Diffraction gratings formed by metasurfaces having differently oriented nanobeams

Abstract

To provide favorable diffraction gratings formed by metasurfaces having differently oriented nanobeams.SOLUTION: Metasurfaces provide compact optical elements in head-mounted display systems to, e.g., incouple light into or outcouple light out of a waveguide. The metasurfaces may be formed by a plurality of repeating unit cells. Each unit cell comprises two or more sets of nanobeams elongated in crossing directions: one or more first nanobeams elongated in a first direction and a plurality of second nanobeams elongated in a second direction. As seen in a top-down view, the first direction may be along a y-axis, and the second direction may be along an x-axis. The unit cells may have periodicity in a range from 10 nm to 1 μm, including 10 nm to 500 nm or 300 nm to 500 nm. Advantageously, the metasurfaces provide diffraction of light with high diffraction angles and high diffraction efficiency over a broad range of incident angles and for incident light with circular polarization.SELECTED DRAWING: Figure 13

Description

[Technical field]

[0001] (Priority Claim) This application claims the benefit of priority under §119(e) of U.S. Provisional Application No. 62 / 451,608, filed January 27, 2017, and U.S. Provisional Application No. 62 / 451,615, filed January 27, 2017. The entire disclosures of each of these priority documents are incorporated herein by reference. (Incorporated by reference)

[0002] This application incorporates by reference the contents of each of the following patent applications: U.S. Application No. 14 / 331,218 (Magic Leap Docket No. 20020.00), U.S. Application No. 14 / 641,376 (Magic Leap Docket No. 20014.00), U.S. Provisional Application No. 62 / 012,273 (Magic Leap Docket No. 30019.00), U.S. Provisional Application No. 62 / 005,807 (Magic Leap Docket No. 30016.00), U.S. Provisional Application No. 62 / 333,067 (Attorney Docket No. MLEAP.066PR), and U.S. Patent Application No. 15 / 342,033 (Attorney Docket No. MLEAP.027A). (Field)

[0003] The present disclosure relates to display systems, and more particularly to augmented reality display systems. [Background technology]

[0004] Modern computing and display technologies have facilitated the development of systems for so-called "virtual reality" or "augmented reality" experiences, in which digitally reproduced images or portions thereof are presented to a user in a manner that appears or may be perceived as real. Virtual reality or "VR" scenarios typically involve the presentation of digital or virtual image information without transparency to other actual real-world visual inputs, while augmented reality or "AR" scenarios typically involve the presentation of digital or virtual image information as an augmentation to the visualization of the real world around the user. Mixed reality or "MR" scenarios are a type of AR scenario, typically involving virtual objects that are integrated into and responsive to the natural world. For example, MR scenarios may include AR image content that appears blocked by or is perceived to otherwise interact with objects in the real world.

[0005] Referring to FIG. 1, an augmented reality scene 1 is depicted. A user of the AR technology sees a real-world park-like setting 20 featuring people, trees, buildings in the background, and a concrete platform 30. The user also perceives that they are "seeing" "virtual content," such as a robotic figure 40 standing on the real-world platform 1120, and a flying cartoon-like avatar character 50 that appears to be an anthropomorphic bumblebee. These elements 50, 40 are "virtual" in that they do not exist in the real world. Because of the complexity of the human visual perception system, producing AR technology that facilitates a comfortable, natural-feeling, and rich presentation of virtual image elements among other virtual or real-world image elements is challenging.

[0006] The systems and methods disclosed herein address various challenges associated with AR or VR technology. Summary of the Invention [Means for solving the problem]

[0007] According to some embodiments, an optical system includes a metasurface configured to diffract visible light having a wavelength. The metasurface includes a plurality of repeating unit cells, each unit cell consisting of two to four sets of nanobeams. The first set of nanobeams is formed by one or more first nanobeams, and the second set of nanobeams is formed by a plurality of second nanobeams disposed adjacent to the one or more first nanobeams and separated from each other by sub-wavelength spacing. The one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuthal directions. The unit cells repeat with a period of about 10 nm to 1 μm or less.

[0008] According to some other embodiments, the optical system includes a waveguide configured to propagate visible light, the waveguide including a substrate having thereon the metasurface of the optical system described above, and the one or more first nanobeams and the second nanobeam are arranged to diffract the light at a diffraction angle relative to the direction of the incident light and propagate the diffracted light within the substrate under total internal reflection.

[0009] According to some embodiments, a head-mounted display device is configured to project light to a user's eye and display augmented reality image content, the head-mounted display device includes a frame configured to be supported on the user's head. The display device additionally includes a display disposed on the frame. At least a portion of the display includes one or more waveguides, the one or more waveguides being transparent and disposed at a location in front of the user's eye when the user wears the head-mounted display device such that the transparent portion transmits light from a portion of the environment in front of the user to the user's eye and provides a view of the portion of the environment in front of the user. The display device additionally includes one or more light sources. The display device further includes at least one diffraction grating configured to couple light from the light source into or out of the one or more waveguides, the diffraction grating including the metasurface of the optical system described above.

[0010] According to yet another embodiment, a method of fabricating an optical system includes providing a substrate and forming a metasurface on the substrate, the metasurface comprising a plurality of unit cells. The step of forming the metasurface includes forming unit cells consisting of two to four sets of nanobeams. The step of forming the unit cells includes forming a first set of nanobeams including one or more first nanobeams and forming a second set of nanobeams adjacent to the one or more first nanobeams. The step of forming the second set of nanobeams includes forming a plurality of second nanobeams separated from each other by sub-wavelength spacing. The one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuth directions. The unit cells repeat with a period of about 10 nm to 1 μm or less.

[0011] According to some embodiments, an optical system includes a metasurface configured to diffract visible light having a wavelength, the metasurface including a plurality of repeating unit cells. Each unit cell includes a first set of nanobeams, where two or more of the first nanobeams have different widths. Each unit cell additionally includes a second set of nanobeams, where two or more of the second nanobeams have different widths. The second nanobeams are disposed adjacent to the first nanobeam and separated from each other by a sub-wavelength spacing. Additionally, the first nanobeam and the second nanobeam of the unit cell have different orientations.

[0012] According to another embodiment, a head-mounted display device is configured to project light to a user's eye and display augmented reality image content, the head-mounted display device includes a frame configured to be supported on the user's head. The display device additionally includes a display disposed on the frame. At least a portion of the display includes one or more waveguides, the one or more waveguides being transparent and disposed at a location in front of the user's eye when the user wears the head-mounted display device such that the transparent portion transmits light to the user's eye and provides a view of a portion of the environment in front of the user. The display device additionally includes one or more light sources. The display device further includes at least one diffraction grating configured to couple light from the light source into or out of the one or more waveguides, the diffraction grating comprising a metasurface according to the optical system described above.

[0013] According to yet another embodiment, a method of fabricating a metasurface includes providing a substrate. The method additionally includes forming a metasurface having a plurality of unit cells on the substrate. The step of forming the metasurface includes forming a first set of nanobeams comprising two or more first nanobeams having different widths. The step of forming the metasurface additionally includes forming a second set of nanobeams comprising two or more second nanobeams having different widths, the second nanobeams disposed adjacent to the first nanobeams and separated from each other by a sub-wavelength spacing. The first nanobeams and the second nanobeams have different orientations.

[0014] Examples of various other embodiments are provided below. 1. An optical system comprising: 1. A metasurface configured to diffract visible light having a wavelength, a plurality of repeating unit cells, each unit cell consisting of 2-4 sets of nanobeams, a first set of nanobeams being formed by one or more first nanobeams; the second set of nanobeams is formed by a plurality of second nanobeams disposed adjacent to the one or more first nanobeams and separated from one another by sub-wavelength spacings; the one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuth directions; The unit cells are repeated at a period of about 10 nm to 1 μm or less. comprising a plurality of repeating unit cells; It has a metasurface. Optical system. 2. The optical system of embodiment 1, wherein the one or more first nanobeams and the second nanobeam are directed at an angle relative to each other, resulting in a phase difference between visible light diffracted by the one or more first nanobeams and visible light diffracted by the second nanobeams. 3. The optical system of embodiment 2, wherein the phase difference is twice the angle. 4. An optical system according to any of embodiments 1-3, wherein the wavelengths in the visible spectrum correspond to blue light, green light, or red light. 5. An optical system according to any of embodiments 1-4, wherein the one or more first and second nanobeams are oriented in azimuth directions rotated approximately 90 degrees relative to each other. 6. An optical system according to any one of embodiments 1-5, wherein each of the first nanobeams has the same width. 7. An optical system according to any of the preceding embodiments, wherein each of the second nanobeams has the same width. 8. An optical system according to any of embodiments 1-7, wherein each of the first nanobeams within each of the second nanobeams has the same spacing between respective ones of the first and second nanobeams. 9. An optical system according to any of the preceding embodiments, wherein the unit cells repeat with a period of less than a wavelength, the wavelength being within the visible spectrum. 10. An optical system according to any of embodiments 1-9, wherein the one or more first nanobeams and the second nanobeam have a height less than the wavelength. 11. An optical system according to any of embodiments 1-10, wherein the one or more first nanobeams and the second nanobeam are formed from a material whose bulk refractive index is greater than 2.0 at the wavelength. 12. An optical system according to any of embodiments 1-11, wherein the one or more first nanobeams and the second nanobeam are formed from a semiconductor material or an insulating material. 13. An optical system according to any of embodiments 1-12, wherein the one or more first nanobeams and the second nanobeam are formed from a material comprising silicon. 14. The optical system of any of embodiments 1-13, wherein the one or more first nanobeams and the second nanobeam are formed from a material selected from the group consisting of polycrystalline silicon, amorphous silicon, silicon carbide, and silicon nitride. 15. An optical system according to any of embodiments 1-14, wherein the one or more first and second nanobeams are configured to diffract visible light at a diffraction angle of greater than 50 degrees relative to the surface normal plane with a diffraction efficiency of greater than 10%. 16. The optical system of embodiment 15, wherein the one or more first nanobeams and the second nanobeam are configured to diffract light with a diffraction efficiency for incident light having a range of incidence angles greater than 40 degrees. 17. The optical system of embodiment 16, wherein the surface normal plane extends in a first azimuthal direction. 18. The optical system of embodiment 17, wherein the one or more first nanobeams and the second nanobeams are configured to diffract light in a transmission mode, and the intensity of the diffracted light on a side opposite to the light incident side of the one or more first nanobeams and the second nanobeams is greater than the intensity of the diffracted light on the same side as the light incident side of the one or more first nanobeams and the second nanobeams. 19. The optical system of embodiment 17, wherein the one or more first nanobeams and the second nanobeams are configured to diffract light in a reflection mode, and the intensity of the diffracted light on the same side as the light incident side of the one or more first nanobeams and the second nanobeams is greater than the intensity of the diffracted light on the opposite side to the light incident side of the one or more first nanobeams and the second nanobeams. 20. An optical system according to any of embodiments 1-19, wherein the one or more first nanobeams and the second nanobeam are formed on a substrate and from a material whose bulk refractive index is at least 0.5 greater than the refractive index of the substrate. 21. The optical system of embodiment 20, wherein the substrate has a refractive index greater than 1.5. 22. The optical system of any of embodiments 20-21, wherein the substrate is configured such that light diffracted by the one or more first nanobeams and the second nanobeam propagates in a second direction under total internal reflection. 23. An optical system according to any of embodiments 1-22, wherein the one or more first nanobeams and the second nanobeam have a substantially rectangular cross-sectional shape. 24. An optical system according to any one of embodiments 1-23, wherein the one or more first nanobeams comprise a pair of first nanobeams. 25. The optical system of embodiment 24, wherein one or more first nanobeams are immediately adjacent to a pair of nanobeams such that the second nanobeam is directly interposed between the first nanobeams of adjacent pairs. 26. An optical system according to any of embodiments 1-23, wherein the one or more first nanobeams consist of one first nanobeam. 27. The optical system of any of embodiments 1-24 and 26, further comprising a third set of nanobeams formed by a plurality of third nanobeams elongated in a different orientation relative to the first one or more first nanobeams and the plurality of second nanobeams, the third nanobeam being interposed between the one or more first nanobeams and the second nanobeams. 28. The optical system of embodiment 27, wherein the third nanobeams have the same length such that the third nanobeams are co-terminus. 29. The optical system of any of embodiments 27-28, wherein adjacent ones of the third nanobeams are separated by a constant space in the first azimuthal direction. 30. An optical system as described in any of embodiments 27-29, wherein the one or more first nanobeams span a distance in a first azimuthal direction corresponding to the plurality of third nanobeams. 31. The optical system of any of embodiments 27-30, wherein each of the third nanobeams has the same width and the spacing between individual ones of the third nanobeams has the same width. 32. An optical system described in any of embodiments 27-31, wherein the third nanobeam extends in a third azimuthal direction that, when viewed from the propagation direction of the incident light, is rotated in a counterclockwise direction relative to the one or more first nanobeams by an angle that is smaller than the minimum rotation angle in the counterclockwise direction of the second nanobeam relative to the one or more first nanobeams. 33. The optical system of any of embodiments 27-32, further comprising a fourth set of nanobeams formed by a plurality of fourth nanobeams elongated in a different orientation relative to the first one or more first nanobeams, the plurality of second nanobeams, and the plurality of third nanobeams, the fourth nanobeam being positioned on a side of the second nanobeam in a second azimuthal direction opposite to the side on which the third nanobeam is positioned. 34. An optical system as described in any of embodiments 33, wherein the fourth nanobeam extends in a fourth azimuthal direction that, when viewed from the propagation direction of the incident light, is rotated in a counterclockwise direction relative to the one or more first nanobeams by an angle that is smaller than the minimum counterclockwise rotation angle of the second nanobeam relative to the one or more first nanobeams. 35. The optical system of embodiment 34, wherein the fourth azimuth direction and the third azimuth direction are rotated approximately 90 degrees relative to each other. 36. An optical system as described in any of embodiments 1-35, wherein the one or more first nanobeams and the second nanobeams comprise a bilayer comprising a lower layer having a first refractive index and an upper layer having a second refractive index lower than the first refractive index. 37. The optical system of embodiment 36, wherein the upper layer is formed from a material having a refractive index less than about 2.0. 38. The optical system of any of embodiments 36-37, wherein the upper layer comprises silicon or carbon. 39. The optical system of any of embodiments 1-38, wherein the one or more first nanobeams and the second nanobeam are embedded in a transparent spacer layer. 40. The optical system of embodiment 39, wherein the transparent spacer layer has a refractive index less than the refractive index of a bulk material of the one or more first nanobeams and the second nanobeam. 41. The optical system of any of embodiments 1-38, wherein a metallic reflective layer is formed over the one or more first nanobeams and the second nanobeam. 42. An optical system comprising: 1. A waveguide configured to propagate visible light, comprising: A substrate having thereon a metasurface according to any of embodiments 1-41, wherein the one or more first nanobeams and the second nanobeam are arranged to diffract light at a diffraction angle relative to the direction of the incident light and to propagate the diffracted light within the substrate under total internal reflection. A waveguide is provided. Optical system. 43. The waveguide of embodiment 42, wherein the substrate is formed from a material whose refractive index is less than the bulk refractive index of the material in which the one or more nanobeams and the second nanobeam are formed, thereby propagating the diffracted light within the substrate under total internal reflection. 44. The waveguide of any one of embodiments 42-43, wherein the diffraction angle is greater than 50 degrees. 45. The waveguide of any of embodiments 42-44, wherein the substrate is formed from a material whose refractive index is at least 0.5 less than the bulk refractive index of the material in which the one or more nanobeams and the second nanobeam are formed. 46. ​​The waveguide of any of embodiments 42-45, wherein the substrate has a refractive index greater than 1.5. 47. A head-mounted display device configured to project light to a user's eye and display augmented reality image content, comprising: a frame configured to be supported on a user's head; A display disposed on the frame, at least a portion of the display comprising: one or more waveguides, the one or more waveguides being transparent and positioned at a location in front of the user's eyes when the user wears the head mounted display device such that the transparent portions transmit light from a portion of the environment in front of the user to the user's eyes to provide a view of the portion of the environment in front of the user; One or more light sources; At least one diffraction grating configured to couple light from a light source into one or more waveguides or out of one or more waveguides, the diffraction grating comprising a metasurface according to any of embodiments 1-41; a display; A head-mounted display device comprising: 48. The device of embodiment 47, wherein the one or more light sources comprise a fiber scanning projector. 49. A device described in any of embodiments 47-48, wherein the display is configured to project light into the user's eye so as to present image content to the user at multiple depth planes. 50. A method of making an optical system, comprising the steps of: Providing a substrate; forming a metasurface on a substrate, the metasurface comprising a plurality of unit cells, the unit cell being composed of 2-4 sets of nanobeams; forming the unit cells, forming a first set of nanobeams comprising one or more first nanobeams; forming a second set of nanobeams adjacent to the one or more first nanobeams, the second set of nanobeams comprising a plurality of second nanobeams separated from one another by sub-wavelength spacing; Including, the one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuth directions; The unit cells are repeated at a period of about 10 nm to 1 μm or less. Steps and A method comprising: 51. The method of embodiment 50, wherein forming one or more first nanobeams and forming a second nanobeam comprises lithographically defining the first and second nanobeams. 52. The method of embodiment 50, wherein forming one or more first nanobeams and forming a second nanobeam comprises forming the first and second nanobeams by nanoimprinting. 53. The method of any of embodiments 50-52, wherein the steps of forming one or more first nanobeams and forming a second nanobeam are performed simultaneously. 54. The method of any of embodiments 50-53, wherein the one or more first nanobeams have the same width. 55. The method of any of embodiments 50-54, wherein the second nanobeam of each unit cell has the same width. 56. The method of any of embodiments 50-55, wherein the unit cell has a period equal to or less than a wavelength in the visible spectrum. 57. An optical system comprising: 1. A metasurface configured to diffract visible light having a wavelength, A plurality of repeating unit cells, each unit cell comprising: a first set of nanobeams formed by one or more first nanobeams; and a second set of nanobeams formed by a plurality of second nanobeams disposed adjacent to the one or more first nanobeams and separated from one another by sub-wavelength spacing; Equipped with the one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuth directions; The unit cell repeats with a periodicity of less than the wavelength. comprising a plurality of repeating unit cells; It has a metasurface. Optical system. 58. The optical system of embodiment 57, further comprising a light source configured to emit light at a wavelength onto the metasurface. 59. The optical system of embodiment 58, further comprising a spatial light modulator configured to modulate light from the light source and output the modulated light to the metasurface. 60. An optical system according to any of embodiments 57-59, wherein the wavelength corresponds to blue light, green light, or red light. 61. An optical system comprising: 1. A metasurface configured to diffract visible light having a wavelength, A plurality of repeating unit cells, each unit cell comprising: a first set of nanobeams, where two or more of the first nanobeams have different widths; a second set of nanobeams, two or more of the second nanobeams having different widths, the second nanobeams disposed adjacent to the first nanobeam and separated from each other by a sub-wavelength spacing; Equipped with The first nanobeam and the second nanobeam have different orientations. comprising a plurality of repeating unit cells; It has a metasurface. Optical system. 62. The optical system of embodiment 61, further comprising a light source configured to emit light at a wavelength onto the metasurface. 63. The optical system of embodiment 62, further comprising a spatial light modulator configured to modulate light from the light source and output the modulated light to the metasurface. 64. An optical system according to any of embodiments 61-63, wherein the wavelength corresponds to blue light, green light, or red light. 65. The optical system of embodiment 61, wherein the first set of nanobeams and the second set of nanobeams are arranged such that the metasurface is configured to diffract visible light into a single order of diffracted light. 66. An optical system as described in any of embodiments 61-65, wherein the first set of nanobeams comprises a pair of first nanobeams each having a first width and a second width, and the second set of nanobeams comprises alternating second nanobeams having a third width and a fourth width. 67. An optical system according to any of embodiments 61-66, wherein the unit cells repeat with a period of about 10 nm to 1 μm or less. 68. An optical system according to any of embodiments 61-68, wherein the unit cells repeat with a period equal to or less than the wavelength, the wavelength being within the visible spectrum. 69. The optical system of any of embodiments 61-68, wherein the first nanobeam and the second nanobeam are oriented at an angle relative to each other, resulting in a phase difference between the visible light diffracted by the first set of nanobeams and the second set of nanobeams. 70. The optical system of embodiment 69, wherein the phase difference is twice the angle. 71. The optical system of any of embodiments 69-70, wherein the orientation angle is approximately 90 degrees. 72. The optical system of any of embodiments 61-67, wherein the first nanobeam and the second nanobeam have a height less than the wavelength. 73. The optical system of any of embodiments 61-72, wherein the first nanobeam and the second nanobeam are formed from a material whose bulk refractive index is greater than 2.0 at the wavelength. 74. The optical system of any of embodiments 61-73, wherein the first nanobeam and the second nanobeam are formed from a semiconductor material or an insulating material. 75. The optical system of any of embodiments 61-74, wherein the first nanobeam and the second nanobeam are formed from titanium dioxide. 76. The optical system of any of embodiments 61-75, wherein the first nanobeam and the second nanobeam are formed from a silicon-containing material. 77. The optical system of any of embodiments 61-76, wherein the first nanobeam and the second nanobeam are formed from a material selected from the group consisting of monocrystalline silicon, polycrystalline silicon, amorphous silicon, silicon carbide, and silicon nitride. 78. An optical system according to any of embodiments 61-77, wherein the first nanobeam and the second nanobeam are configured to diffract visible light with a diffraction efficiency of greater than 10% at a diffraction angle of greater than 50 degrees relative to the surface normal plane. 79. The optical system of embodiment 78, wherein the first nanobeam and the second nanobeam are configured to diffract light with a diffraction efficiency for incident light having a range of incidence angles greater than 40 degrees. 80. The optical system of embodiment 79, wherein the surface normal plane extends in a first azimuthal direction. 81. The optical system of embodiment 80, wherein the first nanobeam and the second nanobeam are configured to diffract light in a transmission mode, and the intensity of the diffracted light on a side opposite to the light incident side of the first nanobeam and the second nanobeam is greater than the intensity of the diffracted light on the same side as the light incident side of the first nanobeam and the second nanobeam. 82. The optical system of embodiment 80, wherein the first nanobeam and the second nanobeam are configured to diffract light in a reflection mode, and the intensity of the diffracted light on the same side as the light incident side of the first nanobeam and the second nanobeam is greater than the intensity of the diffracted light on the opposite side to the light incident side of the first nanobeam and the second nanobeam. 83. The optical system of any of embodiments 61-82, wherein the first nanobeam and the second nanobeam are formed on a substrate and from a material whose bulk refractive index is at least 0.5 greater than the refractive index of the substrate. 84. The optical system of embodiment 83, wherein the substrate has a refractive index greater than 1.5. 85. The optical system of any of embodiments 83-84, wherein the substrate is configured such that light diffracted by the first nanobeam and the second nanobeam propagates in the second direction under total internal reflection. 86. The optical system of any of embodiments 61-85, wherein the first nanobeam and the second nanobeam have a substantially rectangular cross-sectional shape. 87. An optical system according to any of embodiments 61-85, wherein a first nanobeam is directly adjacent to a pair of nanobeams such that the second nanobeam is directly interposed between the first nanobeams of adjacent pairs. 88. The optical system of any of embodiments 61-87, further comprising a waveguide configured to propagate visible light, the metasurface being disposed across the waveguide, the metasurface comprising a first nanobeam and a second nanobeam arranged to diffract the light at a diffraction angle relative to the incident direction of the light and propagate the diffracted light within the substrate under total internal reflection. 89. The optical system of any of embodiments 61-88, wherein the substrate is formed from a material whose refractive index is at least 0.5 less than the bulk refractive index of the material in which the first nanobeam and the second nanobeam are formed. 90. A head-mounted display device configured to project light to a user's eye and display augmented reality image content, comprising: a frame configured to be supported on a user's head; A display disposed on the frame, at least a portion of the display comprising: one or more waveguides, the one or more waveguides being transparent and positioned at locations in front of the user's eyes when the user wears the head mounted display device such that a transparent portion transmits light to the user's eyes to provide a view of a portion of the environment in front of the user; One or more light sources; At least one diffraction grating configured to couple light from a light source into one or more waveguides or out of one or more waveguides, the diffraction grating comprising a metasurface according to any of embodiments 61-87; a display; A head-mounted display device comprising: 91. The display device of embodiment 90, wherein the one or more light sources comprise a fiber scanning projector. 92. A display device as described in any of embodiments 90-91, wherein the display is configured to project light into the user's eye to present image content to the user at multiple depth planes. 93. A method of fabricating a metasurface, comprising: Providing a substrate; forming a metasurface on a substrate, the metasurface having a plurality of unit cells, the forming of the metasurface comprising: forming a first set of nanobeams comprising two or more first nanobeams having different widths; forming a second set of nanobeams comprising two or more second nanobeams having different widths, the second nanobeams disposed adjacent to the first nanobeams and separated from each other by a sub-wavelength spacing; wherein the first nanobeam and the second nanobeam have different orientations; and A method comprising: 94. The method of embodiment 93, wherein forming the first nanobeam and forming the second nanobeam simultaneously include lithographically defining the first and second nanobeams. 95. The method of embodiment 93, wherein forming the first nanobeam and forming the second nanobeam include forming the first and second nanobeams by nanoimprinting. 96. The method of any of embodiments 93-95, wherein the steps of forming the first nanobeam and forming the second nanobeam are performed simultaneously. 97. The method of any of embodiments 93-96, wherein the unit cells have a periodicity equal to or less than a wavelength in the visible spectrum. [Brief description of the drawings]

[0015] [Figure 1] FIG. 1 illustrates a user's view of an augmented reality (AR) device.

[0016] [Diagram 2] FIG. 2 illustrates an example of a wearable display system.

[0017] [Diagram 3] FIG. 3 illustrates a conventional display system for simulating a three-dimensional image for a user.

[0018] [Figure 4] FIG. 4 illustrates aspects of an approach for simulating a three-dimensional image using multiple depth planes.

[0019] [Diagram 5] 5A-5C illustrate the relationship between the radius of curvature and the radius of focus.

[0020] [Figure 6] FIG. 6 illustrates an example of a waveguide stack for outputting image information to a user.

[0021] [Figure 7] FIG. 7 illustrates an example of an output beam output by a waveguide.

[0022] [Figure 8] FIG. 8 illustrates an example of a stacked waveguide assembly where each depth plane includes an image formed using multiple different component colors.

[0023] [Figure 9A] FIG. 9A illustrates a cross-sectional side view of an example set of stacked waveguides, each containing an internal coupling optical element.

[0024] [Figure 9B] FIG. 9B illustrates a perspective view of the example of multiple stacked waveguides of FIG. 9A.

[0025] [Figure 9C] FIG. 9C illustrates a top-down plan view of the multiple stacked waveguide example of FIGS. 9A and 9B.

[0026] [Figure 10A] FIG. 10A diagrammatically illustrates a cross-sectional view of an axicon as an example of a conventional optical element.

[0027] [Figure 10B] FIG. 10B diagrammatically illustrates a cross-sectional view of a metasurface-based axicon as an example of an optical element formed from a metasurface.

[0028] [Figure 10C] FIG. 10C illustrates the resulting transmitted beam profile when the metasurface-based axicon of FIG. 10B is illuminated with a collimated Gaussian left-handed circularly polarized (LCP) light beam.

[0029] [Figure 11A] FIG. 11A illustrates an exemplary waveplate formed from a metasurface comprising multiple nanobeams under top-down illumination with incident light having transverse electric (TE) polarization and orthogonal transverse magnetic (TM) polarization.

[0030] [Figure 11B] FIG. 11B illustrates a simulated phase wavefront resulting from the exemplary waveplate illustrated with reference to FIG. 11A.

[0031] [Figure 11C] FIG. 11C illustrates the simulated phase retardation of a TM-polarized beam relative to a TE-polarized beam resulting from the exemplary waveplate of FIG. 11A.

[0032] [Figure 11D] FIG. 11D illustrates a simulated absorption spectrum of the example waveplate of FIG. 11A corresponding to the simulated phase retardation illustrated in FIG. 11C.

[0033] [Figure 12] 12A-12H illustrate the change in the polarization vector of incident light corresponding to a rotation in the fast axis of the waveplate through angles θ of 0, π / 4, π / 2, 3π / 4, π, 5π / 4, 3π / 2 and 7π / 4, respectively.

[0034] [Figure 13] 13A and 13B illustrate cross-sectional side and top-down views, respectively, of a diffraction grating comprising a metasurface having two-level geometric phase optical elements, according to some embodiments.

[0035] [Figure 14] FIG. 14 illustrates simulated diffraction efficiency versus incidence angle (α) for the example grating described with reference to FIGS. 13A and 13B.

[0036] [Figure 15] 15A and 15B illustrate two-dimensional simulations of the phase wavefront for TE-polarized light upon transmission through the diffraction grating described with reference to FIGS. 13A and 13B.

[0037] [Figure 16A] FIG. 16A illustrates a cross-sectional side view of a diffraction grating comprising a metasurface with geometric phase optical elements, according to some embodiments, where a mask layer is left in place, according to some embodiments.

[0038] [Figure 16B]FIG. 16B illustrates simulated diffraction efficiency (η) versus mask layer thickness for the example grating illustrated in FIG. 16A.

[0039] [Figure 16C] FIG. 16C illustrates simulated diffraction efficiency (η) versus angle of incidence (α) for the example grating illustrated in FIG. 16A where the remaining mask layer is 20 nm thick, according to some embodiments.

[0040] [Figure 16D] FIG. 16D illustrates simulated diffraction efficiency (η) versus incidence angle (α) for the example grating illustrated in FIG. 16A where the remaining mask layer is 40 nm thick, according to some embodiments.

[0041] [Figure 17A] 17A and 17B illustrate simulated diffraction efficiency (η) versus incidence angle (α) for an exemplary grating formed from amorphous silicon for TE and TM polarized green light, respectively, in accordance with some embodiments. [Figure 17B] 17A and 17B illustrate simulated diffraction efficiency (η) versus incidence angle (α) for an exemplary grating formed from amorphous silicon for TE and TM polarized green light, respectively, in accordance with some embodiments.

[0042] [Figure 18] FIG. 18 illustrates simulated diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from polycrystalline silicon and configured to diffract green light, according to some embodiments.

[0043] [Figure 19] FIG. 19 illustrates simulated diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from silicon carbide (SiC) and configured to diffract green light, according to some embodiments.

[0044] [Figure 20] FIG. 20 illustrates simulated diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from silicon nitride (Si3N4) and configured to diffract green light, in accordance with some embodiments.

[0045] [Figure 21] FIG. 21 illustrates simulated diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from polycrystalline silicon and configured to diffract blue light, according to some embodiments.

[0046] [Figure 22] FIG. 22 illustrates simulated diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from amorphous silicon and configured to diffract blue light, according to some embodiments.

[0047] [Diagram 23] FIG. 23 illustrates simulated diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from silicon carbide (SiC) and configured to diffract blue light, according to some embodiments.

[0048] [Figure 24] FIG. 24 illustrates simulated diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from silicon nitride (Si3N4) and configured to diffract blue light, in accordance with some embodiments.

[0049] [Diagram 25] FIG. 25 illustrates a top-down view of a grating comprising a metasurface with four-level geometric phase optical elements, according to some embodiments.

[0050] [Figure 26]FIG. 26 illustrates a cross-sectional view of a diffraction grating comprising a metasurface having a geometric phase optical element configured to diffract in a reflection mode, according to some embodiments.

[0051] [Figure 27] FIG. 27 illustrates simulated diffraction efficiency (η) versus angle of incidence (α) for the example diffraction illustrated in FIG.

[0052] [Figure 28] 28A-28D are cross-sectional views of intermediate structures at various stages in the fabrication of a diffraction grating comprising a metasurface with geometric phase optical elements, according to some embodiments.

[0053] [Figure 29] 29A-29D are cross-sectional views of intermediate structures at various stages in the fabrication of a diffraction grating comprising a metasurface with geometric phase optical elements according to some other embodiments.

[0054] [Diagram 30] 30A and 30B illustrate cross-sectional side and top-down views, respectively, of a diffraction grating comprising a metasurface having a two-level asymmetric geometric phase optical element, according to some embodiments.

[0055] [Figure 31A] 31A and 31B illustrate simulated diffraction efficiency (η) versus incidence angle (α) for an exemplary grating formed from polycrystalline silicon for TE and TM polarized green light, respectively, in accordance with some embodiments. [Figure 31B] 31A and 31B illustrate simulated diffraction efficiency (η) versus incidence angle (α) for an exemplary grating formed from polycrystalline silicon for TE and TM polarized green light, respectively, in accordance with some embodiments.

[0056] [Figure 32A]32A and 32B illustrate simulated diffraction efficiency (η) versus incidence angle (α) for an exemplary grating formed from amorphous silicon for TE and TM polarized green light, respectively, in accordance with some embodiments. [Figure 32B] 32A and 32B illustrate simulated diffraction efficiency (η) versus incidence angle (α) for an exemplary grating formed from amorphous silicon for TE and TM polarized green light, respectively, in accordance with some embodiments.

[0057] [Figure 33A] 33A and 33B illustrate simulated diffraction efficiency (η) versus incidence angle (α) for an exemplary grating formed from amorphous silicon for TE and TM polarized green light, respectively, in accordance with some embodiments. [Figure 33B] 33A and 33B illustrate simulated diffraction efficiency (η) versus incidence angle (α) for an exemplary grating formed from amorphous silicon for TE and TM polarized green light, respectively, in accordance with some embodiments. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0058] Optical systems, such as display systems, often utilize optical elements to control the propagation of light. In some applications, due to the demand for compact optical systems, traditional optical elements may no longer be suitable.

[0059] Metasurfaces, i.e., metamaterial surfaces, offer the opportunity to realize virtually flat, aberration-free optical systems at scales much smaller than geometric optics. Without being limited by theory, in some embodiments, metasurfaces include a dense array of surface structures that act as resonant optical antennas. The resonant nature of the interaction of light with the surface structures provides the ability to manipulate optical wavefronts. In some cases, metasurfaces may enable the replacement of bulky or difficult to manufacture optical components with thin, relatively planar elements formed by simple patterning processes.

[0060] In some embodiments, a metasurface for forming a diffraction grating is disclosed. The metasurface may take the form of a grating formed by a plurality of repeating unit cells. Each unit cell may comprise two or more sets of nanobeams elongated in intersecting directions, i.e., one or more first nanobeams elongated in a first direction and a plurality of second nanobeams elongated in a second direction different from the first direction. For example, as seen in a top-down view, the first direction may be generally along the y-axis and the second direction may be generally along the x-axis. In some embodiments, the unit cell may comprise four sets of nanobeams, i.e., one or more first nanobeams elongated in a first direction, a plurality of second nanobeams elongated in a second direction, a plurality of third nanobeams elongated in a third direction, and a plurality of fourth nanobeams elongated in a fourth direction. By way of example, the first and second directions may form a first angle (e.g., 90°) with respect to one another, and the first and third directions and the first and fourth directions may form opposite angles with one another. In some embodiments, the metasurface may be symmetric in the sense that there are a plurality of first nanobeams, each of the first nanobeams having the same width. In some other embodiments, the metasurface may be described as asymmetric in the sense that there are a plurality of first nanobeams, at least one of the first nanobeams in a unit cell has a width that is different from at least one other of the first nanobeams. In some embodiments, the unit cells of a symmetric or asymmetric metasurface may have a periodicity in the range of 10 nm to 1 μm, including 10 nm to 500 nm or 300 nm to 500 nm, and may be less than a wavelength of light that the metasurface is configured to diffract or that is directed at the metasurface, for example, for coupling in or out of a waveguide. Advantageously, the metasurfaces disclosed herein have been found to provide diffraction of light with high diffraction angles and high diffraction efficiency for incident light with circular polarization over a wide range of incidence angles. In particular, in some embodiments, the asymmetric metasurfaces can steer diffracted light into one of multiple diffraction orders while reducing other of the multiple diffraction orders.Additionally, in some embodiments, the metasurface diffracts light with high wavelength selectivity.

[0061] In some embodiments, metasurfaces may be utilized within a wearable display system to provide a compact optical element. AR systems may display virtual content to a user or viewer while still allowing the user to see the world around them. Preferably, the content is displayed on a wearable head-mounted display, for example as part of eyewear that projects image information to the user's eyes. In addition, the display may also transmit light from the surrounding environment to the user's eyes, allowing a view of the surrounding environment. As used herein, it should be understood that a "head-mounted" display is a display that may be mounted on the viewer's head.

[0062] Reference is now made to the drawings, in which like reference numbers refer to like parts throughout. (Exemplary Display System)

[0063] FIG. 2 illustrates an example of a wearable display system 60. The display system 60 includes a display 70 and various mechanical and electronic modules and systems to support the functionality of the display 70. The display 70 may be coupled to a frame 80, which is wearable by a display system user or viewer 90 and configured to position the display 70 in front of the user's 90 eye. The display 70 may be considered eyewear in some embodiments. In some embodiments, a speaker 100 is coupled to the frame 80 and configured to be positioned adjacent to the ear canal of the user 90 (in some embodiments, another speaker, not shown, may optionally be positioned adjacent the user's other ear canal to provide stereo / shapeable sound control). The display system may also include one or more microphones 110 or other devices to detect sound. In some embodiments, the microphones may be configured to allow a user to provide input or commands (e.g., voice menu command selections, natural language questions, etc.) to the system 60 and / or enable audio communication with other persons (e.g., other users of similar display systems). The microphone may further be configured as an ambient sensor to collect audio data (e.g., sounds from the user and / or the environment). In some embodiments, the display system may also include an ambient sensor 120a, which may be separate from the frame 80 and attached to the body of the user 90 (e.g., on the head, torso, limbs, etc. of the user 90). The ambient sensor 120a, in some embodiments, may be configured to obtain data characterizing a physiological state of the user 90. For example, the sensor 120a may be an electrode.

[0064] 2, the display 70 is operably coupled to the local data processing module 140 by a communication link 130, such as wired or wireless connectivity, which may be mounted in a variety of configurations, such as fixedly attached to the frame 80, fixedly attached to a helmet or hat worn by the user, built into headphones, or otherwise removably attached to the user 90 (e.g., in a backpack configuration, in a belt-connected configuration). Similarly, the sensor 120a may be operably coupled to the local data processing module 140 by a communication link 120b, such as wired or wireless connectivity. The local processing and data module 140 may include a hardware processor and digital memory, such as non-volatile memory (e.g., flash memory or hard disk drive), both of which may be utilized to aid in processing, caching, and storing data. The data includes data a) captured from sensors (e.g., which may be operatively coupled to the frame 80 or otherwise attached to the user 90), such as image capture devices (such as cameras), microphones, inertial measurement units, accelerometers, compasses, GPS units, wireless devices, gyroscopes, and / or other sensors disclosed herein, and / or b) obtained and / or processed using the remote processing module 150 and / or remote data repository 160 (including data related to the virtual content), potentially for passing to the display 70 after processing or retrieval. The local processing and data module 140 may be operatively coupled to the remote processing module 150 and the remote data repository 160 by communication links 170, 180, such as via wired or wireless communication links, such that these remote modules 150, 160 are operatively coupled to each other and available as resources to the local processing and data module 140. In some embodiments, the local processing and data module 140 may include one or more of an image capture device, a microphone, an inertial measurement unit, an accelerometer, a compass, a GPS unit, a wireless device, and / or a gyroscope.In some other embodiments, one or more of these sensors may be mounted on the frame 80 or may be free-standing structures that communicate with the local processing and data module 140 by wired or wireless communication paths.

[0065] 2, in some embodiments, remote processing module 150 may comprise one or more processors configured to analyze and process data and / or image information. In some embodiments, remote data repository 160 may comprise digital data storage facilities that may be available through the Internet or other networking configurations in a "cloud" resource configuration. In some embodiments, remote data repository 160 may include one or more remote servers that provide information, such as information for generating augmented reality content, to local processing and data module 140 and / or remote processing module 150. In some embodiments, all data is stored and all calculations are performed within the local processing and data module, allowing for fully autonomous use from the remote modules.

[0066] Referring now to FIG. 3, the perception of an image as "three-dimensional" or "3-D" may be achieved by providing a slightly different presentation of the image to each eye of a viewer. FIG. 3 illustrates a conventional display system for simulating a three-dimensional image for a user. Two different images 190, 200, one for each eye 210, 220, are output to the user. The images 190, 200 are spaced from the eyes 210, 220 by a distance 230 along an optical or z-axis parallel to the viewer's line of sight. The images 190, 200 are flat, and the eyes 210, 220 may focus on the images by assuming a single accommodated state. Such a 3-D display system relies on the human visual system to combine the images 190, 200 and provide a perception of depth and / or scale of the combined image.

[0067] However, it should be understood that the human visual system is more complex and more difficult to provide a realistic perception of depth. For example, many viewers of conventional "3-D" display systems find such systems uncomfortable or may not perceive any sense of depth at all. Without being limited by theory, it is believed that viewers of an object may perceive the object as "three-dimensional" due to a combination of vergence and accommodation. Vergence of the two eyes relative to each other (i.e., eye rolling, in which the pupils move toward or away from each other to converge the gaze of the eyes and fixate on the object) is closely linked to the focusing (or "accommodation") of the eye's lens and pupil. Under normal conditions, changing the focus of the eye's lens or accommodating the eye to change focus from one object to another at different distances will automatically produce a matching change in vergence to the same distance, under a relationship known as the "accommodation-vergence reflex" and pupil dilation or constriction. Similarly, changes in vergence will induce matching changes in accommodation of lens shape and pupil size under normal conditions. As described herein, many stereoscopic or "3-D" display systems display a scene using a slightly different presentation (and therefore a slightly different image) to each eye so that a three-dimensional perspective is perceived by the human visual system. However, such systems are uncomfortable for many viewers, especially since they simply provide a different presentation of the scene but work against the "accommodation-vergence reflex" when the eyes view the entire image information in a single accommodated state. Display systems that provide better matching between accommodation and vergence can create a more realistic and comfortable simulation of a three-dimensional image.

[0068] FIG. 4 illustrates aspects of an approach for simulating a three-dimensional image using multiple depth planes. With reference to FIG. 4, objects at various distances from the eyes 210, 220 on the z-axis are accommodated by the eyes 210, 220 such that the objects are in focus. The eyes 210, 220 assume a particular accommodated state and focus the objects at different distances along the z-axis. As a result, a particular accommodated state may be said to be associated with a particular one of the depth planes 240 having an associated focal length such that an object or part of an object at a particular depth plane is in focus when the eye is in an accommodated state relative to that depth plane. In some embodiments, a three-dimensional image may be simulated by providing a different presentation of an image for each eye 210, 220 and by providing a different presentation of an image corresponding to each of the depth planes. Although shown as separate for clarity of illustration, it should be understood that the fields of view of the eyes 210, 220 may overlap, for example, as the distance along the z-axis increases. Additionally, while shown to be flat for ease of illustration, it should be understood that the contour of the depth plane may be curved in physical space such that all features within the depth plane are in focus with the eye in a particular accommodated state.

[0069] The distance between an object and the eye 210 or 220 may also change the amount of divergence of light from that object as viewed by that eye. Figures 5A-5C illustrate the relationship between distance and divergence of light rays. The distance between the object and the eye 210 is represented in the order of decreasing distances R1, R2, and R3. As shown in Figures 5A-5C, the light rays become more divergent as the distance to the object decreases. As the distance increases, the light rays become more collimated. In other words, the light field generated by a point (an object or part of an object) may be said to have a spherical wavefront curvature that is a function of the distance the point is away from the user's eye. The curvature increases with decreasing distance between the object and the eye 210. As a result, at different depth planes, the divergence of the light rays is also different, and the divergence increases with decreasing distance between the depth plane and the viewer's eye 210. Although only a monocular 210 is illustrated in FIGS. 5A-5C and various other figures herein for clarity of illustration, it should be understood that the discussion regarding eye 210 may apply to both eyes 210 and 220 of a viewer.

[0070] Without being limited by theory, it is believed that the human eye is typically capable of interpreting a finite number of depth planes to provide depth perception. As a result, a highly realistic simulation of perceived depth can be achieved by providing the eye with different presentations of images corresponding to each of these limited number of depth planes. The different presentations can be focused separately by the viewer's eyes, thereby serving to provide depth cues to the user based on ocular accommodation required to focus on different image features for scenes located on different depth planes and / or based on the observation of different image features on different depth planes that are out of focus.

[0071] FIG. 6 illustrates an example of a waveguide stack for outputting image information to a user. The display system 250 includes a stack of waveguides or a stacked waveguide assembly 260 that may be utilized to provide a three-dimensional perception to the eye / brain using multiple waveguides 270, 280, 290, 300, 310. In some embodiments, the display system 250 is the system 60 of FIG. 2, of which FIG. 6 illustrates several portions in more detail. For example, the waveguide assembly 260 may be part of the display 70 of FIG. 2. It should be understood that the display system 250 may be considered a bright field display in some embodiments.

[0072] Continuing with reference to FIG. 6, the waveguide assembly 260 may also include a number of features 320, 330, 340, 350 between the waveguides. In some embodiments, the features 320, 330, 340, 350 may be one or more lenses. The waveguides 270, 280, 290, 300, 310 and / or the number of lenses 320, 330, 340, 350 may be configured to transmit image information to the eye with various levels of wavefront curvature or light beam divergence. Each waveguide level may be associated with a particular depth plane and may be configured to output image information corresponding to that depth plane. The image input devices 360, 370, 380, 390, 400 may act as light sources for the waveguides and may be utilized to input image information into the waveguides 270, 280, 290, 300, 310, each of which may be configured to disperse incident light across each respective waveguide for output towards the eye 210, as described herein. The light exits output surfaces 410, 420, 430, 440, 450 of the image input devices 360, 370, 380, 390, 400 and is input into corresponding input surfaces 460, 470, 480, 490, 500 of the waveguides 270, 280, 290, 300, 310. In some embodiments, each of the input surfaces 460, 470, 480, 490, 500 may be an edge of the corresponding waveguide or may be a portion of the major surface of the corresponding waveguide (i.e., one of the waveguide surfaces that directly faces the world 510 or the viewer's eye 210). In some embodiments, a single beam of light (e.g., a collimated beam) may be launched into each waveguide, outputting a total field of cloned collimated beams that are directed towards the eye 210 at a particular angle (and divergence) corresponding to the depth plane associated with the particular waveguide. In some embodiments, a single one of the image launch devices 360, 370, 380, 390, 400 may be associated with and launch light into multiple (e.g., three) waveguides 270, 280, 290, 300, 310.

[0073] In some embodiments, each of the image input devices 360, 370, 380, 390, 400 is an individual display that generates image information for input into the corresponding waveguide 270, 280, 290, 300, 310. In some other embodiments, the image input devices 360, 370, 380, 390, 400 are the output of a single multiplexed display that may, for example, send image information via one or more optical conduits (such as fiber optic cables) to each of the image input devices 360, 370, 380, 390, 400. It should be understood that the image information provided by the image input devices 360, 370, 380, 390, 400 may include light of different wavelengths or colors (e.g., different component colors, as discussed herein).

[0074] In some embodiments, the light injected into the waveguides 270, 280, 290, 300, 310 is provided by a light projector system 520, which includes a light module 530, which may include a light emitter such as a light emitting diode (LED). Light from the light module 530 may be directed through a beam splitter 550 to and modified by a light modulator 540, e.g., a spatial light modulator. The light modulator 540 may be configured to change the perceived intensity of the light injected into the waveguides 270, 280, 290, 300, 310. Examples of spatial light modulators include liquid crystal displays (LCDs), including liquid crystal on silicon (LCOS) displays.

[0075] In some embodiments, the display system 250 may be a scanning fiber display comprising one or more scanning fibers configured to project light in various patterns (e.g., raster scan, spiral scan, Lissajous pattern, etc.) into one or more waveguides 270, 280, 290, 300, 310 and ultimately to the viewer's eye 210. In some embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may represent diagrammatically a single scanning fiber or a bundle of scanning fibers configured to inject light into one or more waveguides 270, 280, 290, 300, 310. In some other embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may represent diagrammatically multiple scanning fibers or multiple bundles of scanning fibers, each configured to inject light into an associated one of the waveguides 270, 280, 290, 300, 310. It should be understood that one or more optical fibers may be configured to transmit light from the optical module 530 to one or more of the waveguides 270, 280, 290, 300, 310. It should be understood that one or more intervening optical structures may be provided between the scanning fiber or fibers and one or more of the waveguides 270, 280, 290, 300, 310, for example, to redirect light exiting the scanning fiber into one or more of the waveguides 270, 280, 290, 300, 310.

[0076] The controller 560 controls the operation of one or more of the stacked waveguide assemblies 260, including the operation of the image input devices 360, 370, 380, 390, 400, the light source 530, and the light module 540. In some embodiments, the controller 560 is part of the local data processing module 140. The controller 560 includes programming (e.g., instructions in a non-transient medium) that coordinates the timing and provision of image information to the waveguides 270, 280, 290, 300, 310, for example, according to any of the various schemes disclosed herein. In some embodiments, the controller may be a single integrated device or a distributed system connected by wired or wireless communication channels. The controller 560 may be part of the processing module 140 or 150 (FIG. 2) in some embodiments.

[0077] Continuing with reference to FIG. 6, the waveguides 270, 280, 290, 300, 310 may be configured to propagate light within each respective waveguide by total internal reflection (TIR). Each of the waveguides 270, 280, 290, 300, 310 may be planar or have another shape (e.g., curved) with major top and bottom surfaces and edges extending between their major top and bottom surfaces. In the illustrated configuration, each of the waveguides 270, 280, 290, 300, 310 may include an outcoupling optical element 570, 580, 590, 600, 610 configured to extract light from the waveguide by redirecting light propagating within each respective waveguide out of the waveguide and outputting image information to the eye 210. The extracted light may also be referred to as outcoupling light, and the outcoupling optical element light may also be referred to as a light extraction optical element. The extracted beam of light may be output by the waveguide at a location where the light propagating within the waveguide strikes the light extraction optical element. The outcoupling optical element 570, 580, 590, 600, 610 may be a grating, for example, including diffractive optical features as further discussed herein. Although shown disposed on the bottom major surface of the waveguide 270, 280, 290, 300, 310 for ease of explanation and clarity of the drawings, in some embodiments the outcoupling optical element 570, 580, 590, 600, 610 may be disposed on the top and / or bottom major surfaces and / or directly within the volume of the waveguide 270, 280, 290, 300, 310, as further discussed herein. In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 may be attached to a transparent substrate and formed within a layer of material that forms the waveguide 270, 280, 290, 300, 310. In some other embodiments, the waveguide 270, 280, 290, 300, 310 may be a monolithic piece of material and the outcoupling optical elements 570, 580, 590, 600, 610 may be formed on a surface of and / or within that piece of material.

[0078] With continued reference to FIG. 6, as discussed herein, each waveguide 270, 280, 290, 300, 310 is configured to output light and form an image corresponding to a particular depth plane. For example, the waveguide 270 closest to the eye may be configured to deliver collimated light (injected into such waveguide 270) to the eye 210. The collimated light may represent an optical infinity focal plane. The next upper waveguide 280 may be configured to send collimated light that passes through a first lens 350 (e.g., a negative lens) before it can reach the eye 210. Such a first lens 350 may be configured to generate a slight convex wavefront curvature such that the eye / brain interprets the light originating from the next upper waveguide 280 as originating from a first focal plane closer inward from optical infinity toward the eye 210. Similarly, the third upper waveguide 290 passes its output light through both the first 350 and second 340 lenses before reaching the eye 210. The combined refractive power of the first 350 and second 340 lenses may be configured to produce another incremental amount of wavefront curvature such that the eye / brain interprets the light originating from the third waveguide 290 as originating from a second focal plane closer inward toward the person from optical infinity, which was the light from the next upper waveguide 280.

[0079] The other waveguide layers 300, 310 and lenses 330, 320 are similarly configured, with the highest waveguide 310 in the stack sending its output through all of the lenses between it and the eye for an aggregate focal power that represents the focal plane closest to the person. To compensate the stack of lenses 320, 330, 340, 350 when viewing / interpreting light originating from the world 510 on the other side of the stacked waveguide assembly 260, a compensating lens layer 620 may be placed on top of the stack to compensate for the aggregate power of the lens stacks 320, 330, 340, 350 below. Such a configuration provides as many perceived focal planes as there are waveguide / lens pairs available. Both the outcoupling optical elements of the waveguides and the focusing sides of the lenses may be static (i.e., not dynamic or electroactive). In some alternative embodiments, one or both may be dynamic using electroactive features.

[0080] In some embodiments, two or more of the waveguides 270, 280, 290, 300, 310 may have the same associated depth plane. For example, multiple waveguides 270, 280, 290, 300, 310 may be configured to output images set at the same depth plane, or multiple subsets of the waveguides 270, 280, 290, 300, 310 may be configured to output images set at the same depth planes, with one set per depth plane. This may provide the advantage of forming tiled images to provide an extended field of view at those depth planes.

[0081] Continuing with reference to FIG. 6, the outcoupling optical elements 570, 580, 590, 600, 610 can be configured to both redirect light out of their respective waveguides and output this light with an appropriate amount of divergence or collimation for a particular depth plane associated with the waveguide. As a result, waveguides with different associated depth planes can have different configurations of outcoupling optical elements 570, 580, 590, 600, 610 that output light with different amounts of divergence depending on the associated depth plane. In some embodiments, the light extraction optical elements 570, 580, 590, 600, 610 can be volume or surface features that can be configured to output light at specific angles. For example, the light extraction optical elements 570, 580, 590, 600, 610 can be volume holograms, surface holograms, and / or diffraction gratings. In some embodiments, features 320, 330, 340, 350 may not be lenses. Rather, they may simply be spacers (e.g., cladding layers and / or structures for forming air gaps).

[0082] In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 are diffractive features or "diffractive optical elements" (also referred to herein as "DOEs") that form a diffraction pattern. Preferably, the DOEs have a low enough diffraction efficiency so that only a portion of the light in the beam is deflected towards the eye 210 with each intersection point of the DOE, while the remainder continues to travel through the waveguide via TIR. The light carrying the image information is thus split into several related exit beams that exit the waveguide at various locations, resulting in a very uniform pattern of exit emission towards the eye 210 for this particular collimated beam bouncing within the waveguide.

[0083] In some embodiments, one or more DOEs may be switchable between an "on" state in which they actively diffract and an "off" state in which they do not significantly diffract. For example, a switchable DOE may comprise a layer of polymer dispersed liquid crystal in which microdroplets comprise a diffractive pattern in a host medium, and the refractive index of the microdroplets may be switched to substantially match the refractive index of the host material (in which case the pattern does not significantly diffract incident light), or the microdroplets may be switched to a refractive index that does not match that of the host medium (in which case the pattern actively diffracts incident light).

[0084] In some embodiments, a camera assembly 630 (e.g., a digital camera, including visible and infrared light cameras) may be provided to capture images of the eye 210 and / or tissue surrounding the eye 210, for example, to detect user input and / or monitor a physiological condition of the user. As used herein, a camera may be any image capture device. In some embodiments, the camera assembly 630 may include an image capture device and a light source that projects light (e.g., infrared light) onto the eye, which may then be reflected by the eye and detected by the image capture device. In some embodiments, the camera assembly 630 may be mounted to the frame 80 (FIG. 2) and may be in electrical communication with the processing modules 140 and / or 150, which may process image information from the camera assembly 630. In some embodiments, one camera assembly 630 may be utilized per eye to monitor each eye separately.

[0085] 7, an example of an exit beam output by a waveguide is shown. Although one waveguide is illustrated, it should be understood that other waveguides in the waveguide assembly 260 (FIG. 6) may function similarly and that the waveguide assembly 260 includes multiple waveguides. Light 640 is launched into the waveguide 270 at the input surface 460 of the waveguide 270 and propagates within the waveguide 270 by TIR. At the point where the light 640 impinges on the DOE 570, a portion of the light exits the waveguide as an exit beam 650. The exit beam 650 is illustrated as approximately parallel, but may be redirected to propagate to the eye 210 at an angle (e.g., forming a diverging exit beam) as discussed herein and depending on the depth plane associated with the waveguide 270. It should be understood that a nearly collimated exit beam may refer to a waveguide with outcoupling optics that outcouples light to form an image that appears to be set at a depth plane at a large distance (e.g., optical infinity) from the eye 210. Other sets of waveguides or other outcoupling optics may output a more divergent exit beam pattern, which would require the eye 210 to accommodate to a closer distance and focus on the retina, and would be interpreted by the brain as light from a distance closer to the eye 210 than optical infinity.

[0086] In some embodiments, a full color image may be formed at each depth plane by overlaying an image on each of the component colors, for example, three or more component colors. FIG. 8 illustrates an example of a stacked waveguide assembly, where each depth plane includes an image formed using multiple different component colors. The illustrated embodiment shows depth planes 240a-240f, but more or less depths are also contemplated. Each depth plane may have three or more component color images associated with it, including a first image of a first color G, a second image of a second color R, and a third image of a third color B. The different depth planes are indicated in the diagram by different numbers for diopters (dpt) following the letters G, R, and B. By way of example only, the numbers following each of these letters indicate the diopters (1 / m), i.e., the inverse distance of the depth plane from the viewer, and each box in the diagram represents an individual component color image. In some embodiments, the exact locations of the depth planes for the different component colors may be varied to account for differences in the eye's focusing of different wavelengths of light. For example, different component color images for a given depth plane may be placed on depth planes that correspond to different distances from the user. Such an arrangement may increase visual acuity and user comfort and / or reduce chromatic aberration.

[0087] In some embodiments, the light of each component color may be output by a single dedicated waveguide, such that each depth plane may have multiple waveguides associated with it. In such embodiments, each box in the figure containing the letter G, R, or B may be understood to represent an individual waveguide, and three waveguides may be provided per depth plane, with three component color images provided per depth plane. The waveguides associated with each depth plane are shown adjacent to each other in this drawing for ease of illustration, but it should be understood that in a physical device, the waveguides may all be arranged in a stack with one waveguide per level. In some other embodiments, multiple component colors may be output by the same waveguide, such that, for example, only a single waveguide may be provided per depth plane.

[0088] 8, in some embodiments, G is green, R is red, and B is blue. In some other embodiments, other colors associated with other wavelengths of light, including magenta and cyan, may be used in addition to or in place of one or more of the red, green, or blue colors.

[0089] It should be understood that references throughout this disclosure to a given color of light are understood to encompass light of one or more wavelengths within the range of wavelengths of light that are perceived by a viewer as that given color. For example, red light may include one or more wavelengths of light that are within the range of about 620-780 nm, green light may include one or more wavelengths of light that are within the range of about 492-577 nm, and blue light may include one or more wavelengths of light that are within the range of about 435-493 nm.

[0090] In some embodiments, the light source 530 (FIG. 6) may be configured to emit light at one or more wavelengths outside the range of visual perception of a viewer, e.g., infrared and / or ultraviolet wavelengths. Additionally, the waveguide in-coupling, out-coupling, and other light redirecting structures of the display 250 may be configured to direct and emit this light out of the display toward the user's eye 210, e.g., for imaging and / or user stimulation applications.

[0091] 9A, in some embodiments, light impinging on a waveguide may need to be redirected to in-couple the light into the waveguide. An in-coupling optical element may be used to redirect and in-couple the light into its corresponding waveguide. FIG. 9A illustrates a cross-sectional side view of an example of a plurality or set 660 of stacked waveguides, each including an in-coupling optical element. Each of the waveguides may be configured to output light of one or more different wavelengths or one or more different wavelength ranges. The stack 660 may correspond to the stack 260 (FIG. 6), and the illustrated waveguides of the stack 660 may correspond to a portion of the plurality of waveguides 270, 280, 290, 300, 310, although it should be understood that light from one or more of the image input devices 360, 370, 380, 390, 400 is launched into the waveguide from a position that requires the light to be redirected for in-coupling.

[0092] The illustrated set 660 of stacked waveguides includes waveguides 670, 680, and 690. Each waveguide includes an associated incoupling optical element (which may also be referred to as the light input area on the waveguide), for example, incoupling optical element 700 is disposed on a major surface (e.g., the top major surface) of waveguide 670, incoupling optical element 710 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and incoupling optical element 720 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some embodiments, one or more of the incoupling optical elements 700, 710, 720 may be disposed on a bottom major surface of the respective waveguide 670, 680, 690 (particularly, one or more of the incoupling optical elements are reflective polarizing optical elements). As shown, the incoupling optical elements 700, 710, 720 may be disposed on the upper major surface of their respective waveguides 670, 680, 690 (or on top of the next lower waveguide), and in particular, the incoupling optical elements are transmissive deflecting optical elements. In some embodiments, the incoupling optical elements 700, 710, 720 may be disposed within the body of the respective waveguides 670, 680, 690. In some embodiments, as discussed herein, the incoupling optical elements 700, 710, 720 are wavelength selective such that they selectively redirect one or more wavelengths of light while transmitting other wavelengths of light. Although illustrated on one side or corner of their respective waveguides 670, 680, 690, it should be understood that the incoupling optical elements 700, 710, 720 may be disposed within other areas of their respective waveguides 670, 680, 690 in some embodiments.

[0093] As shown, the in-coupling optical elements 700, 710, 720 may be laterally offset from one another. In some embodiments, each in-coupling optical element may be offset to receive light without that light passing through another in-coupling optical element. For example, each in-coupling optical element 700, 710, 720 may be configured to receive light from a different image input device 360, 370, 380, 390, and 400, as shown in FIG. 6, and may be separated (e.g., laterally spaced) from the other in-coupling optical elements 700, 710, 720 such that it does not receive substantially any light from others of the in-coupling optical elements 700, 710, 720.

[0094] Each waveguide also includes an associated light distribution element, for example light distribution element 730 is disposed on a major surface (e.g., a top major surface) of waveguide 670, light distribution element 740 is disposed on a major surface (e.g., a top major surface) of waveguide 680, and light distribution element 750 is disposed on a major surface (e.g., a top major surface) of waveguide 690. In some other embodiments, light distribution elements 730, 740, 750 may be disposed on the bottom major surface of the associated waveguide 670, 680, 690, respectively. In some other embodiments, light distribution elements 730, 740, 750 may be disposed on both the top and bottom major surfaces of the associated waveguide 670, 680, 690, respectively, or light distribution elements 730, 740, 750 may be disposed on different ones of the top and bottom major surfaces in different associated waveguides 670, 680, 690, respectively.

[0095] The waveguides 670, 680, 690 may be spaced apart and separated by, for example, gas, liquid and / or solid layers of material. For example, as shown, layer 760a may separate waveguides 670 and 680, and layer 760b may separate waveguides 680 and 690. In some embodiments, layers 760a and 760b are formed from a low index material (i.e., a material having a lower index of refraction than the material forming the immediately adjacent ones of the waveguides 670, 680, 690). Preferably, the index of refraction of the material forming layers 760a, 760b is 0.05 or greater, or 0.10 or less, than the index of refraction of the material forming the waveguides 670, 680, 690. Advantageously, the lower refractive index layers 760a, 760b may act as cladding layers to promote total internal reflection (TIR) ​​of light through the waveguides 670, 680, 690 (e.g., TIR between the top and bottom major surfaces of each waveguide). In some embodiments, the layers 760a, 760b are formed from air. Although not shown, it should be understood that the top and bottom of the illustrated set of waveguides 660 may include immediate cladding layers.

[0096] Preferably, for ease of manufacturing and other considerations, the materials forming the waveguides 670, 680, 690 are similar or the same, and the materials forming the layers 760a, 760b are similar or the same. In some embodiments, the materials forming the waveguides 670, 680, 690 may vary between one or more of the waveguides, and / or the materials forming the layers 760a, 760b may differ while still maintaining the various refractive index relationships discussed above.

[0097] 9A, light rays 770, 780, 790 are incident on the set of waveguides 660. It should be understood that light rays 770, 780, 790 may be injected into the waveguides 670, 680, 690 by one or more image injection devices 360, 370, 380, 390, 400 (FIG. 6).

[0098] In some embodiments, the light beams 770, 780, 790 have different properties, e.g., different wavelengths or different wavelength ranges, that may correspond to different colors. Each of the incoupling optical elements 700, 710, 720 deflects incident light such that the light propagates through a respective one of the waveguides 670, 680, 690 by TIR. In some embodiments, each of the incoupling optical elements 700, 710, 720 selectively deflects one or more particular wavelengths of light while transmitting other wavelengths to the underlying waveguide and associated incoupling optical element.

[0099] For example, incoupling optical element 700 may be configured to selectively deflect light beam 770 having a first wavelength or wavelength range while transmitting light beams 1242 and 1244 having different second and third wavelengths or wavelength ranges, respectively. Transmitted light beam 780 impinges on and is deflected by incoupling optical element 710, which is configured to selectively deflect light of the second wavelength or wavelength range. Light beam 790 is deflected by incoupling optical element 720, which is configured to selectively deflect light of the third wavelength or wavelength range.

[0100] 9A, the deflected light rays 770, 780, 790 are deflected to propagate through the corresponding waveguides 670, 680, 690. That is, the incoupling optical element 700, 710, 720 of each waveguide deflects the light into its corresponding waveguide 670, 680, 690 and incouplings the light into its corresponding waveguide. The light rays 770, 780, 790 are deflected at an angle that causes the light to propagate through the respective waveguides 670, 680, 690 by TIR. The light rays 770, 780, 790 propagate through the respective waveguides 670, 680, 690 by TIR until they impinge on the corresponding light distribution element 730, 740, 750 of the waveguide.

[0101]

[0046] Referring now to Figure 9B, a perspective view of the example of multiple stacked waveguides of Figure 9A is illustrated. As previously described, the in-coupled light rays 770, 780, 790 are deflected by the in-coupling optical elements 700, 710, 720, respectively, and then propagate by TIR within the waveguides 670, 680, 690, respectively. The light rays 770, 780, 790 then impinge on the light distribution elements 730, 740, 750, respectively. The light distribution elements 730, 740, 750 deflect the light rays 770, 780, 790 to propagate towards the out-coupling optical elements 800, 810, 820, respectively.

[0102] In some embodiments, the light distribution elements 730, 740, 750 are orthogonal pupil expanders (OPEs). In some embodiments, the OPEs deflect or disperse the light to the out-coupling optical elements 800, 810, 820, and in some embodiments may also increase the beam or spot size of this light as it propagates to the out-coupling optical elements. In some embodiments, the light distribution elements 730, 740, 750 may be omitted and the in-coupling optical elements 700, 710, 720 may be configured to deflect the light directly to the out-coupling optical elements 800, 810, 820. For example, referring to FIG. 9A, the light distribution elements 730, 740, 750 may be replaced with the out-coupling optical elements 800, 810, 820, respectively. In some embodiments, the outcoupling optical elements 800, 810, 820 are exit pupils (EPs) or exit pupil expanders (EPEs) that direct light to the viewer's eye 210 (FIG. 7). It should be understood that the OPEs may be configured to increase the dimensions of the eyebox in at least one axis, and the EPEs may increase the eyebox in an axis that intersects, e.g., perpendicular to, the axis of the OPE. For example, each OPE may be configured to redirect a portion of the light striking the OPE to an EPE of the same waveguide, while allowing the remaining portion of the light to continue propagating down the waveguide. Again, upon impact with the OPE, another portion of the remaining light is redirected to the EPE, and the remaining portion of that portion continues to propagate further down the waveguide, etc. Similarly, in response to striking an EPE, a portion of the impinging light is directed out of the waveguide toward the user, and the remaining portion of the light continues to propagate through the waveguide until it again strikes an EP, at which point another portion of the impinging light is directed out of the waveguide, and so on. As a result, a single beam of internally coupled light may be "replicated" each time a portion of that light is redirected by an OPE or EPE, thereby forming a cloned beam field of light, as shown in Figure 6. In some embodiments, the OPE and / or EPE may be configured to modify the size of the beam of light.

[0103] Thus, referring to Figures 9A and 9B, in some embodiments, the set of waveguides 660 includes, for each component color, a waveguide 670, 680, 690, an in-coupling optical element 700, 710, 720, a light distribution element (e.g., OPE) 730, 740, 750, and an out-coupling optical element (e.g., EP) 800, 810, 820. The waveguides 670, 680, 690 may be stacked with an air gap / cladding layer between each one. The in-coupling optical element 700, 710, 720 redirects or deflects the incoming light into its waveguide (with different in-coupling optical elements receiving different wavelengths of light). The light then propagates at an angle that will result in TIR within the respective waveguide 670, 680, 690. In the example shown, light ray 770 (e.g., blue light) is deflected by the first in-coupling optical element 700 in the manner described above, then continues bouncing back down the waveguide, interacting with the light distribution element (e.g., OPE) 730 and then the out-coupling optical element (e.g., EP) 800. Light rays 780 and 790 (e.g., green and red light, respectively) pass through the waveguide 670, where light ray 780 strikes the in-coupling optical element 710 and is deflected thereby. Light ray 780 will then bounce back down the waveguide 680, via TIR, to its light distribution element (e.g., OPE) 740 and then the out-coupling optical element (e.g., EP) 810. Finally, light ray 790 (e.g., red light) passes through the waveguide 690 and strikes the light in-coupling optical element 720 of the waveguide 690. The light in-coupling optical element 720 deflects the light beam 790 so that it propagates by TIR to the light distribution element (e.g., OPE) 750 and then by TIR to the out-coupling optical element (e.g., EP) 820. The out-coupling optical element 820 then finally out-couples the light beam 790 to a viewer, who also receives the out-coupled light from the other waveguides 670, 680.

[0104] FIG. 9C illustrates a top-down plan view of the example of multiple stacked waveguides of FIGS. 9A and 9B. As shown, the waveguides 670, 680, 690 may be vertically aligned with each waveguide's associated light distribution elements 730, 740, 750 and associated out-coupling optical elements 800, 810, 820. However, as discussed herein, the in-coupling optical elements 700, 710, 720 are not vertically aligned. Rather, the in-coupling optical elements are preferably non-overlapping (e.g., spaced apart laterally as seen in the top-down view). As discussed further herein, this non-overlapping spatial arrangement facilitates the injection of light from different sources into different waveguides on a one-to-one basis, thereby allowing a particular light source to be uniquely coupled to a particular waveguide. In some embodiments, an arrangement including non-overlapping spatially separated in-coupling optical elements may be referred to as a shifted pupil system, and the in-coupling optical elements in these arrangements may correspond to sub-pupils. (Metasurfaces and Metasurface-Based Optical Elements)

[0105] Display systems may employ various optical elements to control the propagation of light. However, in some contexts, such as display systems, including head-mounted display devices (e.g., display system 80 described above with reference to FIG. 2), conventional optical elements may be undesirable or unsuitable due to their relatively heavy weight, large size, manufacturing challenges, and / or deficiencies in optical properties such as diffraction angle and diffraction efficiency.

[0106] For example, as described above with reference to FIGS. 9A-9C, display systems according to various embodiments may include optical elements (e.g., in-coupling optical elements, light distribution elements, and out-coupling optical elements), which may include diffraction gratings. Additionally, as further described above with reference to FIGS. 9A-9C, light coupled into a corresponding waveguide preferably propagates within the waveguide by total internal reflection (TIR). To achieve TIR, it may be desirable for the diffraction grating to have a relatively high diffraction angle with respect to the surface normal. In addition, high diffraction efficiency is desirable to provide good light intensity and image brightness. However, diffraction gratings capable of achieving high diffraction angles and high diffraction efficiency for visible light remain a challenge. To address these and other needs, embodiments of optical elements, e.g., diffraction gratings, disclosed herein utilize metasurfaces.

[0107] Metasurfaces may include surface structures that can locally modify the polarization, phase, and / or amplitude of light in reflection or transmission. Metasurfaces may include arrays of sub-wavelength sized and / or spaced phase-shifting elements whose patterns are configured to control the wavefront of light such that various optical functionalities can be derived therefrom, including beam shaping, lensing, beam bending, and polarization splitting. Factors that can be used to manipulate the wavefront of light include the material, size, geometry, and orientation of the surface structures. By arranging surface structures with different scattering properties on a surface, spatially variant metasurfaces can be created, throughout which the optical wavefront can be substantially manipulated.

[0108] In conventional optical elements such as lenses and waveplates, the wavefront is controlled via the propagation phase in a medium that is much thicker than the wavelength. Unlike conventional optical elements, metasurfaces instead use sub-wavelength sized resonators as phase shifting elements to induce phase changes in light. Because metasurfaces are formed from features that are relatively thin and uniform in thickness, they can be patterned across the surface using thin film processing techniques such as semiconductor processing techniques as well as direct printing techniques such as nanoimprinting techniques. An example of the substitution of conventional optical elements with metasurfaces is illustrated with reference to FIGS. 10A-10C. FIG. 10A diagrammatically illustrates a cross-sectional view of a conventional optical element, e.g., a glass axicon 1102. As illustrated, a typical conventional optical element, such as a glass axicon, formed from, e.g., a glass lens, can be several millimeters thick. In contrast, FIG. 10B diagrammatically illustrates a cross-sectional view of an optical element, e.g., a metasurface axicon 1104, which may be formed from a metal or semiconductor metasurface and disposed on a substrate, e.g., a quartz substrate. Compared to conventional axicons 1102, metasurface axicons 1104 are on the order of tens to hundreds of nanometers thick, making them suitable for optical systems requiring compact optical elements, such as head-mounted display devices. FIG. 10C illustrates a transmitted non-diffracting Bessel beam profile 1106 that results when metasurface axicons 1104 are illuminated with a collimated Gaussian left-handed circularly polarized (LCP) light beam at 550 nm wavelength. As shown, the desired beam profile 1106 can be achieved using metasurface axicons, which can be several orders of magnitude thinner compared to conventional axicons. Similar results can be obtained with various other optical elements, such as gratings. (Waveplates based on geometric phase metasurfaces)

[0109] Without being bound by any theory, when a light beam is traced along a closed cycle in the space of the polarization states of light, the dynamic phase can be obtained from the cumulative path length as well as the geometric phase. The dynamic phase obtained from the geometric phase is due to the local change in the polarization. Some optical elements that rely on the geometric phase to form a desired phase front can be referred to as Pancharatnam Berry Phase Optical Elements (PBOEs). PBOEs can be constructed from waveplate elements whose fast axis orientation depends on the spatial position of the waveplate element.

[0110] Without being limited by theory, by forming a metasurface with a geometric phase optical element, e.g., a half-wave plate formed from PBOE, with their fast axis orientation according to a function θ(x,y), an incident circularly polarized beam can be oriented as Φ g It can be completely transformed into a beam of opposite helicity with a geometric phase equal to (x,y)=+ / -2θ(x,y). By controlling the local orientation of the fast axis of the waveplate element from 0 to π, a phase pickup / delay can be achieved that covers the full 0 to 2π range while maintaining a relatively high and uniform transmission amplitude across the entire optical element, thereby providing the desired wavefront.

[0111] Examples of waveplates based on geometric phase and the resulting phase pickup / retardation and absorptance are illustrated with reference to FIGS. 11A-11D. FIG. 11A illustrates an exemplary waveplate 1100 formed from a metasurface with multiple nanobeams 1104 under top-down illumination with incident light 1108 under transverse electric (TE) polarization (with the electric field polarized perpendicular to the length of the structure) and orthogonal transverse magnetic (TM) polarization. The thickness of the resonant structure can be small compared to the free-space wavelength of the incident light 1104. In the illustrated example, the nanobeams 1104 are 120 nm wide in the x-direction and 100 nm thick in the z-direction. In the illustrated example, the nanobeams 1104 are formed from Si, which has been found to support relatively strong resonances in the wavelength range of interest, as described with reference to FIGS. 11B-11D.

[0112] Figure 11B illustrates a simulated phase wavefront resulting from the waveplate 1100 illustrated above with reference to Figure 11A. In comparison to the finite element simulation 1112 of the incident wavefront, finite element simulation 1116 shows that the wavefront of the TE-polarized beam at 550 nm is retarded by 0.14π. Wavefront simulation 1120 shows that the wavefront of the TM-polarized beam is retarded by an additional 1.15π. As a result, the phase delay between the two orthogonal polarizations is approximately π, and the beam array acts as a half-waveplate.

[0113] FIG. 11C illustrates a simulated spectrum of the phase retardation of TM-polarized versus TE-polarized beams resulting from a waveplate similar to that described above with reference to FIG. 11A. By sweeping the wavelength from 490 nm to 700 nm, the phase retardation of the waveplate varies from approximately 0.4π to 1.2π. Simulated spectra 1128, 1132, and 1136 illustrate the phase retardation for a blazed grating comprising a nanobeam array with beam widths of 100 nm, 120 nm, and 140 nm, respectively, for a nominal thickness of 100 nm for the nanobeams 1104. For comparison, simulated spectrum 1140 shows a relatively small phase retardation of 0.063π for a 100 nm thick film of calcite, a naturally birefringent crystal. The square symbols illustrate experimental measurements for an array of 120 nm beams, showing good agreement with the simulation. The inset shows an EM image of the actual fabricated blazed grating 1100.

[0114] Figure 11D illustrates simulated absorption spectra 1144 and 1148 of a waveplate with a nanobeam array under TM and TE illumination, respectively, with a beam width of 120 nm, corresponding to the phase retardation spectrum 1132 of Figure 11C. Insets 1152 and 1156 illustrate the magnetic field distribution |Hy| for TE illumination and the electric field distribution |Ey| for TM illumination, respectively, at a wavelength of 600 nm.

[0115] 11C and 11D, without being bound by any theory, the substantial variation in phase delay, e.g., as illustrated by phase delay spectrum 1132, can be attributed to a relatively strong resonance under TE illumination, as illustrated by absorption spectrum 1148, and a relatively weak second order TM resonance, as illustrated by absorption spectrum 1144. The order of the resonance is determined by the maximum field number inside the nanobeam (FIG. 11D, inset). As illustrated, the TE absorption resonance of the array, e.g., as illustrated by absorption spectrum 1148, and the associated variation in phase delay, e.g., as illustrated by phase delay spectrum 1132, can be spectrally tuned, in part, by varying the feature size, including width, of the nanobeam 1104.

[0116] In the following, with reference to Figs. 12A-12H, a structure 1200 of a geometric PB phase based on geometrically rotated waveplate elements is described. In particular, a PB phase configured as a half-waveplate with a phase delay π is described. Eight half-waveplate elements may be arranged to be equally spaced and feature a constant orientation angle difference Δθ between neighboring waveplates. For illustrative purposes, the bottom row diagrammatically depicts the rotation of the polarization vector of an incident light beam with left-handed circular polarization, i.e., |LCP> state. The middle row illustrates half-waveplate elements constructed from nanobeam arrays similar to those described with reference to Figs. 11A-11D, with their fast axes oriented at different angles θ relative to the vertical axis. The top row diagrammatically illustrates the corresponding polarization vectors of light transmitted with delay through the waveplate elements. The circular polarization and counterclockwise orientation angle of the fast axes of the waveplates are defined from the perspective of the light source.

[0117] Still referring to Figures 12A-12H, the incident light beam can be described by polarization vectors 1204 and 1208 with equal amplitudes in the x and y directions, respectively, and a phase delay of π / 2 1212 between the polarization vectors. In operation, the half-wave plate acts by shifting the phase between the two perpendicular polarizations by a phase of π. The net result for this work is to reverse the electric field steered along the slow axis and maintain the electric field along the fast axis. This action can also be viewed as the original polarization vector being flipped to its mirror image, with the fast axis acting as a mirror. Considering the helical incidence situation, where the polarization vector rotates in time, it can be seen that the action of the wave plate switches the helicity from |LCP> to |RCP> and vice versa.

[0118] Referring to the bottom row of FIG. 12A, the electric field of the incident |LCP> beam changes at an initial time t=t 0 At |LCP>, the light is steered upwards towards the positive y-axis. After a quarter optical cycle (i.e., π / 2), the light is steered along the negative y-direction, as shown by vector 1208. The action of the waveplate in the middle row of FIG. 12A is to reflect vectors 1204 and 1208 into a mirror placed in the plane of the fast axis and in the direction of light propagation. The action of this mirror is to flip vector 1204 to the positive x-direction and keep vector 1208 in its original direction. As a result, the |LCP> beam is converted to a |RCP> beam.

[0119] 12B-12H illustrate how the polarization vector of the |LCP> beam changes when the fast axis of the waveplate is rotated by angles θ of π / 4, π / 2, 3π / 4, π, 5π / 4, 3π / 2, and 7π / 4, respectively. Independent of the rotation angle, a |RCP> output beam is produced. However, referring to FIG. 12A, the produced phase retardation of vectors 1204 and 1208 is φ gFor example, as shown in FIG. 12E, when θ=π / 2, the effect of the waveplate is to flip vector 1208 from the negative y-direction to the positive y-direction while keeping vector 1204 in the same direction. This is given by φ g = 2θ = π, producing a |RCP> beam that is retarded. Thus, for the half-wave plate shown, it will have spent half an optical cycle well before reaching the state shown in FIG. 12A.

[0120] Thus, as an illustrative example, after passing through eight half-wave plate elements that are equally spaced and characterized by a constant orientation angle difference between neighbors, e.g., Δθ=π / 8, the transmitted RCP wave will have a constant phase difference Δφ between neighboring wave plates. g =π / 4. By using eight waveplate elements with fast axis orientations varying from 0 to π, phase retardation / acceleration covering the full 0 to 2π range can be achieved. However, it can be difficult to fabricate half-waveplate elements with high diffraction angles for visible light. This is because the diffraction angle depends, among other things, on the length of the period of the periodically repeating waveplate elements, and forming a relatively large number of half-waveplate elements within a relatively short period can be difficult due to space constraints. Below are embodiments of diffraction gratings in which phase retardation / acceleration covering the full 0 to 2π range can be achieved at relatively high diffraction angles and diffraction efficiencies, as well as uniformity of diffraction efficiency across a relatively wide angle of incidence. (Diffraction gratings based on geometric phase metasurfaces)

[0121] Applications of metasurfaces comprising PBOEs include diffraction gratings, e.g., blazed gratings, focusing lenses, and axicons, among various other applications. As described herein, blazed gratings are capable of steering a light beam into several diffraction orders. Blazed gratings can be configured to achieve high grating efficiency in one or more diffraction orders, e.g., the +1 and / or -1 diffraction orders, thus concentrating the refractive power in the desired diffraction orders while the residual refractive power in other orders (e.g., the zeroth order) is low. In this disclosure, various embodiments of metasurfaces comprising PBOEs configured as diffraction gratings are described. Diffraction gratings according to various embodiments have a combination of desirable optical properties, including one or more of high diffraction angles, high diffraction efficiency, a wide range of acceptance angles, and highly uniform diffraction efficiency within the range of acceptance angles. These desirable optical properties may result from a combination of various aspects of the invention, including the materials, dimensions, and geometric configurations of the elements of the metasurface.

[0122] As described herein, visible light may include light having one or more wavelengths within various color ranges, including the red, green, or blue ranges. As described herein, red light may include one or more wavelengths of light within a range of about 620-780 nm, green light may include one or more wavelengths of light within a range of about 492-577 nm, and blue light may include one or more wavelengths of light within a range of about 435-493 nm. Thus, visible may include one or more wavelengths of light within a range of about 435 nm to 780 nm.

[0123] As described herein, features that are parallel, nominally parallel, or approximately parallel, e.g., as nanobeams, lines, line segments, or unit cells, refer to features that have longitudinal directions that differ by less than about 10%, less than about 5%, or less than about 3% in the longitudinal direction. Additionally, features that are vertical, nominally vertical, or approximately vertical, refer to features that have longitudinal directions that deviate from 90 degrees in the longitudinal direction by less than about 10%, less than about 5%, or less than about 3%.

[0124] As described herein, a structure configured to diffract light, such as a diffraction grating, may diffract light in a transmission mode and / or a reflection mode. As described herein, a structure configured to diffract light in a transmission mode refers to a structure in which the intensity of the diffracted light on the side opposite the light incident side of the structure is greater than the intensity of the diffracted light on the same side of the structure as the light incident side, for example, by at least 10%, 20%, or 30%. Conversely, a structure configured to diffract light in a reflection mode refers to a structure in which the intensity of the diffracted light on the same side of the structure as the light incident side is greater than the intensity of the diffracted light on the same side of the structure as the light incident side, for example, by at least 10%, 20%, or 30%.

[0125] As described herein, a line, also referred to as a beam or nanobeam, is an elongated structure having a volume. It should be understood that the line is not limited to any particular cross-sectional shape. In some embodiments, the cross-sectional shape is rectangular.

[0126] 13A and 13B respectively illustrate a cross-sectional side view and a top-down view of a diffraction grating 1300 comprising a metasurface with a geometric phase optical element according to some embodiments. The diffraction grating 1300 comprises a two-level geometric phase metasurface. The cross-sectional side view illustrated with reference to FIG. 13A is of section AA′ illustrated in FIG. 13B. The diffraction grating 1300 includes a substrate 1304 having a surface on which a metasurface 1308 is formed, the metasurface 1308 being configured to diffract light having a wavelength within the visible spectrum. The metasurface 1308 includes one or more first lines or nanobeams 1312 having a first orientation and generally extending in a first lateral direction (e.g., y-direction) and a plurality of second lines or nanobeams 1316 having a second orientation generally extending in a second direction (e.g., x-direction). The first lines or nanobeams 1312 may be considered to form a first set of nanobeams, and the second lines or nanobeams 1316 may be considered to form a second set of nanobeams. One or more of the first lines 1312 and second lines 1316 are disposed adjacent to one another in a second direction, and the first lines 1312 and second lines 1316 alternate and repeat in the second direction with a period that is less than the wavelength of light that the metasurface is configured to diffract.

[0127] Preferably, each of the first lines 1312 has the same width. In some embodiments, the second lines 1316 are stacked laterally in the y-direction between one or more of the first lines 1312 of an adjacent pair. Without being limited by theory, the one or more first lines 1312 and the second lines 1316 are oriented at an angle relative to each other, preferably to create a phase difference between the visible light diffracted by the one or more first lines 1312 and the visible light diffracted by the second line 1316, where the phase difference between the visible light diffracted by the one or more first lines 1312 and the visible light diffracted by the second line 1316 is twice the angle.

[0128] In some embodiments, similar to the waveplate combinations illustrated above with reference to Figures 12A-12H, phase pickup / delay covering the full 0-2π range can be achieved by using the phase difference caused by the relative orientation of one or more first lines 1312 with respect to the second lines 1316, which can vary from 0 to π. In some embodiments, when one of the one or more first lines 1312 and second lines 1316 is rotated by π with respect to the other, e.g., perpendicular to each other, a phase pickup / delay of 2π can be achieved between one or more first lines 1312 and second lines 1316. That is, unlike Figures 12A-12H, phase pickup / delay covering the full 0-2π range can be achieved based on a two-level geometric phase metasurface with lines oriented in simply two different directions, according to some embodiments. Advantageously, unlike FIGS. 12A-12H, by using the waveplate combination illustrated with reference to FIGS. 12A-12H, the footprint occupied by the illustrated metasurface 1308 is more compact and has a period that is less than or equal to a wavelength in the visible spectrum, which in turn enables a relatively high diffraction angle θ of the diffracted beams 1338, 1342.

[0129] The first line 1312 and the second line 1316 are formed from an optically transmissive material. As described herein and throughout the specification, a "transmissive" or "transparent" structure, e.g., a transmissive substrate, may allow at least a portion, e.g., at least 20, 30, 50, 70, or 90%, of the incident light to pass therethrough. Thus, the transparent substrate may be a glass, sapphire, or polymer substrate in some embodiments. A "reflective" structure, e.g., a reflective substrate, may reflect and have reflected therefrom at least a portion, e.g., at least 20, 30, 50, 70, 90%, or more, of the incident light.

[0130] One or more of the first lines 1312 and second lines 1316 may be described as being protrusions, ridges, flutes, or nanowires that protrude from the plane of the paper, extend along the plane of the paper, and have a width. Additionally or alternatively, the regions of separation between adjacent first lines 1312 and / or adjacent second lines 1316 may be described as being recesses, troughs, depressions, or trenches that are recessed into the plane of the paper and have a spacing. In some embodiments, the first lines 1312 and second lines 1316 are elongated rectangular structures that have a substantially rectangular cross-sectional shape in the yz plane. However, other embodiments are possible in which the first lines 1312 and second lines 1316 have a cross-sectional shape that may be in the shape of a circle, an ellipse, a triangle, a parallelogram, a rhombus, a trapezoid, a pentagon, or any suitable shape.

[0131] Below, various configurations are described, including the dimensions and geometric arrangements of one or more of the first lines 1312 and second lines 1316, the combined effect of which is to produce a grating based on geometric phase optical elements with desirable optical properties described herein, including one or more of a relatively high diffraction angle, a relatively high diffraction efficiency, a relatively wide range of acceptance angles, and a relatively uniform efficiency within the range of acceptance angles.

[0132] Still referring to FIGS. 13A and 13B , in operation, when an incident light beam 1330, e.g., visible light, is incident on the metasurface 1308 at an incidence angle α, measured normal to the surface 1304S and relative to the first line 1312, e.g., a plane extending parallel to the yz-plane, the grating 1300 partially transmits the incident light as a transmitted light beam 1334 and diffracts it at a diffraction angle θ 1 +1st order diffracted light beam at 1342 and diffraction angle θ 2 The incident light is partially diffracted as a diffracted light beam of −1 order 1338 at α, and the diffraction angle is measured relative to the same plane, e.g., the yz plane, to measure α. One or both of the diffracted light beams 1338 and 1342 are measured relative to the critical angle θ for the occurrence of total internal reflection within the substrate 1304 configured as a waveguide. TIRUpon diffracting at a diffraction angle greater than , the diffracted light beams 1338 and 1342 propagate in their respective opposite directions along the x-axis under total internal reflection (TIR) ​​until the light beam reaches the OPE / EPE 1346, which may correspond to the light distribution elements 730, 740, 750 and the outcoupling optical elements 800, 810, 820 (FIG. 9B).

[0133] According to various embodiments, one or more of the first lines 1312 and the second lines 1316 are formed from a material that provides low ohmic loss of photons such that the diffraction efficiency is at a high level. Without being bound by any theory, among other things, the ohmic loss of photons may depend on whether the first lines 1312 and / or the second lines 1316 are formed from a material that is a metal versus a semiconductor or an insulator. As described herein, whether a material is a metal, a semiconductor, or an insulator may depend on the electronic energy band structure of the material in the energy wave vector space or Ek space. The electronic energy band structure may be described as having a highest occupied molecular orbital (HOMO), which may also be referred to as a valence band, and a lowest unoccupied molecular orbital (LUMO), which may also be referred to as a conduction band. An insulator has an energy difference between the HOMO and the LUMO that is substantially greater than the energy corresponding to the wavelength range that the metasurface is configured to diffract. A semiconductor has an energy difference between the HOMO and the LUMO that is substantially comparable to the energy corresponding to the wavelength range that the metasurface is configured to diffract. As described herein, metals have zero or negative energy difference between HOMO and LUMO. As a result, metals have a substantial concentration of free or delocalized electrons. Collectively, the free or delocalized electrons can interact with light and generate plasmons, which refer to quasiparticles that cause quantization of plasma oscillations of free electrons. When at least one of the dimensions of the first line 1312 and the second line 1316, e.g., width, is sufficiently small, e.g., less than the wavelength of the incident light, the plasmons can become confined to the surface and interact strongly with the light, resulting in surface plasmons. Under some circumstances, when the frequency of the incident photons matches the natural frequency of the surface electrons, which oscillate against the restoring force of the positive atomic nuclei, surface plasmon resonance (SPR) can occur, resulting in resonant oscillation of the conduction electrons.

[0134] Without being bound by any theory, when one or more of the first lines 1312 and / or second lines 1316 are formed from a metal, ohmic loss of photons may occur, at least in part, due to plasmon resonance, which may occur at or near the SPR wavelength. Thus, in some embodiments, each of the one or more of the first lines 1312 and second lines 1316 may have a concentration of free electrons of, for example, about 1×10 19 / cm 3 Less than 1×10 18 / cm 3 Less than 1×10 17 / cm 3 Less than or about 1 × 10 16 / cm 3 The first line 1312 and the second line 1316 are preferably formed from a non-metallic material, such as a semiconductor or insulator, having a thickness less than 100 Å. However, embodiments are not so limited, and in some embodiments, one or both of the first line 1312 and the second line 1316 may be formed from a metal.

[0135] Still referring to Figures 13A, 13B, the inventors have found that in some embodiments it may be advantageous to form the first line 1312 and the second line 1316 using a semiconductor or insulator, which may provide a low level of ohmic losses resulting from plasmon generation and correspondingly increased diffraction efficiency. The resulting first line 1312 and second line 1316 impose a polarization-dependent phase shift on the transmitted light, modifying both its phase and polarization. Without being bound by any theory, when formed from a semiconductor or insulator, each of the one or more first lines 1312 and second lines 1316 may be considered a waveguide, having an effective refractive index and operating as a Fabry-Perot resonator, imposing a polarization-dependent phase shift on the transmitted light. To reduce ohmic losses resulting from plasmon generation and increase diffraction efficiency, one or more of the first lines 1312 and the second lines 1316 are formed from a material having certain material properties, including a relatively low free electron concentration and a relatively high bulk refractive index, as discussed herein.

[0136] As discussed above, in order to provide high diffraction efficiency, in addition to achieving other benefits, it may be desirable to have the first line 1312 and / or the second line 1316 formed from a material having a relatively low concentration of free electrons. Thus, when formed from a semiconductor or insulator, under various embodiments, the first line 1312 and the second line 1316 each are not intentionally doped with a free-electron generating dopant, or when intentionally doped, they have a concentration of free electrons of about 1×10 19 / cm 3 Less than 1×10 18 / cm 3 Less than 1×10 17 / cm 3 Less than or about 1×10 16 / cm 3 The doped dopant is, for example, an n-type dopant, at a concentration of less than 1000 nm. Without being bound by any theory, the relatively low dopant concentration may be advantageous, for example, in reducing ohmic losses resulting from plasmon generation and / or surface plasmon resonance, among other advantages.

[0137] Without being bound by any theory, it is believed that when the first line 1312 and / or the second line 1316 are formed from a semiconductor or insulator, ohmic losses resulting from plasmonic absorption may be reduced, but some ohmic losses still result from optical absorption resulting from photon-absorption electronic transitions, including elastic and inelastic electronic transitions. For example, optical absorption may occur when a photon having an energy above the band gap between the HOMO and LUMO of the semiconductor or insulator is absorbed, resulting in the generation of an electron-hole pair. Thus, it may be advantageous to reduce optical absorption resulting from photoabsorption electronic transitions. Thus, in some embodiments, the first line 1312 and / or the second line 1316 may have an absorption coefficient value of about 5×10 5 / cm, approximately 1×10 5 / cm, less than 5×10 4 / cm, less than 1×10 4 / cm, approximately 5×103 / cm, approximately 1×10 3 / cm, approximately 5×10 2 / cm, or within a range defined by any of the above values, for incident light having a wavelength within the visible spectrum.

[0138] Without being bound by any theory, it has been found that when the first and second lines 1312, 1316, having subwavelength feature sizes, support leaky mode resonance, they can confine light, thereby inducing a phase delay in the scattered light waves produced under TE and TM illumination. The effectiveness of the confinement of light within one or more of the first and second lines 1312, 1316 can result from being configured as a waveguide acting as a resonator, and the resulting diffraction efficiency can depend, among other factors, on the refractive index of the material of the first and second lines 1312, 1316 as well as the subwavelength dimensions.

[0139] Thus, in some embodiments, the bulk refractive index (n 1 bulk )。 In some embodiments, it may be desirable to have the first line 1312 and / or the second line 1316 formed from a material having a 1 bulk is measured at a wavelength, e.g., a visible wavelength, that the diffraction grating 1300 is configured to diffract.

[0140] Among other advantages, a relatively high refractive index may be achieved by using certain semiconductor materials to form the first line 1312 and / or the second line 1316. In some embodiments, when formed from a semiconductor material, the first line 1312 and / or the second line 1316 may be formed from an elemental Group IV material (e.g., Si, Ge, C, or Sn) or an alloy formed from Group IV materials (e.g., SiGe, SiGeC, SiC, SiSn, SiSnC, GeSn, etc.), a Group III-V compound semiconductor material (e.g., GaP, GaAs, GaN, InAs, etc.) or an alloy formed from Group III-V materials, a Group II-VI semiconductor material (CdSe, CdS, ZnSe, etc.) or an alloy formed from Group II-VI materials. Each of these materials may be crystalline, polycrystalline, or amorphous.

[0141] In some embodiments, the first line 1312 and / or the second line 1316 are formed from silicon, such as silicon, amorphous silicon, or polycrystalline silicon. When formed from silicon, it may be more easily processed or integrated using silicon processing techniques.

[0142] Among other advantages, a relatively high refractive index may also be achieved by using an insulator to form the first lines 1312 and / or second lines 1316. When formed from an insulator, one or more of the first lines 1312 and / or second lines 1316 may be formed from oxides, including transition metals such as titanium, tantalum, hafnium, zirconium, etc., including their stoichiometric and sub-stoichiometric forms, according to some embodiments. Examples of such oxides include, for example, titanium oxide, zirconium oxide, and zinc oxide.

[0143] The first line 1312 and / or the second line 1316 may also be formed from oxides, nitrides, or oxynitrides of Group IV elements, such as silicon, including their stoichiometric and substoichiometric forms, according to some other embodiments. Examples of such insulators include, for example, silicon oxide (SiO x ), silicon nitride (SiN x ), and silicon oxynitride (SiO x N y ).

[0144] In some embodiments, the first line 1312 and the second line 1316 may be formed from the same semiconductor or insulator material, which may be advantageous for simplifying the fabrication of the metasurface 1308. However, various embodiments are not so limited, and in some embodiments, the first line 1312 and the second line 1316 may be formed from different semiconductor or insulator materials.

[0145] Continuing to refer to Figures 13A and 13B, in addition to being formed from various materials as described above, one or more of the first lines 1312 and second lines 1316 have a particular combination of dimensions and act as sub-wavelength sized resonators that induce a phase shift in light.

[0146] In various embodiments, the W of the first line 1312 nano1 and the second line 1316 W nano2 Each of W is smaller than the wavelength of light that the metasurface 1308 is configured to diffract, preferably smaller than a wavelength in the visible spectrum. nano1 and W nano2 Each of the first lines 1312 has a width W in the range of 10 nm to 1 μm, 10 nm to 500 nm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm, for example 30 nm. nano1 According to some embodiments, each of the second lines 1316 has the same width W nano2According to some embodiments, one or more of the first lines 1312 and the second lines 1316 have the same width, i.e., W nano1 =W nano2 However, in some other embodiments, W nano1 and W nano2 may be substantially different. Further, in some embodiments, different ones of the one or more first lines 1312 and different ones of the second lines 1316 may have different widths.

[0147] According to some embodiments, immediately adjacent ones of the one or more first lines 1312 in the second direction are spaced apart by a regular interval s 1 In addition, one of the one or more first lines 1312 and one of the second lines 1316 that are directly adjacent to each other in the second direction are separated by a regular interval s 2 According to some embodiments, the s 1 and s 2 One or both of the first and second lines 1312 and 1316 are smaller than the wavelength for which the metasurface 1308 is configured to diffract. nano1 and h nano2 The interval s 1 , s 2 and height h nano1 and h nano2A particular combination of may be selected such that a desired range of incidence angles α (Δα), sometimes referred to as the range of acceptance angles or field of view (FOV), is obtained. As described herein, the desired range Δα may be described by a range of angles spanning negative and positive values ​​of α, outside of which the diffraction efficiency drops by more than 10%, more than 25%, more than 50%, or more than 75% relative to the diffraction efficiency at α=0. For example, if a uniform intensity of diffracted light is desired within Δα, it may be desirable to have Δα where the diffraction efficiency is relatively flat. Referring back to FIG. 13A , an incident light beam 1330 is incident on the surface of the metasurface 1308 and the waveguide 1304 at an angle α with respect to a surface normal, e.g., the yz-plane. According to some embodiments, as described above, Δα is related to an angular bandwidth for the metasurface 1308 such that the light beam 1330 within Δα is efficiently diffracted by the metasurface 1308 at a diffraction angle θ with respect to the surface normal (e.g., the yz-plane). In particular, θ is TIR At or above this, the diffracted light propagates within the substrate 1304 under total internal reflection (TIR).

[0148] It has been found that Δα may depend on the shadowing effect produced by neighbors of one or more of the first lines 1312 in the second direction and directly neighbors of the second lines 1316 in the first direction. That is, when an incident light beam 1330 is incident at an incidence angle α above a certain value, the incident light beam directed towards a feature may be blocked by directly neighboring features. For example, Δα may be determined by the relationship between s 1 / h nano1 , s 2 / h nano1 , and / or s 2 / h nano1 In various embodiments, the ratio s 1 / h nano1 , s 2 / h nano1 , and / or s 2 / h nano1is selected such that Δα is greater than 20 degrees (e.g., + / - 10 degrees), 30 degrees (e.g., + / - 15 degrees), 40 degrees (e.g., + / - 20 degrees), or 50 degrees (e.g., + / - 25 degrees), or is in a range of angles defined by any of these values. 1 / h nano1 , s 2 / h nano1 , and / or s 2 / h nano1 For example, s 1 and s 2 can be realized when s is within the range of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm, for example, 30 nm. 1 and s 2 The relatively low value of h nano1 and h nano2 has a correspondingly relatively low value.

[0149] Advantageously, according to some embodiments, the relatively high refractive index (n 1 ) allows for a relatively thin thickness or low height. Thus, in various embodiments, the first line 1312 and the second line 1316 may be, according to some embodiments, 1 Depending on the, the range may be 10 nm to 1 μm, 10 nm to 500 nm, 10 nm to 300 nm, 10 nm to 100 nm, and 10 nm to 50 nm, for example 107 nm, nano1 and h nano2 For example, h nano1 and h nano2 is n 1 is greater than 3.3, 10nm to 450nm, and n 1 As another example, the height of the first line 1312 and the second line 1316 may be between 10 nm and 450 nm, and the nanobeams are formed from silicon (e.g., amorphous or polysilicon).

[0150] According to various embodiments, s 1 and W nano1 The combination of s 1 and W nano1 The pitch (p nano1 ) is selected from the range of 10 nm to 1 μm, 10 nm to 500 nm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm. nano1 and s selected from the ranges of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm. 1 The value obtained by the sum of, say, p nano1 = 95.5 nm.

[0151] Of course, s 1 and s 2 Relatively small values ​​of h can be realized. nano1 and h nano2 has a correspondingly relatively small value. Advantageously, the relatively high refractive index n 1 forming one or more first lines 1312 and / or second lines 1316 using a material having 1 , s 2 , h nano1 , and h nano2 Relatively small values ​​of h can be obtained, as we have found. nano1 and h nano2 may be inversely proportional to the bulk refractive index of the material forming the first line 1312 and the second line 1316. Thus, for materials having bulk refractive indices between 2.0 and 2.5, between 2.5 and 3.0, between 3.0 and 3.5, and higher than 3.5, h nano1 and h nano2 In various embodiments, the high bulk refractive index n of one or more of the first lines 1312 and the second lines 1316 may be in the range of 500 nm to 1 μm, 300 nm to 500 nm, 100 nm to 300 nm, and 10 nm to 100 nm, respectively. 1 and a material having the corresponding dimension s 1 , s 2 , hnano1 , and h nano2 With a particular combination of a is correspondingly decreased, which in turn may increase the diffraction angle θ, as explained further below.

[0152] Preferably, h nano1 and h nano2 are substantially equal, which may be advantageous for processing. However, embodiments are not so limited, and nano1 and h nano2 can be substantially different.

[0153] In various embodiments, the first line 1312 and / or the second line 1316 may have a bulk refractive index (n 1 bulk ) is the refractive index n of the substrate 1304 2 Higher, i.e., n 1 bulk >n 2 In some embodiments, the substrate 1304 may be configured as a waveguide and may correspond to the waveguides 310, 300, 290, 280, 270 (FIG. 6) and / or the waveguides 670, 680, and 690 (FIG. 9A). In such applications, the substrate is preferably between that of air, but not between n 1 bulk is less than, for example, 1.5, 1.6, 1.7, 1.8, 1.9, or higher, but n 1 bulk The substrate 1304 may have a refractive index that is less than 100 nm, which may provide a benefit for increasing the Δα of a display that forms an image by outputting light from the substrate 1316. Examples of materials for forming the substrate 1304 include silica glass (e.g., doped silica glass), silicon oxynitride, transition metal oxides (e.g., hafnium oxide, tantalum oxide, zirconium oxide, niobium oxide, lithium niobate, aluminum oxide (e.g., sapphire)), plastics, polymers, or other optically transmissive materials having a suitable refractive index, for example, as described herein.

[0154] Without being bound by any theory, it is believed that when one or more of the first lines 1312 and / or the second lines 1316 have sub-wavelength dimensions as described above, the refractive index of the first lines 1312 and / or the second lines 1316a is greater than or equal to their bulk refractive index values, i.e., n 1 bulk For example, for the fundamental mode of resonance, the first line 1312 and / or the second line 1316 may deviate from about 1 (when the light is primarily in air) to about n 1 bulk (when the light is primarily in lines and / or segments) the effective refractive index n 1 eff Thus, in some embodiments, a sufficient value of n 1 eff >n 2 Therefore, in some embodiments, the materials for the first and / or second lines 1312 and 1316 and the substrate 1304 should have a bulk refractive index n 1 bulk and the refractive index n of the substrate 1304 2 The difference between (n 1 bulk -n 2 ) is selected to be sufficiently large, for example, 0.5 or higher, 1.0 or higher, 1.5 or higher, 2.0 or higher, 2.5 or higher, or 3.0 or higher.

[0155] 13A and 13B, the metasurface 1308 may be described as forming a plurality of metasurface unit cells 1320 that repeat in at least the x-direction. As described herein, a metasurface unit cell 1320 may be defined as a footprint having a minimum repeating dimension in the x-direction that includes one or more first lines 1312 and second lines 1316. By way of example, each unit cell 1320 spans a unit cell width 1320a measured from the left vertical side of the left one of the first lines 1312 of one unit cell 1320 to the left vertical side of the left one of the first lines 1312 of an immediately adjacent unit cell 1320, thereby including, in the illustrated embodiment, a pair of first lines 1312 and a row of second lines 1316 stacked in the y-direction.

[0156] As described herein, the lateral dimension of the Metasurface unit cell 1320 or the period of the repeating units of the unit cell 1320 is referred to herein as the unit cell pitch Λ a The pitch Λ a repeats at least twice at regular intervals in the x-direction across the waveguide 1304. In other words, the unit cell pitch Λ a may be the distance between the same points of the nearest neighboring unit cells 1320. In various embodiments, Λ a can be smaller than the wavelength that the grating 1300 is configured to diffract, and can be smaller than a wavelength or any wavelength in the range of about 435 nm to 780 nm. In some embodiments that are configured to diffract at least red light, Λ a can be less than a wavelength (or any wavelength) in the range of about 620-780 nm. In some other embodiments that are configured to diffract at least green light, Λ a can be less than a wavelength (or any wavelength) in the range of about 492-577 nm. In some other embodiments that are configured to diffract at least blue light, Λ a can be less than a wavelength (or any wavelength) in the range of about 435-493 nm. Alternatively, according to various embodiments, Λ acan be in the range of 10 nm to 1 μm, including 10 nm to 500 nm or 300 nm to 500 nm. It should be understood that each of the metasurfaces disclosed herein can be utilized to diffract light and can be part of a display system 250 (FIG. 6), and the display system 1000 can be configured to direct light having a narrow band of wavelengths to the metasurface. Preferably, Λ for a given metasurface is a is less than the minimum wavelength of the band of wavelengths that a light source of the display system is configured to direct at the metasurface.

[0157] In some embodiments, Λ a is the ratio mλ / (sinα+n 2 sinθ), m may be an integer (e.g., 1, 2, 3, . . . ), and α, n 2 Each of θ, α, and θ are found to have values ​​as described elsewhere herein. For example, α may be in the range Δα over 40 degrees, n 2 can be in the range of 1 to 2, and θ can be in the range of 40 to 80 degrees.

[0158] In some embodiments, Λ a may be substantially constant across the surface 1304S of the lattice 1300 formed by the plurality of unit cells. However, embodiments are not so limited, and in some other embodiments, Λ a may vary across surface 1304S.

[0159] 13B, in some embodiments, each of the second lines 1316 is at least 2, 3, 4, or more times shorter than each of the one or more first lines 1312. However, embodiments in which the second lines 1316 are longer than the one or more first lines 1312 are also possible. According to various embodiments, the one or more first lines 1312 have a length L in the range of 200 μm to 5 mm, 200 μm to 1 mm, or 1 mm to 5 mm. 1According to various embodiments, the second line 1316 may have a length L in the range of 100 nm to 500 nm, 100 nm to 300 nm, and 300 nm to 500 nm. 2 In some embodiments, the one or more first lines 1312 may have a length L that corresponds to a total lateral dimension of an optical element formed by the metasurface, e.g., a length of an incoupling or outcoupling optical element formed by the metasurface comprising the lines 1312. 1 In some embodiments, the second lines may have a unit cell pitch Λ a About 40% to about 60% of, for example, Λ a The length L is about 50% of 2 In some embodiments, L 1 is such that the one or more first lines 1312 span a distance in the y-direction corresponding to five second lines 1316. However, it should be understood that the one or more first lines 1312 may span a distance in the y-direction corresponding to more than 1, e.g., more than 10, more than 20, more than 50, or more than 100, or any suitable number of second lines 1316 in the range between any of 10, 20, and 100, according to various embodiments.

[0160] 13A and 13B, in some embodiments, each of the second lines 1316 has the same length, such that the second lines 1316 extend in the x-direction and co-terminate without intersecting with any of the one or more first lines 1312. However, embodiments in which the second lines 1316 have different lengths are also possible.

[0161] Still referring to the illustrated embodiment of FIG. 13A, the extension direction (y-direction) of the one or more first lines 1312 is approximately perpendicular to the extension direction (x-direction) of the second lines 1316. That is, the second lines 1316 are rotated relative to the one or more first lines 1312 by a rotation angle of π / 2 when viewed from the propagation direction of the incident light (i.e., into the page). However, the embodiment is not so limited, and the second lines 1316 may extend in any direction that is rotated counterclockwise by an angle smaller than π / 2 when viewed from the propagation direction of the incident light (i.e., into the page). For example, the second lines 1316 may be rotated relative to the one or more first lines 1312 in a similar manner to the nanobeams of the waveplates illustrated in FIGS. 12B-12H are rotated relative to the waveplates illustrated in FIG. 12A. For example, the second line 1316 may be rotated relative to one or more of the first lines 1312 by rotation angles θ of π / 4, π / 2, 3π / 4, π, 5π / 4, 3π / 2, and 7π / 4, respectively. Thus, when a |LCP> beam is incident on the metasurface 1308 having the first and second lines 1312 and 1316, a |RCP> output beam is produced with a resultant phase delay of the polarization vectors corresponding to TE and TM polarizations of φ g = 2θ, where θ is the change in rotation angle when the fast axis of the waveplate is rotated by the rotation angle θ. In particular, for the illustrated embodiment, a second line 1316, which is rotated by θ = π / 2 relative to the one or more first lines 1312, diffracts an incident light beam, e.g., a |LCP> beam, thereby generating a diffracted |RCP> beam, which is diffracted by the second line 1316 through an angle φ g Thus, after passing through a metasurface 1308, in which one or more alternating first and second lines 1312 and 1316 in the x-direction have a constant orientation angle difference Δθ=π / 2, as in the illustrated embodiment, the transmitted RCP wave is delayed by a constant phase difference Δφ g=π is shown between adjacent ones of one or more first lines 1312 and second lines 1316. As a result, by varying the fast axis orientation from 0 to π, phase pickup / delay covering the full 0 to 2π range can be achieved, but with a much more compact unit cell pitch and higher diffraction angles compared to the illustrated examples in Figures 12A-12H. Display Devices with Geometric Phase Metasurface-Based Gratings

[0162] As disclosed herein, in various embodiments described above, the metasurface 1308 may be implemented as an in-coupling optical element (e.g., one or more of the in-coupling optical elements 700, 710, 720 (FIG. 9A)) to in-couple incident light such that the light propagates through the substrate 1304 via total internal reflection. However, bearing in mind that the metasurface 1308 may also be configured to deflect light impinging thereon from within the substrate 1304, in some embodiments, the metasurfaces disclosed herein may be applied to form out-coupling optical elements, such as one or more of the out-coupling optical elements 570, 580, 590, 600, 610 (FIG. 6) or 800, 810, 820 (FIG. 9B), instead of or in addition to forming in-coupling optical elements at different locations on the surface 2000a. In some other embodiments, the metasurface 1308 may be utilized as a light distribution element (e.g., OPE) 730, 740, 750 (FIG. 9B). It should be understood that where different waveguides have different associated component colors, the out-coupling optical elements and / or in-coupling optical elements associated with each waveguide may have a geometric size and / or periodicity specific to the wavelength or color of light that the waveguide is configured to propagate. Thus, different waveguides may have metasurfaces with different arrangements of one or more first lines 1312 and second lines 1316. In particular, the different arrangements may depend on the wavelength or color of the incident light beam. For example, depending on the color of the incident light beam, Λ amay be configured differently according to the wavelengths that the grating 1300 is configured to diffract. For example, to diffract at least red, green, or blue light, the metasurface 1308 may have a Λ, which is less than wavelengths in the range of about 620-780 nm, less than wavelengths in the range of about 492-577 nm, and less than wavelengths in the range of about 435-493 nm, respectively. a Λ a To scale Λ, parameters such as the refractive index, width, height, and spacing of one or more of the first lines 1312 and / or second lines 1316 may be adjusted proportionately. a is sinα, n 2 , and sin θ may be kept relatively uniform for different wavelengths of incident light by compensating for one or more of

[0163] FIG. 14 illustrates a simulation 1400 of diffraction efficiency versus incidence angle α for an example grating according to various embodiments of the grating 1300 described above with reference to FIGS. 13A and 13B. In particular, the simulation 1400 shows that under transmission mode, n 2 = 1.77, Λ a = 382 nm, h nano1 =h nano2 = 107 nm, W nano1 =W nano2 = 30 nm, p nano1 = 96 nm, and s 1 1 shows the diffraction efficiency (η) of T-1 order diffracted TE polarized green light (λ=520 nm) simulated for a grating having one or more first and second lines formed from polycrystalline silicon on a substrate with α=66 nm. As shown, the range of incidence angles (Δα) or field of view (FOV) is relatively wide, exceeding about 40 degrees, outside which the diffraction efficiency η drops by about 10% from an efficiency of about 32% at α=0.

[0164] Figures 15A and 15B illustrate two-dimensional simulations 1500 and 1504 of the phase wavefront for TE-polarized 520 nm wavelength light transmitted through the diffraction grating 1300 described above with reference to Figures 13A and 13B, which corresponds to the simulation 1400 illustrated above with reference to Figure 14. In particular, simulations 1500 and 1504 correspond to illumination conditions where the angle of incidence α is 0 degrees and 20 degrees, respectively.

[0165] As described in more detail below, fabrication of the diffraction gratings disclosed herein may involve a patterning process, including photolithography and etching. The photolithography process may include depositing a mask layer, such as a photoresist and / or a hard mask (which may act as an anti-reflective coating), on or over the layer of high refractive index material in which one or more first and second lines 1312 and 1316 are formed. The mask layer may then first be developed and / or patterned into a pattern in the mask layer that serves as a template for patterning the underlying layer of high refractive index material. The underlying layer of high refractive index material is then patterned into the first and second lines using the patterned mask layer as a template. In various embodiments, the patterned mask layer is removed, thereby leaving the first and second lines. However, under some circumstances, it may be difficult or undesirable to remove the patterned mask layer from the patterned first and second lines. For example, the removal process for some mask layers may undesirably damage the surfaces of the first and second lines and / or the exposed substrate surface. Thus, the inventors have found that in some circumstances, the patterned mask layer may be left behind. In the following, with reference to Figures 16A-16D, an embodiment of a diffraction grating in which the mask layer is left behind is described.

[0166] FIG. 16A illustrates a cross-sectional side view of a grating 1600 comprising a metasurface with geometric phase optical elements, in which a mask layer is left after forming one or more first and second lines, for example by photolithography and etching, according to some embodiments. In particular, it has been found that leaving a mask layer having a relatively low refractive index can advantageously have little or no effect on the resulting optical response, including diffraction efficiency versus incidence angle (η versus α) behavior. Similar to the grating 1300 illustrated above with reference to FIGS. 13A and 13B, the grating 1600 includes a substrate 1304 having a surface 1304S on which a metasurface 1608 is formed, the metasurface 1608 being configured to diffract light having a wavelength within the visible spectrum. The metasurface 1608 includes one or more first lines 1312 extending in a first lateral direction (e.g., y-direction) and a plurality of second lines 1316 extending in a second direction (e.g., x-direction). The arrangement of the metasurface 1608 may be substantially similar to the arrangement of the metasurface 1308 illustrated above with reference to FIGS. 13A and 13B, except that in the metasurface 1608 of FIG. 16A there is a mask layer 1604 patterned over the one or more first lines 1312 and second lines 1316 as a template for etching and forming the one or more first lines 1312 and second lines 1316. According to some embodiments, the mask layer 1604 may be a photoresist or hard mask layer having a relatively low refractive index that is lower than the refractive index of the material of the one or more first lines 1312 and second lines 1316. According to some embodiments, the mask layer 1604, which may be a hard mask and / or an anti-reflective layer (ARC), has a refractive index whose value is less than about 2.0, less than about 1.8, less than about 1.6, or less than about 1.4, or whose value is within a range defined by any of these values. According to some embodiments, the mask layer 1604 may be formed from a silicon-containing or silica-containing mask layer.

[0167] 16B illustrates a simulation 1610 of diffraction efficiency (η) versus thickness of mask layer 1604 (FIG. 16A) for an example grating similar to the grating illustrated above with reference to FIGS. 13A and 13B, but in which for the simulated grating, a mask layer 1604 is disposed over one or more first lines 1312 and second lines 1316 (FIGS. 13A and 13B). In particular, simulation 1610 illustrates a simulation ... 2 = 1.77, and a SiO 2 and in transmission mode, Λ a = 382 nm, h nano1 =h nano2 = 107 nm, W nano1 =W nano2 = 30 nm, p nano1 = 96 nm, and s 1 16 shows the diffraction efficiency (η) for TE polarized green light (λ=520 nm) simulated for a diffraction grating with α=66 nm. Simulation 1610 illustrates simulated diffraction efficiency curves 1614 and 1618, corresponding to transmitted diffraction orders T1 and T-1, respectively, at α=0. Simulation 1610 illustrates that the presence of a mask layer having a thickness up to 90 nm has an almost negligible effect (about 1% or less) on the diffraction efficiency. For example, η ranges less than about 1% at α=0 for a mask layer having a thickness up to 90 nm.

[0168] FIG. 16C illustrates a simulation 1620 of diffraction efficiency (η) versus incidence angle α for an exemplary diffraction grating, simulated with reference to FIG. 16A, but where a mask layer 1604 having a fixed thickness of 20 nm is disposed on one or more of the first lines 1312 and the second lines 1316 (FIGS. 13A and 13B) for the simulated diffraction grating. The simulation 1620 illustrates simulated diffraction efficiency curves 1614 and 1618 corresponding to transmitted diffraction orders T1 and T-1, respectively. Compared to the simulation 1400 described above with reference to FIG. 14 for the T-1 diffraction order, the simulated diffraction efficiency 1628 illustrates that the presence of the 20 nm thick mask layer has an almost negligible effect (about 1% or less) on the diffraction efficiency or field of view. For example, η is about 32% at α=0, which drops by about 10% at +α=21 degrees.

[0169] FIG. 16D illustrates a simulation 1630 of diffraction efficiency (η) versus incidence angle α for an exemplary diffraction grating, simulated with reference to FIG. 16A, but with a mask layer 1604 having a fixed thickness of 40 nm disposed on one or more of the first lines 1312 and the second lines 1316 (FIGS. 13A and 13B) for the simulated diffraction grating. The simulation 1630 illustrates simulated diffraction efficiency curves 1624 and 1628 corresponding to transmitted diffraction orders T1 and T-1, respectively. Compared to the simulation 1400 described above with reference to FIG. 14 for the T-1 diffraction order, the simulated diffraction efficiency 1628 illustrates that the presence of the 20 nm thick mask layer has an almost negligible effect (about 1% or less) on the diffraction efficiency or field of view. For example, η is about 32% at α=0, which drops by about 10% at +α=21 degrees.

[0170] Below, with reference to Figures 17A-20, simulations of diffraction efficiency (η) versus incidence angle α for example diffraction gratings formed from different high refractive index materials are illustrated, where the diffraction gratings are configured to diffract green light in the visible spectrum (e.g., λ = 520 nm).

[0171] 17A and 17B illustrate simulations 1700, 1704 of diffraction efficiency (η) versus angle of incidence (α) for an example diffraction grating formed from amorphous silicon and configured to diffract green visible light. In particular, simulations 1700 and 1704 show the diffraction efficiency (η) for T-1 order diffracted TE and TM polarized green light, respectively, at λ=520 nm, incident on the diffraction grating at α relative to the surface normal. Simulations 1700 and 1704 illustrate the diffraction efficiency (η) for one or more first and second lines formed from amorphous silicon, 2 = 1.77, and under transmission mode, Λ a = 382 nm, h nano1 =h nano2 = 90 nm, W nano1 =W nano2 = 30 nm, p nano1 = 96 nm, and s 1 = 66 nm. The complex refractive index used for the simulation was n = 5.02 + 0.363i. As shown, for TE polarized green light, the range of incidence angles (Δα) or field of view (FOV) is relatively wide at about 50 (<-30 to > +20) degrees, outside which the diffraction efficiency η drops by about 10% from an efficiency of about 28% at α = 0.

[0172] FIG. 18 illustrates a simulation 1400 of diffraction efficiency (η) versus incidence angle (α) for an example grating formed from polycrystalline silicon and configured to diffract green visible light at λ=520 nm, according to some embodiments. Simulation 1400 is the same simulation as illustrated in FIG. 14, but replotted using a different x-axis range for easy comparison with FIGS. 17A, 19, and 20. The complex index of refraction used for the simulation was n=4.41+0.182i. As illustrated, the range of incidence angles (Δα) or field of view (FOV) is relatively wide, exceeding about 40 degrees, outside which the diffraction efficiency η drops by about 10% from an efficiency of about 32% at α=0.

[0173] 19 illustrates a simulation 1900 of diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from silicon carbide (SiC) and configured to diffract green light, according to some embodiments. In particular, simulation 1900 shows the diffraction efficiency (η) of T-1 order diffracted TE polarized green light at λ=520 nm incident on the grating at α relative to the surface normal. Simulation 1900 illustrates one or more first and second lines formed from silicon carbide (SiC) at n 2 = 1.77, and under transmission mode, Λ a = 382 nm, h nano1 =h nano2 = 260 nm, W nano1 =W nano2 = 65 nm, p nano1 = 96 nm, and s 1 = 31 nm. The complex refractive index used for the simulation was n = 2.65 + 0.005i. As shown, for TE polarized green light, the range of incidence angles (Δα) or field of view (FOV) is relatively wide, about 40 (about -20 to about +20) degrees, outside of which the diffraction efficiency η drops by about 10% from an efficiency of about 27% at α = 0.

[0174] FIG. 20 illustrates a silicon nitride (e.g., Si 3 N 4 2 illustrates a simulation 2000 of diffraction efficiency (η) versus angle of incidence (α) for an exemplary diffraction grating formed from silicon nitride (e.g., Si 3 N 4 ) one or more first lines and second lines formed from 2 = 1.77, and under transmission mode, Λ a = 382 nm, h nano1 =h nano2 = 300 nm, W nano1=W nano2 = 60 nm, p nano1 = 96 nm, and s 1 = 36 nm. The complex refractive index used for the simulation was n = 2.20 + 0.002i. As shown, for TE polarized green light, the range of incidence angles (Δα) or field of view (FOV) is relatively wide > 40 (approximately < -30 to approximately +10) degrees, outside which the diffraction efficiency η drops by approximately 10% from an efficiency of approximately 21% at α = 0.

[0175] Below, with reference to Figures 21-24, simulations of diffraction efficiency (η) versus angle of incidence (α) are illustrated for example diffraction gratings formed from different high refractive index materials, where the diffraction gratings are configured to diffract blue light in the visible spectrum (e.g., λ = 455 nm).

[0176] 21 illustrates a simulation 2200 of diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from polycrystalline silicon and configured to diffract blue light, according to some embodiments. In particular, simulation 2100 shows the diffraction efficiency (η) of T-1 order diffracted TE polarized blue light at λ=455 nm incident on the grating at α relative to the surface normal. Simulation 2100 illustrates one or more first and second lines formed from polycrystalline silicon, each of which is 2 = 1.77, and under transmission mode, Λ a = 334 nm, h nano1 =h nano2 = 75 nm, W nano1 =W nano2 = 30 nm, p nano1 = 96 nm, and s 1 = 66 nm. The complex refractive index used for the simulation was n = 4.67 + 0.636i. As shown, for TE polarized green light, the range of incidence angles (Δα) or field of view (FOV) is relatively wide > 40 (approximately < -30 to approximately > +10) degrees, outside which the diffraction efficiency η drops by approximately 10% from an efficiency of approximately 22% at α = 0.

[0177] 22 illustrates a simulation 2200 of diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from amorphous silicon and configured to diffract blue light, according to some embodiments. In particular, simulation 2200 shows the diffraction efficiency (η) of T-1 order diffracted TE polarized blue light at λ=455 nm incident on the grating at α relative to the surface normal. Simulation 2200 illustrates one or more first and second lines formed from amorphous silicon, each of which is 2 = 1.77, and under transmission mode, Λ a = 334 nm, h nano1 =h nano2 = 60 nm, W nano1 =W nano2 = 30 nm, p nano1 = 96 nm, and s 1 = 66 nm. The complex refractive index used for the simulation was n = 5.363 + 1.015i. As shown, for TE polarized green light, the range of incidence angles (Δα) or field of view (FOV) is relatively wide > 40 (approximately < -30 to approximately > +10) degrees, outside which the diffraction efficiency η drops by approximately 10% from an efficiency of approximately 18% at α = 0.

[0178] 23 illustrates a simulation 2300 of diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from silicon carbide and configured to diffract blue light, according to some embodiments. In particular, simulation 2300 shows the diffraction efficiency (η) of T-1 order diffracted TE polarized blue light at λ=455 nm incident on the grating at α relative to the surface normal. Simulation 2300 illustrates one or more first and second lines formed from silicon carbide at n 2 = 1.77, and under transmission mode, Λ a = 334 nm, h nano1 =h nano2 = 220 nm, W nano1 =W nano2 = 60 nm, p nano1 = 96 nm, and s 1= 36 nm. The complex refractive index used for the simulation was n = 2.67 + 0.01i. As shown, for TE polarized green light, the range of incidence angles (Δα) or field of view (FOV) is relatively wide, about 40 (about -18 to about +18) degrees, outside of which the diffraction efficiency η drops by about 10% from the efficiency of about 30% at α = 0.

[0179] 24 illustrates a simulation 2400 of diffraction efficiency (η) versus angle of incidence (α) for an example grating formed from silicon nitride and configured to diffract blue light, according to some embodiments. In particular, simulation 2400 shows the diffraction efficiency (η) of T-1 order diffracted TE polarized blue light at λ=455 nm incident on the grating at α relative to the surface normal. Simulation 2400 illustrates one or more first and second lines formed from silicon nitride at n 2 = 1.77, and under transmission mode, Λ a = 334 nm, h nano1 =h nano2 = 260 nm, W nano1 =W nano2 = 60 nm, p nano1 = 96 nm and s 1 = 36 nm. The complex refractive index used for the simulation was n = 2.24 + 0.007i. As shown, for TE polarized green light, the range of incidence angles (Δα) or field of view (FOV) is relatively wide, about 20 (about -8 to about +12) degrees, outside of which the diffraction efficiency η drops by about 10% from an efficiency of about 21% at α = 0.

[0180] FIG. 25 illustrates a top-down view of a grating 2500 comprising a metasurface having a geometric phase optical element according to some other embodiments. It should be understood that some embodiments of metasurfaces disclosed herein can be formed from two to four sets of nanobeams, each extending in a different direction. FIGS. 13A-13B illustrate a metasurface having two sets of nanobeams, and FIG. 25 illustrates a metasurface having four sets of nanobeams. In particular, the grating 2500 of FIG. 25 comprises a four-level geometric phase metasurface. Similar to the grating 1300 described above with reference to FIGS. 13A and 13B, the grating 2500 includes a substrate, e.g., a waveguide, on which a metasurface is formed that is configured to diffract light having a wavelength within the visible spectrum. The metasurface includes one or more first lines 2512 extending in a first lateral direction (e.g., y-direction) and a plurality of second lines 2516 extending in a second direction (e.g., x-direction). One or more first lines 2512 and second lines 2516 are disposed adjacent to one another in the second direction, and the first lines 2512 and second lines 2516 alternate in the second direction with a period that is less than the wavelength in the visible spectrum for which the metasurface is configured to diffract. In some embodiments, the second lines 2516 are stacked laterally in the y-direction between adjacent pairs of first lines 2512. Various features of the one or more first lines 1312 and second lines 1316 of the diffraction grating 2500 are similar to the corresponding features of the diffraction grating 1300 described above with reference to Figures 13A and 13B, with the following differences.

[0181] Unlike the diffraction grating 1300 described above with reference to Figures 13A and 13B, the diffraction grating 2500 further comprises one or both of a plurality of third lines 2514, each extending in a third direction, and a plurality of fourth lines 2518, each extending in a fourth direction. Each of the first, second, third, and fourth directions may be different from each other. The plurality of third lines 2514 may be considered to form a third set of nanobeams, and the plurality of fourth lines 2518 may be considered to form a fourth set of nanobeams. The third lines 2514 are disposed on a first side of the second lines 2516 and are interposed in a second direction (e.g., in the x-axis direction) between one or more of the first lines 2512 and the second lines 2516. The fourth line 2518 is disposed on a second side of the second line 2516 opposite the first side and is interposed in a second direction (e.g., the x-direction) between one or more other first lines 2512 and the second line 2516.

[0182] Unlike the diffraction grating 1300 described above with reference to Figures 13A and 13B, the diffraction grating 2500 may have only one first line 2512. In some other embodiments, the diffraction grating 2500 may have multiple first lines 2512, for example, a pair of first lines such as the diffraction grating 1300 described above with reference to Figures 13A and 13B.

[0183] In some embodiments, the third lines 2514 have the same length and / or the fourth lines 2518 have the same length such that the third lines 2514 and / or the fourth lines 2518 co-terminate in the third and fourth directions, respectively. However, other embodiments are possible in which different ones of the third lines 2514 and / or different ones of the fourth lines 2518 do not co-terminate. Additionally, in some embodiments, the co-terminating third lines 2514 and the co-terminating fourth lines 2518 have the same length. However, in other embodiments, the co-terminating third lines 2514 and the co-terminating fourth lines 2518 have different lengths.

[0184] In some embodiments, adjacent ones of the third lines 2514 are separated by a regular interval in a first direction (e.g., the y-direction) and / or adjacent ones of the fourth lines 2518 are separated by a regular interval in the first direction. However, other embodiments are possible in which the third lines 2514 and / or the fourth lines 2518 are not separated by a regular interval. Additionally, in some embodiments, the regularly spaced third lines 2514 and the regularly spaced fourth lines 2518 have the same regular interval. However, in other embodiments, the regularly spaced third lines 2514 and the regularly spaced fourth lines 2518 have different intervals.

[0185] In some embodiments, the third lines 2514 have the same width and / or the fourth lines 2518 have the same width. However, in other embodiments, the third lines 2514 and / or the fourth lines 2518 have different widths. In addition, in some embodiments, the widths of the third lines 2514 having the same width and the fourth lines 2518 having the same width are the same. However, in some other embodiments, the widths of the third lines 2514 having the same width and the fourth lines 2518 having the same width are different. In addition, in some embodiments, the third lines 2514 and the fourth lines 2518 have the same width as one or both of the first lines 2512 and the second lines 2416.

[0186] In some embodiments, the third lines 2514 extend in a third direction that is rotated counterclockwise relative to the one or more first lines 2512 by an angle that is less than the minimum rotation angle of the second lines 2516 relative to the one or more first lines 2512 when viewed from the propagation direction of the incident light (e.g., into the plane of the paper). In some embodiments, the second lines 2516 are rotated 90° or π / 2 relative to the one or more first lines 2512, and the third lines 2514 are rotated 45° or π / 4 relative to the one or more first lines 2512. Additionally, the fourth lines 2518 extend in a fourth direction that is rotated counterclockwise relative to the one or more first lines 2512 by an angle that is greater than the minimum rotation angle of the second lines 2516 relative to the one or more first lines 2512 when viewed from the propagation direction of the incident light. In some embodiments, the second line 2516 is rotated 90 degrees or π / 2 relative to the one or more first lines 2512, and the third line 2514 is rotated 135 degrees or 3π / 4 relative to the one or more first lines 2512.

[0187] In some embodiments, similar to the waveplate combinations illustrated above with reference to Figures 12A-12H, the phase difference caused by the relative orientation of one or more of the first line 2512, second line 2516, third line 2514, and fourth line 2518 may vary from 0 to π. When the third line 2514, fourth line 2518, and second line 2516 are rotated by π / 4, 3π / 4, and π with respect to the one or more of the first line 2512, phase pickup / delay of π / 2, 3π / 2, and 2π, respectively, may be achieved, such that phase pickup / delay covering the full 0 to 2π range may be achieved, according to some embodiments. As a result, by varying the fast axis orientation from 0 to π, phase pickup / delay covering the full 0 to 2π range may be achieved, but with a much more compact unit cell pitch and higher diffraction angles compared to the examples illustrated in Figures 12A-12H. (Display devices based on geometric phase metasurfaces)

[0188] In various embodiments of the display system (e.g., referring back to FIGS. 9A and 9B), the waveguide set 1200 may include a metasurface grating configured to operate in a transmissive mode. In various embodiments, the waveguide set 1200 includes waveguides 670, 680, 690 corresponding to each component color (R, G, B), which in turn form within or on each of the internal coupling optical elements 700, 710, 720 that may include or correspond to the gratings 1300, 2500, described above with reference to FIGS. 13A and 13B and 25. The waveguides 670, 680, 690 additionally have formed therein or thereon one of the light distribution elements (e.g., OPE) 730, 740, 750 and / or outcoupling optical elements (e.g., EPE) 800, 810, 820, respectively, that include or correspond to the EPE / OPE 1346, described above with reference to Figures 13A and 13B. In operation, in some embodiments, when an incident light beam 1330, e.g., visible light, is incident on the metasurface 1308 at an incidence angle α, the grating 1300, 2500 diffracts the incident light into a diffracted light beam 1342, 1338 at a diffraction angle θ 2 One or both of the diffracted light beams 1338 and 1342 are diffracted by an index of refraction n 2 For the occurrence of total internal reflection for the substrate 1304, which is configured as a waveguide having a critical angle θ TIR When the light is diffracted at a diffraction angle exceeding the condition θ 2 >θ TIR and θ 1 >θ TIR are satisfied, one or both of the diffracted light beams 1338 and 1342 propagate in their respective opposite directions along the x-axis by total internal reflection (TIR). Subsequently, in some embodiments, the diffracted light beam 1346 is coupled into the substrate 1304 under the TIR mode until it reaches an orthogonal pupil expander (OPE) 1346 or an exit pupil expander (EPE) 1346, described above with reference to Figures 9A and 9B.

[0189] 13A and 13B and 25, the gratings 1300, 2500 are configured to operate in a transmissive mode, although other embodiments are possible. In some other embodiments, referring back to FIGS. 9A and 9B, some display devices include a set of waveguides 1200 having a grating configured to operate in a reflective mode. In these embodiments, the set of waveguides 1200 includes waveguides 670, 680, 690 corresponding to each component color (R, G, B), which in turn form within or on each of the internal coupling optical elements 700, 710, 720 including or corresponding to the grating 2600, the cross-sectional view of which is described with respect to FIG. The diffraction grating 2600 includes a metasurface 2608 configured to diffract light in a reflective mode, and differs from the diffraction gratings 1300, 2500 described above with reference to Figures 13A and 13B and 25 in that, in operation, light incident on the side of the metasurface 2608 is diffracted toward the same side as the light incident side of the metasurface 2608. The diffraction grating 2600 includes a substrate 1304 having a surface 1304S on which a metasurface 1308 configured to diffract light having wavelengths within the visible spectrum is formed. The metasurface 2608 includes one or more first lines 1312 and a plurality of second lines 1316 whose material composition, dimensions, and lateral arrangement on the surface 1304S are similar to those of the diffraction gratings 1300, 2500 described above with reference to Figures 13A and 13B and 25, respectively. In particular, although a top-down view is not shown, the metasurface 1308 includes one or more first lines 1312 extending in a first lateral direction (e.g., the y-direction) and a plurality of second lines 1316 extending in a second direction (e.g., the x-direction), where the one or more first lines 1312 and second lines 1316 are arranged adjacent to one another in the second direction and alternate in the second direction with a periodicity that is less than a wavelength in the visible spectrum.

[0190] Without being limited by theory, in some embodiments, similar to the metasurface 1308 described above with reference to Figures 13A and 13B, in the metasurface 2608 of the grating 2600, the one or more first lines 1312 and the second lines 1316 are oriented at an angle relative to each other, causing a phase difference between the visible light diffracted by the one or more first lines 1312 and the visible light diffracted by the second lines 1316, where the phase difference between the visible light diffracted by the one or more first lines 1312 and the visible light diffracted by the second lines 1316 is twice the angle.

[0191] 25, in some other embodiments, the diffraction grating 2600 further comprises one or both of a plurality of third lines 2514, each extending in a third direction, and a plurality of fourth lines 2518, each extending in a fourth direction. Additionally, in some embodiments, the illustrated diffraction grating 2600 has only one first line 2512.

[0192] Various other possible arrangements of one or more of the first lines 1312, second lines 1316, third lines 2514, and fourth lines 2518 described above with reference to Figures 13A, 13B, and 25 may also be implemented in the diffraction grating 2600 of Figure 26, the detailed description of which will be omitted.

[0193] 13A and 13B and 25, in grating 2600, an optically transmissive spacer layer 2604 may be formed over or on, e.g., directly on, one or more of the first lines 1312 and second lines 1316. In addition, a reflective layer 2612 may also be formed over or on, e.g., directly on, one or more of the first lines 1312 and second lines 1316 and / or over or on, e.g., directly on, the spacer layer 2604.

[0194] In some embodiments, the spacer layer 2604 is formed directly over and in contact with one or more of the first lines 1312 and second lines 1316 such that the one or more of the first lines 1312 and second lines 1316 are embedded in the spacer layer 2604. The spacer layer 2604 has a height or thickness h that exceeds the height of the one or more of the first lines 1312 and second lines 1326 by a height d. spacer The height d may be in the range of 5 nm to 1 μm, 5 nm to 500 nm, or 10 nm to 300 nm, according to some embodiments. In some embodiments, the spacer layer 2604 has a refractive index n of the bulk material in which the one or more first lines 1312 and second lines 1316 are formed. 1 bulk Lower, refractive index n spacer In some embodiments, n spacer is also the refractive index n of the substrate 1304 2 In various embodiments, n spacer has a refractive index of 1-2, 1.1-1.7, or 1.1-1.5, e.g., 1.2. In various embodiments, the spacer layer 2604 may be formed from materials that may be deposited by spin coating, including poly(methyl methacrylate) (PMMA), spin-on glass, e-beam resist or photoresist, and polymers. It should be appreciated that when deposited by spin coating, the as-spin-coated material may undergo viscous flow, and thus the thickness of the spacer layer 2604 over the one or more first lines 1312 and second lines 1316 may be thinner as compared to the thickness of the spacer layer 2604 in areas where the one or more first lines 1312 and second lines 1316 are not present, e.g., where the spacer layer 2604 is formed directly on the substrate 1304.

[0195] In some embodiments, the reflective layer 2612 is formed directly on the spacer layer 2604. In this embodiment, the reflective layer 2612 is separated from the one or more first lines 2612 and second lines 2616 by the spacer layer 2604 formed thereover. However, in some other embodiments, the reflective layer 2612 may be formed directly on the one or more first lines 1312 and second lines 1316. In these embodiments, the one or more first lines 1312 and second lines 1316 may be embedded in the reflective layer 2612. That is, the reflective layer 2612 may fill the space between the one or more first lines 1312 and / or second lines 1316.

[0196] The reflective layer 2612 may be formed from a material that substantially reflects light, e.g., visible light, such as a metal or metallic material, such as aluminum, silver, gold, and copper. In some other embodiments, the reflective layer 2612 may be formed from other light reflective materials, such as a reflective polymer. When formed directly over the spatial layer 2604, the height or thickness h of the reflective layer 2612 may be 0.1 mm or less. r may be sufficiently thick to be substantially non-transparent and non-porous, for example, greater than 150 nm, greater than 500 nm, or greater than 1 μm, or within ranges between these thicknesses. In embodiments where the reflective layer 2612 is formed directly over the one or more first lines 1312 and second lines 1316, the thickness of the reflective layer 2612 may be sufficient to embed the one or more first lines 1312 and second lines, with a thickness of h nano1 and h nano2 It may exceed.

[0197] 27 illustrates a simulation 2700 of diffraction (η) versus incidence angle (α) for an example grating according to various embodiments of the grating 2600 described above with reference to FIG. 26. In particular, the simulation 2700 illustrates one or more first and second lines formed from polycrystalline silicon, 2 = 1.77, and under reflection mode, Λ a = 382 nm, h nano1 =h nano2= 50 nm, W nano1 =W nano2 = 30 nm, p nano1 = 95.5 nm, s 1 Figure 1 shows the diffraction efficiency (η) of T-1 order diffracted TE polarized green light (λ=520 nm) simulated for a grating with α=65.5 nm, and d=50 nm. As shown, the range of incidence angles (Δα) or field of view (FOV) is relatively wide, exceeding about 45 degrees (-25 to +20 degrees), outside of which the diffraction efficiency η drops off by about 10% from an efficiency of about 40% at α=0. (Methods for fabricating geometric phase metasurfaces)

[0198] In the following, methods of fabricating geometric phase metasurfaces are described. In some embodiments, the geometric phase metasurfaces can be fabricated by using deposition of a high refractive index material onto a lower refractive index substrate 1304 to form one or more first lines 1312 and second lines 1316, followed by patterning using lithography and etching processes. In some other embodiments, the geometric phase metasurfaces can be fabricated by using deposition of a high refractive index material onto a lower refractive index substrate 1304 of one or more first lines 1312 and second lines 1316, followed by patterning using nanoimprinting techniques.

[0199] 28A-28D respectively illustrate cross-sectional views of intermediate structures 2800A-2800D at various stages of fabrication of a diffraction grating having a geometric phase metasurface using lithography and etching, according to some embodiments. Referring to intermediate structure 2800A of FIG. 28A, the method includes providing a substrate 1304 having a surface 1304S suitable for forming a metasurface 1308 thereon. Substrate 1304 includes an optically transmissive material having a refractive index n2 and various other material attributes as described above with reference to FIGS. 13A and 13B. The method additionally includes providing a substrate 1304 having a surface 1304S suitable for forming a metasurface 1308 thereon. Substrate 1304 includes an optically transmissive material having a refractive index n2 and various other material attributes as described above with reference to FIGS. 13A and 13B. 1 bulkand various other material attributes as described above with reference to FIGS. 13A and 13B. The high index layer 1310, when patterned as described above with reference to FIGS. 13A and 13B, is suitable for forming one or more first lines 1312 and second lines 1316. The high index layer 1310 may be deposited using any suitable technique, such as chemical vapor deposition (CVD), including plasma-based CVD processes such as plasma-enhanced chemical vapor deposition (PECVD) and thermal-based CVD processes such as low-pressure chemical vapor deposition (LPCVD), according to some embodiments. The high index layer 1310 may also be deposited using physical vapor deposition (PVD), evaporation, and atomic layer deposition, among other techniques. The method additionally includes forming a mask layer 1604A on the high index layer 1310. The mask layer 1604A may be formed of or include one or more layers of a material suitable for providing a template for subsequent etching of the underlying high index layer 1310. In some embodiments, the mask layer 1604A may be a photoresist, which may be spin coated followed by a post bake. In some other embodiments, the mask layer 1604 may include multiple layers, including a hard mask layer formed on the high refractive index layer 1310 and a photoresist layer formed on the hard mask layer. The hard mask layer may be included, for example, when the photoresist layer may not provide sufficient etch selectivity during the subsequent etch pattern transfer to the underlying high refractive index layer 1310. The hard mask layer may also act as an anti-reflective coating to reduce reflection during the subsequent exposure process. In some embodiments, the hard mask layer may be a film deposited by either a spin coated polymer or deposition technique for depositing the high refractive index layer 1310. When included, the hard mask layer may provide better etch selectivity than the overlying photoresist layer. In some embodiments, the photoresist may be a positive photoresist or a negative photoresist.A positive photoresist is a type of photoresist in which the portions of the photoresist exposed to light become soluble in a photoresist developer, while a negative resist is a type of photoresist in which the portions of the photoresist exposed to light become insoluble in a photoresist developer.

[0200] In some embodiments, the photoresist and / or hard mask layer may be formed from a material including silicon or silicon oxide that may have sufficient etch selectivity to the high index layer 1310 such that the photoresist and / or hard mask layer remains relatively intact through etching of the underlying high index layer 1310. In these embodiments, the silicon or silicon oxide containing photoresist and / or hard mask layer may remain on top of the one or more first lines and / or second lines after patterning, as described above with reference to FIG.

[0201] Referring to intermediate structure 2800B in FIG. 28B, after deposition and post-deposition bake, the method includes patterning the photoresist layer of the mask layer 1604 by selectively exposing portions of the photoresist to a pattern of light. Exposure to light, e.g., coherent UV light or an electron beam, creates chemical changes, e.g., polymer cross-linking, in the photoresist, which allows the exposed portions of the photoresist to be selectively removed by a developer solution for a positive photoresist, or the unexposed portions of the photoresist to be selectively removed by a developer solution for a negative photoresist. Upon selective removal, the resulting patterned mask photoresist remains on the high refractive index layer 1310, thereby serving as a template for subsequent patterning of the underlying hard mask layer, when included, e.g., by etching. The resulting intermediate structure 2800C shows the patterned mask layer 1604, which includes the patterned photoresist and, optionally, the patterned hard mask layer, when included.

[0202] With reference to intermediate structure 2800C of FIG. 28C, the patterned mask layer 1604 may be used as a template to etch the underlying high index layer 1310 into one or more first lines 1312 extending in a first lateral direction (e.g., y-direction) and a plurality of second lines 1306 extending in a second direction (e.g., x-direction), as described in more detail above with reference to FIGS. 13A and 13B. In various embodiments, the high index layer 1310 may be etched, for example, anisotropically dry etched. The etching process employed may have suitable selectivity to the mask layer 1604 and / or substrate 1304 such that portions of the high index layer 1310 are removed without prematurely removing the mask layer 1604 and / or unnecessarily damaging exposed portions of the substrate 1304.

[0203] Referring to intermediate structure 2800D, in some embodiments, the mask layer 1604 on one or more of the first lines 1312 and the second lines 1316 is removed therefrom. The resist portions of the mask layer 1604 may be removed, for example, by using a liquid resist stripper or an oxygen-based plasma in a process referred to as ashing. If desired, the underlying hard mask layer, when included, may then be removed using a wet or dry etching process that selectively removes the hard mask without substantially affecting the one or more of the first lines 1312 and the second lines 1316 or the substrate 1304. However, in some embodiments, such as those described above with reference to FIG. 16A, the mask layer 1604, for example, photoresist / hard mask or hard mask, may be left without being removed.

[0204] 29A-29D respectively illustrate cross-sectional views of intermediate structures 2900A-2900D at various stages of fabrication of a diffraction grating with a geometric phase metasurface nanoimprint technique, according to some embodiments. In some embodiments, the method of forming intermediate structures 2900A, 2900C, and 2900D of Figs. 29A, 29C, and 29D, respectively, is similar to the method of forming intermediate structures 2800A, 2800C, and 2800D of Figs. 28A, 28C, and 28D, respectively. However, the method of forming intermediate structure 2900B of Fig. 29B is different from the method of forming intermediate structure 2800B of Fig. 28B, and the differences are described below.

[0205] Referring to the intermediate structure 2900B in FIG. 29B, unlike the method described above with reference to FIG. 28B, instead of patterning the photoresist layer by selectively exposing and removing parts of the photoresist using light or an electron beam, in the illustrated embodiment, a nanoimprint template 2904 or nanoimprint mold having a predetermined topological pattern according to the formation of one or more first lines 1312 and second lines 1316 is brought into contact with the imprint resist of the mask layer 1604A. In some embodiments, the template 2904 is pressed into the imprint resist formed from a thermoplastic polymer at a temperature, for example above the glass transition temperature of the imprint resist, thereby transferring the pattern of the template 2904 to the softened imprint resist. After cooling, the template 2904 is separated from the imprint resist, and the patterned resist is left on the high refractive index layer 1310. In some other embodiments, after being pressed into the imprint resist, the imprint resist is hardened by cross-linking under UV light.

[0206] Although not shown, a reflection mode metasurface, such as the metasurface 2608 described with reference to FIG. 26, may be formed through additional processing of the intermediate structure shown in FIG. 28D or 29D. For example, a spacer layer 2604 or a reflective layer may be deposited in the open volume between the one or more first lines 1312 and the second lines 1316. In some other embodiments, the one or more first lines 1312 and the second lines 1316 may be formed by etching a trench into a blanket spacer layer 2604 or a blanket reflective layer, followed by filling the trench with the high refractive index material of the one or more first lines 1312 and the second lines 1316.

[0207] It should be understood that the substrate 1304 configured as a waveguide with a metasurface formed thereon according to various embodiments can be used to form a display system such as system 250 (FIG. 6) disclosed herein. For example, the metasurface can be utilized as an incoupling, light dispersing, and / or outcoupling optical element as described herein. In some embodiments, after processing of the metasurface, the waveguide 2000 can be optically coupled to a light pipe, such as a light pipe, for injecting image information from a spatial light modulator into the waveguide. The light pipe can be an optical fiber in some embodiments. Examples of light pipes include image injection devices 360, 370, 380, 390, 400 (FIG. 6) and scanning optical fibers. In some embodiments, multiple waveguides, each having a metasurface 1308, can be provided, and each of these waveguides can be optically coupled to one or more image injection devices. (Geometric Phase Metasurfaces with Asymmetric Optical Elements)

[0208] As described above, applications of metasurfaces comprising PBOEs include their use as diffraction gratings, e.g., blazed gratings, capable of steering a light beam into several diffraction orders. For example, as described above with respect to Figures 13A and 13B, a diffraction grating 1300 can be configured to achieve maximum grating efficiency for multiple diffraction orders, e.g., the +1 and -1 diffraction orders. For example, as described above with respect to Figures 13A and 13B, a PBOE-based blazed grating 1300 partially transmits incident light as a transmitted light beam 1334 and has a diffraction angle θ 1 +1st order diffracted light beam at 1342 and diffraction angle θ 2 diffracted light beams of −1 order 1338 at α, and the diffraction angle is measured relative to the same plane, e.g., the yz plane, to measure α. One or both of the diffracted light beams 1338 and 1342 may be configured to partially diffract the incident light as a diffracted light beam of −1 order 1338 at α, and the diffraction angle is measured relative to the same plane, e.g., the yz plane, to measure α. Due to the occurrence of total internal reflection within the substrate 1304 configured as a waveguide, one or both of the diffracted light beams 1338 and 1342 may be configured to partially diffract the incident light as a diffracted light beam of −1 order 1338 at α, and the diffraction angle is measured relative to the same plane, e.g., the yz plane, to measure α. TIR When diffracted at a diffraction angle greater than 1, the diffracted light beams 1338 and 1342 propagate in their respective opposite directions along the x-axis under total internal reflection (TIR) ​​until the light beams reach the OPE / EPE 1346, which may correspond to the light distribution elements 1214, 1224, 1234 and the outcoupling optical elements 1250, 1252, 1254 ( FIG. 9B ). However, for some applications, it may be desirable to concentrate the diffracted light into one of the multiple diffraction orders, e.g., the +1 order diffracted light 1338 or the −1 order diffracted light 1338, while reducing the other of the multiple diffraction orders, e.g., the other of the +1 order 1338 or the −1 order diffracted light 1338. For example, referring back to Figures 13A / 13B, when substrate 1304 is configured as a waveguide such that diffracted light beams 1338 and 1342 propagate along the x-axis under total internal reflection (TIR) ​​until they reach an OPE / EPE 1346 located to one side, concentrating the diffracted light into a single diffraction order provides a greater amount of light that is actually available to be output to the viewer.

[0209] 30A and 30B, a two-phase level asymmetric geometric phase metasurface configured to steer light into a particular diffraction order is illustrated. FIGS. 30A and 30B respectively illustrate a cross-sectional side view and a top-down view of a diffraction grating 3000 including a metasurface 3008 configured to diffract visible light having a wavelength, the metasurface comprising a plurality of repeating unit cells 1320a. Each unit cell comprises a first set of nanobeams comprising two or more first nanobeams 3012 that are asymmetric in the sense that at least two of the first nanobeams 3012 have different widths compared to one another. Each unit cell also comprises a second set of nanobeams comprising a plurality of second nanobeams 3016, including asymmetric second nanobeams 3016, at least two of which have different widths. The second nanobeam is disposed adjacent to the first nanobeam and separated from each other by a subwavelength interval, with the first nanobeam 3012 and the second nanobeam 3016 having different orientations. Advantageously, it has been found that metasurfaces with these asymmetric nanobeams can diffract light such that the light is more efficiently steered into one of the diffraction orders, e.g., the +1 1st diffraction order 1342 or the −1 1st diffraction order 1338, while reducing the other of the diffraction orders, e.g., the +1 1st diffraction order 1342 or the −1 1st diffraction order 1338.

[0210] In some embodiments, the diffraction grating 3000 comprises a two-level geometric phase metasurface. The cross-sectional side view illustrated with reference to FIG. 30A is of a cross section taken along line AA′ in FIG. 30B. The diffraction grating 3000 includes a substrate 1304 having a surface on which a metasurface 3008 configured to diffract light having a wavelength within the visible spectrum is formed. The metasurface 3008 includes a first line or nanobeam 3012 having a first orientation and generally extending in a first lateral direction (e.g., y-direction) and a plurality of second lines or nanobeams 3016 generally extending in a second direction (e.g., x-direction). The first lines or nanobeams 3012 may be considered to form a first set of nanobeams and the second lines or nanobeams 3016 may be considered to form a second set of nanobeams. The first lines 3012 and the second lines 3016 are disposed adjacent to one another in a second direction, and the first lines 3012 and the second lines 3016 alternately repeat in the second direction with a period, e.g., a period less than the wavelength of light that the metasurface is configured to diffract. Advantageously, compared to structures such as those in US 9,507,064, metasurfaces with spatially-varying orientations can efficiently diffract light having multiple polarizations, e.g., TE and TM polarizations.

[0211] It should be understood that the physical and optical properties of the diffraction grating 3000, including, for example, the refractive indices of the various materials and the operating principles of the grating, are similar to the various embodiments described above, for example, the diffraction grating 1300 described above with respect to Figures 13A / 13B. In addition, the unit cell pitch Λ of the diffraction grating 3000 a and the dimensions, e.g., height, length, and width, of the first nanobeam 3012 and the second nanobeam 3016 are similar to the various embodiments described above, and detailed descriptions thereof are omitted herein for brevity.

[0212] However, unlike some embodiments described above, at least one of the first nanobeams 3012 has a different width than another of the first nanobeams 3012, and at least one of the second nanobeams 3016 has a different width than another of the second nanobeams 3016. In the illustrated embodiment, the unit cells have first widths W nano1-1 and the second width W nano1-2 The unit cell further includes a first set of nanobeams including a pair of first nanobeams 3012 having a third width W nano2-1 and the fourth width W nano2-2 The second set of nanobeams includes a plurality of second nanobeams 3016 having a width of 200 nm. Thus, in the illustrated embodiment, the first set of nanobeams includes alternating nanobeams having two different widths and the second set of nanobeams includes alternating nanobeams having two different widths. However, embodiments are not so limited and the first and / or second sets of nanobeams can include additional nanobeams having other widths.

[0213] Various configurations are described below, including the dimensions and geometric arrangements of the first line 3012 and the second line 3016, the combined effect of which is to steer diffracted light into one of multiple diffraction orders while reducing other of the multiple diffraction orders, and achieve various desirable optical properties described above, including one or more of relatively high diffraction angles, relatively high diffraction efficiency, a relatively wide range of acceptance angles and relatively uniform efficiency within the range of acceptance angles, and relatively high efficiency, for both TE and TM polarization.

[0214] In particular, referring to FIG. 30A , in operation, when an incident light beam 1330, e.g., visible light, is incident on the metasurface 3008 at an incidence angle α measured relative to a plane, e.g., the yz plane, that is normal to the surface 1304S and extends parallel to the first line 1312, the grating 3000 partially transmits the incident light as a transmitted light beam and diffracts it at a diffraction angle θ 1The +1st order diffracted light beam 1342 at the 2 diffracted light beam of +1 order 1342 substantially suppresses the diffraction angle θ for the occurrence of total internal reflection within the substrate 1304 configured as a waveguide, and the diffraction angle is measured relative to the same plane, e.g., the yz plane, for measuring α. Similar to what is described above, the diffraction angle θ for the diffraction angle α for the +1 order 1342 diffracted light beam is measured relative to the critical angle θ for the occurrence of total internal reflection within the substrate 1304 configured as a waveguide. TIR Upon diffracting at a diffraction angle greater than , the diffracted light beam propagates along the x-axis under total internal reflection (TIR) ​​until the light beam reaches the OPE / EPE 1346 (not shown for clarity, see e.g., Figures 13A and 13B).

[0215] In various embodiments, the W of the first line 1312 nano1 and the second line 1316 W nano2 Each of W is smaller than the wavelength of light that the metasurface 1308 is configured to diffract, preferably smaller than a wavelength in the visible spectrum. nano1-1 , W nano1-2 , W nano2-1 , and W nano2-2 Each of is in the range of 10 nm to 1 μm, 10 nm to 500 nm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm, for example, 30 nm. nano1-1 is W nano2-1 is essentially equal to W nano1-2 is W nano2-2 In some other embodiments, W nano1-1 , W nano2-1 , W nano1-2 , and W nano2-2 Each of may be different.

[0216] According to some embodiments, directly adjacent ones of the first lines 1312 in the second direction (x-direction) are spaced apart by a spacing s 1-1 In addition, one of the first lines 1312 is separated by a different regular interval s 1-2 and s 1-313 is separated from one of the second lines 1316 on the opposite side by s 1-1 , s 1-2 , and s 1-3 Each of is smaller than the wavelength that the metasurface 3008 is configured to diffract.

[0217] According to some embodiments, immediately adjacent ones of the second lines 3016 in the first direction (y-direction) have two different widths W nano2-1 and W nano2-2 3016, which alternates with a second line 3016 having a spacing s 2-1 and s 2-2 According to some embodiments, the s 2-1 and s 2-2 Each of is smaller than the wavelength that the metasurface 3008 is configured to diffract.

[0218] Continuing to refer to FIG. 30A, the first line 3012 and the second line 3016 have a height h nano , which may be the same or different, e.g., similar in dimensions to those described above with respect to Figs. 13A / 13B, the description of which in terms of dimensions and, e.g., technical effect on the field of view (FOV), is not described herein for the sake of brevity. Furthermore, the desired ratio of spacing and height of the different nanobeams may be determined, e.g., by the spacing s 1-1 , s 1-2 , s 1-3 , s 2-1 , and s 2-2 can be realized when s is within the range of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm, for example 30 nm. 1-1 , s 1-2 , s 1-3 , s 2-1 , and s 2-2 The relatively low value of h nano1 and h nano2 has a correspondingly relatively low value.

[0219] According to various embodiments, s 1-1 and W nano1-1 Or W nano1-2 One combination of s 1-1 and W nano1-1 or W nano1-2 The pitch (p nano1 ) is selected from the range of 10 nm to 1 μm, 10 nm to 500 nm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm. nano1-1 , W nano1-2 and s selected from the ranges of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm. 1 For example, in some embodiments, p nano1 =95.5 nm.

[0220] Of course, s 1-1 , s 1-2 , s 1-3 , s 2-1 , and s 2-2 Relatively small values ​​of h can be realized. nano may have a correspondingly relatively small value. Advantageously, the relatively high refractive index n 1 By forming the first line 1312 and / or the second line 1316 using a material with 1-1 , s 1-2 , s 1-3 , s 2-1 , and s 2-2 , h nano can be obtained, which, as we have found, is the quantity h nano may be inversely proportional to the bulk refractive index of the material forming the first line 3012 and the second line 3016. Thus, for materials having bulk refractive indices between 2.0 and 2.5, between 2.5 and 3.0, between 3.0 and 3.5, and higher than 3.5, h nanoIn various embodiments, the high bulk refractive index n of the first line 3012 and the second line 3016 can be in the range of 500 nm to 1 μm, 300 nm to 500 nm, 100 nm to 300 nm, and 10 nm to 100 nm, respectively. 1 and the corresponding dimensions 1-1 , s 1-2 , s 1-3 , s 2-1 and s 2-2 , h nano A particular combination of materials has an overall pitch Λ a may be correspondingly decreased, which in turn increases the diffraction angle θ, as explained further below.

[0221] 31A and 31B illustrate simulations 3100, 3104 of diffraction efficiency (η) versus angle of incidence (α) for an exemplary diffraction grating formed from polycrystalline silicon and configured to diffract green visible light. In particular, simulations 3100 and 3104 show the diffraction efficiency (η) for T+1 (3114, FIG. 31A) and T-1 (3118, FIG. 31A) order diffracted TE polarized green light at λ=520 nm and T+1 (3124, FIG. 31B) and T-1 (3128, FIG. 31B) order TM polarized green light at λ=520 nm, respectively, incident on the diffraction grating at α relative to the surface normal. Simulations 3100 and 3104 show the diffraction efficiency (η) for n first and second lines formed from polycrystalline silicon. 2 = 1.77, and under transmission mode, Λ a = 382 nm, h nano1 = 107 nm, W nano1-1 =W nano2-1 = 30 nm, and W nano1-2 =W nano2-2 = 45 nm, s 1-1 = 58 nm, s 1-2 = 23 nm, s 1-3 = 35 nm, s 2-1 =s 2-2 = 58 nm.

[0222] As illustrated in FIG. 31A, for TE polarization, the grating 3000 diffracts the incident light relatively efficiently into the T+1 order diffracted beam 3114 while reducing the T-1 order diffracted beam 3118, with corresponding diffraction efficiencies greater than 50% and about 10% at α=0, respectively. For T+1 order TE polarized green light, the range of incidence angles (Δα) or field of view (FOV) is relatively wide, about 50 (about 20 to >+20) degrees, outside which the diffraction efficiency η drops from greater than 50% efficiency at α=0 to about 10% or more. As illustrated in FIG. 31B, for TM polarization, the grating 3000 diffracts the incident light relatively uniformly between the T+1 order diffracted beam 3124 and the T-1 order diffracted beam 3128, with corresponding diffraction efficiencies less than 20% at α=0.

[0223] 32A and 32B respectively illustrate simulated diffraction efficiency (η) versus angle of incidence (α) for an exemplary grating formed from amorphous silicon for TE and TM polarized green light, according to some embodiments. In particular, simulations 3200 and 3204 show the diffraction efficiency (η) for T+1 (3214, FIG. 32A) and T-1 (3218, FIG. 32A) order diffracted TE polarized green light at λ=520 nm and T+1 (3224, FIG. 32B) and T-1 (3228, FIG. 32B) order TM polarized green light at λ=520 nm, respectively, incident on the grating at α relative to the surface normal. Simulations 3200 and 3204 show the diffraction efficiency (η) for n first and second lines formed from amorphous silicon. 2 = 1.77, and under transmission mode operation, Λ a = 382 nm, h nano = 85 nm, W nano1-1 =W nano2-1 = 25 nm and W nano1-2 =W nano2-2 = 40 nm, s 1-1 = 63 nm, s 1-2 = 25 nm, s 1-3 =38 nm, s 2-1 =s 2-2 = 63 nm.

[0224] As illustrated in FIG. 32A, for TE polarization, the grating 3000 diffracts the incident light relatively efficiently into the T+1 order diffracted beam 3214 while reducing the T-1 order diffracted beam 3218, with corresponding diffraction efficiencies of about 42% and about 13% at α=0, respectively. For T+1 order TE polarized green light, the range of incidence angles (Δα) or field of view (FOV) is relatively wide >40 (<-30 to >+10) degrees, outside which the diffraction efficiency η drops by about 10% or more from greater than 40% efficiency at α=0. As illustrated in FIG. 32B, for TM polarization, the grating 3000 diffracts the incident light relatively evenly between the T+1 order diffracted beam 3224 and the T-1 order diffracted beam 3228, with corresponding diffraction efficiencies of greater than 15% at α=0.

[0225] 33A and 33B respectively illustrate simulated diffraction efficiency (η) versus angle of incidence (α) for an exemplary grating formed from amorphous silicon for TE and TM polarized green light, according to some embodiments. In particular, simulations 3300 and 3304 show the diffraction efficiency (η) for T+1 (3314, FIG. 33A) and T-1 (3318, FIG. 33A) order diffracted TE polarized green light at λ=520 nm and T+1 (3324, FIG. 32B) and T-1 (3328, FIG. 32B) order TM polarized green light at λ=520 nm, respectively, incident on the grating at α relative to the surface normal. Simulations 3300 and 3304 show the diffraction efficiency (η) for n diffracted TE polarized green light at λ=520 nm and n diffracted TM polarized green light at λ=520 nm, respectively, incident on the grating at α relative to the surface normal. 2 = 1.77, and under transmission mode, Λ a = 382 nm, h nano1 85nm, W nano1-1 =W nano2-1 = 30 nm and W nano1-2 =W nano2-2 = 45 nm, s 1-1 = 58 nm, s 1-2 = 23 nm, s 1-3 = 35 nm, s 2-1 =s 2-2 = 58 nm.

[0226] As illustrated in FIG. 33A, for TE polarization, the grating 3000 diffracts the incident light relatively efficiently into the T+1 order diffracted beam 3314 while reducing the T-1 order diffracted beam 3318, with corresponding diffraction efficiencies of about 39% and about 13% at α=0, respectively. For T+1 order TE polarized green light, the range of incidence angles (Δα) or field of view (FOV) is relatively wide >40 (<-30 to >+10) degrees, outside which the diffraction efficiency η drops by about 10% or more from greater than 35% efficiency at α=0. As illustrated in FIG. 33B, for TM polarization, the grating 3000 diffracts the incident light relatively evenly between the T+1 order diffracted beam 3324 and the T-1 order diffracted beam 3328, with corresponding diffraction efficiencies of greater than 15% at α=0.

[0227] Various exemplary embodiments of the present invention are described herein. Reference is made to these examples in a non-limiting sense. They are provided to illustrate the more broadly applicable aspects of the invention. Various modifications may be made to the invention described, and equivalents may be substituted without departing from the true spirit and scope of the invention.

[0228] For example, although advantageously utilized with AR displays that provide images across multiple depth planes, the augmented reality content disclosed herein may also be displayed by systems that provide images on a single depth plane and / or with virtual reality displays. In some embodiments where multiplexed image information (e.g., light of different colors) is directed into the waveguide, multiple metasurfaces may be provided on the waveguide, e.g., one metasurface active for each color of light. In some embodiments, the pitch or periodicity and / or geometric size of the protrusions that form the metasurface may vary across the metasurface. Such metasurfaces may be active in redirecting different wavelengths of light depending on the geometry and pitch at which the light impinges on the metasurface. In some other embodiments, the geometry and pitch of the metasurface features are configured to vary such that deflected light rays, even those of similar wavelengths, propagate away from the metasurface at different angles. It should also be understood that multiple separated metasurfaces may be disposed across the substrate surface, with each of the metasurfaces having the same geometry and pitch in some embodiments, or at least some of the metasurfaces having different geometry and / or pitch than other metasurfaces in some other embodiments.

[0229] Although advantageously applied to displays, such as wearable displays, metasurfaces can also be applied to a variety of other devices where a compact, low-profile light redirecting element is desired. For example, metallic surfaces can be applied to form the light redirecting portions of optical plates (e.g., glass plates), optical fibers, microscopes, sensors, watches, cameras, and image projection devices in general.

[0230] In addition, many modifications may be made to adapt a particular situation, material, composition of matter, process, process acts or steps to the objective, spirit or scope of the present invention. Moreover, as will be understood by those skilled in the art, each of the individual variations described and illustrated herein has separate components and features that can be readily separated from or combined with the features of any of the other several embodiments without departing from the scope or spirit of the present invention. All such modifications are intended to be within the scope of the claims associated with this disclosure.

[0231] The present invention includes a method that may be implemented using the device. The method may include the act of providing such a suitable device. Such provision may be implemented by a user. In other words, the act of "providing" merely requires the user to obtain, access, approach, locate, configure, activate, power on, or otherwise act to provide the required device in the method. The methods described herein may be carried out in any order of the described events that is logically possible, as well as the described order of events.

[0232] Exemplary aspects of the invention have been described above, along with details regarding material selection and manufacturing. As to other details of the invention, these can be understood in conjunction with the above-referenced patents and publications, and generally understood or understood by those skilled in the art. The same may be true with respect to method-based aspects of the invention in terms of additional acts as generally or theoretically adopted.

[0233] For ease of description, various words are used herein to indicate the relative location of features. For example, various features may be described as being "on," "over," "to the side of," "higher" or "lower" other features. Other words of relative location may also be used. All such words of relative location assume that the aggregate structure or system formed by the features as a whole is in a certain orientation as a reference point for purposes of description, but it should be understood that when used, the structures may be positioned parallel, inverted, or in any number of other orientations.

[0234] In addition, although the present invention has been described with reference to several examples that optionally incorporate various features, the present invention is not limited to those described or indicated as being considered with respect to each variation of the present invention. Various modifications may be made to the invention described, and equivalents may be substituted (whether described herein or not included for some brevity) without departing from the true spirit and scope of the invention. In addition, when a range of values ​​is provided, it is to be understood that all intervening values ​​between the upper and lower limits of that range, and any other stated or intervening values ​​within that stated range, are encompassed within the present invention.

[0235] It is also contemplated that any optional features of the described inventive variations may be described and claimed independently or in combination with any one or more of the features described herein. Reference to a singular item includes the possibility that there are multiple identical items. More specifically, as used herein and in the claims associated therewith, the singular forms "a," "an," "said," and "the" include multiple referents unless specifically stated otherwise. In other words, the use of articles allows for "at least one" of the subject item in the above description as well as in the claims associated with this disclosure. Furthermore, it is noted that such claims may be drafted to exclude any optional element. Thus, this statement is intended to serve as a predicate for the use of such exclusive language, such as "only," "only," and the like, in connection with the recitation of claim elements, or the use of a "negative" limitation.

[0236] Without using such exclusive terms, the term "comprising" in the claims associated with this disclosure is intended to permit the inclusion of any additional elements, regardless of whether a given number of elements are recited in such claim or whether the addition of features can be considered to change the nature of the elements recited in such claim. Except as specifically defined herein, all technical and scientific terms used herein are to be given their broadest possible commonly understood meanings while maintaining the validity of the claims.

[0237] The scope of the present invention is not limited to the examples provided and / or the present specification, but rather is limited only by the scope of the terms of the claims associated with this disclosure. Indeed, the novel apparatus, methods, and systems described herein may be embodied in various other forms. Furthermore, various omissions, substitutions, and changes in the form of the systems and methods described herein may be made without departing from the spirit of the present disclosure. For example, although blocks are presented in a given arrangement, alternative embodiments may implement similar functionality with different components and / or circuit topologies, and some blocks may be deleted, moved, added, sub-divided, combined, and / or modified. Each of these blocks may be implemented in a variety of different ways. Any suitable combination of elements and acts of the various embodiments described above may be combined to provide further embodiments. The various features and processes described above may be implemented independently of each other or combined in various ways. All suitable combinations and sub-combinations of features of the present disclosure are intended to be within the scope of the present disclosure. The present specification also provides, for example, the following items: (Item 1) 1. An optical system comprising: the optical system comprises a metasurface configured to diffract visible light having a wavelength, the metasurface comprising a plurality of repeating unit cells, each unit cell consisting of two to four sets of nanobeams; a first set of nanobeams is formed by one or more first nanobeams; a second set of nanobeams is formed by a plurality of second nanobeams disposed adjacent to the one or more first nanobeams and separated from one another by sub-wavelength spacings; the one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuth directions; The unit cells are repeated at a period of about 10 nm to 1 μm or less. Optical system. (Item 2) 2. The optical system of claim 1, wherein the one or more first nanobeams and the second nanobeam are directed at an angle relative to each other, resulting in a phase difference between visible light diffracted by the one or more first nanobeams and visible light diffracted by the second nanobeam. (Item 3) 2. The optical system of claim 1, wherein the phase difference is twice the angle. (Item 4) 2. The optical system of claim 1, wherein the wavelengths in the visible spectrum correspond to blue light, green light, or red light. (Item 5) 2. The optical system of claim 1, wherein the one or more first nanobeams and the second nanobeam are oriented in azimuth directions rotated approximately 90 degrees relative to each other. (Item 6) Item 2. The optical system of item 1, wherein each of the first nanobeams has the same width. (Item 7) Item 2. The optical system of item 1, wherein each of the second nanobeams has the same width. (Item 8) 2. The optical system of claim 1, wherein each of the first nanobeams within each of the second nanobeams has the same spacing between respective ones of the first and second nanobeams. (Item 9) 2. The optical system of claim 1, wherein the unit cells repeat with a period equal to or less than the wavelength, the wavelength being within the visible spectrum. (Item 10) 2. The optical system of claim 1, wherein the one or more first nanobeams and the second nanobeam have a height less than the wavelength. (Item 11) Item 2. The optical system of item 1, wherein the one or more first nanobeams and the second nanobeam are formed from a material whose bulk refractive index is greater than 2.0 at the wavelength. (Item 12) Item 2. The optical system of item 1, wherein the one or more first nanobeams and the second nanobeam are formed from a semiconductor material or an insulating material. (Item 13) Item 2. The optical system of item 1, wherein the one or more first nanobeams and the second nanobeam are formed from a material comprising silicon. (Item 14) Item 14. The optical system of item 13, wherein the one or more first nanobeams and the second nanobeam are formed from a material selected from the group consisting of polycrystalline silicon, amorphous silicon, silicon carbide, and silicon nitride. (Item 15) 2. The optical system of claim 1, wherein the one or more first nanobeams and the second nanobeam are configured to diffract the visible light at a diffraction angle greater than 50 degrees relative to a surface normal plane with a diffraction efficiency greater than 10%. (Item 16) Item 16. The optical system of item 15, wherein the one or more first nanobeams and the second nanobeam are configured to diffract light at the diffraction efficiency for incident light having a range of incidence angles greater than 40 degrees. (Item 17) Item 17. The optical system of item 16, wherein the surface normal plane extends in the first azimuthal direction. (Item 18) Item 18. The optical system of item 17, wherein the one or more first nanobeams and the second nanobeam are configured to diffract light in a transmission mode, and an intensity of diffracted light on a side opposite to a light incident side of the one or more first nanobeams and the second nanobeams is greater than an intensity of diffracted light on a side the same as the light incident side of the one or more first nanobeams and the second nanobeams. (Item 19) Item 18. The optical system of item 17, wherein the one or more first nanobeams and the second nanobeam are configured to diffract light in a reflection mode, and an intensity of diffracted light on a side same as a light incident side of the one or more first nanobeams and the second nanobeams is greater than an intensity of diffracted light on an opposite side to the light incident side of the one or more first nanobeams and the second nanobeams. (Item 20) 2. The optical system of claim 1, wherein the one or more first nanobeams and the second nanobeam are formed on a substrate and are formed from a material whose bulk refractive index is at least 0.5 greater than the refractive index of the substrate. (Item 21) 21. The optical system of claim 20, wherein the substrate has a refractive index greater than 1.5. (Item 22) 21. The optical system of claim 20, wherein the substrate is configured such that light diffracted by the one or more first nanobeams and the second nanobeam propagates in the second direction under total internal reflection. (Item 23) 2. The optical system of claim 1, wherein the one or more first nanobeams and the second nanobeam have a substantially rectangular cross-sectional shape. (Item 24) Item 2. The optical system of item 1, wherein the one or more first nanobeams comprise a pair of first nanobeams. (Item 25) 25. The optical system of claim 24, wherein the one or more first nanobeams are immediately adjacent to a pair of nanobeams such that the second nanobeam is directly interposed between adjacent pairs of first nanobeams. (Item 26) 2. The optical system of item 1, wherein the one or more first nanobeams consist of one first nanobeam. (Item 27) 2. The optical system of claim 1, further comprising a third set of nanobeams formed by a plurality of third nanobeams elongated in a different orientation relative to the first one or more first nanobeams and the plurality of second nanobeams, the third nanobeam being interposed between the one or more first nanobeams and the second nanobeams. (Item 28) 27. The optical system of claim 26, wherein the third nanobeams have the same length such that the third nanobeams are co-terminus. (Item 29) Item 28. The optical system of item 27, wherein adjacent ones of the third nanobeams are separated by a constant space in the first azimuthal direction. (Item 30) Item 28. The optical system of item 27, wherein the one or more first nanobeams span a distance in the first azimuthal direction corresponding to a plurality of third nanobeams. (Item 31) Item 28. The optical system of item 27, wherein each of the third nanobeams has the same width and the spacing between individual ones of the third nanobeams has the same width. (Item 32) 28. The optical system of item 27, wherein the third nanobeam extends in a third azimuthal direction, which, when viewed from the propagation direction of the incident light, is rotated counterclockwise relative to the one or more first nanobeams by an angle that is smaller than a minimum counterclockwise rotation angle of the second nanobeam relative to the one or more first nanobeams. (Item 33) 28. The optical system of item 27, further comprising a fourth set of nanobeams formed by a plurality of fourth nanobeams elongated in a different orientation relative to the one or more first nanobeams, the plurality of second nanobeams, and the plurality of third nanobeams, the fourth nanobeam being positioned on a side of the second nanobeam opposite to the side on which the third nanobeam is positioned in the second azimuthal direction. (Item 34) Item 34. The optical system of item 33, wherein the fourth nanobeam extends in a fourth azimuthal direction, which, when viewed from the propagation direction of the incident light, is rotated counterclockwise relative to the one or more first nanobeams by an angle that exceeds a minimum counterclockwise rotation angle of the second nanobeam relative to the one or more first nanobeams. (Item 35) Item 35. The optical system of item 34, wherein the fourth azimuth direction and the third azimuth direction are rotated approximately 90 degrees relative to each other. (Item 36) 2. The optical system of claim 1, wherein the one or more first nanobeams and the second nanobeam comprise a bilayer, the bilayer comprising a lower layer having a first refractive index and an upper layer having a second refractive index lower than the first refractive index. (Item 37) Item 37. The optical system of item 36, wherein the upper layer is formed from a material having a refractive index less than about 2.0. (Item 38) Item 37. The optical system of item 36, wherein the upper layer comprises silicon or carbon. (Item 39) 2. The optical system of claim 1, wherein the one or more first nanobeams and the second nanobeam are embedded in a transparent spacer layer. (Item 40) 40. The optical system of claim 39, wherein the transparent spacer layer has a refractive index less than the refractive index of a bulk material of the one or more first nanobeams and the second nanobeam. (Item 41) Item 14. The optical system of item 1, wherein a metallic reflective layer is formed over the one or more first nanobeams and the second nanobeam. (Item 42) 2. The optical system of claim 1, further comprising a waveguide configured to propagate visible light, the waveguide comprising a substrate having the metasurface thereon, the one or more first nanobeams and the second nanobeam being arranged to diffract light at a diffraction angle relative to a direction of incident light and cause the diffracted light to propagate within the substrate under total internal reflection. (Item 43) 43. The waveguide of claim 42, wherein the substrate is formed from a material whose refractive index is less than the bulk refractive index of a material from which the one or more nanobeams and the second nanobeam are formed, thereby causing the diffracted light to propagate within the substrate under total internal reflection. (Item 44) Item 43. The waveguide of item 42, wherein the diffraction angle is greater than 50 degrees. (Item 45) Item 43. The waveguide of item 42, wherein the substrate is formed from a material whose refractive index is at least 0.5 less than the bulk refractive index of the material from which the one or more nanobeams and the second nanobeam are formed. (Item 46) Item 43. The waveguide of item 42, wherein the substrate has a refractive index greater than 1.5. (Item 47) The optical system is a head mounted display device configured to project light to an eye of a user and display augmented reality image content, the head mounted display device comprising: a frame configured to be supported on a head of the user; a display disposed on the frame; Equipped with At least a portion of the display comprises: one or more waveguides, the one or more waveguides being transparent and positioned at a location in front of an eye of the user when the user is wearing the head mounted display device, whereby the transparent portions transmit light from a portion of an environment in front of the user to the user's eye to provide a view of the portion of the environment in front of the user; One or more light sources; At least one diffraction grating; Equipped with 2. The optical system of claim 1, wherein the at least one diffraction grating is configured to couple light from the light source into or out of the one or more waveguides, the diffraction grating comprising a metasurface. (Item 48) Item 48. The device of item 47, wherein the one or more light sources comprise a fiber scanning projector. (Item 49) Item 48. The device of item 47, wherein the display is configured to project light into the user's eye to present image content to the user at multiple depth planes. (Item 50) 1. A method of fabricating an optical system, the method comprising: Providing a substrate; forming a metasurface on the substrate comprising a plurality of unit cells; Including, The unit cell is composed of 2 to 4 sets of nanobeams, and forming the unit cell includes: forming a first set of nanobeams comprising one or more first nanobeams; forming a second set of nanobeams adjacent to the one or more first nanobeams; Including, the second set of nanobeams comprises a plurality of second nanobeams separated from one another by sub-wavelength spacing; the one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuth directions; The unit cells repeat with a period of about 10 nm to 1 μm or less. (Item 51) Item 51. The method of item 50, wherein forming the one or more first nanobeams and forming the second nanobeam comprises lithographically defining the first and second nanobeams. (Item 52) Item 51. The method of item 50, wherein forming the one or more first nanobeams and forming the second nanobeam comprises forming the first and second nanobeams by nanoimprinting. (Item 53) Item 51. The method of item 50, wherein forming the one or more first nanobeams and forming the second nanobeam are performed simultaneously. (Item 54) Item 51. The method of item 50, wherein the one or more first nanobeams have the same width. (Item 55) Item 51. The method of item 50, wherein the second nanobeam of each unit cell has the same width. (Item 56) Item 51. The method of item 50, wherein the unit cell has a period equal to or less than a wavelength in the visible spectrum. (Item 57) 1. An optical system comprising: The optical system comprises a metasurface configured to diffract visible light having a wavelength, the metasurface comprising a plurality of repeating unit cells; Each unit cell is a first set of nanobeams formed by one or more first nanobeams; and a second set of nanobeams formed by the plurality of second nanobeams; Equipped with the plurality of second nanobeams are disposed adjacent to the one or more first nanobeams and are separated from one another by sub-wavelength spacings; the one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuth directions; The unit cell repeats with a period equal to or less than the wavelength. Optical system. (Item 58) Item 58. The optical system of item 57, further comprising a light source configured to emit light at said wavelength onto said metasurface. (Item 59) Item 59. The optical system of item 58, further comprising a spatial light modulator configured to modulate light from the light source and output the modulated light to the metasurface. (Item 60) Item 58. The optical system of item 57, wherein the wavelengths correspond to blue light, green light, or red light.

Claims

1. An optical system comprising: the optical system comprises a metasurface configured to diffract visible light having a wavelength; the metasurface comprises a plurality of repeating unit cells; Each unit cell is a first set of nanobeams, wherein two or more of the nanobeams in the first set have different widths; a second set of nanobeams, two or more of the nanobeams in the second set having different widths, the nanobeams in the second set being disposed adjacent to the nanobeams in the first set and separated from each other by a sub-wavelength spacing; Equipped with The optical system, wherein the first set of nanobeams and the second set of nanobeams have different orientations.

2. The optical system of claim 1, wherein the first set of nanobeams comprises a pair of first nanobeams each having a first width and a second width, and the second set of nanobeams comprises alternating second nanobeams having a third width and a fourth width.

3. The optical system of claim 1, wherein the first set of nanobeams and the second set of nanobeams have heights less than the wavelength.

4. The optical system of claim 1, wherein the first set of nanobeams comprises a pair of first nanobeams, and the second set of nanobeams is between first nanobeams of pairs of adjacent unit cells.

5. An optical system as described in any one of claims 1 to 4, wherein the first set of nanobeams and the second set of nanobeams are formed from a material whose bulk refractive index is greater than 2.0 at the wavelength.

6. The optical system of claim 1, wherein the first set of nanobeams and the second set of nanobeams are formed on a substrate and are formed from a material whose bulk refractive index is at least 0.5 greater than the refractive index of the substrate.

7. The optical system of claim 6, wherein the substrate has a refractive index greater than 1.

5.

8. An optical system as described in claim 6 or claim 7, wherein the substrate is configured so that light diffracted by the first set of nanobeams and the second set of nanobeams propagates in a second direction under total internal reflection.

9. The optical system of claim 1, wherein the first set of nanobeams and the second set of nanobeams are formed from a semiconductor material.

10. The optical system of claim 1, wherein the unit cells are repeated with a period in the range of 10 nm to 1 μm.

11. The optical system of claim 1, wherein the first set of nanobeams and the second set of nanobeams are directed at an angle of 90 degrees to each other.

12. The optical system of claim 1, wherein the first set of nanobeams and the second set of nanobeams are configured to diffract visible light incident on a surface of the metasurface such that visible light having an angle of incidence greater than +20 degrees or less than -20 degrees has a diffraction efficiency that is reduced by more than 10% relative to the diffraction efficiency of visible light having an angle of incidence of 0 degrees, the angle of incidence being the angle between the visible light and a plane perpendicular to the surface.

13. A light source configured to emit light at said wavelength onto said metasurface; and a spatial light modulator configured to modulate light from the light source and output the modulated light to the metasurface; The optical system of claim 1 further comprising:

14. The optical system of claim 1, wherein the wavelengths correspond to blue light, green light, or red light.

15. The optical system of claim 1, wherein the first set of nanobeams and the second set of nanobeams are configured to diffract visible light into a single order of diffracted light.

16. A head mounted display device configured to project light onto a user's eye and display augmented reality image content, the head mounted display device comprising: a frame configured to be supported on a head of the user; a display disposed on the frame; Equipped with At least a portion of the display comprises: one or more waveguides, the one or more waveguides being transparent, the one or more waveguides being positioned at a location in front of an eye of the user when the user wears the head mounted display device, whereby the transparent portions transmit light to the user's eyes and provide a view of a portion of the environment in front of the user; one or more light sources; At least one diffraction grating; Equipped with the at least one diffraction grating is configured to couple visible light from the one or more light sources into the one or more waveguides or to couple light out of the one or more waveguides, the diffraction grating comprising a metasurface configured to diffract the light from the one or more light sources, the light having a wavelength; the metasurface comprises a plurality of repeating unit cells; Each unit cell is a first set of nanobeams, wherein two or more of the nanobeams in the first set have different widths; a second set of nanobeams, two or more of the nanobeams in the second set having different widths, the nanobeams in the second set being disposed adjacent to the nanobeams in the first set and separated from each other by a sub-wavelength spacing; Equipped with A head mounted display device, wherein the first set of nanobeams and the second set of nanobeams have different orientations.

17. The display device of claim 16, wherein the one or more light sources comprise a fiber scanning projector.

18. A display device as described in claim 16 or claim 17, wherein the display is configured to project light into the user's eye with multiple levels of wavefront divergence corresponding to multiple depth planes.

19. A method of fabricating a metasurface, the method comprising: Providing a substrate; forming a metasurface on the substrate, the metasurface having a plurality of unit cells; Including, forming the metasurface comprises: forming a first set of nanobeams comprising two or more first nanobeams having different widths; forming a second set of nanobeams comprising two or more second nanobeams having different widths, the second set of nanobeams disposed adjacent to the first set of nanobeams and separated from one another by sub-wavelength spacings; wherein the first set of nanobeams and the second set of nanobeams have different orientations.

20. The method of claim 19, wherein forming the first set of nanobeams and forming the second set of nanobeams are performed simultaneously.

Images