] The diffraction grating in the OPE region 1450 is oriented obliquely 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 inclination 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 be more clearly seen in the k-space diagram, which will be found and discussed later in Figure 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. Therefore, in order to redirect the 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.

[0222] Figure 14C is a three-dimensional illustration of the optical operation 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 waveguide side closer to the viewer. The grid lines are not visible because they are microscopic. In this case, a single input beam 1401 is illustrated, but the image would consist of many such input beams propagating through the eyepiece waveguide 1400 in slightly different directions. The input beam 1401 is incident from the ICG region 1440 into the OPE region 1450. 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.

[0223] When the input beam 1401 interacts with the diffraction grating formed within the OPE region 1450, some of its refractive power is diffracted toward the EPE region, while another portion of its refractive power continues through the OPE region 1450 along the same path. As already mentioned, this is partly due to the grating's relatively low diffraction efficiency. Furthermore, the beam 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 shown by arrows in Figure 14C. The effect is replicated as the input beam propagates through the OPE region 1450, resulting in an expansion of the spatial range of the light. This is evident from Figure 14C, which shows that the input beam 1401 is replicated into many light beams, ultimately propagating toward the EPE region, generally in the -y-direction.

[0224] The EPE region 1460 also includes diffraction features that can perform at least two functions. First, they can duplicate the beam along another direction (e.g., a direction substantially perpendicular to the direction in which the beam is duplicated by the OPE region 1450). Second, they can diffract each beam of light out of the eyepiece waveguide 1400 toward the user's eye. The EPE region 1460 can duplicate the light beam in the same manner as the OPE region 1450. That is, as the beam propagates through the EPE region 1460, it repeatedly interacts with the diffraction grating, diffracting a portion of its refractive power to a first order of diffraction, thereby externally coupling toward the user's eye. The remaining portion of the beam's refractive power undergoes zero-order diffraction and continues to propagate in the same direction within the EPE region 1460 until it interacts with the grating again. The diffraction optics features of the EPE region 1460 can also impart some refractive power to the duplicated output beam of light so that they appear as if they originated from a desired depth plane, as discussed elsewhere in this specification. This can be accomplished by using a lens function to impart curvature to the lines of the diffraction grating within the EPE region 1460.

[0225] Figure 14B illustrates the k-space behavior of the eyepiece waveguide 1400. Specifically, Figure 14B includes component-specific k-space diagrams (KSDs) of the eyepiece waveguide 1400, illustrating the k-space effects of each component. The FOV rectangles and arrows indicating the corresponding propagation directions of light through the eyepiece waveguide in the k-space diagrams have corresponding shading. The first k-space diagram KSD1 shows the k-space representation of the input beam incident on the ICG region 1440 from the input device. As already discussed, the set of input beams has its k x and k y It can be represented in k-space by an FOV rectangle 1430 whose dimensions correspond to the angular spread of the input beam in the x- and y-directions. Each specific point within the FOV rectangle in KSD1 corresponds to a k-vector associated with one of the input beams, and k x The component indicates the propagation angle of the input beam in the x-direction, and k y The component indicates the propagation angle of the input beam in the y-direction. More precisely, k x =sin(θ x ) and in the formula, θ x k is the angle formed by the input beam and the yz plane. y =sin(θ y ) and in the formula, θ y is the angle formed by the input beam and the xz plane. The FOV rectangle within KSD1 is shown in the schematic diagram. z -The fact that the beams are aligned on the -z axis means that the represented input light beam has a propagation angle that aligns with the input beam propagating in the -z direction, and therefore all input beams generally propagate in the -z direction. (Although not illustrated here, any of the waveguide displays described herein can also be designed for FOVs that are off-axis with respect to the ±z directions.)

[0226] The second k-space diagram KSD2 shows the k-space action of the ICG region 1440. As already discussed, the diffraction grating is associated with the grating vectors (e.g., G1, G -1 ) has. KSD2 has the G1 lattice vector and G-1 The grid vectors are shown, which are of equal magnitude and opposite in direction along the periodic axis of the ICG. The ICG region 1440 diffracts the input beam to ±1 diffraction order. Also, in k-space, this means that the ICG is G1 and G -1 This means copying the FOV rectangle to two new locations by using both grid vectors and translating it. In the illustrated instance, ICG is the grid vector G1, G -1 The size is designed using a period Λ based on the angular frequency ω of the input beam, so that the copied FOV rectangle is completely placed within the k-space ring of the waveguide. Therefore, all of the diffracted input beam enters the inductive propagation mode.

[0227] -k x A copy of the FOV rectangle centered on a point on the -axis (the 9 o'clock position in the k-space ring) shows that the corresponding diffracted beams have a propagation angle such that their propagation component in the plane of the eyepiece waveguide 1400 is centered around the beam in the -x direction. Thus, all of these beams generally propagate toward the OPE region 1450, reflecting back and forth between the front and back surfaces of the eyepiece waveguide 1400 via TIR. Meanwhile, +k x A copy of the FOV rectangle centered on a point on the -axis (at the 3 o'clock position in the k-space ring) indicates that the corresponding diffracted beam has a propagation angle such that its propagation component in the plane of the eyepiece waveguide 1400 is centered around the beam in the +x-direction. Thus, all of these 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, these beams are generally lost and do not contribute meaningfully to the projection of an image toward the user's eye.

[0228] KSD2 is the illustrated linear lattice vector G1, G -1Higher-order lattice vectors that are multiples of k are not illustrated. ICG does not diffract the light beam to those diffraction orders because doing so would translate the k-vectors, which in this instance constitute an FOV rectangle that extends beyond the periphery of the k-space disk defining the allowed k-vectors. Therefore, higher diffraction orders do not occur in this embodiment.

[0229] The third k-space diagram KSD3 shows the k-space action of OPE region 1450. Again, since OPE region 1450 contains a diffraction grating, the associated grating vectors (e.g., G1, G) are... -1 ) has, which may be of equal magnitude and opposite in direction along the periodic axis of the OPE grating. In this case, the periodic axis of the diffraction grating is at a 45° angle with respect to the x-axis. Therefore, the grating vectors of the OPE diffraction grating (e.g., G1, G) -1 ) is k x -Points at a 45° angle with respect to the axis. As shown in KSD3, one of the grid vectors defines the FOV rectangle, -k y - It is translated to a new location where it is aligned with a point located on the - axis (the 6 o'clock position in the k-space ring). 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 aligned with the beam in the -y-direction toward the EPE region 1460. On the other hand, other illustrated OPE grating vectors would place the FOV rectangle outside the outer periphery of the k-space disk. However, k-vectors outside the disk are not allowed, and therefore the OPE diffraction grating will not diffract the beam to its diffraction order. The periodic axis of the diffraction grating within the OPE region 1450 does not necessarily have to be exactly 45°. For example, as can be seen by examining KSD3, the periodic axis can still be an angle somewhat greater or less than 45°, while translating the FOV rectangle to the 6 o'clock position where the FOV rectangle can fit entirely within the k-space ring. This means that the FOV rectangle does not necessarily have to be -k y - The FOV rectangle will be positioned at the 6 o'clock position without being centered within the k-space ring along the axis.

[0230] In the illustrated instance, the OPE diffraction grating has grating vectors G1 and G -1 One of these is designed using a period Λ based on the angular frequency ω of the input beam, such that a copied FOV rectangle, which is perfectly located within the k-space ring of the waveguide, is positioned at the 6 o'clock position. Therefore, all of the diffracted input beam remains in the induced propagation mode. The k-space distance from the 9 o'clock position to the 6 o'clock position in the k-space ring, which is a translation performed by the OPE grating, exceeds the distance from the origin of the k-space diagram to the ring, which is a translation performed by the ICG. Therefore, the OPE grating vector must have a different magnitude from the ICG grating vector. In particular, the OPE grating vector is longer than the ICG grating vector, which means that the OPE grating has a shorter period Λ than the ICG grating.

[0231] The fourth k-space diagram KSD4 shows the k-space action of the EPE region 1460. Again, since the EPE region 1460 contains a diffraction grating, the associated grating vectors (e.g., G1, G) -1 ) has, which are of equal magnitude and opposite in direction along the periodic axis of the EPE grating. In this case, the periodic axis of the diffraction grating is along the y-axis of the eyepiece waveguide 1400. Therefore, the grating vector of the EPE diffraction grating (e.g., G1, G) -1 ) is ±k y-Points in the 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 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 +z- direction toward the user's eye. On the other hand, the other primary EPE grating vector places the FOV rectangle outside the outer periphery of the k-space disk, and therefore the EPE diffraction grating will not diffract the beam to its diffraction order. However, one of the secondary EPE grating vectors will translate the FOV rectangle to the 12 o'clock position in the k-space ring. Therefore, the EPE grating may diffract a portion of the light to one of the second diffraction orders. The secondary diffraction direction may correspond to the induced propagation direction along the +y- direction, which is typically an undesirable effect. For example, secondary diffraction, as discussed below, can introduce visual artifacts and flare or smear effects into the image presented to the user when the EPE grating is perturbed and refractive forces are introduced.

[0232] In the illustrated instance, the EPE diffraction grating has grating vectors G1 and G -1 One of the gratings is designed with a period Λ based on the angular frequency ω of the input beam so that the copied FOV rectangle is positioned entirely inside the k-space disk of the waveguide. Therefore, all beam diffracted by the EPE grating is no longer in induced propagation mode and thus exits the eyepiece waveguide 1400. Furthermore, the EPE grating shifts the FOV rectangle back to the origin of the k-space diagram (where the FOV rectangle corresponding to the input beam was located), so the output beam has the same propagation angle as its corresponding input beam. In the illustrated embodiment, the EPE gratings have the same period Λ as the ICG because both of these gratings shift the FOV rectangle by the same k-space distance. However, this is not a requirement. y The dimension is the k of the k-space ring at the 6 o'clock position. y If the dimension is less than the FOV rectangle, the different k within the ring yThe possible locations can have a range of positions corresponding to the 6 o'clock position. Therefore, there can be numerous engineering options for the EPE grid vector, and consequently the OPE vector, to position the FOV rectangle in a location within the k-space ring and / or near the origin of the k-space diagram.

[0233] In some embodiments, the lines of the EPE diffraction grating may be slightly curved to impart refractive power to the output beam emanating from the EPE region 1460. For example, the lines of the diffraction grating within the EPE region 1460 can be bent toward the OPE region in the waveguide plane to impart negative refractive power. This can be used to make the output beam follow a divergent path, as shown, for example, in Figure 12B. This causes the projected image to appear in a depth plane closer than optical infinity. The specific curvature can be determined by the lens function. In k-space, this means that different spatial regions within the EPE region 1460 will have grating vectors pointing in slightly different directions depending on the curvature of the grating lines within their specific regions. In these embodiments, this translates the FOV rectangle to various different locations centered around the origin of the k-space diagram. This, in turn, centers the set of output beams corresponding to each of the translated FOV rectangles around different propagation angles, which in turn creates the illusion of depth.

[0234] Figure 14D illustrates the technique for determining the size and shape of the OPE region 1450 and the EPE region 1460. Figure 14D illustrates the same eyepiece waveguide 1400 as shown in Figures 14A and 14B, including the ICG region 1440, the OPE region 1450, and the EPE region 1460. Figure 14D also includes simplified versions of the k-space diagrams KSD1, KSD2, and KSD3. Referring to the first k-space diagram KSD1, the four corner k-vectors of the FOV rectangle correspond to the input beams incident on the ICG at the most oblique angle from the corners of the image in the input plane (see Figures 12A and 12B). Since the propagation angles of these input beams are the most extreme of all things in the field of view, their k-vectors are located at the four corners of the FOV rectangle in k-space.

[0235] Figure 14D shows rays defining four diffracted beams from ICG region 1440, corresponding to the four corners of the input image. In particular, the ray near the top of OPE region 1450 defines a diffracted beam (i.e., a k-vector located at the upper right corner of the FOV rectangle) corresponding to an input beam incident on ICG region 1440 at a steepest propagation angle that is upward and away from the OPE region. Similarly, the ray near the bottom of OPE region 1450 defines a diffracted beam (i.e., a k-vector located at the lower right corner of the FOV rectangle) corresponding to an input beam incident on ICG region 1450 at a steepest propagation angle that is downward and away from the OPE region. These two beams define the spread of the diffracted beam from ICG region 1440. To create these two beams and all other replicated instances between them and project them toward the user's eye, the upper and bottom boundaries of the OPE region should encompass the propagation paths of these two beams. The specific propagation paths can be determined by referring to the second k-space diagram KSD2.

[0236] KSD2 shows the resulting k-vectors of the beam diffracting from the ICG region 1440 towards the OPE region 1450. The arrows in KSD2 indicate the beam propagation angles corresponding to the k-vector located in the upper right corner of the FOV rectangle.

[0237] The size, shape, and location of the EPE region 1460 can be determined by performing a backray trace using propagation angles, which are evident from the k-vectors in the third k-space diagram KSD3. As is evident from KSD3, the left and right-right corner k-vectors of the FOV rectangle define the spread of the propagation path that the beam follows as it propagates from the OPE region 1450 toward the EPE region 1460. Using these propagation angles, the origin of those rays in the OPE region can be determined by backtracing from the portion of the EPE region 1460 furthest from the OPE region 1450 (i.e., the lower corner of the EPE region), which will arrive at the lower corner of the EPE region with propagation angles defined by the left and right-right corner k-vectors. 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 toward the left-lower corner of the EPE region 1460, the worst-case propagation angle is that indicated by the right-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 the beam from the OPE region 1450 to the lower right corner of the EPE region, the worst-case propagation angle is indicated by the k-vector of the upper left corner of the FOV rectangle. Therefore, the propagation path with that angle can be used to define the right boundary of the OPE region 1450.

[0238] As shown in Figure 14D, in the illustrated eyepiece waveguide 1400, the EPE region 1460 is located in the -x and -y directions from the ICG region 1440. Additionally, some of the diffracted beams spread from the ICG region 1440 along their paths in the 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 sufficiently far from the EPE region in the +y direction so that the spreading 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. Figure 15A illustrates an exemplary embodiment that achieves these objectives.

[0239] Figure 15A illustrates an exemplary embodiment of a waveguide eyepiece 1500 in which the OPE region 1550 is inclined 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 Figure 14A.

[0240] 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 grid lines of the ICG region 1540 can be oriented so that the diffracted beam does not exit the ICG region in the propagation direction having a component in the -y-direction. In addition, the ICG region 1540 can be positioned near the shared boundary of the OPE region 1550 and the EPE region 1560, but so that no portion of the ICG region extends beyond that shared boundary in the -y-direction. The action of the ICG region 1540 can be seen in the k-space diagram shown in Figure 15B.

[0241] Figure 15B includes a k-space diagram illustrating the operation of the eyepiece waveguide 1500 shown in Figure 15A. The first k-space diagram KSD1 shows an FOV rectangle corresponding to the 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 around the -z direction. Thus, in k-space, they are k at the origin of KSD1. z - It can be represented by an FOV rectangle centered on the axis.

[0242] The second k-space diagram KSD2 shows the effect of the ICG region 1540 on the input beam. The ICG region 1540 diffracts the input beam and redirects it toward the OPE region 1550. In k-space, this corresponds to translating the FOV rectangle using the lattice vector associated with the ICG region 1540. In this embodiment, the lattice lines within the ICG region 1540 are oriented with a periodic axis having a component in the +y- direction. This means that the lattice vector associated with ICG 1540 is also +k y - This means that it has a component in the direction of +k y - The magnitude of this component in the direction is k y- The width of the FOV rectangle in the direction may be greater than or equal to half. This means that no portion of the FOV rectangle extends below the horizontal axis of the k-space diagram KSD2 after being translated by ICG region 1540. This, in turn, means that none of the diffracted beams from ICG region 1540 are -k y - This means that there is no propagation angle with a component in the direction. Therefore, none of the diffracted beams propagate 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.

[0243] The third k-space diagram, KSD3, shows the effect of the OPE region 1550 on the diffracted beam from the ICG region 1540. As shown, the diffraction grating of the OPE region 1550 can be oriented to redirect the beam of light at an angle corresponding to an FOV rectangle that has been translated 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 may depend on the layout of the various regions of the eyepiece waveguide relative to each other.

[0244] The translated FOV rectangle in KSD3 is -k xBecause it is centered around a k-vector having a component in the --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 Figure 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. Since the tip portion 1555 of the OPE region 1550 may contribute to 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.

[0245] 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. The design of the diffraction grating in the EPE region 1560 is also somewhat different because the starting location of the FOV rectangle in KSD4 for the eyepiece waveguide embodiment shown in Figure 15A is slightly different from the starting location of the FOV rectangle in KSD4 for the eyepiece waveguide embodiment shown in Figure 14A. 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 -It has a component in the direction and can be tilted such that the OPE region 1550 does not need to extend beyond the left edge of the EPE region 1560 (see the discussion in Figure 14D and compare the location of the upper right corner k-vector in KSD3 in Figure 14D with the location of the corresponding k-vector in KSD3 in Figure 15B). This results in the FOV rectangle in KSD4 in Figure 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 with the same propagation angle as its corresponding input beam, as already described herein (i.e., the FOV rectangle representing the output beam is in the same location in the k-space diagram as the FOV rectangle representing the input beam).

[0246] 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-space. x - The propagation angle in the direction (as represented by the FOV rectangle located near the 9 o'clock position of the k-space ring), and generally, -k y The propagation angle in the - direction can also be switched back and forth between this direction and the FOV rectangle located near the 6 o'clock position of the k-space ring. This is indicated by a grid vector with double arrows between the FOV rectangle near the 9 o'clock position and the FOV rectangle near the 6 o'clock position of the k-space ring. Figures 15D-15F illustrate this behavior in more detail.

[0247] Figure 15D is a schematic diagram of the first occurrence of the interaction between the input beam and the OPE region 1550 of the eyepiece waveguide embodiment shown in Figure 15A. The OPE region 1550 of the eyepiece waveguide 1500 includes a diffraction grating consisting of parallel grid lines that repeat in the direction of periodicity. The direction of periodicity determines the direction of the grid vector associated with the diffraction grating. In this instance, the grid vector with double arrows in Figure 15C illustrates the action of the OPE region 1550 and points along the direction of periodicity of the grid lines shown in Figures 15D-15F.

[0248] Figure 15D shows the input beam incident from ICG region 1540 into OPE region 1550. The input beam is shown propagating in the direction corresponding to the k-vector, i.e., the center point of the FOV rectangle located near the 9 o'clock position of the k-space ring in Figure 15C. As shown, the first occurrence of interaction between the input beam and OPE region 1550 results in two diffracted output beams. That is, a portion of the refractive power of the input beam is simply reflected from the upper or bottom surface of the eyepiece waveguide 1500 as output 1, continuing in the same xy direction as the input beam (i.e., zero-order diffraction), and a portion of the refractive power of the input beam is diffracted downward as output 2, firstly (e.g., by the first-order lattice vector G1 of the OPE region). The output 2 beam is shown propagating in the direction corresponding to the k-vector, i.e., the center point of the FOV rectangle located near the 6 o'clock position of the k-space ring in Figure 15C. Following the first occurrence of the interaction, output beam 1 and output beam 2, although having different propagation angles, still propagate within the OPE region 1550 and therefore may have additional interactions with the OPE region, as shown in Figures 15E and 15F. Other input beams, not shown, that are incident on the OPE region 1550 using different propagation angles will behave similarly, but with slightly different input and output angles.

[0249] Figure 15E is a schematic diagram of the second occurrence of interaction between the input beam and the OPE region 1550 of the eyepiece waveguide embodiment shown in Figure 15A. The beam associated with the first occurrence of interaction is shown using a dashed line, while the beam associated with the second occurrence of interaction is shown using a solid line. As shown in Figure 15E, the output beams from the first occurrence of interaction, i.e., output 1 and output 2, can each undergo interaction with the OPE region 1550 similar to that that occurred in the first occurrence. That is, a portion of the refractive power from the output 1 beam from Figure 15D simply continues in the same xy direction (i.e., zero-order diffraction), while another portion of the refractive 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 refractive power from the two output beams from Figure 15D simply continues downward toward the EPE region 1560 (i.e., zero-order diffraction), while another portion of the refractive 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 (Therefore), it continues to propagate further in the same direction as the initial input beam within the OPE region 1550.

[0250] After a second interaction occurs within the OPE region 1550, an interference node 1556 exists where two of the resulting beams intersect. The optical paths followed by each of these beams to reach the interference node 1556 are substantially the same length. Therefore, beams emitting from the interference node 1556 propagating in the same direction may have the same or similar phase and thus may undergo constructive or destructive wave interference with each other. This can result in image artifacts, which are discussed below.

[0251] Figure 15F is a schematic diagram of the third occurrence of interaction between the input beam and the OPE region 1550 in the eyepiece waveguide embodiment shown in Figure 15A. The beams associated with the first and second occurrences of interaction are shown with dashed lines, while the beam associated with the third occurrence of interaction is shown with solid lines. As shown in Figure 15F, each output beam resulting from the second occurrence of interaction may again undergo interaction with the OPE region 1550 similar to that in the previous occurrence. Some of the refractive power of these beams continues in the same direction (i.e., zero-order diffraction), while other parts of the refractive power of these beams are, in part, generally in the -x- direction and in part, generally in the -y- direction (i.e., the first-order lattice vectors G1 and G of the OPE region). -1 The beam is redirected (by...). Generally, all beams propagating in the -x- direction are represented by the FOV rectangle located near the 9 o'clock position in the k-space ring of the k-space diagram in Figure 15C, while generally, all beams propagating in the -y- direction are represented by the FOV rectangle located near the 6 o'clock position. As can be seen from Figure 15C, in the case of the OPE region 1550 consisting of a 1D periodic diffraction grating, for any given input beam, the duplicate beam of light corresponding to that input beam propagates in only two directions within the OPE region (however, the two directions will differ for different input beams incident on the OPE region at different propagation angles).

[0252] A third occurrence of interaction with the OPE region results in the creation of additional interference nodes 1556, where beams with identical or similar optical path lengths intersect each other, potentially leading to 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 grating pattern, which can therefore result in image artifacts, as shown in Figure 15G.

[0253] Figure 15G is a schematic diagram illustrating how a single input beam 1545 from the ICG region 1540 is duplicated by the OPE region 1550 and redirected as multiple beams 1565 toward the EPE region 1560. Each duplicated beam 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, all duplicated beams 1565 illuminating the EPE region are separated by the same spacing, although the beams may have non-monotonically fluctuating intensity. As a result, the duplicated light beams 1565 from the OPE region 1550 can illuminate the EPE region 1560 with a relatively sparsely spaced non-uniform distribution. In some embodiments, it may be advantageous if the duplicated light beams illuminating the EPE region of the eyepiece waveguide can be more uniformly distributed. Figure 16 illustrates such an embodiment. (Exemplary AR eyepiece waveguide with multidirectional pupil expander)

[0254] Figure 16A illustrates an exemplary eyepiece waveguide 1600 having a multidirectional pupil expander (MPE) region 1650 instead of an OPE region. At a macroscopic level, the illustrated embodiment of the eyepiece waveguide 1600 is analogous to the eyepiece waveguide 1500 shown in Figure 15A. The input beam is coupled into the eyepiece waveguide 1600 by the ICG region 1640. The diffracted beam from the ICG region 1640 propagates toward and through the MPE region 1650, which replaces the OPE region. Finally, the MPE region 1650 diffracts the beam of light toward the EPE region 1660, where they are externally coupled 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 respect to Figures 15A–15G. However, the MPE region 1650 differs distinctly from the OPE region 1550 in that it diffracts light in more directions. This feature is advantageous because it reduces the periodic uniformity in the distribution of the light beam within the EPE region 1660, which in turn allows for more uniform illumination of the EPE region.

[0255] The MPE region 1650 consists of diffraction features exhibiting periodicity in multiple directions. The MPE region 1650 may also consist of an array of scattering features arranged in a 2D grating. Individual scattering features can be, for example, depressions or protrusions of any shape. The 2D array of scattering features has associated grating vectors derived from the reciprocal grating of its 2D grating. In one embodiment, the MPE region 1650 may be a 2D periodic diffraction grating consisting of a cross grating with grating lines repeating along two or more distinctly different directions of periodicity. This can be accomplished by superimposing two 1D gratings with different directions of periodicity.

[0256] Figure 16B illustrates a portion of an exemplary 2D periodic lattice that may be used within the MPE region 1650 shown in Figure 16A, along with its associated lattice vectors. The 2D periodic lattice 1650 can be a spatial lattice of diffraction features whose periodicity directions are illustrated by vectors u and v. Such a 2D periodic lattice is associated with lattice vectors. The two fundamental lattice vectors G and H, corresponding to the periodicity directions u and v, are mathematically defined as follows: [ka] Mathematically, vectors u and v define a spatial lattice, and G and H correspond to the fundamental double, i.e., 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.

[0257] As one embodiment, a 2D periodic grid can be designed or formed by superimposing two sets of 1D periodic grid lines, as shown in Figure 16B (wherein the 2D periodic grid may instead consist of individual scattering features located at the intersections of the grid lines shown in Figure 16B, for example). The first set of grid lines 1656 can be repeated along the direction of the fundamental grid vector G, which can have a magnitude equal to 2π / a, where a is the period of the first set of grid lines 1656. The 2D grid shown in Figure 16B is also associated with harmonics of the first fundamental grid vector G, which include higher harmonics such as -G and 2G, -2G, etc. The second set of grid lines 1657 can be repeated along the direction of the fundamental grid vector H, which can have a magnitude equal to 2π / b, where b is the period of the second set of grid lines 1657. The 2D grid shown in Figure 16B is also associated with harmonics of the second fundamental grid vector H. These include higher harmonics such as -H and 2H, -2H, etc.

[0258] Any 2D periodic array of diffraction features will have associated lattice vectors that correspond to the entire reciprocal lattice and point in a direction determined by an integer linear combination (superposition) of the fundamental lattice vectors G and H. In the illustrated embodiments, these superpositions result in additional lattice vectors, which are also shown in Figure 16B. These include, for example, -G, -H, H+G, HG, GH, and -(H+G). Typically, these vectors are described using two indices such as (±1,0), (0,±1), (±1,±1), (±2,0), etc. Although Figure 16B illustrates only the first-order lattice vectors and their superpositions associated with the 2D diffraction grating, higher-order lattice vectors may also exist.

[0259] As has already been discussed elsewhere in this specification, the k-space effect of a grating on the set of light beams that constitute an image is to translate the FOV rectangle corresponding to the image using the grating vector associated with the grating. This is shown in Figures 16C and 16D with respect to an exemplary 2D MPE diffraction grating shown in Figure 16B.

[0260] Figure 16C is a k-space diagram illustrating the k-space action of the MPE region 1650 of the eyepiece waveguide 1600 shown in Figure 16A. The k-space diagram includes a shaded FOV rectangle located near the 9 o'clock position of the k-space ring. This is the location of the FOV rectangle after the ICG region 1640 couples the input beam into the eyepiece waveguide 1600 and redirects them toward the MPE region 1650. Figure 16C shows how the 2D grid within the MPE region 1650 translates the FOV rectangle using the grid vectors shown in Figure 16B. Since 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 one of eight possible new k-space locations. Of these eight possible k-space locations, six are outside the periphery of the k-space diagram. These are illustrated using unshaded FOV rectangles. Since k-vectors outside the boundary of the k-space diagram are not allowed, none of the six lattice vectors result in diffraction. However, there are two lattice vectors (i.e., -G and -(H+G)) that result in a translation of the FOV rectangle to new positions within the boundary of the k-space diagram. One of these locations is near the 6 o'clock position in the k-space ring, and the other is near the 2 o'clock position. Since k-vectors at these locations are allowed and result in induced propagation modes, the FOV rectangles at these locations are shaded to indicate that the beam of light is diffracted into those two states. Thus, the refractive power of a beam of light incident on the MPE region 1650 with a propagation angle indicated by the FOV rectangle located near the 9 o'clock position in the k-space ring is partially diffracted into both 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).

[0261] Figure 16D is a k-space diagram further illustrating the k-space action of the MPE region 1650 of the eyepiece waveguide 1600 shown in Figure 16A. This particular k-space diagram illustrates the action of the MPE region 1650 on a beam of light in a propagating state, illustrated by an FOV rectangle located near the 2 o'clock position of the k-space ring. Again, the 2D diffraction grating within the MPE region 1650 attempts to diffract these beams of light to diffraction orders defined by its eight associated grating vectors. As shown, six of the grating vectors will shift the FOV rectangle to a position outside the boundary of the k-space diagram. Therefore, those diffraction orders do not occur. These positions are illustrated using an unshaded FOV rectangle. However, two of the grating vectors (i.e., H and HG) will shift the FOV rectangle to a position within the boundary of the k-space diagram. These are illustrated by shaded FOV rectangles located near the 9 o'clock and 6 o'clock positions of the k-space ring. Therefore, the 2D diffraction grating within the 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 ring to both 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).

[0262] Although not shown, a similar k-space diagram can be derived to illustrate the k-space effect of the MPE region 1650 on a beam of light traveling with a propagation angle indicated by an FOV rectangle located near the 6 o'clock position of the k-space ring. That k-space diagram would show that a 2D periodic diffraction grating within the MPE region 1650 partially diffracts the refractive power of their beams to both states indicated by two shaded FOV rectangles located near the 9 o'clock and 2 o'clock positions of the k-space ring.

[0263] Figure 16E is a k-space diagram illustrating the k-space action of the eyepiece waveguide 1600 shown in Figure 16A. As already mentioned, the eyepiece waveguide 1600 can generally receive input beams of light that propagate in the -z-direction and are incident on the ICG region 1640 of the waveguide 1600 from an external source. These input beams are k at the origin of the k-space diagram. z - Represented by an FOV rectangle centered on the axis. The ICG region 1640 then diffracts the input beam such that they have propagation angles that are induced and centered around the propagation direction corresponding to the center point of the FOV rectangle located near the 9 o'clock position of the k-space ring.

[0264] The guided beams are incident on the MPE region 1650, where they can have multiple interactions. During each occurrence of interaction, a portion of the refractive power of each beam can undergo zero-order diffraction and continue to propagate in the same direction through the MPE region 1650. In the first occurrence of interaction, for example, this zero-order diffraction corresponds to that portion of the refractive power of those beams, remaining in the state indicated by the FOV rectangle located near the 9 o'clock position of the k-space ring. The other portion of the refractive power of the beams can be diffracted in a new direction. Again, in the first occurrence of interaction, this creates separate diffracted beams having a propagation angle centered around the propagation direction corresponding to the center point of the FOV rectangle located near the 2 o'clock position of the k-space ring, and a propagation direction corresponding to the center point of the FOV rectangle located near the 6 o'clock position.

[0265] As long as the beams remain within the MPE region 1650, they undergo additional interactions, resulting in portions of the beam's refractive power that undergo zero-order diffraction, continuing in the same direction or being diffracted in a new direction. This results in a set of spatially dispersed diffracted beams with propagation angles centered around each propagation direction, indicated by the center point of the FOV rectangle in the k-space ring shown in Figure 16E. This behavior is represented by double arrows between each pair of FOV rectangles in the k-space ring.

[0266] As an arbitrary given input beam of light propagates within the MPE region 1650, it splits into many diffracted beams that can only travel in three permissible directions, each direction defined by the corresponding k-vector, i.e., point, within the FOV rectangle in the ring of the k-space diagram in Figure 16E. (This applies to any input beam of light propagating within the MPE region 1650; however, the three permissible directions will differ slightly depending on the propagation angle at which each initial input beam is incident on the MPE region 1650.) Furthermore, since a portion of the refractive power of an arbitrary given input beam of light is diffracted into one of the same three propagation directions after any number of interactions with the MPE region 1650, image information is preserved throughout these interactions.

[0267] In contrast to the two permissible propagation directions of the OPE region 1550, there are advantages associated with the MPE region 1650, which has three permissible propagation directions per input beam. These advantages will be discussed further below, but here we will only say that the increased number of propagation directions within the MPE region 1650 can result in a more complex distribution of interference nodes within the MPE region 1650, which in turn can improve the uniformity of illumination within the EPE region 1660.

[0268] It should be understood that Figure 16E illustrates the k-space action of an exemplary embodiment of the MPE region 1650. In other embodiments, the MPE region 1650 may be designed so that each input beam of light can diffract in more than three directions within the MPE region. For example, in some embodiments, the MPE region 1650 may be designed to allow diffraction of each input beam of light in four, five, six, seven, eight, etc. As already discussed, the diffraction features within the MPE region 1650 may be designed to provide a lattice vector that copies the FOV rectangle to a location in the k-space ring corresponding to the selected diffraction direction. In addition, the diffraction features within the MPE region 1650 may be designed with a period corresponding to the magnitude of the lattice vector, which results in these copies of the FOV rectangle being entirely within the k-space ring (while other attempted copies of the FOV rectangle are entirely outside the periphery of the k-space diagram).

[0269] In some embodiments, the angular separation between each of the allowable propagation directions with respect to a given beam of light inside the MPE region 1650 is at least 45 degrees. If the angular separation between any pair of selected directions is less than this amount, the diffraction features within the MPE region 1650 would need to be designed to provide lattice vectors for their angular transitions to occur within the k-space ring. Such lattice vectors would be relatively short compared to the size of the k-space ring, due to the smaller angular separation. This increases the likelihood that the superposition of the basic MPE lattice vectors will create a copy of the FOV rectangle that is only partially within the k-space ring, which can result in a loss of image information (if not done carefully, as will be discussed further herein). In addition, if the angular separation between any pair of allowable propagation directions within the MPE region 1650 is too small, the resulting relatively short lattice vectors also increase the likelihood that the lattice vector superposition will create a copy of the FOV rectangle that is only partially inside the central disk of the k-space diagram. This is undesirable because it could result in light being externally coupled from the eyepiece waveguide 1600 toward the user's eye, from a location outside the designated EPE region 1660.

[0270] When determining acceptable propagation directions within the MPE region 1650, various design guidelines can be used as a model. For example, one acceptable propagation direction can be selected so that it corresponds to the direction from the ICG region 1640 to the MPE region 1650. In addition, one acceptable propagation direction can be selected so that only one beam of light propagating from a location inside the MPE region 1650 in that direction will intersect the EPE region 1660. This ensures that the duplicate beams of light corresponding to each input beam are incident on the EPE region 1660 with the same propagation angle. Furthermore, the acceptable propagation directions inside the MPE region 1650 can be selected so that the FOV rectangles do not overlap. Overlapping FOV rectangles can result in a mixture of image information from different image points, which can produce afterimages.

[0271] Figure 16F is a schematic diagram of the first occurrence of interaction between the input beam and the MPE region 1650 of the eyepiece waveguide embodiment shown in Figure 16A. Figure 16F shows the input beam incident from the ICG region 1640 into the MPE region 1650. The input beam is shown propagating in the direction corresponding to the k-vector, i.e., the center point of the FOV rectangle located near the 9 o'clock position of the k-space ring in Figure 16E.

[0272] The MPE region 1650 can contain many sub-1 μm features. Furthermore, with each interaction with the MPE region, the input beam, approximately 1 mm in diameter, will split into three beams (of the same diameter but with a certain proportion of the original refractive power of the input beam) propagating in three different directions in the TIR. One direction corresponds to zero-order diffraction and is the original propagation angle in the waveguide plane. The other two directions depend on the lattice vectors G and H of the MPE region 1650. As shown, the first occurrence of interaction between the input beam and the MPE region 1650 results in three beams. That is, a portion of the refractive power of the input beam is simply reflected as output 1 from the upper or lower surface of the eyepiece waveguide 1600 and continues in the same xy direction as the input beam (i.e., zero-order diffraction), a portion of the refractive power of the input beam interacts with the 2D grating in the MPE region 1650 and is diffracted downward as output 2, and a portion of the refractive power of the input beam interacts with the grating and is diffracted upward and to the right as output 3. The output 2 beam is shown propagating in the direction corresponding to the k-vector, i.e., to the center point of the FOV rectangle located near the 6 o'clock position of the k-space ring in Figure 16E, while the output 3 beam is shown propagating in the direction corresponding to the k-vector, i.e., to the center point of the FOV rectangle located near the 2 o'clock position. Following the first occurrence of this interaction, output beams 1, 2, and 3, although having different propagation angles as shown in Figures 16G-16I, still propagate within the MPE region 1650 and therefore may have additional interactions with the MPE region. Other input beams, not shown, that enter the MPE region 1650 with different propagation angles will behave similarly, but with slightly different input and output angles.

[0273] Figure 16G is a schematic diagram of a second occurrence of interaction between the input beam and the MPE region 1650 of the eyepiece waveguide embodiment shown in Figure 16A. The beam associated with the first occurrence of interaction is shown using a dashed line, while the beam associated with the second occurrence of interaction is shown using a solid line. As shown in Figure 16G, the output beams, output 1, output 2, and output 3 from the first occurrence of interaction can each undergo an interaction with the MPE region 1650 similar to that which occurred in the previous occurrence. That is, a portion of the refractive power of the output 1 beam from Figure 16F simply continues in the same xy direction, while another portion of the refractive power of that beam interacts with the grating and is diffracted in a direction corresponding to the FOV rectangle located near the 6 o'clock position, and yet another portion of the refractive power of that beam interacts with the grating and is diffracted in a direction corresponding to the FOV rectangle located near the 2 o'clock position. Similarly, a portion of the refractive power of output beam 2 from Figure 16F simply continues toward the EPE region 1660, while another portion of the refractive power of that beam interacts with the grating and is diffracted in the direction indicated by the FOV rectangle located near the 9 o'clock position, and yet another portion of the refractive power of that beam interacts with the grating and is diffracted in the direction corresponding to the FOV rectangle located near the 2 o'clock position. Furthermore, a portion of the refractive power of output beam 3 from Figure 16F simply continues toward the direction indicated by the FOV rectangle located near the 2 o'clock position, while another portion of the refractive power of that beam interacts with the grating and is diffracted in the direction indicated by the FOV rectangle located near the 9 o'clock position, and yet another portion of the refractive power of that beam interacts with the grating and is diffracted in the direction corresponding to the FOV rectangle located near the 6 o'clock position.

[0274] Figure 16H is a schematic diagram of the third occurrence of interaction between the input beam and the MPE region 1650 of the eyepiece waveguide embodiment shown in Figure 16A. The beams associated with the first and second occurrences of interaction are shown using dashed lines, while the beam associated with the third occurrence of interaction is shown using solid lines. As shown in Figure 16H, each output beam resulting from the second occurrence of interaction may again undergo interaction with the MPE region 1650 similar to that in the previous occurrence.

[0275] Figure 16I is a schematic diagram of the fourth occurrence of interaction between the input beam and the MPE region 1650 of the eyepiece waveguide embodiment shown in Figure 16A. The beams associated with the first, second, and third occurrences of 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, all resulting beams propagate in one of three directions allowed inside the MPE region 1650 with respect to any given input beam: namely, the direction corresponding to the FOV rectangle located near the 9 o'clock position of the k-space ring, the direction corresponding to the FOV rectangle located near the 2 o'clock position, or the direction corresponding to the FOV rectangle located near the 6 o'clock position. 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 case of the OPE region 1550 as illustrated in Figures 15D-15G. Furthermore, beams may arrive at each of these nodes via different paths and therefore will not necessarily be in phase with each other. Therefore, image artifacts that may arise from the ordered distribution of interference nodes can be reduced within the eyepiece waveguide embodiment 1600 by using the MPE region 1650 instead of the OPE region (e.g., 1550). This can be seen in Figures 16J and 16K.

[0276] Figure 16J is a schematic diagram illustrating various paths the beam can take to eventually follow the EPE region 1660 through the MPE region 1650. Several paths exist that involve changes in multiple directions, while others involve changes in multiple directions (although some of the longer and more complex paths will inevitably carry less refractive force). Due to the complexity introduced by the presence of different diffraction angles within the MPE region 1650, there are many different spacings between the light beams 1665 that ultimately illuminate the EPE region 1660. In fact, any possible spacing between the light beams 1665 can be achieved through a sufficient number of interactions within the MPE region 1650. As shown in Figure 16K, this can result in more uniform illumination of the EPE region 1660.

[0277] Figure 16K is a schematic diagram illustrating how a single input beam 1645 from the ICG region 1640 is duplicated by the MPE region 1650 and redirected as multiple beams 1665 toward the EPE region 1660. Each of these beams 1665 originates from the dense grid of the node. Gaps may still exist between some of these duplicate beams 1665, but they are generally smaller and less regular than the gaps between duplicate beams output from the OPE region (e.g., 1550 as shown in Figure 15G). Because there are so many paths toward the EPE region 1660, all at different locations, the MPE region 1650 provides a complex exit pupil pattern, which allows for more uniform illumination of the EPE region 1560.

[0278] Figure 16L is a comparative illustration of the performance of an eyepiece waveguide with an OPE region versus an eyepiece waveguide with an MPE region. On the left is the eyepiece waveguide 1500, which includes an OPE region 1550 with a 1D periodic diffraction grating. As already discussed, the OPE region 1550 illuminates the EPE region 1560 using a sparse set of regularly spaced replicated light beams. Below the eyepiece waveguide 1500 is a simulated output image. This is the simulated output image that would be projected from the EPE region 1560 of the eyepiece waveguide 1500 in response to an input image consisting of pixels of all the same color and brightness.

[0279] Figure 16L shows, on the right, the eyepiece waveguide 1600, which includes an MPE region 1650 with a 2D periodic diffraction grating. As can be seen from the figure, the MPE region 1650 illuminates the EPE region 1660 more uniformly. Below the eyepiece waveguide 1600 is a simulated output image, which 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 a 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, which result from a sparse and ordered set of replicated light beams illuminating its EPE region 1560.

[0280] Figure 16M further illustrates the performance of an eyepiece waveguide with an MPE region versus an eyepiece waveguide with an OPE region. The upper line of the graph in Figure 16M illustrates the performance of eyepiece waveguide 1500 shown in Figure 15A. The graph of the horizontal cross-section of the image projected from this eyepiece waveguide shows relatively high spatial frequency fluctuations, which were visible as striations in the simulated output image shown in Figure 16L. Figure 16M shows that eyepiece waveguide 1500 has an eyebox efficiency of 1.2%. It also shows the point spreading function associated with this eyepiece waveguide. The point spreading function illustrates the output image acquired from the eyepiece waveguide in response to an input image of a single bright point. This shows that eyepiece waveguide 1500 is very sharp, having only 2.5 to 5 arcs of blur.

[0281] One approach to overcome high spatial frequency fluctuations in the output image from the eyepiece waveguide 1500 is to introduce some degree of dithering into the OPE region 1550. For example, small fluctuations can be introduced into the orientation angle and / or lattice period of the OPE region 1550. This is done in an attempt to disrupt the ordered nature of interference nodes that may exist within the OPE region 1550. The second and third rows in Figure 16M illustrate the performance of the eyepiece waveguide 1500 with two different types of dithering. As can be seen from the horizontal cross-section of the image projected with respect to these waveguides, high spatial frequency fluctuations still exist. Furthermore, the point spreading function with respect to these dithered embodiments shows a much larger amount of blurring, in some cases as much as 45 arcs.

[0282] The lower row of Figure 16M illustrates the performance of the eyepiece waveguide 1600 with the MPE region 1650. The cross-section of the projected image with respect to this waveguide shows much less high spatial frequency variation. Low-frequency spatial variation is still present, but this can be corrected much more easily via software than high spatial frequency variation. The eyebox efficiency of this eyepiece waveguide is 0.9%, slightly lower than others. This may be due to the fact that the MPE region 1650 redirects some of the input light in a general direction corresponding to the FOV rectangle located near the 2 o'clock position in the ring of the k-space diagram shown in Figure 16E. Due to the macroscopic layout of the eyepiece waveguide 1600, light emanating from 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 edge of the waveguide 1600. However, this loss of light results in only a relatively small decrease in eyebox efficiency. On the other hand, the point spreading function for the eyepiece waveguide 1600 shows that it is very sharp, with blurring only for 2.5 to 5 arcs.

[0283] Figures 16A–16M illustrate an eyepiece waveguide 1600 with an MPE region 1650 having three permissible propagation directions for each input beam. However, other embodiments of the MPE region can be designed to allow even more propagation directions for each input beam. One such embodiment is illustrated in Figures 17A–17G. These figures illustrate an eyepiece waveguide 1700, which in its macroscopic design is identical to that of the eyepiece waveguide 1600. That is, the eyepiece waveguide 1700 includes an ICG region 1740, an MPE region 1750, and an EPE region 1760, all of which are arranged in the same manner as the corresponding regions in the eyepiece waveguide 1600 shown in Figure 16A. However, the eyepiece waveguide 1700 differs in the microscopic design of its MPE region 1750.

[0284] Figure 17A illustrates a portion of an exemplary 2D grating that may be used within the MPE region 1750 of an eyepiece waveguide 1700, along with its associated grating vectors. The 2D periodic grating 1750 can be a spatial grating of diffraction features whose periodicity directions are u and v. As already discussed, such a 2D periodic grating is associated with fundamental grating vectors G and H. In one embodiment, the 2D periodic grating 1750 can be designed or formed by superimposing two sets of 1D periodic grating lines (wherein the 2D periodic grating may instead consist of individual scattering features located at the intersections of the grating lines shown, for example, in Figure 17A). The first set of grating lines 1756 can be repeated along the direction of the fundamental grating vector G. The fundamental grating vector G may have a magnitude equal to 2π / a, where a is the period of the first set of grating lines 1756. The 2D lattice shown in Figure 17B is also associated with harmonics of the first fundamental lattice vector G. These include higher harmonics such as -G and 2G, -2G, etc. The second set of lattice lines 1757 can be repeated along the direction of the fundamental lattice vector H. The fundamental lattice vector H can have a magnitude equal to 2π / b, where b is the period of the second set of lattice lines 1657. The 2D lattice shown in Figure 17B is also associated with harmonics of the second fundamental lattice vector H. These include higher harmonics such as -H and 2H, -2H, etc. Also, as already discussed, any 2D periodic array of diffraction features will have associated lattice vectors pointing in a direction determined by an integer linear combination (superposition) of the fundamental lattice vectors. In this case, these superpositions result in additional lattice vectors. These include, for example, -G, -H, H+G, HG, GH, and -(H+G). Figure 17A illustrates only the superposition of a first-order lattice vector and its relationship to a 2D diffraction grating, but higher-order lattice vectors may also exist.

[0285] Figure 17B is a k-space diagram illustrating the k-space action of the MPE region 1750 of the eyepiece waveguide 1700. The k-space diagram includes a shaded FOV rectangle located near the 9 o'clock position of the k-space ring. This is the location of the FOV rectangle after the ICG region 1740 couples the input beam into the eyepiece waveguide 1700 and redirects them toward the MPE region 1750. Figure 17B shows how the 2D grid within the MPE region 1750 translates the FOV rectangle using the grid vectors shown in Figure 17A. Since there are eight grid vectors, the MPE region 1750 attempts to translate the FOV rectangle to new locations that can be considered as eight possible locations within the k-space diagram. Of these eight possible locations, five are outside the periphery of the k-space diagram. These locations are illustrated using an unshaded FOV rectangle. k-vectors outside the periphery of the k-space diagram are not allowed, so none of those five lattice vectors result in diffraction. However, there are three lattice vectors (i.e., -H, -G, and -(H+G)) that result in a translation of the FOV rectangle to a new position within the boundary of the k-space diagram. One of these locations is near the 6 o'clock position in the k-space ring, another is near the 12 o'clock position, and the last is near the 3 o'clock position. Since k-vectors at these locations are allowed and result in stimulated propagation modes, the FOV rectangle at these locations is shaded to indicate that the beam of light is diffracted into those three states. Therefore, a beam of light incident on the MPE region 1750 with a propagation angle indicated by the FOV rectangle located near the 9 o'clock position of the k-space ring is diffracted into all 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).

[0286] Although not shown, similar k-space diagrams can be derived to illustrate the k-space effects of the MPE region 1750 on a beam of light traveling with propagation angles indicated by FOV rectangles located near the 12 o'clock, 3 o'clock, and 6 o'clock positions of the k-space ring. These k-space diagrams would show that a 2D diffraction grating within the MPE region 1750 diffracts those beams to all the remaining states indicated by the shaded FOV rectangles within the ring of the k-space diagram in Figure 17B.

[0287] Figure 17C is a k-space diagram illustrating the k-space action of the eyepiece waveguide 1700. The eyepiece waveguide 1700 can generally receive input beams of light that propagate in the -z-direction and are incident on the ICG region 1740 of the waveguide 1700 from an external source. These input beams are k at the origin of the k-space diagram. z - Represented by an FOV rectangle centered on the axis. The ICG region 1740 then diffracts the input beam such that they have propagation angles centered around the propagation direction, corresponding to the center point of the FOV rectangle located near the 9 o'clock position of the k-space ring.

[0288] The diffracted beams are incident on the MPE region 1750, where they may have multiple interactions. During each occurrence of an interaction, a portion of the refractive power of each beam continues to propagate in the same direction through the MPE region 1750. In the first occurrence of an interaction, for example, this would correspond to that portion of the refractive power of those beams remaining in the state indicated by the FOV rectangle located near the 9 o'clock position. The other portion of the refractive power of the beams can be diffracted in a new direction. Again, in the first occurrence of an interaction, this creates separate 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 of the k-space ring.

[0289] After each interaction, the diffracted beam, still remaining within the MPE region 1750, may undergo additional interactions. Each of these additional interactions results in some of the beam's refractive power undergoing zero-order diffraction and continuing in the same direction, while other parts of the beam's refractive power are diffracted in a new direction. This results in a set of spatially dispersed diffracted beams with propagation angles centered around each propagation direction, indicated by the center point of the FOV rectangle in the k-space ring shown in Figure 17C. This is represented by double arrows between each pair of FOV rectangles in the k-space ring. In other words, a beam of light propagating within the MPE region 1750 can transition from any propagation state represented by one of the FOV rectangles in the k-space ring to any other of these propagation states.

[0290] As an arbitrary given input beam of light propagates within the MPE region 1750, it splits into many diffracted beams, which can only propagate in four possible directions. Each direction is defined by the corresponding k-vector, i.e., point, within the FOV rectangle in the ring of the k-space diagram in Figure 17C. (This applies to any input beam of light propagating within the MPE region 1750; however, the four possible directions will differ slightly depending on the propagation angle at which each initial input beam is incident on the MPE region 1750.) Also, since a portion of the refractive power of any arbitrary given input beam of light is diffracted in 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 Figures 16A-16M, the additional propagation directions allowed within the MPE region 1750 can result in further improvement in the uniformity of illumination within the EPE region 1760. This can be seen in the schematic diagrams shown in Figures 17D-17G.

[0291] Figure 17D is a schematic diagram of the first occurrence of interaction between the input beam and the MPE region 1750 of the eyepiece waveguide 1700. Figure 17D shows the input beam incident from the ICG region 1740 into the MPE region 1750. The input beam is shown propagating in the direction corresponding to the k-vector, i.e., the center point of the FOV rectangle located near the 9 o'clock position of the k-space ring in Figure 17C.

[0292] The MPE region 1750 can contain many sub-1 μm features. Furthermore, with each interaction with the MPE region, a beam of approximately 1 mm in diameter will split into four beams (of the same diameter but with a certain proportion of the original refractive power of the input beam) propagating in four different directions in the TIR. One direction corresponds to zero-order diffraction and is the original angle in the waveguide plane. The other three directions depend on the lattice vectors G and H of the MPE region 1750. As shown, the first occurrence of interaction between the input beam and the MPE region 1750 results in four beams. In other words, a portion of the refractive power of the input beam is simply reflected as output 1 from the upper or lower surface of the eyepiece waveguide 1700 and continues in the same xy direction as the input beam (i.e., zero-order diffraction), a portion of the refractive power of the input beam interacts with the grating and is diffracted downward as output 2, a portion of the refractive power of the input beam interacts with the grating and is diffracted upward as output 3, and a portion of the refractive power of the input beam interacts with the grating and is diffracted to the right as output 4. The output 2 beam is shown to propagate in the direction corresponding to the center point of the FOV rectangle located near the 6 o'clock position of the k-space ring in Figure 17C, i.e., the k-vector, while the output 3 beam is shown to propagate in the direction corresponding to the center point of the FOV rectangle located near the 12 o'clock position, i.e., the k-vector, and the output 4 beam is shown to propagate in the direction corresponding to the center point of the FOV rectangle located near the 3 o'clock position, i.e., the k-vector. Following the first occurrence of this interaction, output beams 1, 2, 3, and 4, although having different propagation angles as shown in Figures 17E-17G, still propagate within the MPE region 1750 and therefore may have additional interactions with the MPE region. Other input beams, not shown, that are incident on the MPE region 1750 with different propagation angles will behave similarly, but with slightly different input and output angles.

[0293] Figure 17E is a schematic diagram of the second occurrence of interaction between the input beam and the MPE region 1750 of the eyepiece waveguide 1700. The beam associated with the first occurrence of interaction is shown with a dashed line, while the beam associated with the second occurrence of interaction is shown with a solid line. As shown in Figure 17D, the output beams from the first occurrence of interaction, namely output 1, output 2, output 3, and output 4, can each undergo interaction with the MPE region 1750, similar to that that occurred in the previous occurrence. That is, a portion of the refractive power of the output 1 beam from Figure 17D simply continues in the same xy direction, while the other portion of the refractive power of that beam interacts with the grating and is diffracted in directions corresponding to the FOV rectangles located near the 12 o'clock, 3 o'clock, and 6 o'clock positions. Similarly, a portion of the refractive power of output beam 2 from Figure 17D simply continues toward the EPE region 1760, while the other portion of the refractive power of that beam interacts with the grating and is diffracted in the directions indicated by the FOV rectangles located near the 9 o'clock, 12 o'clock, and 3 o'clock positions. Furthermore, a portion of the refractive power of output beam 3 from Figure 17D simply continues toward the direction indicated by the FOV rectangle located near the 12 o'clock position, while the other portion of the refractive power of that beam interacts with the grating and is diffracted in the directions indicated by the FOV rectangles located near the 3 o'clock, 6 o'clock, and 9 o'clock positions. Finally, a portion of the refractive power of output beam 4 from Figure 17D simply continues toward the direction indicated by the FOV rectangle located near the 3 o'clock position, while the other portion of the refractive power of that beam interacts with the grating and is diffracted in the directions indicated by the FOV rectangles located near the 6 o'clock, 9 o'clock, and 12 o'clock positions.

[0294] Figure 17F is a schematic diagram of the third occurrence of interaction between the input beam and the MPE region 1750 of the eyepiece waveguide embodiment 1700. The beams associated with the first and second occurrences of interaction are shown using dashed lines, while the beam associated with the third occurrence of interaction is shown using solid lines. As shown in Figure 17F, each output beam resulting from the second occurrence of interaction may again undergo interaction with the MPE region 1750 similar to that in the previous occurrence.

[0295] Figure 17G is a schematic diagram of the fourth occurrence of interaction between the input beam and the MPE region 1750 of the eyepiece waveguide embodiment 1700. The beams associated with the first, second, and third occurrences of 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, all resulting beams propagate in one of four possible propagation directions with respect to the MPE region 1750 with respect to any given input beam: namely, the direction corresponding to the FOV rectangle located near the 9 o'clock position of the k-space ring, the direction corresponding to the FOV rectangle located near the 12 o'clock position, the direction corresponding to the FOV rectangle located near the 3 o'clock position, or the direction corresponding to the FOV rectangle located near the 6 o'clock position. 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 as illustrated in Figures 16A-16M. Furthermore, these nodes are even less likely to result in interference between two in-phase beams. Therefore, the MPE region 1750 can provide even more uniform illumination in the EPE region 1760.

[0296] In summary, the MPE regions described herein offer some or all of the following advantages: The MPE region can extend the image pupil in multiple directions simultaneously. The MPE region can create a dense, non-periodic array of output pupils. The MPE region can reduce interference effects between optical paths through the waveguide. MPE-based eyepiece waveguides can achieve improved brightness uniformity with reduced high-frequency striations and high image sharpness. (An exemplary AR eyepiece waveguide with multiple distinctly different regions for replicating the input beam)

[0297] Figure 18A illustrates an exemplary eyepiece waveguide 1800, comprising an ICG region 1840, two orthogonal pupil expander (OPE) regions 1850a and 1850b, and an exit pupil expander (EPE) region 1860. Figure 18A also includes a k-space diagram illustrating the effect of each of these components of the eyepiece waveguide 1800 in k-space. The ICG region 1840, OPE regions 1850a and 1850b, and EPE region 1860 of the eyepiece waveguide 1800 contain various diffraction features that couple the input beam into the eyepiece waveguide 1800, propagate it through inductive 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 contains multiple distinctly different and / or discontinuous regions for replicating the input beam. These replicated beams from distinctly different regions can be combined again within a common exit pupil region.

[0298] The eyepiece waveguide 1800 illustrated in Figure 18A is similar to the eyepiece waveguide 1400 illustrated in Figure 14A, but instead of one, it includes two OPE regions 1850a and 1850b. It should be recalled that the ICG region 1440 in the eyepiece waveguide 1400 diffracted the input beam to +1 and -1 diffraction orders, but the beam at one of these diffraction orders propagated away from the OPE region 1450 and was eventually lost from the eyepiece waveguide. Thus, some of the light from the input beam was lost. The eyepiece waveguide 1800 shown in Figure 18A corrects this by including two OPE regions 1850a and 1850b, one on each side of the ICG region 1840. In this way, the eyepiece waveguide 1800 can utilize both the +1 and -1 diffraction orders of the ICG 1840.

[0299] The operation of ICG region 1840 is similar to that described for 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 aligned to the origin of the k-space diagram.

[0300] The k-space diagram KSD2 in Figure 18A illustrates the k-space action 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 ring, respectively. The translated FOV rectangle at the 3 o'clock position represents a diffracted beam propagating toward the right OPE region 1850b, while the translated FOV rectangle at the 9 o'clock position represents a diffracted beam propagating toward the left OPE region 1850a.

[0301] The action of the left OPE region 1850a is also similar to that described for OPE region 1450 in Figures 14A and 14B. The k-space diagram KSD3a illustrates the k-space action of the left OPE region 1850a, showing that its diffraction grating shifts the FOV rectangle from the 9 o'clock position to the 6 o'clock position in the k-space ring. The FOV rectangle located at the 6 o'clock position represents the diffracted beam propagating in the -y-direction toward EPE region 1860.

[0302] The operation of the right OPE region 1850b is similar to that of the left OPE region 1850a, but its associated grating vectors are mirrored around the perpendicular line with respect to those of the left OPE region 1850a. This is due to the fact that the lines of the diffraction grating in the right OPE region 1850b are mirrored around the perpendicular line with respect to those of the diffraction grating in the left OPE region 1850a. As a result of the orientation of the lines of the diffraction grating in the right OPE region 1850b, the effect of the grating in k-space is to translate the FOV rectangle from the 3 o'clock position to the 6 o'clock position in the k-space ring, as shown in the k-space diagram KSD3b. The translated FOVs in KSD3a and KSD3b are in the same location at the 6 o'clock position in the k-space ring. Therefore, the refractive power of each input beam is split by the ICG region 1840 into +1 and -1 diffraction orders, and these distinctly different diffraction orders propagate through the eyepiece waveguide 1800 along different paths, but nevertheless arrive at the EPE region 1860 with the same propagation angle. This means that the distinct diffraction orders of each input beam, following different propagation paths through the eyepiece waveguide 1800, ultimately exit the EPE region 1860 with the same angle and thus represent the same point in the projected image.

[0303] Finally, the action of EPE region 1860 is also similar to that described for EPE region 1460 in Figures 14A and 14B. The k-space diagram KSD4 illustrates the k-space action of EPE region 1860, showing that its diffraction grating translates the FOV rectangle (consisting of light beams from both OPE regions 1850a and 1850b) located at the 6 o'clock position of the k-space ring back to the center of the k-space diagram. As has already been discussed elsewhere, this represents that EPE region 1860 externally couples the light beam, generally in the z-direction, toward the user's eye.

[0304] Figures 18B and 18C illustrate a top view 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 in any part of this specification (see Figures 12A and 12B), the EPE region 1860 projects a set of replicated output beams, each set of replicated output beams having a propagation angle corresponding to one of the input beams projected into the eyepiece waveguide.

[0305] Figure 18B illustrates one of these sets of replicated power beams. In this particular case, the replicated power beam 1861 emanating from the EPE region 1860 propagates from left to right. In other words, the replicated power beam 1861 has a propagation direction with a component in the +x- direction. The propagation angles of the replicated power beams 1861 result in some of them being more likely to intersect the user's eye 210 than others. In particular, the replicated power beam 1861 emanating from the left portion of the EPE region 1860 is more likely to intersect the user's eye 210 due to the center position of the eye 210 and the left / right propagation of the light beam. These light beams are illustrated using solid lines. On the other hand, the replicated power beam 1861 emanating from the right portion of the EPE region 1860 is more likely to miss the eye 210. These light beams are illustrated using dashed lines.

[0306] Figure 18B also includes a k-space diagram KSD5 illustrating the state of the output beam in k-space after the EPE region has been translated so that the FOV rectangle returns to the origin of the schematic diagram. The FOV rectangle is illustrated using two halves, each representing half of the horizontal field of view of the eyepiece waveguide 1800. The shaded right half of the FOV rectangle 1832 represents +k x -Includes k-vectors with components in the direction. These are the k-vectors corresponding to the output beam 1861 that exits the EPE region 1860 with the left / right propagation type illustrated in Figure 18B. Only one set of duplicate output beams 1861 is illustrated to exit the EPE region 1860, but all output beams whose k-vectors lie within the shaded right half 1832 of the FOV rectangle will similarly exit the EPE region with a left / right propagation direction. Therefore, for all output beams whose k-vectors lie 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 the eye 210 than those output beams exiting from the right side of the EPE region.

[0307] Figure 18C illustrates another set of replicated light beams 1862 emanating from the EPE region 1860 of the eyepiece waveguide 1800. However, in this case, the replicated power beam 1862 emanating from the EPE region 1860 propagates from right to left. In other words, the replicated power beam 1862 has a propagation direction with a component in the -x- direction. The actual propagation angle of the replicated power beam 1862 leads to the opposite observation of what is derived from Figure 18B. That is, with respect to the power beam 1862 propagating right / left, the beam emanating from the right portion of the EPE region 1860 (illustrated with solid lines) has a strong tendency to intersect the eye 210, while the light beams emanating from the left portion of the EPE region (illustrated with dashed lines) have a strong tendency to lose sight of the eye.

[0308] Referring to the k-space diagram KSD5 included with Figure 18C, the output beam whose k-vector lies within the shaded left half 1831 of the FOV rectangle originates from the EPE region 1860 with the right / left propagation type shown in Figure 18C. Although all output beams whose k-vector lies within the shaded left half 1831 of the FOV rectangle will have different propagation angles, they all share the property that beams originating from the right side of the EPE region 1860 will have a stronger tendency to intersect the eye 210 than output beams originating from the left side of the EPE region.

[0309] The 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, half of the EPE region 1860 mainly contributes to half of the horizontal field of view, while the other half of the EPE region mainly contributes to the remaining half of the horizontal field of view. Based on this observation, 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 the induction mode, since it is unnecessary to project the entire FOV rectangle from all parts of the EPE region 1960. This is illustrated in Figure 19. (Exemplary AR eyepiece waveguide with expanded field of view)

[0310] Figure 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 Figure 19 can be the same as the eyepiece waveguide 1800 shown in Figure 18A. However, some of the diffraction features within the eyepiece waveguide 1900 can be designed with properties that enable an increased field of view in at least one dimension. These features can be clearly understood based on the k-space action of the eyepiece waveguide 1900, illustrated by the k-space diagram shown in Figure 19.

[0311] The k-space diagram shown in Figure 19 has a larger FOV rectangle than that shown in Figure 18A. This is because the FOV rectangles in the k-space diagram in Figure 18A were constrained so that they do not have any dimensions greater than the width of the k-space ring. This constraint ensured that these FOV rectangles could fit entirely within the k-space ring at any position around the ring, and therefore all beams represented by the k-vectors within the FOV rectangles could undergo induced propagation within the eyepiece waveguide 1800 while propagating in any direction in the eyepiece plane. However, in the exemplary embodiment of Figure 19, the FOV rectangle has at least one dimension (e.g., k) greater than the width of the k-space ring. x It has dimensions. In some embodiments, one or more dimensions of the FOV rectangle can be up to 20%, up to 40%, up to 60%, up to 80%, or up to 100% larger than the width of the k-space ring.

[0312] In a particular embodiment illustrated in the k-space diagram of Figure 19, the horizontal dimension of the FOV rectangle is wider than the k-space ring. The horizontal dimension of the FOV rectangle corresponds to the horizontal spread within the propagation angle of the input beam, projected into the eyepiece waveguide. Thus, since the eyepiece waveguide 1900 is illustrated to be usable with an FOV rectangle having a larger horizontal dimension, this means that the horizontal field of view of the eyepiece waveguide is increased. For an eyepiece waveguide (enclosed by air) with a refractive index of 1.8, the eyepiece waveguide 1800 shown in Figure 18A can generally achieve a 45° × 45° FOV, while the eyepiece waveguide 1900 shown in Figure 19 can achieve a maximum FOV of 90° × 45°. However, some embodiments of the eyepiece waveguide may be designed for a smaller FOV of about 60° × 45° to satisfy typical design constraints of eyebox volume (it may be advantageous to send a portion of the FOV to both sides of the eyepiece waveguide to provide a properly sized eyebox) and to avoid screen door artifacts resulting from sparsely spaced output beams. Techniques for extending the field of view of the eyepiece waveguide 1900 are described in the context of an extended horizontal field of view, but the same techniques can also be used to extend the vertical field of view of the eyepiece waveguide 1900. Furthermore, in later embodiments, similar techniques are demonstrated to extend both the horizontal and vertical fields of view of the eyepiece waveguide.

[0313] A close examination of the k-space diagram in Figure 19 reveals that while the illustrated FOV rectangles, when located at certain positions around the ring, cannot fit entirely within the k-space ring, they can still fit entirely within the ring when located at other positions. For example, if one dimension of the FOV rectangle is larger than the width of the k-space ring, the FOV rectangle cannot fit entirely within the ring when it is located on or near the axis of the enlarged dimension. x If the dimensions of the FOV rectangle are greater than the width of the k-space ring, then the FOV rectangle is k x -When located on or near the axis (i.e., at or near the 3 o'clock and 9 o'clock positions), it cannot be fitted entirely within the ring. Similarly, ky If the dimensions of the FOV rectangle are greater than the width of the k-space ring, then the FOV rectangle is k y -When located on or near the axis (i.e., at or near the 12 o'clock and 6 o'clock positions), it cannot fit entirely within the ring. However, when located on or near the opposite axis, such an FOV rectangle can still fit entirely within the k-space ring. x If the dimensions are greater than the width of the k-space ring, the FOV rectangle is still k y -When located on or near the axis (i.e., at or near the 12 o'clock and 6 o'clock positions), it can fit entirely within the ring. Similarly, k y If the dimensions of the FOV rectangle are greater than the width of the k-space ring, then the FOV rectangle is k x -When located on or near the axis (i.e., at or near the 3 o'clock and 9 o'clock positions), it can still fit entirely within the ring. This is because there is area within the k-space ring to accommodate an FOV rectangle that is larger in the azimuthal direction than in the radial direction.

[0314] The radial size of the k-space ring corresponds to the range of propagation angles in the direction normal to the waveguide plane (i.e., the thickness direction) that support the inductive 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 the k-vector in the azimuthal dimension of the k-space ring corresponds to various propagation angles in the in-plane direction of the plane waveguide. Since the spread of propagation angles in the plane waveguide is not limited by the same constraints as in the thickness direction, a wider range of beam propagation angles can be supported.

[0315] Furthermore, it is possible to convert the propagation angle spread in the thickness direction of the eyepiece waveguide to the propagation angle spread in the in-plane direction, and vice versa. When a diffraction grating (or other set of diffraction features) translates the FOV rectangle from one position to another in the k-space ring so that the set of beams represented by the FOV rectangle then propagates in a new direction, this also causes a portion of the beam that was previously diffused in the thickness direction of the plane waveguide to instead diffuse 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 ring. While at the 9 o'clock position, k x The beam spread in the direction is, at that location, k x Since the direction corresponds to the radial direction of the k-space ring, it corresponds to the physical spread in the thickness direction of the waveguide. However, at the 6 o'clock position, k x The beam spread in the direction is, at that location, k x Since the direction corresponds to the azimuthal angle direction of the k-space ring, it corresponds to the physical extent of the waveguide in the in-plane direction.

[0316] Using these observations, the field of view (FOV) of an eyepiece waveguide can be increased by dividing the FOV rectangle into multiple sub-parts, using diffraction features to replicate the beams belonging to the multiple sub-parts of the FOV in a spatially dispersed manner, and using diffraction features to reassemble the multiple sub-parts of the FOV in the exit pupil of the eyepiece waveguide so that the beams corresponding to each sub-part of the FOV have the correct propagation angles and recreate the original image. For example, diffraction features can be used to translate each sub-part of the FOV rectangle to one or more locations in k-space so that they ultimately have the same relative position as in the original image with respect to the other sub-parts of the FOV rectangle.

[0317] In some embodiments, multiple sub-parts of the FOV may partially overlap each other, which may help to alleviate the constraints on reassembling the entire FOV in the waveguide exit pupil and to ensure that the entire beam is present (for example, different pairs of FOV sub-parts may contain portions of the same input beam). For example, in some embodiments, a pair of sub-parts of the input image FOV may overlap by 10%, 20%, 30%, 40%, 50%, or more.

[0318] The k-space diagram KSD2 in Figure 19 illustrates the k-space effect of the ICG region 1940 on the input beam projected into the eyepiece waveguide 1900. As discussed elsewhere in this specification, the input beam projected into the eyepiece waveguide 1900 can be represented by an FOV rectangle centered on 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 vectors. In the case of the ICG region 1840 illustrated in Figure 18A, the ICG region is centered on its associated grid vectors G1, G -1 The ICG region 1940, shown in Figure 19, was designed to have a magnitude equal to the distance from the origin of the k-space diagram to the midpoint of the k-space ring. This centered the FOV rectangle within the k-space ring. However, the ICG region 1940 shown in Figure 19 can be designed to have a larger grid vector. Also, as already discussed, the set of input beams projected into the eyepiece waveguide 1900 can have at least one dimension in k-space that is greater than the width of the k-space ring.

[0319] In some embodiments, the ICG region 1940 has its lattice vectors G1, G -1 However, the enlarged FOV rectangle can be designed to be translated so that it is sufficiently far from the origin of the k-space diagram, so that no part of the enlarged FOV rectangle lies inside the inner disk of the k-space diagram. For an FOV rectangle whose horizontal dimension is twice the width of the k-space ring, to achieve this goal, the grid vectors G1 and G of ICG1940 are used.-1 The size of the k-space diagram will need to be approximately equal to the radius of the outer disk. On the other hand, in the case of an FOV rectangle whose horizontal dimension is simply slightly larger than the width of the k-space ring, to achieve this goal, the grid vectors G1 and G of the ICG region 1940 will need to be -1 The magnitude of must exceed the distance from the origin of the k-space diagram to the midpoint of the k-space ring. Mathematically, this means the following: [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 Figure 20-22 and described below.)

[0320] In other words, this technique for extending the field of view of the eyepiece waveguide 1900 involves the lattice vectors G1 and G in the ICG region 1940. -1 However, this means that the field of view is designed to be longer than in embodiments where it is constrained in all dimensions by a range of propagation angles that can fit within the radial dimension of the k-space ring of a given eyepiece waveguide. Grid vectors G1, G -1 Since the length is increased by decreasing the lattice period Λ, this means that the ICG region 1940 has a finer pitch than what would conventionally be used for light of a given angular frequency ω, ensuring that the input beam can be diffracted entirely into the stimulated modes.

[0321] Naturally, according to the embodiment illustrated in Figure 19, the FOV rectangle is larger in size and the grid vectors G1, G are longer. -1A part of the translated FOV rectangle extends beyond the outer periphery of a larger disc in the k-space diagram after diffraction by the ICG region 1940. Since the k-vectors outside this disc are not allowed, the input beams corresponding to those k-vectors are not diffracted by the ICG region 1940. Instead, only the input beams corresponding to the k-vectors within the shaded portion of the translated FOV rectangle in KSD2 enter the guided propagation mode within the eyepiece waveguide 1900. Input beams that would diffract in the +1 order with k-vectors that would be outside the outer disc of the k-space diagram are not allowed to diffract and are thus lost. Similarly, input beams that would diffract in the -1 order with k-vectors that would be outside the outer disc of the k-space diagram are not allowed to diffract and are thus lost. Fortunately, the beams lost from each of these diffraction orders are not the same. This enables the full field of view to be restored in the EPE region 1960. Even if either the clipped FOV rectangle located at the 3 o'clock position of the k-space diagram KSD2 or the clipped FOV rectangle located at the 9 o'clock position does not contain the full set of input beams, when these clipped FOV rectangles are properly recombined in the EPE region 1960, the full set of input beams can be restored.

[0322] The k-space diagrams KSD3a and KSD3b each illustrate the k-space action of the diffraction gratings within the left OPE region 1950a and the right OPE region 1950b. As discussed with respect to FIG. 18A, these OPE regions can include diffraction gratings that are oriented to translate the FOV rectangles located at the 3 o'clock and 9 o'clock positions to the 6 o'clock position. However, in the embodiment illustrated in FIG. 19, the orientation of the diffraction gratings within the OPE regions 1950a, 1950b may need to be adjusted to accomplish this purpose. Specifically, since the lattice vectors G1, G associated with the ICG region 1940 -1 can no longer terminate at the midpoints of the k-space rings at the 3 o'clock and 9 o'clock positions, the magnitude and direction of the lattice vectors associated with the OPE regions are such that the FOV rectangle is translated to a location at the 6 o'clock position (e.g., k yIt may need to be adjusted to translate to (those centered within the k-space ring in the direction). These adjustments can be achieved by altering the orientation of the grid lines within the OPE regions 1950a, 1950b, and / or by changing the grid period Λ compared to the OPE region in embodiments without extended FOV.

[0323] The shaded right portion of the FOV rectangle in KSD3a represents a first sub-part of the FOV, while the shaded left portion of the FOV rectangle in KSD3b represents a second sub-part of the FOV. In the illustrated embodiment, these FOV sub-parts overlap within the central region of the FOV rectangle.

[0324] k-space diagram KSD3a illustrates that when the FOV rectangle located at the 9 o'clock position is translated to the 6 o'clock position, only the beam corresponding to the shaded right-hand region of the FOV rectangle exists. k-space diagram KSD3b shows the same phenomenon, but the absent beam is one whose k-vector is located on the opposite side of the FOV rectangle. Finally, k-space diagram KSD4 shows that when the two truncated FOV rectangles are superimposed at the 6 o'clock position of the k-space ring, the unshaded portion of the FOV rectangle is filled, meaning that all the beams constituting the complete FOV of the input image are present here and can be projected out of the eyepiece waveguide 1900 toward the user's eye by the diffraction grating in the EPE region 1960. Similar to the embodiment in Figure 18A, the 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 such a manner that they maintain the relative positions of the shaded areas within the original FOV rectangle. This ensures that the beams of light within each sub-part of the FOV have the correct propagation angles so as to recreate the original image.

[0325] From a physical standpoint, this means that the eyepiece waveguide 1900 divides the image field into multiple parts. The light beams corresponding to each of these parts of the image field propagate through the eyepiece waveguide 1900 along different paths, where they can be replicated in a spatially dispersed manner by different OPE regions 1950a and 1950b. Finally, these separate parts of the image field are recombined within the EPE region 1960 and projected toward the user's eye.

[0326] In some embodiments, the various diffraction gratings of the eyepiece 1900 can be designed such that there is overlap between the subsets of beam supplied to the EPE region 1960 by the separate OPE regions 1950a and 1950b. However, in other embodiments, the diffraction grating can be designed such that each OPE region 1950a and 1950b supplies a unique subset of beam required to completely recreate the input image. (Exemplary AR eyepiece waveguide with extended field of view and overlapping MPE and EPE regions)

[0327] Figure 19 illustrates an embodiment of an eyepiece waveguide with an extended field of view (FOV) that replicates the input beam using the OPE region, although other embodiments may, advantageously, use the MPE region. Figures 20A–20L illustrate one such exemplary embodiment.

[0328] Figure 20A illustrates an embodiment of an extended FOV eyepiece waveguide 2000, with an MPE region 2050 overlapping with 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 in the induced propagation mode in the thickness direction of the waveguide. The eyepiece waveguide 2000 has a first surface 2000a and a second surface 2000b. Further, as will be discussed below, different diffraction features can be formed on or within the opposite surfaces 2000a, 2000b of the eyepiece waveguide 2000. In Figure 20A, the two surfaces 2000a, 2000b of the eyepiece waveguide 2000 are shown displaced relative to each other in the xy plane. However, this is for illustrative purposes only, and it is possible to show different diffraction features formed on or within each surface. It should be understood that the first surface 2000a and the second surface 2000b are aligned with each other in the xy plane. In addition, the MPE region 2050 and the EPE region 2060 are shown to be the same size and precisely aligned in the xy plane, but in other embodiments they may have somewhat different sizes and may be partially misaligned. In some embodiments, the MPE region 2050 and the EPE region 2060 overlap with each other by at least 70%, at least 80%, at least 90%, or at least 95%.

[0329] The eyepiece waveguide 2000 includes an ICG region 2040, an MPE region 2050, and an EPE region 2060. The ICG region 2040 receives a set of input beams from the projector device. As described in one of the specifications, the input beams can propagate from the projector device through free space, generally in the z-direction, until they are incident on the ICG region 2040. The ICG region 2040 diffracts the input beams so that all or at least some of them enter an inductive propagation mode within the eyepiece waveguide 2000. The grating lines of the ICG region 2040 can be oriented to direct the diffracted beams toward the MPE region 2050 in the -y-direction.

[0330] The MPE region 2050 may include multiple diffraction features exhibiting periodicity along multiple axes. The MPE region 2050 may consist of an array of scattering features arranged in a 2D grating. Individual scattering features can be, for example, depressions or protrusions of any shape. The 2D array of scattering features has associated grating vectors derived from the reciprocal grating of its 2D grating. In one embodiment, the MPE region 2050 may be a 2D diffraction grating consisting of a cross grating with grating lines repeating along two or more directions of periodicity. The diffraction features constituting the MPE region 2050 may have a relatively low diffraction efficiency (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.

[0331] Figure 20B illustrates a portion of an exemplary 2D grid that may be used within the MPE region 2050 of an eyepiece waveguide 2000, along with its associated grid vectors. While a cross-grid is illustrated, a 2D periodic grid may instead consist of individual scattering features located, for example, at the intersections of the illustrated grid lines. The 2D grid has a first set of grid lines 2056 that repeat along a first periodicity direction. These grid lines 2056 have associated fundamental grid vectors G that point along the periodicity direction of the first set of grid lines 2056 and have a magnitude equal to 2π / a (where a is the period of the first set of grid lines 2056). The 2D grid shown in Figure 20B is also associated with harmonics of the first fundamental grid vectors G. These include higher harmonics such as -G and 2G, -2G, etc. The 2D grid within the MPE region 2050 also has a second set of grid lines 2057 that repeat along the direction of the second periodicity. In some embodiments, the directions of the first and second periodicity are not perpendicular. The second set of grid lines 2057 has associated fundamental grid vectors H that point along the direction of periodicity of the second set of grid lines and have a magnitude equal to 2π / b (where b is the period of the second set of grid lines 2057). The 2D grid shown in Figure 20B is also associated with harmonics of the second fundamental grid vectors H. These include higher harmonics such as -H and 2H, -2H, etc. Finally, any 2D array of diffraction features will also have associated grid vectors that point in directions determined by integer linear combinations (superpositions) of the fundamental grid vectors G and H. In the illustrated embodiments, these superpositions result in additional grid vectors, which are also shown in Figure 20B. These include, for example, -G, -H, H+G, HG, GH, and -(H+G). Figure 20B illustrates only the first-order lattice vectors and their superpositions associated with 2D diffraction gratings, but higher-order lattice vectors may also exist.

[0332] Figure 20C is a k-space diagram KSD1 illustrating the k-space action of the ICG region 2040 of the eyepiece waveguide 2000. The FOV rectangle centered on the origin of KSD1 represents the set of input beams projected toward the ICG region 2040 by the projector device. x - The dimensions of the FOV rectangle in the x-direction represent the FOV of the input beam in the x-direction, while k y The dimensions of the FOV rectangle in the - direction represent the FOV of the input beam in the y- direction. As shown in the illustration, in this particular embodiment, the k of the FOV rectangle x The dimensions are greater than the width of the k-space ring.

[0333] 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 within the ICG region 2040 can be designed to diffract the input beam in that direction. Thus, KSD1 in Figure 20C is the ICG region 2040 with its FOV rectangle at the 6 o'clock position in the k-space ring from the origin of the k-space diagram. y - Indicates a parallel shift to a location on the axis. At this particular location, the wider dimension of the FOV rectangle is oriented in the azimuthal direction of the k-space ring, and therefore the FOV rectangle fits entirely within the ring. This means that all beams represented by the FOV rectangle enter the inductive propagation mode within the eyepiece waveguide 2000 and generally propagate toward the MPE region 2050 in the -y direction.

[0334] As in other MPE regions discussed herein (e.g., 1650, 1750), the MPE region 2050 expands the image pupil in multiple directions by replicating the input beam in a spatially dispersed manner as they propagate through it. Figures 20D–20F and 20H illustrate this behavior of the MPE region 2050 in k-space.

[0335] Figure 20D is the k-space diagram KSD2, illustrating a portion of the k-space action of the MPE region 2050 of the eyepiece waveguide 2000. The k-space diagram includes a shaded FOV rectangle located at the 6 o'clock position of the k-space ring. This is the location of the FOV rectangle after the ICG region 2040 couples the input beam into the eyepiece waveguide 2000 and diffracts them toward the MPE region 2050. Figure 20D shows how the 2D grating within the MPE region 2050 translates the FOV rectangle using the grating vectors shown in Figure 20B. Since 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 ring to eight possible new locations in the k-space diagram. Of these eight possible locations, five are entirely outside the outer perimeter of the k-space diagram. These locations are illustrated using an unshaded FOV rectangle. k-vectors outside the periphery of the k-space diagram are not allowed, so none of those five lattice vectors result in diffraction. However, there are three lattice vectors (i.e., G, -H, and GH) that result in a translation of the FOV rectangle to new positions within the boundaries of the k-space diagram, at least partially. 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 at the 3 o'clock position. Since k-vectors at these locations are allowed and result in stimulated propagation modes, the FOV rectangle at these locations is shaded to indicate that the beam of light is diffracted into those three states.

[0336] For the 9 o'clock and 3 o'clock positions in the k-space ring, the translated FOV rectangle is its k xBecause the dimensions are larger than the width of the ring, they do not fit perfectly within the ring. Therefore, the translated FOV rectangle at these locations is truncated, meaning that beams are not induced, and their k-vectors lie outside the perimeter of the k-space diagram. 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 spreading through the MPE region 2050 in the +x and -x directions, respectively, do not contain all of the original set of input beams. The set of beams propagating through the MPE region 2050 in the +x direction loses the beam corresponding to the right side of the FOV rectangle, while the set of beams propagating in the -x direction loses the beam corresponding to the left side of the FOV rectangle. However, collectively, all beams that make up the FOV still exist.

[0337] The shaded right portion of the translated FOV rectangle at the 9 o'clock position represents the first sub-part of the FOV, while the shaded left portion of the FOV rectangle at the 3 o'clock position represents the second sub-part of the FOV. In the illustrated embodiment, these FOV sub-parts overlap in the central region of the FOV rectangle (although overlap is not necessarily required).

[0338] As already stated, in some embodiments, the first and second periodic axes in the 2D grid of the MPE region 2050 are not orthogonal. This, in turn, means that the fundamental grid vectors G and H are also not orthogonal. This allows the 2D grid in the MPE region 2050 to be translated such that the centers of the FOV rectangles at the 3 o'clock and 9 o'clock positions are located beyond the midpoint of the k-space ring, while the centers of the FOV rectangles at the 6 o'clock and 12 o'clock positions are located at or near the midpoint of the ring. As a result, the translated FOV rectangles at the 3 o'clock and 9 o'clock positions are truncated, which results in the FOV being divided into first and second sub-parts. This is noteworthy in the illustrated embodiments, as dividing the FOV into first and second sub-parts is part of the process for increasing the FOV of the eyepiece waveguide 2000.

[0339] Figure 20E is the k-space diagram KSD3, illustrating another portion of the k-space interaction in the MPE region 2050 of the eyepiece waveguide 2000. KSD3 contains a partially shaded FOV rectangle located at the 3 o'clock position in the k-space ring. This is one of the locations of the translated FOV rectangle after the first interaction in the MPE region 2050. Figure 20E shows how, during subsequent interactions, the 2D grid in the MPE region 2050 translates this FOV rectangle using the grid vectors shown in Figure 20B. Again, with eight grid vectors present, the MPE region 2050 attempts to translate the FOV rectangle from the 3 o'clock position in the k-space ring to a new location that can be considered as eight possible locations in 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 an unshaded FOV rectangle. k-vectors outside the periphery of the k-space diagram are not allowed, so none of those five lattice vectors result in diffraction. However, there are three lattice vectors (i.e., G, H, and H+G) that result in a translation of the FOV rectangle to new positions within the boundaries of the k-space diagram, at least partially. 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 one returns to the 6 o'clock position. Since k-vectors at these locations are allowed and result in stimulated propagation modes, the FOV rectangle at these locations is 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).

[0340] As shown in FIG. 20E, the translated FOV rectangle at the 3 o'clock position of the k-space ring has already been clipped as a result of the first diffraction interaction within the MPE region 2050 shown in FIG. 20D. Thus, only the clipped FOV rectangles are translated to the 9 o'clock, 12 o'clock, and 6 o'clock positions of the k-space ring. In the case of the 9 o'clock position, the FOV rectangle is further clipped, meaning that only the beam corresponding to the centered shaded portion of that particular translated FOV rectangle is actually diffracted into this state.

[0341] FIG. 20F is similar to FIG. 20E and shows the k-space action 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 action of the MPE region 2050 on the beam in this state is the mirror image (about the k y -axis) of that shown in FIG. 20E.

[0342] Although not shown, a similar k-space diagram can be derived to illustrate the k-space action of the MPE region 2050 on a beam of light traveling with the propagation angle shown by the FOV rectangle located at the 12 o'clock position of the k-space ring. That k-space diagram would show that the 2D diffraction grating within the MPE region 2050 would diffract those beams into the states represented by the FOV rectangles at the 3 o'clock, 6 o'clock, and 9 o'clock positions within the rings of the k-space diagrams in FIGS. 20D, 20E, and 20F.

[0343] As shown by the k-space diagram in Figures 20D-20F, when the diffracted light beam from ICG region 2040 arrives in MPE region 2050, many duplicate beams are formed in a spatially dispersed manner. Furthermore, all of these duplicate beams propagate in one of the directions indicated by the FOV rectangles at the 3 o'clock, 6 o'clock, 9 o'clock, and 12 o'clock positions in the k-space ring. As the light beam propagates through MPE region 2050, it undergoes any number of interactions with the diffracting features of the MPE region, resulting in any number of changes in propagation direction. Thus, the light beam is duplicated along both the x-direction and y-direction throughout MPE region 2050. This is represented by the arrows in MPE region 2050 of the eyepiece waveguide 2000 in Figure 20A.

[0344] Since the EPE region 2060 overlaps with the MPE region 2050 in the xy plane of the eyepiece waveguide 2000, the replicated light beams also interact with the EPE region 2060 as they diffuse through the waveguide and reflect back and forth between the first surface 2000a and the second surface 2000b via total internal reflection. When one of the light beams interacts with the EPE region 2060, a portion of its refractive power is diffracted, as indicated by the arrow in the EPE region 2060 of the eyepiece waveguide 2000 in Figure 20A, and exits the eyepiece waveguide toward the user's eye.

[0345] In some embodiments, the EPE region 2060 includes a diffraction grating whose lines are oriented perpendicular to the lines of the diffraction grating that constitute the ICG region 2040. An embodiment of this is shown in Figure 20A, where the ICG region 2040 has grating lines extending in the x-direction and periodically repeating in the y-direction, while the EPE region 2060 has grating lines extending in the y-direction and periodically repeating 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 it is coupled out of the eyepiece waveguide 2000 by the EPE region 2060. This behavior is shown in k-space in Figure 20G.

[0346] Figure 20G is a k-space diagram KSD5 illustrating the k-space action of the EPE region 2060 within the eyepiece waveguide 2000 shown in Figure 20A. As already discussed, the beam of light propagates through the MPE region 2050 in all directions indicated by the FOV rectangles located at the 12, 3, 6, and 9 o'clock positions of the k-space ring. Furthermore, since the EPE region 2060 physically overlaps with the MPE region 2050, the beam of light in all of these propagation states diffuses through the MPE region and comes into contact with the diffraction grating within the EPE region.

[0347] The periodicity axis of the diffraction grating within the EPE region 2060 is ±k x -Since they point in the same direction, the grid vectors associated with the EPE region also point in the same direction. Figure 20G shows how the EPE region 2060 attempts to use these grid vectors to translate the FOV rectangle to the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positions. ±k x Due to its orientation in the -direction, the lattice vector associated with the EPE region 2060 can only translate the FOV rectangles located at the 3 o'clock and 6 o'clock positions of the k-space ring back to the origin of the k-space diagram. Therefore, the EPE region 2060 can only externally couple beams of light that are in one of those two propagation states. That is, the EPE region does not externally couple beams of light propagating in states corresponding to the FOV rectangles at the 12 o'clock and 6 o'clock positions of the k-space ring.

[0348] If the periodic axis for the grid lines in the EPE region 2060 is parallel to, and not perpendicular to, the periodic axis for the grid lines in the ICG region 2040, then the grid vector associated with the EPE region is ±k yIt is important to note that this will point in a direction. This will, in turn, allow the light beam in the propagation state corresponding to the FOV rectangle at the 12 o'clock and 6 o'clock positions of the k-space ring to be externally coupled by the EPE region. Since the input beam arrives in the MPE / EPE region in the propagation state corresponding to the 6 o'clock position, this will mean that the light beam may be externally coupled by the EPE region 2060 before it interacts with the MPE region 2050 and is thereby diffused, which would typically be undesirable. The fact that the periodic axis for the grid 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 a change of direction within the MPE region, possibly over it, at least once before being externally coupled. This allows for an improved spread of the light beam within the MPE region 2050.

[0349] Figure 20H is a k-space diagram KSD6 summarizing the k-space action of the eyepiece waveguide 2000 shown in Figure 20A. This is essentially a superposition of the k-space diagrams shown in Figures 20C-20G. Again, the k-space diagram in Figure 20H shows an FOV rectangle having 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 approximately twice the width of the k-space ring. In the illustrated embodiments, 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.

[0350] KSD6 includes an FOV rectangle centered on the origin of the schematic diagram. Again, the location of the FOV rectangle can explain either the input beam being projected into the eyepiece waveguide 2000 or the replicated output beam being projected out of the waveguide toward the user's eye. In the illustrated embodiment, the action 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 has one of its grid vectors set to -k yIt can be designed to be oriented in the -y direction. This causes the diffracted beam to propagate toward the MPE region 2050 in the -y direction. Furthermore, the ICG region 2040 can be designed such that the magnitude of its lattice vector copies the FOV rectangle to a position that does not fit perfectly within the k-space ring at the 6 o'clock position. This can be done, for example, by designing the ICG region 2040 with a pitch such that the magnitude of its first lattice vector is equal to the distance from the origin of the k-space diagram to the midpoint of the k-space ring. Since the FOV rectangle at the 6 o'clock position is perfectly within the k-space ring, all of the diffracted beam enters the guided mode of propagation.

[0351] As already discussed, the MPE region contains multiple diffraction features exhibiting periodicity along multiple different axes. This means that the MPE region has multiple associated lattice 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 double arrows between their propagation states. As shown in Figure 20H, the FOV rectangles at the 3 o'clock and 6 o'clock positions of the k-space ring are truncated, meaning that not all beams of light associated with the complete FOV exist in each of their propagation states. However, when those sub-parts of the FOV are considered collectively, all beams of light that constitute the complete FOV do exist. Therefore, when the FOV rectangle is ultimately translated back from the 3 o'clock or 6 o'clock position to the origin of the k-space diagram so that the beam of light is externally coupled toward the user's eye, all the beams required to constitute the full FOV of the input image are present and projected from the eyepiece waveguide 2000.

[0352] Figure 20I is a schematic diagram illustrating how a beam of light diffuses through the eyepiece waveguide 2000 shown in Figure 20A. The guided beam, incident on the MPE region 2050 and propagating from the ICG region 2040 in the -y-direction, is duplicated into many beams in a spatially dispersed manner, some of which propagate in the ±y-direction (corresponding to the FOV rectangles at the 6 o'clock and 12 o'clock positions in the k-space ring) and some propagate in the ±x-direction (corresponding to the FOV rectangles at the 3 o'clock and 9 o'clock positions in the k-space ring). In this way, the light beam diffuses laterally throughout the entire eyepiece waveguide 2000.

[0353] Figure 20J illustrates how the diffraction efficiency of the MPE region 2050 within the eyepiece waveguide 2000 can be spatially varied to improve the uniformity of brightness within the waveguide. In the figure, darker shades within the MPE region 2050 represent higher diffraction efficiency, while brighter shades represent lower diffraction efficiency. Spatial variation in the diffraction efficiency of the MPE region 2050 can be achieved by introducing spatial variations in lattice characteristics such as lattice depth, duty cycle, blaze angle, and tilt angle.

[0354] As shown in Figure 20J, the uniformity of brightness within the waveguide can be improved by designing the portion of the MPE region 2050 closer to the ICG region 2040 to have a higher diffraction efficiency. This is because, since 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, so that the light is diffused more effectively to other parts of the MPE region 2050 where less light is present. In addition, 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 uniformity of brightness within the waveguide.

[0355] Brightness uniformity can also be improved by designing the central portion of the MPE region 2050 to have a higher diffraction efficiency along the direction in which the beam propagates from the ICG region 2040 into the MPE region 2050. Again, because the ICG region 2040 is located along the axis in which the light enters, more light is present within this area of ​​the MPE region 2050. Because more light is present within this area, the diffraction efficiency can be higher, allowing the light to diffuse more effectively to the other parts of the MPE region 2050.

[0356] Figure 20K illustrates how the diffraction efficiency of the EPE region 2060 within the eyepiece waveguide 2000 can be spatially varied to improve the uniformity of brightness within the waveguide. Darker shades within the EPE region 2060 again represent higher diffraction efficiency, while brighter shades represent lower diffraction efficiency. The EPE region 2060 can be designed to have higher diffraction efficiency within its peripheral area. Higher diffraction efficiency within the peripheral area of ​​the EPE region 2060 helps to externally couple the light to the user's eye before the light is lost outside the edge of the waveguide.

[0357] Figure 20L illustrates an embodiment of an eyepiece waveguide 2000, which includes one or more diffracting mirrors 2070 around the peripheral edge of the waveguide. The diffracting mirrors 2070 can receive light that propagates through the MPE / EPE region and exits from the edge of the waveguide 2000. The diffracting mirrors can then diffract the light back into the MPE / EPE region so that it can be used to contribute to the projection of an image from the eyepiece waveguide 2000. As already discussed, the MPE region 2050 allows beam propagation in four general directions: generally, the x-direction (i.e., represented by the FOV rectangle at the 3 o'clock position of the k-space ring), generally, the -x-direction (i.e., represented by the FOV rectangle at the 9 o'clock position), generally, the y-direction (i.e., represented by the FOV rectangle at the 12 o'clock position), and generally, the -y-direction (i.e., represented by the FOV rectangle at the 6 o'clock position). The diffraction mirror 2070 can be designed to diffract the beam to one of these identical propagation states.

[0358] For example, the diffraction mirror 2070 on the left side of the eyepiece waveguide 2000 can generally diffract a beam incident from the -x- direction into a propagation state represented by the FOV rectangle at the 3 o'clock position, such that they generally propagate back through the OPE region 2050 in the x-direction. Similarly, the diffraction mirror 2070 at the bottom of the eyepiece waveguide 2010 can generally diffract a beam incident from the -y- direction into a propagation state represented by the FOV rectangle at the 12 o'clock position, such that they generally propagate back through the OPE region 2050 in the y-direction.

[0359] Figure 20L illustrates the k-space action of the bottom diffraction mirror 2070. As shown in the k-space diagram, the bottom diffraction mirror 2070 can be designed with a period that is half that of the grating in the ICG region 2040. A finer period results in a bottom diffraction mirror with an associated grating vector twice the length of 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 ring. Although illustrated for the eyepiece waveguide 2000, the same technique (i.e., spatial variation of diffraction efficiency in the OPE, MPE, EPE regions, etc., and the use of diffraction mirrors along the peripheral edge) can also be used in combination with any of the other embodiments described herein.

[0360] Figure 20M illustrates an exemplary embodiment of eyeglasses 70 incorporating one or more instances of an eyepiece waveguide 2000. The first instance of the eyepiece waveguide 2000 is integrated into the left viewing portion of the eyeglasses 70, while the second instance of the eyepiece waveguide 2000 is integrated into the right viewing portion. In the illustrated embodiment, each waveguide 2000 measures approximately 50 × 30 mm. 2 However, many different sizes can be used. Each waveguide 2000 may be accompanied by a separate projector 2020 that projects an image into the corresponding waveguide. Assuming that the eyepiece waveguide is fabricated from a material with a refractive index of 1.8, some embodiments of the eyepiece waveguide 2000 are capable of achieving an FOV of 90° × 45°, however, some embodiments of the eyepiece waveguide may be designed for a smaller FOV of about 60° × 45° to satisfy typical design constraints of eyebox volume (it may be advantageous to send part of the FOV to both sides of the eyepiece waveguide to provide a properly sized eyebox) and to avoid screen door artifacts resulting from sparsely spaced output beams.

[0361] Figure 20N illustrates another exemplary embodiment of the eyeglasses 70 incorporating one or more instances of the eyepiece waveguide 2000. This embodiment of the eyeglasses 70 is similar to that shown in Figure 20M, except that the orientation of the waveguide 2000 and the accompanying projector 2020 is rotated 90° toward the temples of the eyeglasses 70. In this configuration, several embodiments of the eyepiece waveguide 2000 are capable of achieving an FOV of 45° × 90°, assuming the eyepiece waveguide is fabricated from a material with a refractive index of 1.8, although some embodiments may be designed for a smaller FOV of approximately 45° × 60° to satisfy other design constraints.

[0362] Figure 21A illustrates another embodiment of the eyepiece waveguide 2100, with an MPE region 2150 overlapping with an EPE region 2160. Similar to the eyepiece waveguide 2000 shown in Figure 20A, the eyepiece waveguide 2100 shown in Figure 21A can achieve an extended field of view, which may be greater than the range of propagation angles that can be supported in the inductive propagation mode in the thickness direction of the waveguide. The eyepiece waveguide 2100 has a first surface 2100a and a second surface 2100b. Different diffraction features can be formed on or within the opposite surfaces 2100a, 2100b of the eyepiece waveguide 2100, as will be discussed further below. The two surfaces 2100a, 2100b of the eyepiece waveguide 2100 are shown in Figure 21A as being displaced relative to each other in the xy plane. However, this is for illustrative purposes only, and it is possible to show different diffraction features formed on or within each surface. It should be understood that the first surface 2100a and the second surface 2100b are aligned with each other in the xy plane. In addition, the MPE region 2150 and the EPE region 2160 are shown to be the same size and precisely aligned in the xy plane, but in other embodiments they may have somewhat different sizes and may be partially misaligned. In some embodiments, the MPE region 2150 and the EPE region 2160 overlap with each other by at least 70%, at least 80%, at least 90%, or at least 95%.

[0363] Like the eyepiece waveguide 2000 shown in Figure 20A, the eyepiece waveguide 2100 shown in Figure 21A includes an MPE region 2150 and an EPE region 2160. Unlike the eyepiece waveguide 2000 shown in Figure 20A, the eyepiece waveguide 2100 shown in Figure 21A includes two ICG regions 2140a and 2140b, located on opposite sides of the MPE / EPE region, rather than a single ICG region. Each of the ICG regions 2140a and 2140b may have its own associated projector. Each of the two projectors can input a sub-portion of the full input image FOV into the eyepiece waveguide 2100. Thus, each of the ICG regions 2140a and 2140b can similarly be used to internally couple input beams corresponding to sub-portions of the FOV. These sub-parts can then be assembled in the exit pupil of the eyepiece waveguide 2100.

[0364] The left ICG region 2140a receives a first set of input beams corresponding to a first sub-part of the FOV from a first projector device, while the right ICG region 2140b receives a second set of input beams corresponding to a second sub-part of the FOV from a second projector device. The first and second sub-parts of the FOV may be unique, or they may partially overlap. The first set of input beams may be centered around an input beam that is generally projected along the -z-direction but has a component propagating in the -x-direction toward the left ICG region 2140a, while the second set of input beams may be centered around an input beam that is generally projected along the -z-direction but has a component propagating in the +x-direction toward the right ICG region 2140b. The left ICG region 2140a diffracts the first set of input beams so that at least a portion of them enters an induction mode propagating in the +x- direction, and the right ICG region 2140b diffracts the second set of input beams so that at least a portion of them enters an induction mode propagating in the -x- direction. In this way, both the first and second sets of input beams, corresponding to the first and second sub-parts 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 and 2140b.

[0365] Similar to the eyepiece waveguide 2000 shown in Figure 20A, the eyepiece waveguide 2100 shown in Figure 21A may also include an MPE region 2150 formed on or within a first side 2100a of the waveguide, and an overlapping EPE region 2160 formed on or within a second side 2100b of the waveguide. The MPE region 2150 in the eyepiece waveguide 2100 shown in Figure 21A may be analogous to the MPE region 2050 in the eyepiece waveguide 2000 shown in Figure 20A. That is, the MPE region 2150 may include multiple diffraction features exhibiting periodicity along multiple axes. Similarly, the EPE region 2160 in the eyepiece waveguide 2100 shown in Figure 21A may be analogous to the EPE region 2060 in the eyepiece waveguide 2000 shown in Figure 20A. That is, the EPE region 2160 may contain a diffraction grating whose periodicity axis is orthogonal to that of the two ICG regions 2140a and 2140b. The actions of the MPE region 2150 and EPE region 2160 in Figure 21A can also be analogous to those of the MPE region 2050 and EPE region 2060 in Figure 20A, as shown in Figures 21B-21D.

[0366] Figure 21B is a k-space diagram KSD1 illustrating the k-space effect of the eyepiece waveguide 2100 on a set of first input beams corresponding to a first sub-part of the input image's FOV. The FOV rectangle centered at the origin of KSD1 represents the beam of light corresponding to the full input image FOV to be projected toward the user's eye by the eyepiece waveguide 2100. The overall size of the FOV rectangle is up to approximately twice the width of the k-space ring. Thus, the eyepiece waveguide 2100 shown in Figure 21A is designed to have an improved FOV similar to the embodiments shown in Figures 19 and 20A. However, the set of first input beams projected toward the left ICG region 2140a corresponds only to the shaded sub-part of the FOV rectangle. As shown in Figure 21B, the shaded part of the FOV rectangle corresponding to the set of first input beams is the left-side part of the FOV rectangle. The center of the shaded part of the FOV rectangle is -k x-In the direction of -, because it is offset from the origin of the k-space diagram, the first set of input beams from the first projector is centered not on a beam that propagates precisely in the -z- direction (which would correspond to the case where the shaded portion of the FOV rectangle is centered on the origin of the k-space diagram), but rather on an oblique beam with a component propagating in the -x- direction.

[0367] The left ICG region 2140a has a lattice vector of ±k x It can be designed to be oriented in the x-direction. The a...

Claims

[Claim 1] The invention as described in the drawings of this application.

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