PATENT DOCUMENT

Publication Number: US-11994672-B2
Application Number: US-202017423196-A
Country: US
Kind Code: B2

Title: Optical systems with light-expanding couplers

Abstract:
An electronic device may include a display that generates light for an optical system that redirects the light towards an eye box. The optical system may include a waveguide, a non-diffractive input coupler, a cross coupler, and an output coupler. The cross coupler may expand the light in a first direction. The cross coupler may perform an even number of diffractions on the light and may couple the light back into the waveguide at an angle suitable for total internal reflection. The output coupler may expand the light in a second direction while coupling the light out of the waveguide. The cross coupler may include surface relief gratings or holographic gratings embedded within the waveguide or formed in a separate substrate. The optical system may direct the light towards the eye box without chromatic dispersion and while supporting an expanded field of view and optical bandwidth.

Claims:
What is claimed is: 
     
       1. An optical system configured to redirect light, the optical system comprising:
 a waveguide, wherein the waveguide comprises a first waveguide substrate, a second waveguide substrate, and a medium interposed between the first and second waveguide substrates; 
 an input coupler configured to couple the light into the waveguide; 
 a cross coupler on the waveguide, wherein the cross coupler comprises a first surface relief grating and a second surface relief grating that at least partially overlaps the first surface relief grating, wherein the first surface relief grating is formed in the first waveguide substrate, wherein the second surface relief grating is formed in the second waveguide substrate, wherein the cross coupler is configured to expand the light coupled into the waveguide by the input coupler in a first direction, and wherein the waveguide is configured to propagate the light expanded in the first direction via total internal reflection; and 
 an output coupler on the waveguide, wherein the output coupler is configured to couple the light expanded in the first direction by the cross coupler out of the waveguide while expanding the light in a second direction that is different from the first direction. 
 
     
     
       2. The optical system of  claim 1 , wherein the first surface relief grating has fringes oriented in a first direction. 
     
     
       3. The optical system of  claim 2 , wherein the second surface relief grating has fringes oriented in a second direction different from the first direction. 
     
     
       4. The optical system of  claim 3 , wherein the first surface relief grating overlaps the second surface relief grating within an overlap region of the cross coupler. 
     
     
       5. The optical system defined in  claim 4 , wherein the overlap region has a non-uniform width. 
     
     
       6. The optical system of  claim 1 , wherein the first surface relief grating has a non-binary profile. 
     
     
       7. The optical system of  claim 1 , wherein the output coupler has a diffraction efficiency that varies as a function of position along the first direction, wherein the output coupler has a first diffraction efficiency along a central axis of the output coupler and a second diffraction efficiency at a peripheral edge of the output coupler that is greater than the first diffraction efficiency. 
     
     
       8. The optical system of  claim 1 , wherein the cross coupler has a diffraction efficiency that varies as a function of position. 
     
     
       9. The optical system of  claim 1 , further comprising:
 a partially reflective beam splitter embedded in the waveguide, wherein the light coupled into the waveguide by the input coupler is configured to hit the partially reflective beam splitter prior to being received at the cross coupler. 
 
     
     
       10. The optical system of  claim 1 , wherein the cross coupler comprises a meta-grating on the waveguide. 
     
     
       11. The optical system of  claim 1 , wherein the input coupler comprises diffractive gratings. 
     
     
       12. The optical system of  claim 1 , wherein the output coupler comprises diffractive grating structures. 
     
     
       13. An optical system configured to redirect light, the optical system comprising:
 a waveguide; 
 an input coupler configured to couple the light into the waveguide; 
 a cross coupler on the waveguide, wherein the cross coupler comprises a first surface relief grating having fringes oriented in a first direction and a second surface relief grating having fringes oriented in a second direction different from the first direction, wherein the first surface relief grating overlaps the second surface relief grating within an overlap region of the cross coupler, wherein the first surface relief grating and the second surface relief grating are formed in a first surface relief grating substrate, wherein the cross coupler further comprises a second surface relief grating substrate that includes at least one additional surface relief grating and that is layered over the first surface relief grating substrate, wherein the cross coupler is configured to expand the light coupled into the waveguide by the input coupler in a first direction, and wherein the waveguide is configured to propagate the light expanded in the first direction via total internal reflection; and 
 an output coupler on the waveguide, wherein the output coupler is configured to couple the light expanded in the first direction by the cross coupler out of the waveguide while expanding the light in a second direction that is different from the first direction. 
 
     
     
       14. The optical system of  claim 13 , wherein the waveguide comprises first and second waveguide substrates and a medium interposed between the first and second waveguide substrates, and wherein the first surface relief grating substrate is layered on the first waveguide substrate. 
     
     
       15. The optical system of  claim 14 , wherein the output coupler comprises a louvered mirror embedded in the medium. 
     
     
       16. The optical system of  claim 14 , wherein the medium comprises a grating medium and wherein the output coupler comprises a set of volume holograms recorded in the grating medium. 
     
     
       17. The optical system of  claim 16 , further comprising an antireflection layer on a surface of the first waveguide substrate at the output coupler. 
     
     
       18. The optical system defined in  claim 13 , wherein the waveguide comprises a medium having first and second surfaces and a waveguide substrate layered on the first surface, wherein the first surface relief grating substrate is layered on the second surface of the medium, and wherein the first surface relief grating is embedded in the medium. 
     
     
       19. The optical system defined in  claim 18 , wherein the medium comprises a grating medium and wherein the output coupler comprises a set of volume holograms recorded in the grating medium. 
     
     
       20. The optical system of  claim 19 , further comprising an optically transparent coating on the first surface relief grating and interposed between the first surface relief grating and the grating medium. 
     
     
       21. The optical system defined in  claim 18 , wherein the grating medium has a bulk index of refraction and wherein the surface relief grating substrate has an index of refraction that is greater than the bulk index of refraction of the grating medium. 
     
     
       22. The optical system of  claim 13 , wherein the input coupler comprises diffractive gratings. 
     
     
       23. The optical system of  claim 13 , wherein the output coupler comprises diffractive grating structures. 
     
     
       24. The optical system of  claim 13 , wherein the cross coupler has a diffraction efficiency that varies as a function of position. 
     
     
       25. The optical system of  claim 13 , wherein the output coupler has a diffraction efficiency that varies as a function of position along the first direction. 
     
     
       26. An optical system configured to redirect light, the optical system comprising:
 a waveguide; 
 an input coupler configured to couple the light into the waveguide; 
 a cross coupler on the waveguide, wherein the cross coupler comprises a first surface relief grating and a second surface relief grating that at least partially overlaps the first surface relief grating, wherein the waveguide comprises a first waveguide substrate, a second waveguide substrate, and a medium interposed between the first and second waveguide substrates, wherein the first surface relief grating is formed in a surface relief grating substrate layered on the first waveguide substrate, wherein the second surface relief grating is formed in the second waveguide substrate, wherein the cross coupler is configured to expand the light coupled into the waveguide by the input coupler in a first direction, and wherein the waveguide is configured to propagate the light expanded in the first direction via total internal reflection; and 
 an output coupler on the waveguide, wherein the output coupler is configured to couple the light expanded in the first direction by the cross coupler out of the waveguide while expanding the light in a second direction that is different from the first direction. 
 
     
     
       27. The head-mounted device of  claim 26 , wherein the first surface relief grating comprises first fringes with a first orientation, wherein the second surface relief grating comprises second fringes with a second orientation that is non-parallel with respect to the first orientation, and wherein the first and second surface relief gratings overlap within an overlap region of the cross coupler. 
     
     
       28. The head-mounted device of  claim 27 , further comprising an optically-transparent coating on the first and second surface relief gratings and interposed between the second waveguide substrate and the medium. 
     
     
       29. The head-mounted device of  claim 27 , further comprising a partially reflective beam splitter on the medium, wherein the cross coupler is configured to receive the image light from the partially reflective beam splitter. 
     
     
       30. The optical system of  claim 26 , wherein the second surface relief grating is embedded within the medium. 
     
     
       31. The optical system of  claim 26 , wherein the input coupler comprises diffractive gratings. 
     
     
       32. The optical system of  claim 26 , wherein the output coupler comprises diffractive grating structures. 
     
     
       33. The optical system of  claim 26 , wherein the medium comprises a grating medium and the output coupler comprises a set of volume holograms recorded in the grating medium. 
     
     
       34. The optical system of  claim 26 , wherein the cross coupler has a diffraction efficiency that varies as a function of position and the output coupler has a diffraction efficiency that varies as a function of position along the first direction.

Description:
This application claims priority to U.S. patent application Ser. No. 16/831,147, filed on Mar. 26, 2020, and U.S. provisional patent application No. 62/854,905, filed May 30, 2019, which are hereby incorporated by reference herein in their entireties. 
    
    
     BACKGROUND 
     This relates generally to optical systems and, more particularly, to optical systems for displays. 
     Electronic devices may include displays that present images close to a user&#39;s eyes. For example, devices such as virtual reality and augmented reality headsets may include displays with optical elements that allow users to view the displays. 
     It can be challenging to design devices such as these. If care is not taken, the components used in displaying content may be unsightly and bulky and may not exhibit desired levels of optical performance. 
     SUMMARY 
     An electronic device such as a head-mounted device may have one or more near-eye displays that produce images for a user. The head-mounted device may be a pair of virtual reality glasses or may be an augmented reality headset that allows a viewer to view both computer-generated images and real-world objects in the viewer&#39;s surrounding environment. 
     The near-eye display may include a display unit that generates light and an optical system that redirects the light from the display unit towards an eye box. The optical system may include a waveguide, an input coupler on the waveguide, a cross coupler on the waveguide, and an output coupler on the waveguide. The input coupler may be a non-diffractive input coupler such as an input prism that couples the light into the waveguide and towards the cross coupler. The cross coupler may expand the light coupled into the waveguide in a first direction. The cross coupler may perform an even number of diffractions on the light and may couple the diffracted light back into the waveguide at an angle suitable for total internal reflection in the waveguide. The output coupler may receive the light from the cross coupler. The output coupler may expand the light in a second direction perpendicular to the first direction while coupling the light out of the waveguide. 
     The cross coupler may include surface relief gratings, meta-gratings, or holographic phase gratings such as volume holograms embedded within the waveguide or formed in a separate substrate adhered to an external surface of the waveguide. The optical system may direct the light towards the eye box without chromatic dispersion and while supporting an expanded field of view and optical bandwidth. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a diagram of an illustrative system having a display in accordance with some embodiments. 
         FIG.  2    is a top view of an illustrative optical system for a display that includes an input coupler, a cross coupler, and an output coupler in accordance with some embodiments. 
         FIG.  3    is a front view of an illustrative optical system having a cross coupler that diffracts in-coupled light an even number of times while expanding the light in a first direction and having an output coupler that expands the light in a second direction in accordance with some embodiments. 
         FIG.  4    is a diagram of an illustrative cross coupler having a non-rectangular shape in accordance with some embodiments. 
         FIG.  5    is a cross-sectional top view of an illustrative waveguide having a cross coupler formed from a surface relief grating structure on the waveguide in accordance with some embodiments. 
         FIG.  6    is a cross-sectional top view of an illustrative waveguide having a cross coupler formed from a surface relief grating structure embedded in a grating medium that is used to form an output coupler for the waveguide in accordance with some embodiments. 
         FIG.  7    is a cross-sectional top view of an illustrative waveguide having a cross coupler formed from a surface relief grating structure on the same side of the waveguide as an input coupling prism in accordance with some embodiments. 
         FIG.  8    is a cross-sectional top view of an illustrative waveguide having a cross coupler formed from a surface relief grating structure embedded in a grating medium at the same side of the waveguide as an input coupling prism in accordance with some embodiments. 
         FIG.  9    is a k-space diagram illustrating how surface relief grating structures of the types shown in  FIGS.  5 - 8    may be formed in a substrate having a relatively high index of refraction for ensuring that in-coupled light of different wavelengths propagates through a waveguide in accordance with some embodiments. 
         FIG.  10    is a cross-sectional top view of an illustrative waveguide having a cross coupler formed from volume holographic grating structures in accordance with some embodiments. 
         FIG.  11    is a front view of an illustrative output coupler having a variable diffraction efficiency in accordance with some embodiments. 
         FIGS.  12  and  13    are front views of an illustrative optical system having a cross coupler with a single grating structure that diffracts in-coupled light an even number of times while expanding the light in a first direction and having an output coupler that expands the light in a second direction in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     An illustrative system having a device with one or more near-eye display systems is shown in  FIG.  1   . System  10  may be a head-mounted device having one or more displays such as near-eye displays  20  mounted within support structure (housing)  8 . Support structure  8  may have the shape of a pair of eyeglasses (e.g., supporting frames), may form a housing having a helmet shape, or may have other configurations to help in mounting and securing the components of near-eye displays  20  on the head or near the eye of a user. Near-eye displays  20  may include one or more display modules such as display modules  20 A and one or more optical systems such as optical systems  20 B. Display modules  20 A may be mounted in a support structure such as support structure  8 . Each display module  20 A may emit light  38  (image light) that is redirected towards a user&#39;s eyes at eye box  24  using an associated one of optical systems  20 B. 
     The operation of system  10  may be controlled using control circuitry  16 . Control circuitry  16  may include storage and processing circuitry for controlling the operation of system  10 . Circuitry  16  may include storage such as hard disk drive storage, nonvolatile memory (e.g., electrically-programmable-read-only memory configured to form a solid-state drive), volatile memory (e.g., static or dynamic random-access-memory), etc. Processing circuitry in control circuitry  16  may be based on one or more microprocessors, microcontrollers, digital signal processors, baseband processors, power management units, audio chips, graphics processing units, application specific integrated circuits, and other integrated circuits. Software code may be stored on storage in circuitry  16  and run on processing circuitry in circuitry  16  to implement operations for system  10  (e.g., data gathering operations, operations involving the adjustment of components using control signals, image rendering operations to produce image content to be displayed for a user, etc.). 
     System  10  may include input-output circuitry such as input-output devices  12 . Input-output devices  12  may be used to allow data to be received by system  10  from external equipment (e.g., a tethered computer, a portable device such as a handheld device or laptop computer, or other electrical equipment) and to allow a user to provide head-mounted device  10  with user input. Input-output devices  12  may also be used to gather information on the environment in which system  10  (e.g., head-mounted device  10 ) is operating. Output components in devices  12  may allow system  10  to provide a user with output and may be used to communicate with external electrical equipment. Input-output devices  12  may include sensors and other components  18  (e.g., image sensors for gathering images of real-world object that are digitally merged with virtual objects on a display in system  10 , accelerometers, depth sensors, light sensors, haptic output devices, speakers, batteries, wireless communications circuits for communicating between system  10  and external electronic equipment, etc.). 
     Display modules  20 A may be liquid crystal displays, organic light-emitting diode displays, laser-based displays, reflective displays, or displays of other types. Optical systems  20 B may form lenses that allow a viewer (e.g., a viewer&#39;s eyes at eye box  24 ) to view images on display(s)  20 . There may be two optical systems  20 B (e.g., for forming left and right lenses) associated with respective left and right eyes of the user. A single display  20  may produce images for both eyes or a pair of displays  20  may be used to display images. In configurations with multiple displays (e.g., left and right eye displays), the focal length and positions of the lenses formed by optical system  20 B may be selected so that any gap present between the displays will not be visible to a user (e.g., so that the images of the left and right displays overlap or merge seamlessly). 
     If desired, optical system  20 B may contain components (e.g., an optical combiner, etc.) to allow real-world image light from real-world images or objects  28  to be combined optically with virtual (computer-generated) images such as virtual images in image light  38 . In this type of system, which is sometimes referred to as an augmented reality system, a user of system  10  may view both real-world content and computer-generated content that is overlaid on top of the real-world content. Camera-based augmented reality systems may also be used in device  10  (e.g., in an arrangement which a camera captures real-world images of object  28  and this content is digitally merged with virtual content at optical system  20 B). 
     System  10  may, if desired, include wireless circuitry and/or other circuitry to support communications with a computer or other external equipment (e.g., a computer that supplies display  20  with image content). During operation, control circuitry  16  may supply image content to display  20 . The content may be remotely received (e.g., from a computer or other content source coupled to system  10 ) and/or may be generated by control circuitry  16  (e.g., text, other computer-generated content, etc.). The content that is supplied to display  20  by control circuitry  16  may be viewed by a viewer at eye box  24 . 
       FIG.  2    is a top view of an illustrative optical system  20 B that may be used in system  10  of  FIG.  1   . As shown in  FIG.  2   , optical system  20 B may include optical elements such as waveguide  50 , input optics  58 , output optics  60 , input coupler  52 , cross coupler  54 , and output coupler  56 . Input optics  58  may include collimating lenses or other optical components that pass image light  38  to input coupler  52 . Image light  38  may be provided to optical system  20 B by a display unit in display module  20 A ( FIG.  1   ). The display unit may be a display unit based on a liquid crystal display, organic light-emitting diode display, cathode ray tube, plasma display, projector display (e.g., a projector based on an array of micromirrors), liquid crystal on silicon display, or other suitable type of display. Optical system  20 B may be used to present light  38  output from the display unit to eye box  24 . 
     Waveguide structures such as waveguide  50  in optical system  20 B may be formed from one or more stacked layers of polymer, glass, or other transparent substrates capable of guiding light via total internal reflection. Input coupler  52 , cross coupler  54 , and output coupler  56  may each be partially or completely embedded within waveguide  50  or mounted to a surface of waveguide  50 . Some of optical couplers  52 ,  54 , and  56  may be mounted to a surface of waveguide  50  whereas others of couplers  52 ,  54 , and  56  are embedded within waveguide  50 . Output optics  60  may include lenses that help to focus light  38  coupled out of waveguide  50  by output coupler  56  onto eye box  24 . Input optics  58  and/or output optics  60  may be omitted if desired. 
     Input coupler  52  may be configured to couple light  38  from the display module into waveguide  50 , whereas output coupler  32  may be configured to couple light  38  from within waveguide  50  out of waveguide  50  and towards eye box  24 . For example, when light  38  from input optics  58  strikes input coupler  52 , input coupler  52  may redirect light  38  so that the light propagates within waveguide  50  via total internal reflection towards output coupler  56  (e.g., in the direction of the X axis). When light  38  strikes output coupler  56 , output coupler  56  may redirect light  38  out of waveguide  50  towards eye box  24  (e.g., along the Z axis). 
     In the example of  FIG.  2   , cross coupler  54  is optically interposed between input coupler  52  and output coupler  56 . In this example, input coupler  52  may redirect light  38  towards cross coupler  54 . Cross coupler  54  may expand light  38  in a first direction and may also couple (redirect) the expanded light back into waveguide  50 . Waveguide  50  propagates the light expanded by cross coupler  54  via total internal reflection to output coupler  56 . If desired, output coupler  56  may then expand the light received from cross coupler  54  in a second direction that is different from (e.g., perpendicular to) the first direction. Output coupler  56  may, if desired, provide an optical power to the light coupled out of the waveguide. Consider an example in which the light  38  coupled into waveguide  50  by input coupler  52  includes a pupil of light. Expansion of light  38  by cross coupler  54  and output coupler  56  may serve to expand the pupil in multiple (e.g., orthogonal) dimensions, thereby allowing a relatively large eye box  24  to be filled with pupils of light  38  with a sufficient and substantially uniform intensity across the entire area of the eye box. 
     Input coupler  52 , cross coupler  54 , and output coupler  56  may be based on reflective and refractive optics or may be based on holographic (e.g., diffractive) optics. In arrangements where couplers  52 ,  54 , or  56  are formed from reflective and refractive optics, the couplers may include one or more reflectors (e.g., an array of micromirrors, partial mirrors, or other reflectors). In arrangements where couplers  52 ,  54 , or  56  are based on holographic optics, couplers  52 ,  54 , and  56  may include holographic media such as photopolymers, gelatin such as dichromated gelatin, silver halides, holographic polymer dispersed liquid crystal, or other suitable volume holographic media. Holographic recordings (e.g., holographic phase gratings sometimes referred to herein as holograms) may be stored in the holographic media. The holographic media may sometimes be referred to herein as grating media. 
     A holographic recording may be stored as an optical interference pattern (e.g., alternating regions of different indices of refraction) within a photosensitive optical material such as the holographic media. The optical interference pattern may create a holographic phase grating that, when illuminated with a given light source, diffracts light to create a three-dimensional reconstruction of the holographic recording. The holographic phase grating may be a non-switchable diffractive grating that is encoded with a permanent interference pattern or may be a switchable diffractive grating in which the diffracted light can be modulated by controlling an electric field applied to the holographic recording medium. Multiple holographic phase gratings (holograms) may be recorded within (e.g., superimposed within) the same volume of grating medium if desired. The holographic phase gratings may be, for example, volume holograms in the grating medium. 
     If desired, one or more of couplers  52 ,  54 , and  56  may be implemented using other types of diffraction grating structures such as surface relief grating structures. Surface relief grating structures include diffraction gratings (e.g., surface relief gratings) that are mechanically cut, etched, or otherwise formed in a surface relief grating medium. The surface relief gratings diffract light that is incident upon the surface relief gratings. Rather than modulating index of refraction in the grating medium (as performed to create holographic phase gratings such as volume holograms), surface relief gratings are produced by varying the physical thickness of the medium across its lateral area. Multiple surface relief gratings (e.g., two surface relief gratings) may be multiplexed within the same volume of surface relief grating medium if desired. 
     In one suitable arrangement that is sometimes described herein as an example, input coupler  52  is a non-diffractive input coupler (e.g., an input coupler that does not include diffraction gratings such as surface relief gratings or holographic phase gratings). For example, input coupler  52  may include an input prism, an angled surface (edge) of waveguide  50 , etc. Use of a non-diffractive input coupler such as an input prism may allow light  38  to be coupled into waveguide  50  without producing the chromatic dispersion that is otherwise associated with input-coupling using diffractive elements. In another suitable arrangement, input coupler  52  may be formed using diffraction gratings such as volume holograms or other grating structures. In these scenarios, any chromatic dispersion introduced by the input coupler may be reversed by the output coupler in diffracting the light out of the waveguide (e.g., in a scenario where the output coupler includes holographic phase gratings such as volume holograms). 
     Cross coupler  54  may include diffractive grating structures that diffract the light  38  coupled into waveguide  50  by the (non-diffractive) input coupler  52 . The grating structures in cross coupler  54  may include surface relief grating structures (e.g., one or more surface relief gratings) or phase grating structures such as volume holographic grating structures (e.g., a set of at least partially overlapping volume holograms). The grating structures in cross coupler  54  may be configured to diffract light  38  an even number of times. At least one of the diffractions may serve to expand light  38  in a first direction (e.g., along the Y axis into and/or out of the plane of  FIG.  2   ). At least one of the diffractions may serve to redirect the expanded light back into waveguide  50  at an angle such that the light propagates by total internal reflection to output coupler  54 . By diffracting the light an even number of times, any chromatic dispersion effects associated with diffracting the light one time can be reversed by diffracting the light a corresponding subsequent time. This may serve to mitigate chromatic dispersion of the light that is conveyed to output coupler  56 . 
     Output coupler  56  may include diffractive grating structures such as volume holographic grating structures or other holographic phase gratings. In another suitable arrangement, output coupler  56  may include reflective mirror structures such as a louvered mirror. Output coupler  56  may reflect or diffract light  38 . The reflection/diffraction of light  38  by output coupler  56  may serve to expand light  38  in a second direction (e.g., along the X axis) and to couple the expanded light out of waveguide  50  towards eye box  24 . 
       FIG.  3    is a front view of waveguide  50  showing how cross coupler  54  may include grating structures that expand light  38  while also diffracting light  38  an even number of times to mitigate chromatic dispersion. As shown in  FIG.  3   , waveguide  50  may include a waveguide substrate with a lateral (external) surface  114 . A non-diffractive input coupler  52  such as input prism  70  may be mounted to surface  114 . Input prism  70  may couple light  38  downwards (e.g., in the +Z direction) into waveguide  50  and towards cross coupler  54 . Cross coupler  54  may be formed on a lateral surface of a waveguide substrate in waveguide  50  or may be embedded within waveguide  50 . 
     Cross coupler  54  may include a first diffractive grating structure  72  and a second diffractive grating structure  74 . First grating structure  72  may at least partially overlap second grating structure  74  (e.g., within overlap region  76 ). Grating structures  72  and  74  may, for example, be superimposed over each other within the same volume (area) of grating medium within overlap region  76 . Overlap region  76  may have a width (e.g., parallel to the Y axis) that is approximately equal to (e.g., greater than or equal to) the width of input prism  70 . This is merely illustrative. Overlap region  76  may have a width that is less than or equal to the width of input prism  70  or may have other shapes. Overlap region  76  need not have a uniform width. 
     Light  38  that is coupled into waveguide  50  parallel to the X-axis (sometimes referred to herein as DC light  86 ) may be directed by cross coupler  54  back into waveguide  50  and towards output coupler  56  without being expanded in the vertical direction. DC light  86  may propagate down the length of waveguide  50  to output coupler  56  via total internal reflection. Light  38  that is coupled into waveguide  50  at a non-zero angle with respect to the X-axis may be vertically expanded by first grating structure  72  and/or second grating structure  74  (e.g., by diffracting the light vertically in a direction parallel to the Y axis, sometimes referred to herein as a “first direction”). First grating structure  72  and/or second grating structure  74  may be configured to cumulatively diffract light  38  an even number of times by the time the light re-enters waveguide  50  for propagation to output coupler  56  by total internal reflection (e.g., to mitigate chromatic dispersion generated by a single instance of diffraction). 
     As an example, light  38  at a positive angle with respect to DC light  86  may be coupled into waveguide  50  and directed towards cross coupler  54 , as shown by arrow  88 . First grating structure  72  may include fringes  78  that are oriented at a non-parallel angle with respect to the fringes  78  in second grating structure  74 . First grating structure  72  and second grating structure  74  may include surface relief gratings or holographic phase gratings such as volume holograms. In scenarios where grating structures  72  and  74  are formed from holographic phase gratings, fringes  78  may represent lines of constant index of refraction of the grating medium. In scenarios where grating structures  72  and  74  are formed using surface relief gratings, fringes  78  may represent lines of constant thickness of the grating medium. Fringes  78  are characterized by a period A (e.g., the period of the modulations in refractive index or the period of the modulations in thickness of the grating medium) and an orientation (e.g., defined by the direction of a grating vector for grating structures  72  and  74 , where the grating vector is oriented perpendicular to fringes  78 ). Fringes  78  may also have an associated fringe angle defined with respect to the normal surface of lateral surface  114 . 
     The periods, orientations, and fringe angles of grating structures  72  and  74  may configure the grating structures to diffract light from particular ranges of incident angles and at a particular range of wavelengths over particular ranges of output angles. These factors may be selected to configure cross coupler  54  to vertically expand light  38  while diffracting the light an even number of times and while diffracting the light back into waveguide  50  at an angle at which the light can be propagated down waveguide  50  via total internal reflection, for the wavelengths (colors) included in light  38  and over the incident angles with which the light is provided to the cross coupler by input prism  70 . 
     Consider an example in which grating structures  72  and  74  are formed using surface relief gratings. In this example, grating structure  74  may be configured to perform a first diffraction in which light at the incident angle associated with arrow  88  (e.g., light incident in the +X, −Y, and −Z directions) is diffracted at a corresponding output angle, as shown by arrow  90  (e.g., an output angle in the +Y and +X directions). Grating structure  74  may also be configured to perform a (subsequent) second diffraction in which the light at the incident angle associated with arrow  90  (e.g., the output angle of the first diffraction) is diffracted at a corresponding output angle, as shown by arrow  92  (e.g., an output angle in the +X, −Y, and +Z directions). The first diffraction may introduce chromatic dispersion in which different wavelengths of incident light  38  are diffracted at slightly different output angles. The second diffraction may reverse the chromatic dispersion introduced by the first diffraction (e.g., by diffracting the light from the first diffraction back into waveguide  50  at the same output angle for each wavelength). The second diffraction that produced arrow  92  may direct the light back into waveguide  50  at an angle such that the light is able to propagate down the length of waveguide  50  by total internal reflection to output coupler  56 . 
     Similarly, grating structure  72  may be configured to perform a first diffraction in which light at the incident angle associated with arrow  88 ′ (e.g., light incident in the +X, +Y, and −Z directions) is diffracted at a corresponding output angle, as shown by arrow  90 ′ (e.g., an output angle in the −Y and +X directions). Grating structure  72  may also be configured to perform a (subsequent) second diffraction in which the light at the incident angle associated with arrow  90 ′ (e.g., the output angle of the first diffraction) is diffracted at a corresponding output angle, as shown by arrow  92 ′ (e.g., an output angle in the +X, +Y, and +Z direction). The first diffraction may introduce chromatic dispersion in which different wavelengths of incident light  38  are diffracted at slightly different output angles. The second diffraction may reverse the chromatic dispersion introduced by the first diffraction. The second diffraction associated with arrow  92 ′ may direct the light back into waveguide  50  at an angle such that the light is able to propagate down the length of waveguide  50  by total internal reflection to output coupler  56 . 
     Diffraction in the vertical direction (e.g., in the +Y/−Y direction) by grating structures  72  and  74  may serve to expand light  38  in the vertical direction (e.g., parallel to the Y axis). Output coupler  56  may diffract or reflect the light received from cross coupler  54  towards the eye box, as shown by arrows  84 , while also expanding the light in a horizontal direction that is different from (e.g., orthogonal to) the vertical direction (e.g., output coupler  56  may expand the light in a direction parallel to the X axis, as shown by arrows  82 ). This may allow pupils in the light coupled into waveguide  50  to be expanded in two dimensions by the time the light is received at the eye box. 
     Grating structures  72  and  74  may each perform the first diffraction over a range of angles about DC light  86  (e.g., grating structures  72  may diffract light  38  over a continuous range of incident angles between arrow  88  and the X axis whereas grating structures  74  diffract light  38  over a continuous range of incident angles between arrow  88 ′ and the X axis). The second diffraction performed by grating structures  72  and  74  may similarly be performed over a corresponding range of incident angles. If desired, diffraction grating structures (e.g., volume holograms, surface relief gratings, etc.) such as optional diffractive beam dump  77  may be formed on waveguide  50 . Diffractive beam dump  77  may be configured to diffract low angle light such as DC light  86  to locations other than output coupler  56  (e.g., towards other optics, a light sink such as an absorptive material, etc.), as shown by arrows  79 . This may help to ensure that light of uniform intensity is provided to output coupler  56 , for example (e.g., because DC light  86  may be brighter than diffracted light  92 ′ and  92 ). 
     Surface relief gratings exhibit a relatively wide bandwidth in wavelength. This may allow grating structures  72  and  74  to each be implemented using a single surface relief grating, if desired, while still exhibiting satisfactory diffraction efficiency for each wavelength of light  38  (e.g., across the visible spectrum). In other words, cross coupler  54  may diffract and expand light  38  for each wavelength in light  38  using only two surface relief gratings (e.g., one surface relief grating in grating structure  72  and another surface relief grating in grating structure  74 ). In another suitable arrangement, more than two surface relief gratings may be included in cross coupler  54 . In these scenarios, additional layers of surface relief grating medium may be stacked on top of each other, where each layer includes one or two associated surface relief gratings. 
     In scenarios where grating structures  72  and  74  are implemented using holographic phase gratings such as volume holograms, each volume hologram exhibits a much narrower bandwidth in wavelength than a surface relief grating. For example, volume holograms diffract light from a particular range of incident angles at a particular range of output angles for a particular range of wavelengths that is much narrower than the range of wavelengths diffracted by a similar surface relief grating. To diffract each wavelength in light  38 , grating structures  72  and  74  may each include a corresponding set of multiplexed volume holograms (or other holographic phase gratings). Each volume hologram in the set may be configured to diffract (e.g., may be Bragg-matched to) light from a different respective range of wavelengths and/or range of incident angles, but may each diffract the incident light at the same range of output angles. Each volume hologram in the set may be at least partially overlapping. For example, each volume hologram in the set may be superimposed within the same volume of grating medium or may be divided between different layers of grating medium (e.g., where each layer includes at least one volume hologram from the set). In this way, the holographic phase gratings (e.g., volume holograms) in cross coupler  54  may collectively perform an even number of diffractions (e.g., the diffractions represented by arrows  88 ,  90 ,  92 ,  88 ′,  90 ′, and  92 ′) on incident light over a wide range of wavelengths and over each of the incident angles provided by input prism  70 . The set of volume holograms in grating structures  72  may sometimes be referred to herein as volume hologram structures. Similarly, the set of volume holograms in grating structures  74  may sometimes be referred to herein as volume hologram structures. 
     The example of  FIG.  3    shows only two diffraction operations being performed by each grating structure. This is merely illustrative. If desired, each grating structure may perform four diffraction operations, six diffraction operations, eight diffraction operations, or any other desired even number of diffractions. Performing an even number of diffractions in this way may allow any chromatic dispersion associated with a first diffraction to be reversed by a corresponding additional diffraction and may allow the light to be redirected towards output coupler  56 . If only a single diffraction operation (or any other odd number of diffraction operations) were performed, the light may be directed elsewhere in the system (e.g., away from output coupler  56 , as shown by arrow  94 ). In these scenarios, if desired, output coupler  56  may be repositioned or expanded in size so that stray light associated with arrow  94  is also received at the output coupler. In addition to light that has been diffracted an even number of times, some of the image light coupled into the waveguide may pass to the output coupler without ever being diffracted by the cross coupler (e.g., the architecture of  FIG.  3    may not require an interaction with the cross coupler for certain parts of the image). 
     In another suitable arrangement, cross coupler  54  may be implemented using meta-grating structures (e.g., grating structures  72  and  74  may each be formed using respective meta-grating). Other types of diffraction gratings (e.g., non-meta-gratings) typically exhibit a periodic structure and chromatic dispersion. For example, propagation angle on the first diffraction by the grating changes as a function of wavelength and consequentially, pupil replications at different wavelengths will be spatially separated inside the waveguide. The propagation angle is restored on the second diffraction by the grating (e.g., compensating for dispersion). However, pupil separation may produce color non-uniformity to the image. 
     In contrast, meta-gratings are aperiodic assemblies of high index dielectric resonators (e.g., formed on surface  114  of waveguide  50  or other surfaces on or in the waveguide). Meta-gratings in grating structures  72  and  74  may, for example, be formed on surface  114  of waveguide  50 . Each dielectric resonator in the meta-gratings may be designed to impart a phase delay to the incident light. The phase delay of each dielectric resonator may be independently controlled for a different wavelength. Through suitable configuration of the distribution of the dielectric resonators, a wavelength dependent phase profile may be obtained such that all the wavelengths are diffracted at the same output angle. In this way, the pupil can propagate and expand without introducing color separation. 
     The example of  FIG.  3    in which cross coupler  54  has a rectangular shape is merely illustrative. In general, cross coupler  54  (e.g., first grating structure  72 , second grating structure  74 , and/or overlap region  76 ) may have any desired shape having any desired number of straight and/or curved edges (e.g., a triangular shape, a trapezoidal shape, other polygonal shapes, a circular shape, an elliptical shape, combinations of these, etc.).  FIG.  4    is a diagram of one possible shape for cross coupler  54 . As shown in  FIG.  4   , cross coupler  54  may have five sides and overlap region  76  may have five sides. First grating structure  72  and second grating structure  74  may have non-uniform lengths (e.g., parallel to the X axis). The shape of cross coupler  54  may be selected to maximize the amount of light received at output coupler  56  ( FIG.  3   ), for example. Other shapes may be used. Output coupler  56  may also be provided with any desired shape and need not be rectangular. If desired, cross coupler  54  may be formed using only one of first grating structure  72  or second grating structure  74 . If desired, grating structures  72  and  74  may be non-overlapping (e.g., overlap region  76  may be omitted). 
       FIG.  5    is a cross-sectional top view of waveguide  50  in an example where cross coupler  54  is formed using a surface relief grating structure (e.g., as viewed in the direction of arrow  95  of  FIG.  3   ). As shown in  FIG.  5   , waveguide  50  may include one or more waveguide substrates such as substrate  108  and substrate  110 . A holographic recording medium such as grating medium  106  may be interposed (layered) between substrates  108  and  110 . Lateral (e.g., planar) surface  120  of grating medium  106  may contact substrate  108 . Lateral surface  122  of grating medium  106  may contact substrate  110 . Output coupler  56  may be formed within grating medium  106  (e.g., using volume holograms or other holographic phase gratings recorded in grating medium  106 , louvered mirrors embedded in grating medium  106 , etc.). If desired, an optional antireflection coating  118  may be layered onto surface  120  and/or surface  122  at output coupler  56 . Antireflection coating  118  may prevent unwanted light reflections within grating medium  106  during the writing (recording) of the holographic phase gratings within output coupler  56 , for example. 
     Input prism  70  may be mounted to external surface  114  of substrate  108 . Input prism  70  may couple image light  38  into waveguide  50  and towards cross coupler  54 . Cross coupler  54  may include a surface relief grating structure such as surface relief grating structure  100 . Surface relief grating structure  100  may be used to form first grating structure  72  (e.g., surface relief grating structure  100  may include a surface relief grating that performs at least the first and second diffractions associated with arrows  88 ′,  90 ′, and  92 ′ of  FIG.  3   ), may be used to form second grating structure  74  (e.g., surface relief grating structure  100  may include a surface relief grating that performs at least the first and second diffractions associated with arrows  88 ,  90 , and  92  of  FIG.  3   ), or may be used to form overlap region  76  (e.g., surface relief grating structure  100  may include a surface relief grating used to form first grating structure  72  and a surface relief grating used to form second grating structure  74  that are superimposed within the same area). 
     As shown in  FIG.  5   , surface relief grating structure  100  may be formed within a substrate such as surface relief grating substrate (medium)  112 . As an example, the surface relief grating(s) in surface relief grating structure  100  may be defined by ridges (peaks)  102  and troughs (minima  104 ) in the thickness of surface relief grating substrate  112 . In the example of  FIG.  5   , surface relief grating structure  100  is a binary structure in which the grating is defined either by a first thickness associated with peaks  102  or a second thickness associated with troughs  104 . This is merely illustrative. If desired, surface relief grating structure  100  may be non-binary (e.g., may include any desired number of thicknesses following any desired profile, may include peaks  102  that are angled at non-parallel fringe angles with respect to the Y axis, etc.). Surface relief grating substrate  112  may exhibit a relatively high index of refraction (e.g., an index of refraction greater than the bulk index of refraction of grating medium  106 ). Surface relief grating substrate  112  may be adhered to surface  116  of waveguide substrate  110  using adhesive layer  115 . Adhesive layer  115  may have a relatively low index of refraction (e.g., less than the index of refraction of surface relief grating substrate  112 ). Surface relief grating structure  100  may be fabricated separately from output coupler  56  in waveguide  50  and may be adhered to waveguide  50  after fabrication, for example. 
     Input prism  70  may image couple light  38  into waveguide  50  and towards surface relief grating structure  100 . Surface relief grating structure  100  may diffract light  38  and even number of times while serving to expand light  38  in a direction parallel to the Y axis. The final diffraction performed by surface relief grating structure  100  may couple light  38  (e.g., as expanded light) back into waveguide  50  at an angle such that the light continues to propagate along the length of waveguide  50  by total internal reflection. Light  38  is then coupled out of waveguide  50  by output coupler  56 , as shown by arrows  38 ′. Output coupler  56  may also expand light  38  in a direction parallel to the X axis. In this way, output coupler  56  and cross coupler  54  may collectively expand light  38  in two dimensions prior to providing the expanded light to the eye box. 
     Forming cross coupler  54  using a surface relief grating structure may allow for higher light throughput relative to scenarios where volume holograms are used. Performing an even number of diffractions using cross coupler  54  may mitigate any chromatic dispersion produced by the surface relief grating structure. Use of a non-diffractive input coupler such as input prism  70  may allow light  38  to be coupled into waveguide  50  without introducing chromatic dispersion. These examples are merely illustrative and, if desired, cross coupler  54  may be implemented using volume holograms and input prism  70  may be implemented using other input coupling structures (e.g., holograms or other diffraction gratings, an angled surface of waveguide  50 , etc.). In another arrangement, substrate  110  may be omitted and surface relief grating substrate  112  may be placed in contact with surface  122  of grating medium  106 . 
     If desired, optional light homogenization structures such as one or more layers of beam splitters  124  may be embedded within grating medium  106 . Beam splitters  124  may be formed using metallic coatings, dielectric coatings, dielectric layers having different refractive indices, or other partially reflective structures. One or more beam splitters  124  may be mounted to surface  120 , surface  122 , surface  114 , and/or surface  116  if desired. Beam splitters  124  may transmit a first portion of light  38  while reflecting a second portion of light  38 . This may serve to laterally replicate the pupils of light  38  that are provided to surface relief grating structure  100 , to output coupler  56 , and eventually to the eye box (e.g., to ensure that a uniform intensity of light fills the eye box). In scenarios where more than one beam splitter  124  is provided in waveguide  50 , the beam splitters may be partially overlapping, completely overlapping, or non-overlapping. The beam splitters may exhibit a variable reflectivity if desired (e.g., the beam splitters may exhibit greater reflectivity at one end than at an opposing end of the beamsplitters). The reflectivity may be continuously varied or varied in discrete steps. 
     In another suitable arrangement, surface relief grating structure  100  may be embedded within grating medium  106 .  FIG.  6    is a diagram showing how surface relief grating structure  100  may be embedded within grating medium  106 . As shown in  FIG.  6   , substrate  110  may be omitted and surface relief grating substrate  112  may be placed into contact with surface  122  of grating medium  106  (e.g., grating medium  106  may be molded over surface relief grating substrate  112 ). Surface relief grating structure  100  may be embedded within grating medium  106 . If desired, an optional transparent dielectric coating  130  may be layered over surface relief grating structure  100  (e.g., coating  130  may be interposed between surface relief grating structure  100  and grating medium  106 ). Coating  130  may serve to increase diffraction efficiency and broaden the angular response of surface relief grating structure  100 . Coating  130  may be formed from titanium oxide, silicon nitride, tantalum pentoxide, or any other desired materials. 
     The examples of  FIGS.  5  and  6    in which surface relief grating structure  100  is formed on the side of waveguide  50  opposite input prism  70  is merely illustrative. If desired, surface relief grating structure  100  may be formed on the same side of waveguide  50  as input prism  70 , as shown in  FIGS.  7  and  8   . 
     As shown in the example of  FIG.  7   , surface relief grating substrate  112  may be mounted to surface  114  of substrate  108  using adhesive layer  115 . Input prism  70  may be mounted to surface relief grating substrate  112 . Input prism  70  may couple light into waveguide  50 . The in-coupled light may reflect off of one or more surfaces of waveguide  50  to surface relief grating structure  100 . 
     As shown in the example of  FIG.  8   , substrate  108  may be omitted and surface relief grating substrate  112  may be placed into contact with surface  120  of grating medium  106 . Surface relief grating structure  100  may be embedded within grating medium  106 . Input prism  70  may be mounted to surface relief grating substrate  112 . Input prism  70  may couple light into waveguide  50 . The in-coupled light may be received directly at surface relief grating structure  100  or may be reflected off of one or more surfaces of waveguide  50  towards surface relief grating structure  100 . 
     These examples are merely illustrative. If desired, more than one surface relief grating structure may be provided on waveguide  50 . In these scenarios, multiple surface relief grating substrates  112  having associated surface relief grating structures may be layered over each other. Any desired input coupling structures may be used. Beam splitters  124  and/or antireflection coating  118  of  FIG.  5    may be provided in the waveguides of  FIGS.  6 - 8    if desired. Coating  130  of  FIG.  6    may be layered under surface relief grating structure  100  of  FIG.  8    if desired. 
     Surface relief grating substrate  112  may be provided with a relatively high index of refraction (e.g., an index of refraction greater than that of substrates  108  and  110  and greater than the bulk index of grating medium  106 ).  FIG.  9    is a k-space diagram showing how forming surface relief grating substrate  112  with a relatively high index of refraction may allow the entire field of view of input prism  70  to be coupled back into waveguide  50  for propagation to output coupler  56  by total internal reflection for each wavelength of light  38 . 
     As shown in  FIG.  9   , the horizontal axis plots k x /k media  and the vertical axis plots k y /k media , where k x /k media  represents the X component and k y /k media  represents the Y component of the k-vector for light propagating through optical system  20 B. The Z component is omitted from  FIG.  9    for the sake of clarity (e.g.,  FIG.  9    illustrates a two-dimensional projection of three-dimensional k-space). Region  150  represents the field of view from output coupler  56  (e.g., as provided at the eye box). Region  158  represents the light  38  that is coupled into waveguide  50  by input prism  70 . Because input prism  70  does not introduce chromatic dispersion, the light coupled into waveguide  50  is represented by the same region  158  in k-space regardless of wavelength. Similarly, because any chromatic dispersion introduced into the system is mitigated by the time the light is coupled out of the waveguide, the field of view from output coupler  56  is represented by the same region  150  in k-space regardless of wavelength. 
     The first diffraction performed by surface relief grating structure  100  is schematically represented by arrow  168 . Because the first diffraction introduces chromatic dispersion, different wavelengths of light are diffracted to different regions in k space such as regions  162 ,  164 , and  166 . Region  162  may correspond to a blue wavelength, region  164  may correspond to a green wavelength, and region  166  may correspond to a red wavelength, as just one example. The example of  FIG.  9    only illustrates diffraction of the portion of region  158  below the horizontal axis for the sake of clarity. In practice, the portion of region  158  above the horizontal axis is also diffracted in the first diffraction to additional regions (e.g., additional regions corresponding to regions  162 ,  164 , and  166 ) below the horizontal axis. 
     Curve  152  represents the lower limit at which total internal reflection can still be supported by waveguide  50 . If the diffraction from region  158  produces light that falls within curve  152 , the light will be diffracted at an angle at which waveguide  50  is incapable of supporting total internal reflection, and the light will not properly propagate to the output coupler. Curve  154  represents the upper limit of diffraction supported by surface relief grating substrate  112 . If the diffraction from region  158  produces light that falls outside of curve  154 , surface relief grating structure  100  will be unable to perform additional diffractions on the light (e.g., to couple the light back into the waveguide). In other words, the first diffraction from region  158  needs to produce light that falls between curves  152  and  154  for the light to be provided to output coupler  56 . However, as shown in  FIG.  9   , the chromatic dispersion produced by the first diffraction may produce light that falls outside of this region for some wavelengths (e.g., for the wavelength associated with region  166 ). This may cause the cross coupler to fail to direct some of the wavelengths of light  38  to output coupler  56 . 
     In order to mitigate these effects, surface relief grating substrate  112  may be provided with a material having a relatively high index of refraction (e.g., a relatively high index glass or other material). The refractive index of surface relief grating substrate  112  may be, for example, greater than the bulk index of refraction of grating medium  106 . Providing the surface relief grating medium with a relatively high refractive index in this way may expand curve  154  to curve  154 ′, as shown by arrow  160 . As each of regions  162 ,  164 , and  166  falls between curves  154 ′ and  152 , each wavelength of light from the first diffraction may be satisfactorily diffracted back into the waveguide at an angle suitable for total internal reflection (e.g., so that the light is properly directed towards the output coupler). Because surface relief grating structure  100  performs an even number of diffractions, the chromatic dispersion associated with arrow  168  is reversed by a corresponding subsequent diffraction in surface relief grating structure  100  (e.g., by the second diffraction associated with arrows  92  and  92 ′ of  FIG.  3   ). 
       FIG.  10    is a diagram showing how cross coupler  54  may be formed holographic phase gratings such as volume holograms. As shown in  FIG.  10   , an additional grating medium  180  may be layered on surface  116  of substrate  110 . An additional waveguide substrate  182  may be provided under grating medium  180 . Cross coupler  54  may include volume hologram structures  184  in grating medium  180 . Volume hologram structures  184  may include one or more at least partially overlapping volume holograms (e.g., a set of volume holograms that each diffract a respective range of wavelengths and/or incident angles at the same range of output angles). The volume holograms may be provided in separate layers of grating medium or may be superimposed with the same volume of the same layer of grating medium. 
     Input prism  70  may couple light  38  into waveguide  50  and towards volume hologram structures  184 . Volume hologram structures  184  may perform an even number of diffractions on the in-coupled light, may expand the light in a direction parallel to the Y axis, and may diffract the light back into waveguide  50  at an angle suitable for total internal reflection. If desired, the volume holograms in volume hologram structures  184  may have fringes with constant pitch, a variable period, and/or a variable fringe angle. The period (e.g., A) refers to the spacing between fringes as measured along the grating vector (i.e., the vector orthogonal to the fringes); the pitch (e.g., p) refers to the distance between fringes as measured along the grating surface (e.g., surface  116  or the surface of substrate  182 ); and the fringe angle refers to the angle between the grating surface normal (e.g., the Z axis) and the grating vector. In other words, the period may vary across structures  184  (e.g., may vary as a function of position along the X-axis of  FIG.  10   ), the pitch may be constant across the structures  184 , and the fringe angle may vary across structures  184  (e.g., may vary as a function of position along the X-axis of  FIG.  10   ). Constant-pitch, variable-period gratings may help maintain high diffraction efficiency across a range of angles of incidence for a given wavelength. This type of volume phase holographic grating may in turn help avoid undesirable color shifts, efficiency losses, and brightness variations in the optical system. This example is merely illustrative and, if desired, other types of volume holograms or other holographic phase gratings may be used. If desired, grating medium  180  may be provided at surface  114  of substrate  108 . Additional grating media may be layered over grating medium  180  if desired. One or more beam splitters  124  ( FIG.  5   ) may be provided within grating medium  106  of  FIG.  10    or elsewhere in or on waveguide  50  if desired. Antireflection coating  130  of  FIG.  5    may be provided at output coupler  56  of  FIG.  10    if desired. 
     In practice, DC light  86  ( FIG.  3   ) may have a greater brightness than the vertically expanded light that is provided to output coupler  56  (e.g., as shown by arrows  92  and  92 ′ of  FIG.  3   ). In order to mitigate this difference in brightness, output coupler  56  may be provided with a diffraction efficiency that varies as a function of position along the Y axis.  FIG.  11    is a diagram showing how output coupler  56  may be provided with a variable diffraction efficiency. 
     As shown in  FIG.  11   , output coupler  200  may have a central region  200  that receives DC light  86 . The DC light may have greater brightness than diffracted light that is incident upon output coupler  200  within peripheral regions  202 . To mitigate this difference in brightness, output coupler  56  may be provided with greater diffraction efficiency within peripheral regions  202  than within central region  200 . This may allow the light provided to the eye box to exhibit uniform brightness across an entirety of the eye box. 
     If desired, output coupler  56  may include any desired number of regions having different diffraction efficiencies (e.g., where the regions closer to the central horizontal axis of output coupler  56  exhibit greater diffraction efficiency than regions farther from the central horizontal axis). In another suitable arrangement, the diffraction efficiency of output coupler  56  may be continuously varied as a function of position along the Y axis. Plot  206  shows one exemplary continuous diffraction efficiency for output coupler  56 . As shown by curve  204 , the diffraction efficiency may be a smoothly varying curve that exhibits a minimum at the center of output coupler  56  and maxima at the edges of output coupler  56 . This is merely illustrative and, in general, curve  204  may exhibit any other desired shape. The diffraction efficiency of output coupler  56  may vary discretely or continuously along the X axis or any other axis if desired. 
     The example of  FIG.  11    in which the diffraction efficiency of output coupler  56  varies as a function of position is merely illustrative. If desired, the diffraction efficiency of cross coupler  54  may vary as a function of position. Output coupler  56  of  FIG.  11    may, for example, be replaced with cross coupler  54  (e.g., cross coupler  54  may have a variable diffraction efficiency as described above in connection with output coupler  56  of  FIG.  11   ). Cross coupler  54  and output coupler  56  may both have a diffraction efficiency that varies continuously or discretely as a function of position along one or more axes, if desired. Holograms used to form cross coupler  54  and/or output coupler  56  may be comb-shifted if desired. Comb-shifted holograms may include a set of holograms in a first region of grating medium and a second set of holograms in an adjacent second region of the grating medium. The grating frequencies of the second set may each lie within adjacent frequency gaps between the grating frequencies of the first set (e.g., where the grating vectors for the first and second sets are oriented in the same direction). This may allow for more homogenous diffraction across the eye box, for example. 
     The examples above in which cross coupler  54  has two grating structures  72  and  74  for expanding light  38  while also diffracting light  38  an even number of times to mitigate chromatic dispersion is merely illustrative. In another suitable arrangement, cross coupler  54  may include a single grating structure having fringes oriented in the same direction for expanding light  38  while also diffracting light  38  an even number of times to mitigate chromatic dispersion.  FIG.  12    is a diagram showing how cross coupler  54  may include a single grating structure having fringes oriented in the same direction for expanding light  38  while also diffracting light  38  an even number of times to mitigate chromatic dispersion 
     As shown in  FIG.  12   , cross coupler  54  may include a single grating structure  236  having fringes  78  oriented in a single direction (e.g., fringes having grating vectors oriented in a single direction and characterized by a period A). At least some of cross coupler  54  may be laterally interposed (e.g., along the X axis) between input prism  70  and output coupler  56  (e.g., wherein input prism  70  is laterally interposed between at least some of cross coupler  54  and left edge  220  of waveguide  50 ). Input prism  70  may couple light  38  into waveguide  50 , as shown by arrows  222 . Grating structure  236  may expand the in-coupled light  38  in a first direction (whereas output coupler  56  may expand the light in a second direction) and may provide the light to output coupler  56 , as shown by arrows  226 . Grating structure  236  may be configured to diffract light  38  an even number of times by the time the light reaches output coupler  56 , or by the time the light is coupled back into the waveguide for propagation by total internal reflection (e.g., to mitigate chromatic dispersion generated by a single instance of diffraction). 
     The example of  FIG.  12    is merely illustrative. Cross coupler  54  having grating structure  224  may be interposed between other edges of waveguide  50  and output coupler  56 . For example, as shown in  FIG.  13   , at least some of grating structure  224  for cross coupler  54  may be laterally interposed between top edge  230  of waveguide  50  and output coupler  56 . Input prism  70  may be laterally interposed between at least some of grating structure  224  and edge  230 . Input prism  38  may couple light  38  into waveguide  50  along the direction of the Y axis in this example, as shown by arrows  232 . Grating structure  224  may expand light  38  and may diffract light  38  an even number of times before providing the light to output coupler  56 , as shown by arrows  234 . Output coupler  56  may expand the light in a direction different to the direction of expansion provided by grating structure  224 . In the examples of  FIGS.  12  and  13   , grating structure  224  may include surface relief gratings, meta-gratings, holographic phase gratings such as volume holograms, etc. Grating structure  224  may be provided in the layers of waveguide  50  as shown by  FIGS.  5 - 8  and  10    or at any other desired location on waveguide  50 . 
     A physical environment refers to a physical world that people can sense and/or interact with without aid of electronic systems. Physical environments, such as a physical park, include physical articles, such as physical trees, physical buildings, and physical people. People can directly sense and/or interact with the physical environment, such as through sight, touch, hearing, taste, and smell. 
     In contrast, a computer-generated reality (CGR) environment refers to a wholly or partially simulated environment that people sense and/or interact with via an electronic system (e.g., an electronic system including the display systems described herein). In CGR, a subset of a person&#39;s physical motions, or representations thereof, are tracked, and, in response, one or more characteristics of one or more virtual objects simulated in the CGR environment are adjusted in a manner that comports with at least one law of physics. For example, a CGR system may detect a person&#39;s head turning and, in response, adjust graphical content and an acoustic field presented to the person in a manner similar to how such views and sounds would change in a physical environment. In some situations (e.g., for accessibility reasons), adjustments to characteristic(s) of virtual object(s) in a CGR environment may be made in response to representations of physical motions (e.g., vocal commands). 
     A person may sense and/or interact with a CGR object using any one of their senses, including sight, sound, touch, taste, and smell. For example, a person may sense and/or interact with audio objects that create 3D or spatial audio environment that provides the perception of point audio sources in 3D space. In another example, audio objects may enable audio transparency, which selectively incorporates ambient sounds from the physical environment with or without computer-generated audio. In some CGR environments, a person may sense and/or interact only with audio objects. Examples of CGR include virtual reality and mixed reality. 
     A virtual reality (VR) environment refers to a simulated environment that is designed to be based entirely on computer-generated sensory inputs for one or more senses. A VR environment comprises a plurality of virtual objects with which a person may sense and/or interact. For example, computer-generated imagery of trees, buildings, and avatars representing people are examples of virtual objects. A person may sense and/or interact with virtual objects in the VR environment through a simulation of the person&#39;s presence within the computer-generated environment, and/or through a simulation of a subset of the person&#39;s physical movements within the computer-generated environment. 
     In contrast to a VR environment, which is designed to be based entirely on computer-generated sensory inputs, a mixed reality (MR) environment refers to a simulated environment that is designed to incorporate sensory inputs from the physical environment, or a representation thereof, in addition to including computer-generated sensory inputs (e.g., virtual objects). On a virtuality continuum, a mixed reality environment is anywhere between, but not including, a wholly physical environment at one end and virtual reality environment at the other end. 
     In some MR environments, computer-generated sensory inputs may respond to changes in sensory inputs from the physical environment. Also, some electronic systems for presenting an MR environment may track location and/or orientation with respect to the physical environment to enable virtual objects to interact with real objects (that is, physical articles from the physical environment or representations thereof). For example, a system may account for movements so that a virtual tree appears stationery with respect to the physical ground. Examples of mixed realities include augmented reality and augmented virtuality. 
     An augmented reality (AR) environment refers to a simulated environment in which one or more virtual objects are superimposed over a physical environment, or a representation thereof. For example, an electronic system for presenting an AR environment may have a transparent or translucent display through which a person may directly view the physical environment. The system may be configured to present virtual objects on the transparent or translucent display, so that a person, using the system, perceives the virtual objects superimposed over the physical environment. Alternatively, a system may have an opaque display and one or more imaging sensors that capture images or video of the physical environment, which are representations of the physical environment. The system composites the images or video with virtual objects, and presents the composition on the opaque display. A person, using the system, indirectly views the physical environment by way of the images or video of the physical environment, and perceives the virtual objects superimposed over the physical environment. As used herein, a video of the physical environment shown on an opaque display is called “pass-through video,” meaning a system uses one or more image sensor(s) to capture images of the physical environment, and uses those images in presenting the AR environment on the opaque display. Further alternatively, a system may have a projection system that projects virtual objects into the physical environment, for example, as a hologram or on a physical surface, so that a person, using the system, perceives the virtual objects superimposed over the physical environment. 
     An augmented reality environment also refers to a simulated environment in which a representation of a physical environment is transformed by computer-generated sensory information. For example, in providing pass-through video, a system may transform one or more sensor images to impose a select perspective (e.g., viewpoint) different than the perspective captured by the imaging sensors. As another example, a representation of a physical environment may be transformed by graphically modifying (e.g., enlarging) portions thereof, such that the modified portion may be representative but not photorealistic versions of the originally captured images. As a further example, a representation of a physical environment may be transformed by graphically eliminating or obfuscating portions thereof. 
     An augmented virtuality (AV) environment refers to a simulated environment in which a virtual or computer generated environment incorporates one or more sensory inputs from the physical environment. The sensory inputs may be representations of one or more characteristics of the physical environment. For example, an AV park may have virtual trees and virtual buildings, but people with faces photorealistically reproduced from images taken of physical people. As another example, a virtual object may adopt a shape or color of a physical article imaged by one or more imaging sensors. As a further example, a virtual object may adopt shadows consistent with the position of the sun in the physical environment. 
     There are many different types of electronic systems that enable a person to sense and/or interact with various CGR environments. Examples include head mounted systems, projection-based systems, heads-up displays (HUDs), vehicle windshields having integrated display capability, windows having integrated display capability, displays formed as lenses designed to be placed on a person&#39;s eyes (e.g., similar to contact lenses), headphones/earphones, speaker arrays, input systems (e.g., wearable or handheld controllers with or without haptic feedback), smartphones, tablets, and desktop/laptop computers. A head mounted system may have one or more speaker(s) and an integrated opaque display. Alternatively, a head mounted system may be configured to accept an external opaque display (e.g., a smartphone). The head mounted system may incorporate one or more imaging sensors to capture images or video of the physical environment, and/or one or more microphones to capture audio of the physical environment. Rather than an opaque display, a head mounted system may have a transparent or translucent display. The transparent or translucent display may have a medium through which light representative of images is directed to a person&#39;s eyes. The display may utilize digital light projection, OLEDs, LEDs, uLEDs, liquid crystal on silicon, laser scanning light source, or any combination of these technologies. The medium may be an optical waveguide, a hologram medium, an optical combiner, an optical reflector, or any combination thereof. In one embodiment, the transparent or translucent display may be configured to become opaque selectively. Projection-based systems may employ retinal projection technology that projects graphical images onto a person&#39;s retina. Projection systems also may be configured to project virtual objects into the physical environment, for example, as a hologram or on a physical surface. The display systems described herein may be used for these types of systems and for any other desired display arrangements. 
     In accordance with an embodiment, an optical system that redirects light produced by a display module towards an eye box, the optical system is provided that includes a waveguide, a non-diffractive input coupler configured to couple the light produced the display module into the waveguide, a cross coupler on the waveguide, the cross coupler is configured to perform an even number of diffractions on the light coupled into the waveguide by the non-diffractive input coupler, the even number of diffractions are configured to expand the light in a first direction and the waveguide is configured to propagate the light expanded in the first direction via total internal reflection and an output coupler on the waveguide, the output coupler is configured to couple the light expanded in the first direction by the cross coupler out of the waveguide while expanding the light in a second direction that is different from the first direction. 
     In accordance with another embodiment, the cross coupler includes a surface relief grating. 
     In accordance with another embodiment, the surface relief grating has fringes oriented in a first direction. 
     In accordance with another embodiment, the cross coupler further includes an additional surface relief grating having fringes oriented in a second direction different from the first direction. 
     In accordance with another embodiment, the surface relief grating overlaps the additional surface relief grating within an overlap region of the cross coupler. 
     In accordance with another embodiment, the overlap region has a non-uniform width. 
     In accordance with another embodiment, the surface relief grating and the additional surface relief grating are formed in a first surface relief grating substrate and the cross coupler further includes a second surface relief grating substrate that includes at least one additional surface relief grating and that is layered over the first surface relief grating substrate. 
     In accordance with another embodiment, the waveguide includes first and second waveguide substrates and a medium interposed between the first and second waveguide substrates and the surface relief grating and the additional surface relief grating are formed in a surface relief grating substrate layered on the first waveguide substrate. 
     In accordance with another embodiment, the output coupler includes a louvered mirror embedded in the medium. 
     In accordance with another embodiment, the medium includes a grating medium and the output coupler includes a set of volume holograms recorded in the grating medium. 
     In accordance with another embodiment, the surface relief grating has a non-binary profile. 
     In accordance with another embodiment, the waveguide includes a medium having first and second surfaces and a waveguide substrate layered on the first surface medium, the surface relief grating is formed in a surface relief grating medium layered on the second surface of the medium and the surface relief grating is embedded in the medium. 
     In accordance with another embodiment, the medium includes a grating medium and the output coupler includes a set of volume holograms recorded in the grating medium. 
     In accordance with another embodiment, the optical system includes an optically transparent coating on the surface relief grating and interposed between the surface relief grating and the grating medium. 
     In accordance with another embodiment, the optical system includes an antireflection layer on a surface of the waveguide substrate at the output coupler. 
     In accordance with another embodiment, the grating medium has a bulk index of refraction and the surface relief grating medium has an index of refraction that is greater than the bulk index of refraction of the grating medium. 
     In accordance with another embodiment, the output coupler has a diffraction efficiency that varies as a function of position along the first direction. 
     In accordance with another embodiment, the output coupler has a first diffraction efficiency along a central axis of the output coupler and a second diffraction efficiency at a peripheral edge of the output coupler that is greater than the first diffraction efficiency. 
     In accordance with another embodiment, the cross coupler has a diffraction efficiency that varies as a function of position. 
     In accordance with another embodiment, the waveguide includes first and second waveguide substrates and a first grating medium interposed between the first and second waveguide substrates, the cross coupler includes a substrate, a second grating medium, and a set of holographic phase gratings in the second grating medium and the second grating medium is interposed between the substrate and the first waveguide substrate. 
     In accordance with another embodiment, the set of holographic phase gratings include a plurality of at least partially overlapping volume holograms. 
     In accordance with another embodiment, the output coupler includes an additional set of holographic phase gratings in the first grating medium. 
     In accordance with another embodiment, the set of holographic phase gratings have fringes with a constant pitch at the substrate and a variable period. 
     In accordance with another embodiment, the non-diffractive input coupler includes a non-diffractive input coupler selected from the group consisting of: a prism mounted to the waveguide and an angled edge of the waveguide. 
     In accordance with another embodiment, the optical system includes a partially reflective beam splitter embedded in the waveguide, the light coupled into the waveguide by the non-diffractive input coupler is configured to hit the partially reflective beam splitter prior to being received at the cross coupler. 
     In accordance with another embodiment, the cross coupler includes a meta-grating on the waveguide. 
     In accordance with an embodiment, a head-mounted device is provided that includes, a display module that produces image light, a waveguide having first and second waveguide substrates and a grating medium interposed between the first and second waveguide substrates, a surface relief grating structure that is formed from the second waveguide substrate and that is embedded within the grating medium, an input prism mounted to the first waveguide substrate, the input prism is configured to couple the image light into the waveguide and towards the surface relief grating structure and an output coupler having a set of volume holograms in the grating medium, the surface relief grating structure is configured to: expand the image light along a first axis, perform an even number of diffractions on the image light and direct the image light into the waveguide and towards the output coupler, the output coupler being configured to expand the image light along a second axis perpendicular to the first axis and being configured to couple the image light out of the waveguide. 
     In accordance with another embodiment, the surface relief grating structure includes first and second surface relief gratings formed in the second waveguide substrate, the first surface relief grating includes first fringes with a first orientation, the second surface relief grating includes second fringes with a second orientation that is non-parallel with respect to the first orientation and the first and second surface relief gratings overlap within an overlap region of the surface relief grating structure. 
     In accordance with another embodiment, the head-mounted device includes an optically-transparent coating on the first and second surface relief gratings and interposed between the second waveguide substrate and the grating medium. 
     In accordance with another embodiment, the head-mounted device includes a partially reflective beam splitter on the grating medium, the surface relief grating structure is configured to receive the image light from the partially reflective beam splitter. 
     In accordance with another embodiment, the set of volume holograms has a diffraction efficiency that varies as a function of position along the first axis. 
     In accordance with an embodiment, a display system is provided that includes a waveguide, an input coupler configured to couple light into the waveguide, a cross coupler on the waveguide, the cross coupler includes a first diffractive grating structure having first fringes oriented in a first direction and a second diffractive grating structure having second fringes oriented in a second direction, the first diffractive grating structure overlaps the second diffractive grating structure within an overlap region of the cross coupler, the overlap region is aligned with the input coupler and the first and second diffractive grating structures are each configured to diffract the light coupled into the waveguide by the input coupler an even number of times and an output coupler on the waveguide, the output coupler is configured to receive the light diffracted by the cross coupler, expand the light in a given direction, and couple the light out of the waveguide. 
     In accordance with another embodiment, the first diffractive grating structure includes a first surface relief grating, the second diffractive grating structure includes a second surface relief grating, the first and second surface relief gratings are both formed in a surface relief grating substrate layer adhered to an external surface of the waveguide, the first and second surface relief gratings are configured to expand the light coupled into the waveguide by the input coupler in an additional direction perpendicular to the given direction, and the output coupler includes a set of volume holograms embedded in the waveguide. 
     In accordance with another embodiment, the first diffractive grating structure includes a first meta-grating on the waveguide and the second diffractive grating structure includes a second meta-grating on the waveguide. 
     The foregoing is merely illustrative and various modifications can be made to the described embodiments. The foregoing embodiments may be implemented individually or in any combination.

Metadata:
Filing Date: 20200526
Publication Date: 20240528
Grant Date: 20240528
Priority Date: 20190530
Inventors: PFEIFFER, JONATHAN B.
AIETA, Francesco
OH, SE BAEK
SCHLOTTAU, FRISO
Urness, Adam C.
Assignee: APPLE INC
CPC Classifications: [{"code": "G02B2027/0178", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B27/0101", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/0081", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B5/1814", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B5/32", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B6/0016", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B6/125", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/0103", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/0172", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/4211", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/4272", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B6/0011", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B6/0015", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2006/12107", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2006/12114", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2006/12147", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B6/124", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2027/0123", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2027/0134", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2027/0174", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B6/124", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B27/0081", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B27/0172", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B27/0081", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B6/125", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/0103", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B2006/12107", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2006/12114", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2006/12147", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B27/0101", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/0172", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B2027/0178", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B27/4211", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/0172", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/4272", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B2027/0174", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2027/0134", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B6/0011", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B6/0015", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B27/0081", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/4211", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/4272", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B6/0011", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B6/0015", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2027/0134", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2027/0174", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B5/1814", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B5/32", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B6/0016", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/0172", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B2027/0123", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2027/0174", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B6/125", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/4211", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/0103", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/4272", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B6/0011", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B6/0015", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2027/0134", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B6/124", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2006/12107", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2006/12114", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B2006/12147", "inventive": false, "first": false, "tree": "[]"}]
Family ID: 71083774