Diffraction gratings formed by metasurfaces with differently directed 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 disclosure of each of these priority documents is 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 technology has 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 can 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 input, while augmented reality or "AR" scenarios typically involve the presentation of digital or virtual image information as an augmentation to the user's visualization of the real world around them. Mixed reality or "MR" scenarios are a type of AR scenario and typically involve virtual objects 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 AR technology views a real-world park-like setting 20 featuring people, trees, a building 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. Due to 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 positioned adjacent to the one or more first nanobeams and separated from each other by subwavelength 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 one or more first nanobeams and second nanobeams 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 eyes and display augmented reality image content, the head-mounted display device including a frame configured to be supported on the user's head. The display device also 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 positioned in front of the user's eyes 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 eyes and provides a view of the portion of the environment in front of the user. The display device also includes one or more light sources. The display device further includes at least one diffraction grating configured to couple light from the light sources 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 for fabricating an optical system includes providing a substrate and forming a metasurface on the substrate, the metasurface comprising a plurality of unit cells. Forming the metasurface includes forming unit cells consisting of two to four sets of nanobeams. 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. Forming the second set of nanobeams includes forming a plurality of second nanobeams separated from each other by subwavelength 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 approximately 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, two or more of the first nanobeams having different widths. Each unit cell additionally includes a second set of nanobeams, two or more of the second nanobeams having different widths. The second nanobeams are positioned adjacent to the first nanobeam and separated from each other by a subwavelength spacing. Furthermore, the first nanobeam and the second nanobeam of a unit cell have different orientations.

[0012] According to another embodiment, a head-mounted display device is configured to project light to a user's eyes and display augmented reality image content, the head-mounted display device including a frame configured to be supported on the user's head. The display device also 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 positioned in front of the user's eyes when the user wears the head-mounted display device, such that 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. The display device also includes one or more light sources. The display device further includes at least one diffraction grating configured to couple light from the light sources 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 for fabricating a metasurface includes providing a substrate. The method additionally includes forming a metasurface having a plurality of unit cells on the substrate. Forming the metasurface includes forming a first set of nanobeams comprising two or more first nanobeams having different widths. Forming the metasurface also includes forming a second set of nanobeams comprising two or more second nanobeams having different widths, the second nanobeams being positioned adjacent to the first nanobeams and separated from each other by a subwavelength spacing. The first nanobeams and 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 two to four 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 spacing; the one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuthal directions; The unit cells are repeated at a period of approximately 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 the visible light diffracted by the one or more first nanobeams and the 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 one 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 one of embodiments 1-6, 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 each of the first and second nanobeams. 9. An optical system according to any of embodiments 1-7, 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 one of embodiments 1-9, wherein the one or more first nanobeams and the second nanobeam have a height that is less than the wavelength. 11. An optical system according to any of embodiments 1-10, wherein the one or more first nanobeams and second nanobeams are formed from a material whose bulk refractive index is greater than 2.0 at the wavelength. 12. An optical system according to any one 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 one of embodiments 1-12, wherein the one or more first nanobeams and the second nanobeam are formed from a silicon-containing material. 14. The optical system of any of embodiments 1-13, wherein the one or more first nanobeams and second nanobeams are formed from a material selected from the group consisting of polycrystalline silicon, amorphous silicon, silicon carbide, and silicon nitride. 15. An optical system described in any of embodiments 1-14, wherein the one or more first nanobeams and second nanobeams are configured to diffract visible light at a diffraction angle greater than 50 degrees relative to the surface normal plane with a diffraction efficiency greater than 10%. 16. The optical system of embodiment 15, wherein the one or more first nanobeams and second nanobeams are configured to diffract light at a diffraction efficiency for incident light having a range of incident angles greater than 40 degrees. 17. An optical system as described in embodiment 16, wherein the surface normal plane extends in the first azimuthal direction. 18. An optical system as described in embodiment 17, wherein the one or more first nanobeams and 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 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 second nanobeams. 19. An optical system as described in embodiment 17, wherein the one or more first nanobeams and 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 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 second nanobeams. 20. An optical system according to any of embodiments 1-19, wherein the one or more first nanobeams and second 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. 21. The optical system of embodiment 20, wherein the substrate has a refractive index greater than 1.5. 22. An optical system according to 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 the second direction under total internal reflection. 23. An optical system according to any one 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 one 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 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 co-terminate. 29. An optical system according to 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 described in any of embodiments 27-29, wherein the one or more first nanobeams span a distance corresponding to the plurality of third nanobeams in the first azimuthal direction. 31. An optical system according to 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 counterclockwise 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. 33. An optical system described in 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, a plurality of second nanobeams, and a plurality of third nanobeams, wherein the fourth nanobeam is 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 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 counterclockwise 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 azimuthal direction and the third azimuthal direction are rotated approximately 90 degrees relative to each other. 36. An optical system according to any one of embodiments 1-35, wherein the one or more first and 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. An optical system according to any one 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 that is less than the refractive index of the bulk material of the one or more first and second nanobeams. 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 nanobeams 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. It comprises a waveguide, 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 from 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. A waveguide according to 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 from which the one or more nanobeams and the second nanobeam are formed. 46. ​​The waveguide of any one 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 into 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 that are transparent and positioned at locations 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 or out of one or more waveguides, the diffraction grating comprising a metasurface according to any of embodiments 1-41; a display comprising: 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 fabricating an optical system, comprising: providing a substrate; forming a metasurface on a substrate, the metasurface comprising a plurality of unit cells, each unit cell consisting of two to four sets of nanobeams; 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 azimuthal directions; The unit cells are repeated at a period of approximately 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; 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 azimuthal directions; The unit cell repeats with a period equal to or 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 of 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, wherein 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 of 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 diffraction light. 66. An optical system 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 one 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, and the wavelength is within the visible spectrum. 69. An optical system described in any of embodiments 61-68, wherein the first nanobeam and the second nanobeam are oriented at an angle relative to each other, creating 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 heights that are smaller 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. An optical system according to any one 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 described in any of embodiments 61-77, wherein the first nanobeam and the second nanobeam are configured to diffract visible light with a diffraction efficiency greater than 10% at a diffraction angle 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 at a diffraction efficiency for incident light having a range of incident angles greater than 40 degrees. 80. The optical system of embodiment 79, wherein the surface normal plane extends in the first azimuthal direction. 81. An optical system as described in 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 the 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. An optical system as described in 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 are formed 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. An optical system according to 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. An optical system according to any one 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 a second nanobeam is directly interposed between the first nanobeams of adjacent pairs. 88. An optical system described in 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 from which the first nanobeam and the second nanobeam are formed. 90. A head-mounted display device configured to project light into 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 that are transparent and positioned at locations in front of the user's eyes when the user wears the head mounted display device such that 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 configured to couple light from a light source into or out of one or more waveguides, the diffraction grating comprising a metasurface according to any of embodiments 61-87; and a display comprising: 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 described in any of embodiments 90-91, wherein the display is configured to project light into the user's eye so as to present image content to the user on 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 being disposed adjacent to the first nanobeams and separated from each other by 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 includes lithographically defining the first and second nanobeams. 95. The method of embodiment 93, wherein forming the first nanobeam and forming the second nanobeam comprises 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 explanation of the drawings]

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

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

[0017] [Figure 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] [Figure 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 contains 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 multiple stacked waveguide example 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 schematically illustrates a cross-sectional view of a metasurface-based axicon as an example of an optical element formed from a metasurface.

[0028] [Figure 10C] Figure 10C illustrates the resulting transmitted beam profile when the metasurface-based axicon of Figure 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-to-bottom 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 TM-polarized light relative to a TE-polarized beam resulting from the exemplary waveplate of FIG. 11A.

[0032] [Figure 11D] FIG. 11D illustrates the 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 with two-level geometric phase optical elements, according to some embodiments.

[0035] [Figure 14] FIG. 14 illustrates simulated diffraction efficiency versus angle of incidence (α) for the exemplary diffraction 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 in response to 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, with the mask layer remaining, according to some embodiments.

[0038] [Figure 16B]FIG. 16B illustrates the 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 angle of incidence (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 angle of incidence (α) for an exemplary diffraction grating formed from amorphous silicon for TE and TM polarized green light, respectively, according to some embodiments. [Figure 17B] 17A and 17B illustrate simulated diffraction efficiency (η) versus angle of incidence (α) for an exemplary diffraction grating formed from amorphous silicon for TE and TM polarized green light, respectively, according to some embodiments.

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

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

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

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

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

[0051] [Figure 27] FIG. 27 illustrates the simulated diffraction efficiency (η) versus angle of incidence (α) for the exemplary 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] [Figure 30] 30A and 30B illustrate cross-sectional side and top-down views, respectively, of a diffraction grating comprising a metasurface with a two-phase-level asymmetric geometric phase optical element, according to some embodiments.

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

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

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

[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 comprise dense arrays of surface structures that function as resonant optical antennas. The resonant nature of the interaction between light and 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 can take the form of a grating formed by a plurality of repeating unit cells. Each unit cell can include 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 viewed from above, the first direction can be generally along the y-axis, and the second direction can be generally along the x-axis. In some embodiments, a unit cell can include 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 multiple 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 multiple first nanobeams, and at least one of the first nanobeams within a unit cell has a width that is different from at least one other of the first nanobeams. In some embodiments, the unit cell 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, which may be less than the wavelength of light that the metasurface is configured to diffract or that is guided onto 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 efficiencies for incident light with circular polarization over a wide range of incident 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 wearable display systems to provide compact optical elements. AR systems may display virtual content to a user or viewer while still allowing the user to see the world around them. Preferably, this 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 that 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, wherein like reference numerals refer to like parts throughout. Exemplary Display Systems

[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 directly in front of the user's 90 eyes. The display 70 may, in some embodiments, be considered eyewear. In some embodiments, a speaker 100 is coupled to the frame 80 and configured to be positioned adjacent to the user's 90 ear canal (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 queries, 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 a local data processing module 140 by a communication link 130, such as a 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, integrated into headphones, or otherwise removably attached to the user 90 (e.g., in a backpack-type configuration, in a belt-type configuration). Similarly, the sensor 120a may be operably coupled to the local data processing module 140 by a communication link 120b, e.g., a wired or wireless connectivity. The local processing and data module 140 may include a hardware processor and digital memory, such as non-volatile memory (e.g., flash memory or a hard disk drive), both of which may be utilized to aid in processing, caching, and storing data. The data includes data a) captured from sensors (e.g., which may be operatively coupled to frame 80 or otherwise attached to 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 remote processing module 150 and / or remote data repository 160 (including data related to virtual content), possibly for passing to display 70 after processing or retrieval. Local processing and data module 140 may be operatively coupled to remote processing module 150 and remote data repository 160 by communication links 170, 180, such as via wired or wireless communication links, such that these remote modules 150, 160 are operatively coupled to each other and available as resources to local processing and data module 140. In some embodiments, 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 freestanding 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 a digital data storage facility that may be available through the Internet or other networking configuration in a “cloud” resource configuration. In some embodiments, remote data repository 160 may include one or more remote servers that provide information, for example, 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 computations are performed within the local processing and data module, allowing for fully autonomous use from the remote module.

[0066] Referring now to FIG. 3, the perception of an image as “three-dimensional” or “3-D” can be achieved by providing a slightly different presentation of the image to each eye of a 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 the optical or z-axis parallel to the viewer's line of sight. The images 190, 200 are flat, and the eyes 210, 220 can focus on the images by assuming a single accommodative state. Such a 3-D display system relies on the human visual system to combine the images 190, 200 and provide the perception of depth and / or scale of the combined image.

[0067] However, it should be understood that the human visual system is more complex and providing a realistic perception of depth is more difficult. 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 eyes’ lines of sight and fixate on an 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 slightly different presentations (and therefore slightly different images) to each eye so that a three-dimensional perspective is perceived by the human visual system. However, such systems are uncomfortable for many viewers, particularly because they simply provide different presentations of the scene but work against the "accommodation-vergence reflex" when the eyes view all image information in a single accommodated state. Display systems that provide better matching between accommodation and vergence can produce more realistic and comfortable simulations of three-dimensional images.

[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 so that the objects are in focus. The eyes 210, 220 assume particular accommodated states and focus 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 portion 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. While 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, although shown as flat for ease of illustration, it should be understood that the contours of the depth plane may be curved in physical space so 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 can also change the amount of divergence of light from the object as viewed by that eye. Figures 5A-5C illustrate the relationship between distance and divergence of light rays. The distance between the object and the eye 210 is represented in the order of decreasing distances R1, R2, and R3. As shown in Figures 5A-5C, light rays become more divergent as the distance to the object decreases. As the distance increases, the light rays become more collimated. In other words, the light field generated by a point (an object or part of an object) can be said to have a spherical wavefront curvature that is a function of the distance the point is from the user's eye. The curvature increases as the distance between the object and the eye 210 decreases. As a result, the divergence of light rays at different depth planes also differs, and the divergence increases as the distance between the depth plane and the viewer's eye 210 decreases. While only a single eye 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 can typically interpret 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 representations of images corresponding to each of these limited number of depth planes. The different representations can be focused separately by the viewer's eyes, thereby serving to provide depth cues to the user based on the ocular accommodation required to focus on different image features for a scene 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. Display system 250 includes a stack of waveguides or stacked waveguide assembly 260 that can be utilized to provide a three-dimensional perception to the eye / brain using multiple waveguides 270, 280, 290, 300, 310. In some embodiments, display system 250 is system 60 of FIG. 2, and FIG. 6 diagrammatically illustrates some portions of system 60 in greater detail. For example, waveguide assembly 260 can be part of display 70 of FIG. 2. It should be understood that display system 250 can be considered a bright field display in some embodiments.

[0072] Continuing with reference to FIG. 6, the waveguide assembly 260 may also include multiple features 320, 330, 340, 350 between the waveguides. In some embodiments, the features 320, 330, 340, 350 may be one or more lenses. The waveguides 270, 280, 290, 300, 310 and / or multiple lenses 320, 330, 340, 350 may be configured to transmit image information to the eye with various levels of wavefront curvature or ray divergence. Each waveguide level may be associated with a particular depth plane and configured to output image information corresponding to that depth plane. Image injection devices 360, 370, 380, 390, 400 may function as light sources for the waveguides and may be utilized to inject image information into waveguides 270, 280, 290, 300, 310, each configured as described herein to disperse incident light across each respective waveguide for output toward eye 210. Light exits output surfaces 410, 420, 430, 440, 450 of image injection devices 360, 370, 380, 390, 400 and is injected into corresponding input surfaces 460, 470, 480, 490, 500 of 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 a 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 toward 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, 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 via a beam splitter 550 to and modified by a light modulator 540, such as 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 diagrammatically represent a single scanning fiber or a bundle of scanning fibers configured to inject light into one or more waveguides 270, 280, 290, 300, 310. In some other embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may diagrammatically represent multiple scanning fibers or multiple bundles of scanning fibers, each configured to inject light into an associated one of the waveguides 270, 280, 290, 300, 310. 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 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 waveguides 270, 280, 290, 300, 310, for example, to redirect light exiting the scanning fiber into one or more waveguides 270, 280, 290, 300, 310.

[0076] Controller 560 controls the operation of one or more of stacked waveguide assemblies 260, including the operation of image input devices 360, 370, 380, 390, 400, light source 530, and light module 540. In some embodiments, controller 560 is part of local data processing module 140. Controller 560 contains programming (e.g., instructions in a non-transitory medium) that coordinates the timing and provision of image information to waveguides 270, 280, 290, 300, 310, for example, according to any of the various schemes disclosed herein. In some embodiments, controller 560 may be a single integrated device or a distributed system connected by wired or wireless communication channels. Controller 560 may be part of 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 the major top and bottom surfaces. In the illustrated configuration, each of the waveguides 270, 280, 290, 300, 310 may include outcoupling optical elements 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 light propagating within the waveguide strikes the light extraction optical element. The outcoupling optical element 570, 580, 590, 600, 610 may be, for example, a grating including diffractive optical features as discussed further herein. While shown disposed on the bottom major surface of the waveguides 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 waveguides 270, 280, 290, 300, 310, as discussed further herein. In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 may be formed within a layer of material that is attached to a transparent substrate and forms the waveguides 270, 280, 290, 300, 310. In some other embodiments, the waveguides 270, 280, 290, 300, 310 may be monolithic pieces 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] Continuing with 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 reaching the eye 210. Such first lens 350 may be configured to generate a slight convex wavefront curvature so that the eye / brain interprets light emerging from the next upper waveguide 280 as emerging from a first focal plane closer inward from optical infinity toward the eye 210. Similarly, the third upper waveguide 290 passes its output light through both the first 350 and second 340 lenses before reaching the eye 210. The combined refractive power of the first 350 and second 340 lenses can be configured to produce another, increasing amount of wavefront curvature so that the eye / brain interprets the light emerging 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 due to the aggregate focal power representing the focal plane closest to the person. To compensate for the stack of lenses 320, 330, 340, 350 when viewing / interpreting light originating from the world 510 on the other side of the stacked waveguide assembly 260, a compensating lens layer 620 may be placed on top of the stack to compensate for the aggregate power of the lower lens stacks 320, 330, 340, 350. Such a configuration provides as many perceived focal planes as there are available waveguide / lens pairs. Both the waveguide outcoupling optical elements and the focusing sides of the lenses may be static (i.e., not dynamic or electro-active). In some alternative embodiments, one or both may be dynamic using electro-active features.

[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 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 the appropriate amount of divergence or collimation for the particular depth plane associated with the waveguide. As a result, waveguides with different associated depth planes can have different configurations of the outcoupling optical elements 570, 580, 590, 600, 610, which output light with different amounts of divergence depending on the associated depth plane. In some embodiments, the light-extracting optical elements 570, 580, 590, 600, 610 can be volume or surface features, which can be configured to output light at specific angles. For example, the light-extracting 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 sufficiently low diffraction efficiency so that only a portion of the light in the beam is deflected toward the eye 210 with each intersection point of the DOE, while the remainder continues traveling through the waveguide via TIR. The light carrying the image information is thus split into several related output beams that exit the waveguide at various locations, resulting in a fairly uniform pattern of output emission toward 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 can 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 can 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 the physiological state 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 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, monitoring each eye separately.

[0085] 7, an example of an output beam output by a waveguide is shown. While one waveguide is illustrated, it should be understood that other waveguides in waveguide assembly 260 (FIG. 6) may function similarly, and that waveguide assembly 260 includes multiple waveguides. Light 640 is launched into waveguide 270 at input surface 460 of waveguide 270 and propagates within waveguide 270 by TIR. At the point where light 640 impinges on DOE 570, a portion of the light exits the waveguide as output beam 650. Output beam 650 is illustrated as approximately parallel, but may be redirected to propagate to eye 210 at an angle (e.g., forming a diverging output beam), as discussed herein, and depending on the depth plane associated with waveguide 270. It should be understood that a substantially 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 waveguides or other sets of 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 can be formed at each depth plane by overlaying an image in each of the component colors, for example, three or more component colors. FIG. 8 illustrates an example of a stacked waveguide assembly, with each depth plane including an image formed using multiple different component colors. The illustrated embodiment shows depth planes 240a-240f, but more or fewer depths are also contemplated. Each depth plane can have three or more component color images associated with it, including a first image in a first color G, a second image in a second color R, and a third image in a third color B. Different depth planes are indicated in the diagram by different numbers in diopters (dpt) following the letters G, R, and B. By way of example only, the number following each of these letters indicates the diopter (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 can be varied to account for differences in the eye's focusing of light of different wavelengths. For example, different component color images for a given depth plane may be placed on depth planes corresponding to different distances from the user. Such an arrangement may increase visual acuity and user comfort and / or reduce chromatic aberration.

[0087] In some embodiments, light for 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 diagram containing the letter G, R, or B may be understood to represent an individual waveguide, and three waveguides may be provided per depth plane, resulting in three component color images per depth plane. While the waveguides associated with each depth plane are shown adjacent to each other in this drawing for ease of illustration, it should be understood that in a physical device, the waveguides may all be arranged in a stack with one waveguide per level. In some other embodiments, multiple 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 replace one or more of red, green, or blue.

[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, light source 530 (FIG. 6) may be configured to emit light at one or more wavelengths outside the range of a viewer's visual perception, e.g., infrared and / or ultraviolet wavelengths. Additionally, the waveguide in-coupling, out-coupling, and other light redirecting structures of 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] Referring now to FIG. 9A , in some embodiments, light impinging on a waveguide may need to be redirected to incoupling the light into the waveguide. An incoupling optical element may be used to redirect and incoupling the light into its corresponding waveguide. FIG. 9A illustrates a cross-sectional side view of an example of a plurality or set 660 of stacked waveguides, each including an incoupling 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. While stack 660 may correspond to stack 260 ( FIG. 6 ), and the illustrated waveguides of stack 660 may correspond to a portion of multiple waveguides 270, 280, 290, 300, 310, it should be understood that light from one or more of image injection devices 360, 370, 380, 390, 400 is injected into the waveguide from a location requiring the light to be redirected for incoupling.

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

[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 so as to receive substantially no 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., the top major surface) of waveguide 670, light distribution element 740 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and light distribution element 750 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some other embodiments, light distribution elements 730, 740, 750 may be disposed on the bottom major surfaces of associated waveguides 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 associated waveguides 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] Waveguides 670, 680, 690 may be spaced apart and separated, for example, by gas, liquid, and / or solid layers of material. For example, as shown, layer 760a may separate waveguides 670 and 680, and layer 760b may separate waveguides 680 and 690. In some embodiments, layers 760a and 760b are formed from a low refractive index material (i.e., a material having a lower refractive index than the material forming the immediately adjacent ones of waveguides 670, 680, 690). Preferably, the refractive index of the material forming layers 760a, 760b is 0.05 or greater, or 0.10 or less, than the refractive index of the material forming waveguides 670, 680, 690. Advantageously, the lower refractive index layers 760a, 760b may function as cladding layers that 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 waveguides 670, 680, 690 are similar or the same, and the materials forming layers 760a, 760b are similar or the same. In some embodiments, the materials forming waveguides 670, 680, 690 may vary between one or more waveguides, and / or the materials forming layers 760a, 760b may vary while still maintaining the various refractive index relationships discussed above.

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

[0098] In some embodiments, the light rays 770, 780, 790 have different properties, such as different wavelengths or different wavelength ranges, which may correspond to different colors. Each of the in-coupling 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 in-coupling optical elements 700, 710, 720 selectively deflects one or more particular wavelengths of light while transmitting other wavelengths to the underlying waveguide and associated in-coupling optical element.

[0099] For example, in-coupling optical element 700 may be configured to selectively deflect light ray 770 having a first wavelength or wavelength range while transmitting light rays 1242 and 1244 having different second and third wavelengths or wavelength ranges, respectively. Transmitted light ray 780 impinges on and is deflected by in-coupling optical element 710, which is configured to selectively deflect light of the second wavelength or wavelength range. Light ray 790 is deflected by in-coupling 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 in-coupling optical element 700, 710, 720 of each waveguide deflects the light into its corresponding waveguide 670, 680, 690 and in-couples 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 waveguide's corresponding light distribution element 730, 740, 750.

[0101] 9B, a perspective view of the example multiple stacked waveguides of FIG. 9A is illustrated. As previously described, in-coupled light rays 770, 780, 790 are deflected by in-coupling optical elements 700, 710, 720, respectively, and then propagate by TIR within waveguides 670, 680, 690, respectively. Light rays 770, 780, 790 then impinge on light distribution elements 730, 740, 750, respectively. Light distribution elements 730, 740, 750 deflect light rays 770, 780, 790 to propagate toward 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 light into 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 into 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 light directly into the out-coupling optical elements 800, 810, 820. For example, with reference 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 an OPE can be configured to increase the size of the eyebox in at least one axis, and that an EPE can increase the eyebox in an axis that intersects the axis of the OPE, e.g., orthogonal to the axis of the OPE. For example, each OPE can be configured to redirect a portion of the light striking the OPE to an EPE in the same waveguide, while allowing the remaining portion of the light to continue propagating down the waveguide. Again, upon impingement on the OPE, another portion of the remaining light is redirected to the EPE, and the remainder 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 remainder of that light continues to propagate through the waveguide until it again strikes an EPE, 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 the 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] 9A and 9B, in some embodiments, a waveguide set 660 includes, for each component color, waveguides 670, 680, 690, in-coupling optical elements 700, 710, 720, light distribution elements (e.g., OPEs) 730, 740, 750, and out-coupling optical elements (e.g., EPs) 800, 810, 820. The waveguides 670, 680, 690 may be stacked with an air gap / cladding layer between each one. The in-coupling optical elements 700, 710, 720 redirect or deflect incident light into that waveguide (with different in-coupling optical elements receiving light of different wavelengths). The light then propagates at an angle that will result in TIR within each 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 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 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 ray 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 ray 790 to a viewer, who also receives 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, waveguides 670, 680, 690 may be vertically aligned, along 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., laterally spaced apart, as seen in a 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 specific light source to be uniquely coupled to a specific waveguide. In some embodiments, arrays including non-overlapping, spatially separated in-coupling optical elements may be referred to as shifted-pupil systems, and the in-coupling optical elements in these arrays may correspond to sub-pupils. (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 shortcomings 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. Furthermore, as further described above with reference to FIGS. 9A-9C , light coupled into corresponding waveguides preferably propagates within the waveguides by total internal reflection (TIR). To achieve TIR, it may be desirable for the diffraction gratings 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 can include surface structures that can locally modify the polarization, phase, and / or amplitude of light in reflection or transmission. Metasurfaces can include arrays of subwavelength-sized and / or subwavelength-spaced phase-shifting elements whose patterns are configured to control the wavefront of light so 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 varying metasurfaces can be created, throughout which the optical wavefront can be substantially manipulated.

[0108] In conventional optical elements, such as lenses and waveplates, wavefronts are controlled via the propagation phase in media much thicker than the wavelength. Unlike conventional optical elements, metasurfaces instead use subwavelength-sized resonators as phase-shifting elements to induce phase changes in light. Because metasurfaces are formed from relatively thin, uniform-thickness features, they can be patterned across the surface using thin-film processing techniques, such as semiconductor processing techniques, and direct printing techniques, such as nanoimprinting. An example of the replacement of a conventional optical element with a metasurface is illustrated with reference to FIGS. 10A-10C. FIG. 10A schematically illustrates a cross-section 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 a glass lens, can be several millimeters thick. In contrast, FIG. 10B schematically illustrates a cross-section of an optical element, e.g., a metasurface axicon 1104, 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. Figure 10C illustrates the 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 a 550 nm wavelength. As shown, the desired beam profile 1106 can be achieved using metasurface axicons, which can be several orders of magnitude thinner than 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 the 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 local changes in polarization. Some optical elements that rely on 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, 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 geometric phase-based waveplates and the resulting phase pickup / delay and absorptance are illustrated with reference to FIGS. 11A-11D. FIG. 11A illustrates an exemplary waveplate 1100 formed from a metasurface comprising multiple nanobeams 1104 under top-to-bottom illumination with incident light 1108 under transverse electric (TE) polarization (with an 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 within the wavelength range of interest, as described with reference to FIGS. 11B-11D.

[0112] Figure 11B illustrates simulated phase wavefronts resulting from the waveplate 1100 illustrated above with reference to Figure 11A. Compared 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 light relative to TE-polarized light 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 nanobeam 1104 thickness of 100 nm. 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. Square symbols illustrate experimental measurements for an array of 120-nm beams, demonstrating 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 in 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, as illustrated, for example, by phase delay spectrum 1132, can be attributed to a relatively strong resonance under TE illumination, as shown by absorption spectrum 1148, and a relatively weak second-order TM resonance, as shown by absorption spectrum 1144. The order of the resonance is determined by the maximum field number inside the nanobeam (FIG. 11D, inset). As shown, the TE absorption resonance of the array, as illustrated, for example, by absorption spectrum 1148, and the associated variation in phase delay, as illustrated, for example, by phase delay spectrum 1132, can be spectrally tuned, in part, by varying the feature size, including width, of nanobeam 1104.

[0116] Below, with reference to Figures 12A-12H, a geometric PB phase structure 1200 based on geometrically rotated waveplate elements is described. In particular, a PB phase structure configured as a half-waveplate with a phase delay π is described. Eight half-waveplate elements are arranged to be equally spaced and may 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 Figures 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 delayed and transmitted through the waveplate elements. The circular polarization and counterclockwise orientation angle of the waveplate's fast axis 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> or vice versa.

[0118] Referring to the bottom row of Figure 12A, the electric field of an incident |LCP> beam is steered upward toward the positive y-axis at an initial time t = t0, as shown by vector 1204. After one-quarter of an 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 Figure 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 into an |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, an |RCP> output beam is produced. However, referring to FIG. 12A, the produced phase delay of vectors 1204 and 1208 is φ g = 2θ. For 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 results in a φg = 2θ = π, producing a |RCP> beam. Thus, for the half-wave plate shown, it will have spent half an optical cycle well before reaching the state shown in Figure 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, fabricating half-waveplate elements with high diffraction angles for visible light can be difficult. This is because the diffraction angle depends, among other things, on the period length 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 efficiencies, and with 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, thereby concentrating optical power in desired diffraction orders while leaving low residual optical power in other orders (e.g., the zeroth order). Various embodiments of metasurfaces comprising PBOEs configured as diffraction gratings are described in this disclosure. According to various embodiments, the diffraction gratings have a combination of desirable optical properties, including one or more of a high diffraction angle, high diffraction efficiency, a wide range of acceptance angles, and highly uniform diffraction efficiency within the acceptance angle range. These desirable optical properties can result from a combination of various aspects of the invention, including the materials, dimensions, and geometric configurations of the metasurface elements.

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

[0123] As described herein, features that are parallel, nominally parallel, or nearly 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 perpendicular, nominally perpendicular, or nearly perpendicular 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, can 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 diffracted light on the side opposite the light incident side of the structure is greater than the intensity of 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 diffracted light on the same side of the structure as the light incident side is greater than the intensity of diffracted light on the side opposite the light incident side of the structure, 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 illustrate cross-sectional side and top-down views, respectively, of a diffraction grating 1300 comprising a metasurface with geometric phase optical elements, 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 configured to diffract light having wavelengths within the visible spectrum is formed. 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., the y-direction) and a plurality of second lines or nanobeams 1316 having a second orientation and generally extending in a second direction (e.g., the x-direction). The first lines or nanobeams 1312 can be considered to form a first set of nanobeams, and the second lines or nanobeams 1316 can be considered to form a second set of nanobeams. One or more of the first lines 1312 and second lines 1316 are arranged adjacent to one another in the second direction, and the first lines 1312 and second lines 1316 alternate 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 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 a 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 one another, 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, according to some embodiments, based on a two-level geometric phase metasurface with lines oriented in simply two different directions. Advantageously, unlike Figures 12A-12H, by using the wave plate combination illustrated with reference to Figures 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 allows for 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 this 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 incident light to pass through it. Thus, a transparent substrate may, in some embodiments, be a glass, sapphire, or polymer substrate. 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 incident light.

[0130] One or more of the first lines 1312 and second lines 1316 may be described as protrusions, ridges, flutes, or nanowires that protrude from the plane of the page, extend along the plane of the page, 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 recesses, troughs, depressions, or trenches that are recessed into the plane of the page and have a spacing. In some embodiments, the first lines 1312 and second lines 1316 are elongated rectangular structures having 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 cross-sectional shapes that may be circular, elliptical, triangular, parallelogram, rhombus, trapezoidal, pentagonal, or any suitable shape.

[0131] Below, various configurations are described, including the dimensions and geometric arrangement of one or more first lines 1312 and second lines 1316, the combined effect of which is to produce a grating based on a geometric phase optical element with the 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] 13A and 13B, in operation, when an incident light beam 1330, e.g., visible light, is incident on the metasurface 1308 at an angle of incidence α, measured relative to a plane that is normal to the surface 1304S and extends parallel to the first line 1312, e.g., the yz-plane, the grating 1300 partially transmits the incident light as a transmitted light beam 1334 and partially diffracts the incident light as a diffracted light beam of a +1st order 1342 at a diffraction angle θ1 and a −1st order 1338 at a diffraction angle θ2, the diffraction angles being 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 incident at a 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 beams reach the OPE / EPE 1346, which may correspond to the light distribution elements 730, 740, 750 and the out-coupling 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 so that 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 material's electronic energy band structure in 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 its HOMO and LUMO that substantially exceeds the energy corresponding to the wavelength range over which the metasurface is configured to diffract. A semiconductor has an energy difference between its HOMO and LUMO that substantially matches the energy corresponding to the wavelength range over which the metasurface is configured to diffract. As described herein, metals have a zero or negative energy difference between their 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 to 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., the 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 surface electrons, which oscillate against the restoring force of positive atomic nuclei, surface plasmon resonance (SPR) can occur, resulting in resonant oscillation of 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 first lines 1312 and second lines 1316 may have a free electron concentration of, for example, about 1×10 19 / cm 3 Less than 1 x 10 18 / cm 3 Less than 1 x 10 17 / cm 3 Less than, or about 1 × 10 16 / cm 3 The first line 1312 and the second line 1316 may be formed from a non-metallic material, such as a semiconductor or an insulator, that is less than 1000 . 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] 13A and 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 loss 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 cavity, 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 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 realizing other benefits, it may be desirable to have the first lines 1312 and / or the second lines 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 lines 1312 and the second lines 1316 are each 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 x 10 18 / cm 3 Less than 1 x 10 17 / cm 3 Less than or about 1 x 10 16 / cm 3 The doped layer is doped with a dopant, e.g., an n-type dopant, at a concentration less than 1000 . 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 benefits.

[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 an insulator, ohmic losses resulting from plasmonic absorption can 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 can occur when a photon with energy above the band gap between the HOMO and LUMO of a semiconductor or an insulator is absorbed, resulting in the creation of an electron-hole pair. Therefore, it can 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 has 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 and 1316, having subwavelength feature sizes, support leaky mode resonance, they can confine light, thereby introducing a phase delay into scattered light waves produced under TE and TM illumination. The effectiveness of the light confinement within one or more of the first and second lines 1312 and 1316 can result from being configured as a waveguide that acts as a resonator, and the resulting diffraction efficiency can depend, among other factors, on the refractive index and subwavelength dimensions of the materials of the first and second lines 1312 and 1316.

[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 n 1 bulk is measured at a wavelength, eg, 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 lines 1312 and / or the second lines 1316. In some embodiments, when formed from semiconductor materials, the first lines 1312 and / or the second lines 1316 may be formed from an elemental Group IV material (e.g., Si, Ge, C, or Sn) or an alloy formed from a Group IV material (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 a Group III-V material, a Group II-VI semiconductor material (CdSe, CdS, ZnSe, etc.) or an alloy formed from a Group II-VI material. 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 fabricated 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, according to some embodiments, may be formed from oxides including transition metals such as titanium, tantalum, hafnium, zirconium, etc., including their stoichiometric and sub-stoichiometric forms. 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 sub-stoichiometric 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 ) is included.

[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 with reference 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 the 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, preferably smaller than the wavelength in the visible spectrum, that the metasurface 1308 is configured to diffract. 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. Additionally, 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 separated by a regular interval s1. Additionally, one of the one or more first lines 1312 and one of the second lines 1316 that are immediately adjacent to each other in the second direction are separated by a regular interval s2. According to some embodiments, one or both of s1 and s2 are smaller than the wavelength at which the metasurface 1308 is configured to diffract. Additionally, the first lines 1312 and the second lines 1316 each have a height h nano1 and h nano2 The spacing s1, s2 and the height h nano1 and h nano2A particular combination of may be selected to obtain a desired range of incident angles α (Δα), sometimes referred to as the range of acceptance angles or field of view (FOV). 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 a Δα over which 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 waveguide 1304 at an angle α relative to the surface normal, e.g., the yz-plane. According to some embodiments, as described above, Δα is related to the 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 relative to the surface normal (e.g., the yz-plane). In particular, when 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 first lines 1312 in the second direction and directly neighbors of second lines 1316 in the first direction. That is, when an incident light beam 1330 is incident at an incident 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 calculated as s / h nano1 , s2 / h nano1 , and / or s2 / h nano1 In various embodiments, the ratio s1 / h nano1 , s2 / h nano1 , and / or s2 / h nano1 is 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. nano1, s2 / h nano1 , and / or s2 / h nano1 can be achieved, for example, when s1 and s2 are each in the range of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm, e.g., 30 nm. Of course, relatively low values ​​of s1 and s2 can be achieved by reducing h nano1 and h nano2 has a correspondingly relatively low value.

[0149] Advantageously, according to some embodiments, the relatively high refractive index (n1) of the material of one or more of the first lines 1312 and / or second lines 1316 allows for a relatively small thickness or height. Thus, in various embodiments, the first lines 1312 and second lines 1316 may have a thickness in the range of 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, e.g., 107 nm, depending on n1, according to some embodiments. nano1 and h nano2 For example, h nano1 and h nano2 can be 10 nm to 450 nm where n1 is greater than 3.3, and 10 nm to 1 μm where n1 is less than or equal to 3.3. As another example, the height of the first line 1312 and the second line 1316 can be 10 nm to 450 nm, and the nanobeams are formed from silicon (e.g., amorphous or polysilicon).

[0150] According to various embodiments, s1 and W nano1 The combination of s1 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 a value obtained by adding s1 selected from 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, p nano1= 95.5 nm.

[0151] Of course, relatively small values ​​of s1 and s2 can be realized, and h nano1 and h nano2 Advantageously, one or more of the first lines 1312 and / or the second lines 1316 may be formed using a material with a relatively high refractive index n1, thereby reducing the refractive indices s1, s2, h nano1 , and h nano2 A relatively small value of h can be obtained, which, 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 with bulk refractive indices between 2.0 and 2.5, between 2.5 and 3.0, between 3.0 and 3.5, and above 3.5, h nano1 and h nano2 In various embodiments, the thicknesses s1, s2, h1, and s3 of the first and second lines 1312 and 1316 may be in the ranges of 500 nm to 1 μm, 300 nm to 500 nm, 100 nm to 300 nm, and 10 nm to 100 nm, respectively. nano1 , and h nano2 The overall pitch Λ a is correspondingly reduced, 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 h nano1 and h nano2 may 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 higher than the refractive index n2 of the substrate 1304, i.e., n1 bulk 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 made of a material such that 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 has a refractive index that is less than Δα, which may provide benefits 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)), plastic, polymer, or other optically transmissive material with a suitable refractive index, for example, as described herein.

[0154] Without being bound by any theory, when one or more of the first lines 1312 and / or second lines 1316 have sub-wavelength dimensions as described above, the refractive index of the first lines 1312 and / or second lines 1316a is smaller than 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 The effective refractive index n can vary (when the light is primarily in lines and / or segments) 1 eff Thus, in some embodiments, a sufficient value of n 1 eff Therefore, in some embodiments, the materials for the first lines 1312 and / or second lines 1316 and the substrate 1304 should have a bulk refractive index n 1 bulkand the refractive index n2 of the substrate 1304 (n 1 bulk −n2) 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 smallest 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 a 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 Λ can be smaller than the wavelength that grating 1300 is configured to diffract, and can be smaller than a wavelength in the range of about 435 nm to 780 nm, or any wavelength. In some embodiments, Λ is configured to diffract at least red light. acan be less than a wavelength (or any wavelength) in the range of about 620-780 nm. In some other embodiments 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 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 a can 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 that 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 a is less than the smallest wavelength of the band of wavelengths that the light source of the display system is configured to direct at the metasurface.

[0157] In some embodiments, Λ a may have a value that is less than the ratio mλ / (sinα+n2sinθ), where m is an integer (e.g., 1, 2, 3...), and α, n2, and θ each have values ​​described elsewhere herein. For example, α may be in the range Δα over 40 degrees, n2 may be in the range of 1 to 2, and θ may 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] Still referring to FIG. 13B , in some embodiments, each of the second lines 1316 is at least two, three, four, 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 can have a length L1 in the range of 200 μm to 5 mm, 200 μm to 1 mm, or 1 mm to 5 mm. According to various embodiments, the second lines 1316 can have a length L2 in the range of 100 nm to 500 nm, 100 nm to 300 nm, and 300 nm to 500 nm. In some embodiments, the one or more first lines 1312 can have a length L1 corresponding to the total lateral dimension of the optical element formed by the metasurface, e.g., the length of an internal or external coupling optical element formed by the metasurface comprising the lines 1312. In some embodiments, the second lines have a unit cell pitch Λ a About 40% to about 60% of, for example, Λ a In some embodiments, L1 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 second lines 1316, 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 with one or more of the first lines 1312 without crossing any of them. 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 less 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 how the nanobeams of the waveplates illustrated in FIGS. 12B-12H are rotated relative to the waveplate illustrated in FIG. 12A . For example, the second lines 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, and the resulting phase delay of the polarization vectors corresponding to TE and TM polarizations is φ g = 2θ, where θ is the change in rotation angle when the fast axis of the wave plate 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., an |LCP> beam, thereby generating a diffracted |RCP> beam, which is diffracted by the second line 1316 through 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 internal coupling optical element (e.g., one or more of internal coupling optical elements 700, 710, 720 (FIG. 9A)) to internally couple incident light such that the light propagates through the substrate 1304 via total internal reflection. However, given 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 external coupling optical elements, such as one or more of external coupling optical elements 570, 580, 590, 600, 610 (FIG. 6) or 800, 810, 820 (FIG. 9B), instead of or in addition to forming internal 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 when different waveguides have different associated component colors, the external and / or internal coupling optical elements associated with each waveguide may have a geometric size and / or periodicity specific to the wavelength or color of light 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 grating 1300 is configured to diffract. For example, to diffract at least red, green, or blue light, metasurface 1308 may have 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 proportionally. a may be kept relatively uniform for different wavelengths of incident light by compensating for one or more of sin α, n 2 , and sin θ, as described above.

[0163] 14 illustrates a simulation 1400 of diffraction efficiency versus angle of incidence α for an example diffraction grating according to various embodiments of the diffraction grating 1300 described above with reference to FIGS. 13A and 13B. In particular, the simulation 1400 is performed under transmission mode with n=1.77, Λ a = 382 nm, h nano1 =h nano2 = 107 nm, W nano1 =W nano2 = 30 nm, p nano1 1 shows the simulated diffraction efficiency (η) for T-1 order diffracted TE-polarized green light (λ=520 nm) for a diffraction grating having one or more first and second lines formed from polycrystalline silicon on a substrate with α=96 nm and s1=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 correspond 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 serve as an anti-reflective coating), on or over a layer of high-refractive-index material in which one or more first lines 1312 and second lines 1316 are formed. The mask layer may then be first 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. Using the patterned mask layer as a template, the underlying layer of high-refractive-index material is then patterned into the first and second lines. In various embodiments, the patterned mask layer is removed, thereby leaving the first and second lines. However, in 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 discovered that, under some circumstances, the patterned mask layer can be left behind. Below, with reference to Figures 16A-16D, embodiments of diffraction gratings in which the mask layer is left behind are described.

[0166] FIG. 16A illustrates a cross-sectional side view of a diffraction grating 1600 comprising a metasurface with a geometric phase optical element, in which a mask layer is left behind after forming one or more first and second lines, e.g., by photolithography and etching, according to some embodiments. In particular, it has been found that leaving the mask layer with a relatively low refractive index advantageously can have little or no effect on the resulting optical response, including diffraction efficiency versus angle of incidence (η vs. α) behavior. Similar to the diffraction grating 1300 illustrated above with reference to FIGS. 13A and 13B, the diffraction grating 1600 includes a substrate 1304 having a surface 1304S on which a metasurface 1608 configured to diffract light having wavelengths within the visible spectrum is formed. The metasurface 1608 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). 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 the metasurface 1608 of FIG. 16A has 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 antireflective layer (ARC), has a refractive index that is less than about 2.0, less than about 1.8, less than about 1.6, or less than about 1.4, or 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 where 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 grating having one or more first and second lines formed from silicon on a substrate with n = 1.77, and having a mask layer formed thereon, ranging in thickness from 0 to 90 nm, and where, under transmission mode, Λ a = 382 nm, h nano1 =h nano2 = 107 nm, W nano1 =W nano2 = 30 nm, p nano1 16 shows the diffraction efficiency (η) for TE-polarized green light (λ=520 nm) simulated for a diffraction grating with α=96 nm and s1=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 a nearly negligible effect (about 1% or less) on the diffraction efficiency. For example, η amounts to 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 incident angle α for an exemplary diffraction grating, simulated with reference to FIG. 16A , but in which a mask layer 1604 having a fixed thickness of 20 nm is disposed on one or more first lines 1312 and second lines 1316 ( FIGS. 13A and 13B ). Simulation 1620 illustrates simulated diffraction efficiency curves 1614 and 1618, corresponding to transmitted diffraction orders T1 and T−1, respectively. Compared to simulation 1400 described above with reference to FIG. 14 for the T−1 diffraction order, simulated diffraction efficiency 1628 illustrates that the presence of the 20 nm thick mask layer has a nearly negligible effect (approximately 1% or less) on the diffraction efficiency or field of view. For example, η is approximately 32% at α=0, and it drops by approximately 10% at +α=21 degrees.

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

[0170] Below, with reference to Figures 17A-20, simulations of diffraction efficiency (η) versus angle of incidence α for exemplary 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 exemplary 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 also show the diffraction efficiency (η) for an exemplary diffraction grating having one or more first and second lines formed from amorphous silicon on a substrate with n=1.77 and under transmission mode, Λ a = 382 nm, h nano1 =h nano2 = 90 nm, W nano1 =W nano2 = 30 nm, p nano1 Simulations were performed for a diffraction grating with α = 96 nm and s1 = 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 degrees (<-30 to > +20), outside which the diffraction efficiency η drops by about 10% from the approximately 28% efficiency at α = 0.

[0172] FIG. 18 illustrates a simulation 1400 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 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 refractive index used for the simulation was n=4.41+0.182i. As illustrated, the range of angles of incidence (Δα), or field of view (FOV), is relatively wide, exceeding approximately 40 degrees, outside which the diffraction efficiency η drops by approximately 10% from an efficiency of approximately 32% at α=0.

[0173] 19 illustrates a simulation 1900 of diffraction efficiency (η) versus angle of incidence (α) for an exemplary diffraction 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 diffraction grating at α relative to the surface normal. Simulation 1900 illustrates a diffraction efficiency (η) of one or more first and second lines formed from silicon carbide (SiC) on a substrate with n=1.77, under transmission mode, Λ a = 382 nm, h nano1 =h nano2 = 260 nm, W nano1 =W nano2 = 65 nm, p nano1 Simulations were performed for a diffraction grating with α = 96 nm and s1 = 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 degrees (about -20 to about +20), and outside that range, the diffraction efficiency η drops by about 10% from the efficiency of about 27% at α = 0.

[0174] 20 illustrates a simulation 2000 of diffraction efficiency (η) versus angle of incidence (α) for an exemplary diffraction grating formed from silicon nitride (e.g., Si3N4) and configured to diffract green light, according to some embodiments. In particular, simulation 2000 shows the diffraction efficiency (η) of T-1 order diffracted TE-polarized green light at λ=520 nm, incident on the diffraction grating at α relative to the surface normal. Simulation 2000 illustrates a diffraction efficiency (η) of a T-1 order diffracted TE-polarized green light at λ=520 nm, having one or more first and second lines formed from silicon nitride (e.g., Si3N4) on a substrate with n2=1.77, under transmission mode, Λ a = 382 nm, h nano1 =h nano2 = 300 nm, W nano1 =W nano2 = 60 nm, p nano1Simulations were performed for a diffraction grating with α = 96 nm and s1 = 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 degrees (approximately < -30 to approximately +10), and outside that range, the diffraction efficiency η drops by approximately 10% from the approximately 21% efficiency at α = 0.

[0175] Below, with reference to Figures 21-24, simulations of diffraction efficiency (η) versus angle of incidence (α) for exemplary diffraction gratings formed from different high refractive index materials are illustrated, 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 exemplary diffraction 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 diffraction grating at α relative to the surface normal. Simulation 2100 also illustrates a diffraction efficiency (η) of a T-1 order diffracted TE-polarized blue light at λ=455 nm, having one or more first and second lines formed from polycrystalline silicon on a substrate with n=1.77, under transmission mode. a = 334 nm, h nano1 =h nano2 = 75 nm, W nano1 =W nano2 = 30 nm, p nano1 Simulations were performed for a diffraction grating with α = 96 nm and s1 = 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 degrees (approximately < -30 to approximately > +10), outside of 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 exemplary diffraction 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 diffraction grating at α relative to the surface normal. Simulation 2200 also illustrates a diffraction efficiency (η) of one or more first and second lines formed from amorphous silicon on a substrate with n=1.77, under transmission mode, Λ a = 334 nm, h nano1 =h nano2 = 60 nm, W nano1 =W nano2 = 30 nm, p nano1 Simulations were performed for a diffraction grating with α = 96 nm and s = 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 degrees (approximately < -30 to approximately > +10), and outside that range, 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 exemplary diffraction 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 diffraction grating at α relative to the surface normal. Simulation 2300 also illustrates a diffraction efficiency (η) of one or more first and second lines formed from silicon carbide on a substrate with n=1.77, under transmission mode, Λ a = 334 nm, h nano1 =h nano2 = 220 nm, W nano1 =W nano2 = 60 nm, p nano1Simulations were performed for a diffraction grating with α = 96 nm and s1 = 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 degrees (about -18 to about +18), and outside that range, the diffraction efficiency η drops by about 10% from the approximately 30% efficiency at α = 0.

[0179] 24 illustrates a simulation 2400 of diffraction efficiency (η) versus angle of incidence (α) for an exemplary diffraction 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 diffraction grating at α relative to the surface normal. Simulation 2400 also illustrates a diffraction efficiency (η) of one or more first and second lines formed from silicon nitride on a substrate with n=1.77, under transmission mode, Λ a = 334 nm, h nano1 =h nano2 = 260 nm, W nano1 =W nano2 = 60 nm, p nano1 Simulations were performed for a diffraction grating with α = 96 nm and s1 = 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 degrees (about -8 to about +12), and outside that range, the diffraction efficiency η drops by about 10% from the efficiency of about 21% at α = 0.

[0180] FIG. 25 illustrates a top-down view of a diffraction grating 2500 comprising a metasurface with geometric phase optical elements 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 with two sets of nanobeams, and FIG. 25 illustrates a metasurface with four sets of nanobeams. In particular, the diffraction grating 2500 of FIG. 25 comprises a four-level geometric phase metasurface. Similar to the diffraction grating 1300 described above with reference to FIGS. 13A and 13B, the diffraction grating 2500 includes a substrate, e.g., a waveguide, on which a metasurface configured to diffract light having wavelengths within the visible spectrum is formed. The metasurface includes one or more first lines 2512 extending in a first lateral direction (e.g., the y-direction) and a plurality of second lines 2516 extending in a second direction (e.g., the 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 at 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, except for the following differences.

[0181] 13A and 13B , the diffraction grating 2500 further includes 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 one another. 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., 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 another one or more 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. Additionally, in some embodiments, the widths of the third lines 2514 and the fourth lines 2518 having the same width are the same. However, in some other embodiments, the widths of the third lines 2514 and the fourth lines 2518 having the same width are different. Additionally, 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, when viewed from the propagation direction of the incident light (e.g., into the plane of the page), 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. In some embodiments, the second lines 2516 are rotated 90 degrees or π / 2 relative to the one or more first lines 2512, and the third lines 2514 are rotated 45 degrees or π / 4 relative to the one or more first lines 2512. Additionally, the fourth lines 2518 extend in a fourth direction that, when viewed from the propagation direction of the incident light, 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. In some embodiments, the second line 2516 is rotated 90° or π / 2 relative to one or more of the first lines 2512, and the third line 2514 is rotated 135° or 3π / 4 relative to one or more of the first lines 2512.

[0187] In some embodiments, similar to the waveplate combinations illustrated above with reference to FIGS. 12A-12H , the phase difference caused by the relative orientation of one or more of first lines 2512, second lines 2516, third lines 2514, and fourth lines 2518 can vary from 0 to π. When third lines 2514, fourth lines 2518, and second lines 2516 are rotated by π / 4, 3π / 4, and π relative to one or more of first lines 2512, phase pickup / delays of π / 2, 3π / 2, and 2π, respectively, can be achieved, according to some embodiments, such that phase pickup / delays covering the full 0 to 2π range can be achieved. As a result, by varying the fast axis orientation from 0 to π, phase pickup / delays 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 examples illustrated in FIGS. 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 can 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 respective ones of the internal coupling optical elements 700, 710, 720 therein or thereon, which can include or correspond to the gratings 1300, 2500 described above with reference to FIGS. 13A and 13B and 25. Waveguides 670, 680, 690 additionally form within or on one of light distribution elements (e.g., OPEs) 730, 740, 750 and / or outcoupling optical elements (e.g., EPEs) 800, 810, 820, respectively, including or corresponding to 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 metasurface 1308 at an incident angle α, grating 1300, 2500 diffracts the incident light into diffracted light beams 1342, 1338 at a diffraction angle θ2. One or both of diffracted light beams 1338 and 1342 are diffracted at a critical angle θ2 due to the occurrence of total internal reflection for substrate 1304, which is configured as a waveguide having a refractive index n2. TIR When the light is diffracted at a diffraction angle greater than θ, the condition θ2>θ TIR and θ1>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 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 are configured to operate in a transmissive mode, other embodiments are possible. In some other embodiments, referring back to FIGS. 9A and 9B, some display devices include a waveguide set 1200 having a diffraction grating configured to operate in a reflective mode. In these 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, the cross-sectional view of which includes or corresponds to the diffraction grating 2600 described with respect to FIG. Diffraction grating 2600 includes a metasurface 2608 configured to diffract light in a reflective mode, and differs from diffraction gratings 1300, 2500 described above with reference to Figures 13A, 13B, and 25 in that, in operation, light incident on the side of metasurface 2608 is diffracted toward the same side as the light-incident side of metasurface 2608. 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. Metasurface 2608 includes one or more first lines 1312 and a plurality of second lines 1316, the material composition, dimensions, and lateral arrangement on surface 1304S of which are similar to those of diffraction gratings 1300, 2500 described above with reference to Figures 13A, 13B, and 25, respectively. In particular, although a top-down view is not shown, 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 one or more first lines 1312 and second lines 1316 are arranged adjacent to each other 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 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, and 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] Although not shown, similar to the diffraction grating 2500 described above with reference to Figure 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, detailed descriptions 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 over, one or more of the first lines 1312 and second lines 1316. Additionally, a reflective layer 2612 may also be formed over or on, e.g., directly over, one or more of the first lines 1312 and second lines 1316 and / or over or on, e.g., directly over, 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 1316 by a height d. spacer The height d can 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 lower than the refractive index n2 of the substrate 1304. In various embodiments, n spacer has a refractive index of 1 to 2, 1.1 to 1.7, or 1.1 to 1.5, e.g., 1.2. In various embodiments, the spacer layer 2604 may be formed from a material that can be deposited by spin coating, including poly(methyl methacrylate) (PMMA), spin-on glass, electron beam resist or photoresist, and polymers. It should be understood that when deposited by spin coating, the as-spin-coated material may undergo viscous flow, and therefore the thickness of the spacer layer 2604 across the one or more first lines 1312 and second lines 1316 may be thinner than 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., areas 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 spaces 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-reflecting 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 0.015 to 0.015. r may be sufficiently thick to be substantially non-transparent and pore-free, 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, each having a thickness h nano1 and h nano2 It can exceed.

[0197] Figure 27 illustrates a simulation 2700 of diffraction (η) versus angle of incidence (α) for an example diffraction grating according to various embodiments of the diffraction grating 2600 described above with reference to Figure 26. In particular, the simulation 2700 illustrates a diffraction grating having one or more first and second lines formed from polycrystalline silicon on a substrate with n = 1.77, under reflection mode, where Λ a = 382 nm, h nano1 =h nano2 = 50 nm, Wnano1 =W nano2 = 30 nm, p nano1 Figure 1 shows the diffraction efficiency (η) of T-1 order diffracted TE-polarized green light (λ = 520 nm) simulated for a diffraction grating with α = 95.5 nm, s = 65.5 nm, and d = 50 nm. As shown, the range of incidence angles (Δα) or field of view (FOV) is relatively wide, exceeding approximately 45 degrees (-25 to +20 degrees), outside of which the diffraction efficiency η drops by approximately 10% from an efficiency of approximately 40% at α = 0. (Method for fabricating geometric phase metasurfaces)

[0198] Below, methods of fabricating geometric phase metasurfaces are described. In some embodiments, a geometric phase metasurface 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, a geometric phase metasurface 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 illustrate cross-sectional views of intermediate structures 2800A-2800D, respectively, at various stages of fabricating a diffraction grating with 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 forming a diffraction grating with a refractive index n2 on surface 1304S. 1 bulkThe method includes forming a high-index layer 1310 having a thickness of 1000 nm and 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, according to some embodiments, can 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). The high-index layer 1310 can 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 over the high-index layer 1310. The mask layer 1604A can be formed from 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 1604A 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 subsequent etch pattern transfer to the underlying high refractive index layer 1310. The hard mask layer may also serve as an anti-reflective coating, reducing reflection during subsequent exposure processes. In some embodiments, the hard mask layer may be a spin-coated polymer or a film deposited by either a 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, which may have sufficient etch selectivity to the high refractive index layer 1310 such that the photoresist and / or hard mask layer remains relatively intact through etching of the underlying high refractive 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 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, causes 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 positive photoresist, or the unexposed portions of the photoresist to be selectively removed by a developer solution for negative photoresist. Upon selective removal, the resulting patterned mask photoresist remains on high refractive index layer 1310, thereby serving as a template for subsequent patterning of the underlying hard mask layer, if included, e.g., by etching. The resulting intermediate structure 2800C shows patterned mask layer 1604, which includes patterned photoresist and, optionally, a patterned hard mask layer, if included.

[0202] 28C , the patterned mask layer 1604 can 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., the y-direction) and a plurality of second lines 1306 extending in a second direction (e.g., the x-direction), as described in more detail above with reference to FIGS. 13A and 13B . In various embodiments, the high-index layer 1310 can be etched, for example, anisotropically dry etched. The etching process employed can have suitable selectivity to the mask layer 1604 and / or the 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 over one or more of the first lines 1312 and 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. Optionally, when included, the underlying hard mask layer 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 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, e.g., photoresist / hard mask or hard mask, may be left unremoved.

[0204] 29A-29D illustrate cross-sectional views of intermediate structures 2900A-2900D, respectively, 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 differs from the method of forming intermediate structure 2800B of FIG. 28B, and the differences are described below.

[0205] 29B , instead of patterning a photoresist layer by selectively exposing and removing portions 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 above the glass transition temperature of the imprint resist, for example, thereby transferring the pattern of the template 2904 to the softened imprint resist. After cooling, the template 2904 is separated from the imprint resist, leaving the patterned resist 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 reflective-mode metasurface, such as the metasurface 2608 described with reference to FIG. 26, can 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 can be deposited in the open volume between one or more first lines 1312 and second lines 1316. In some other embodiments, one or more first lines 1312 and second lines 1316 can be formed by etching trenches into a blanket spacer layer 2604 or a blanket reflective layer, followed by filling the trenches with the high refractive index material of the one or more first lines 1312 and second lines 1316.

[0207] It should be understood that 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 metasurface fabrication, 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, in some embodiments, can be an optical fiber. 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 FIGS. 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 FIGS. 13A and 13B , a PBOE-based blazed grating 1300 can be configured to partially transmit incident light as a transmitted light beam 1334 and partially diffract the incident light as a diffracted light beam of a +1 order 1342 at a diffraction angle θ1 and a diffracted light beam of a −1 order 1338 at a diffraction angle θ2, where the diffraction angles are measured relative to the same plane, e.g., the yz plane, for measuring α. One or both of the diffracted light beams 1338 and 1342 may be oriented beyond a critical angle θ due to the occurrence of total internal reflection within a substrate 1304 configured as a waveguide. TIR When diffracted 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 beams reach the OPE / EPE 1346, which may correspond to the light distribution elements 1214, 1224, 1234 and the out-coupling 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 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 specific diffraction orders 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 each other. 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 spacing, 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 multiple diffraction orders, e.g., the +1st diffraction order 1342 or the −1st diffraction order 1338, while reducing the other of the multiple diffraction orders, e.g., the +1st diffraction order 1342 or the −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 wavelengths 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., the y-direction) and a plurality of second lines or nanobeams 3016 generally extending in a second direction (e.g., the x-direction). The first line or nanobeam 3012 may be considered to form a first set of nanobeams, and the second line or nanobeam 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 the 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 U.S. Pat. No. 9,507,064, metasurfaces with spatially varied 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 principles of operation 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 the sake of brevity.

[0212] However, unlike some embodiments described above, at least one of the first nanobeams 3012 has a width that is different from another of the first nanobeams 3012, and at least one of the second nanobeams 3016 has a width that is different from 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, the first set comprising 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 1 / 2. 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] Below, various configurations are described, 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 a relatively high diffraction angle, a relatively high diffraction efficiency, a relatively wide range of acceptance angles and relatively uniform efficiency within the acceptance angle range, and a relatively high efficiency, for both TE and TM polarization.

[0214] 30A , in operation, when an incident light beam 1330, e.g., visible light, is incident on the metasurface 3008 at an angle of incidence α measured relative to a plane, e.g., the yz-plane, normal to the surface 1304S and extending parallel to the first line 1312, the grating 3000 partially transmits the incident light as a transmitted light beam and partially diffracts the incident light as a diffracted light beam of +1 order 1342 at a diffraction angle θ1 while substantially suppressing a diffracted light beam of −1 order (not shown for clarity) at a diffraction angle θ2, where 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 diffracted light beam of +1 order 1342 falls within the critical angle θ2 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, preferably smaller than the wavelength in the visible spectrum, that the metasurface 1308 is configured to diffract. nano1-1 , W nano1-2 , W nano2-1 , and W nano2-2 Each of the W 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 the may be different.

[0216] According to some embodiments, immediately 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 1-3 1316 on the opposite side. 1-1 , s 1-2 , and s 1-3 Each of these 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 alternate with a second line 3016 having a spacing s 2-1 and s 2-2 According to some embodiments, s 2-1 and s 2-2 Each of these is smaller than the wavelength that the metasurface 3008 is configured to diffract.

[0218] Continuing with reference to FIG. 30A, the first line 3012 and the second line 3016 are spaced apart from each other by a height h nano , which may be the same or different, e.g., similar in dimensions to those described above with respect to Figures 13A / 13B, the description of which in terms of dimensions and, e.g., technical effect on the field of view (FOV), will not be described herein for the sake of brevity. Furthermore, the desired ratio of the 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 , s2-1 , and s 2-2 The relatively low value of h nano1 and h nano2 This can be achieved when Θ 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 s1 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. For example, in some embodiments, p nano1 =95.5nm.

[0220] Naturally, 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 Advantageously, by forming the first line 1312 and / or the second line 1316 using a material with a relatively high refractive index n1, s 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 nanoThis is because h 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 nano In various embodiments, the thicknesses n and m may be in the ranges of 500 nm to 1 μm, 300 nm to 500 nm, 100 nm to 300 nm, and 10 nm to 100 nm, respectively. Therefore, the high bulk refractive index n1 of the first line 3012 and the second line 3016 and the corresponding dimensions 1-1 , s 1-2 , s 1-3 , s 2-1 and s 2-2 , h nano and a particular combination of materials having an overall pitch Λ a may be correspondingly reduced, 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) of T+1 (3114, FIG. 31A) and T-1 (3118, FIG. 31A) orders of diffracted TE-polarized green light at λ=520 nm and T+1 (3124, FIG. 31B) and T-1 (3128, FIG. 31B) orders of 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 also show the diffraction efficiency (η) of an exemplary diffraction grating formed from polycrystalline silicon on a substrate with n = 1.77, 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 =58nm, s 1-2 =23 nm, s 1-3 =35nm, s 2-1 =s 2-2= 58 nm.

[0222] As shown in FIG. 31A , for TE polarization, the diffraction grating 3000 diffracts 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 of greater than 50% at α=0 and approximately 10%, respectively. For T+1 order TE polarized green light, the range of incident angles (Δα) or field of view (FOV) is relatively wide, about 50 (about 20 to >+20) degrees, outside of which the diffraction efficiency η drops from greater than 50% at α=0 to approximately 10% or more. As shown in FIG. 31B , for TM polarization, the diffraction grating 3000 diffracts incident light relatively evenly 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 illustrate simulated diffraction efficiency (η) versus angle of incidence (α) for an exemplary diffraction grating formed from amorphous silicon for TE and TM polarized green light, respectively, 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, respectively, incident on the diffraction grating at α relative to the surface normal. 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 diffraction grating at α relative to the surface normal. Simulations 3200 and 3204 show the diffraction efficiency (η) for an exemplary diffraction grating formed from amorphous silicon, having first and second lines on a substrate with n=1.77, 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 =38nm, s 2-1 =s 2-2= 63 nm.

[0224] As shown in FIG. 32A , for TE polarization, the diffraction grating 3000 diffracts incident light relatively efficiently into a T+1 order diffracted beam 3214 while attenuating a 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 incident 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% at α=0. As shown in FIG. 32B , for TM polarization, the diffraction grating 3000 diffracts incident light relatively evenly between a T+1 order diffracted beam 3224 and a T−1 order diffracted beam 3228, with corresponding diffraction efficiencies greater than 15% at α=0.

[0225] 33A and 33B 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, respectively, 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, respectively, incident on the grating at α relative to the surface normal. Simulations 3300 and 3304 show the diffraction efficiency (η) for an exemplary grating formed from amorphous silicon, having first and second lines on a substrate with n=1.77, 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 =58nm, s 1-2 =23 nm, s 1-3 =35nm, s 2-1 =s 2-2= 58 nm.

[0226] As shown in FIG. 33A , for TE polarization, the diffraction grating 3000 diffracts incident light relatively efficiently into a T+1 order diffracted beam 3314 while attenuating a 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 incident angles (Δα) or field of view (FOV) is relatively wide >40 (<−30 to >+10) degrees, outside which the diffraction efficiency η drops to about 10% or more from greater than 35% at α=0. As shown in FIG. 33B , for TM polarization, the diffraction grating 3000 diffracts incident light relatively evenly between a T+1 order diffracted beam 3324 and a T−1 order diffracted beam 3328, with corresponding diffraction efficiencies 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, while advantageously utilized with AR displays that provide images across multiple depth planes, the augmented reality content disclosed herein can 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 guided into a waveguide, multiple metasurfaces can 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 forming the metasurface can vary across the metasurface. Such metasurfaces can be active in redirecting light of different wavelengths 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 so that deflected light rays, even those of similar wavelengths, propagate away from the metasurface at different angles. It should also be understood that multiple isolated metasurfaces may be disposed across the substrate surface, each of the metasurfaces having the same geometry and pitch in some embodiments, or at least some of the metasurfaces having a different geometry and / or pitch than the 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, thin light-redirecting element is desired. For example, metallic surfaces can generally 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.

[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 individual 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 methods that may be implemented using the present device. The methods may include the act of providing such a suitable device. Such provisioning may be performed 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 necessary device in the present 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, along with details regarding material selection and manufacturing, have been described above. As for other details of the invention, these may be understood in connection with the above-referenced patents and publications and may generally be known 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 employed.

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

[0235] It is also contemplated that any optional features of the described inventive variations may be set forth 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 plural of the same items. More specifically, as used herein and in the claims associated therewith, the singular forms "a," "an," "said," and "the" include plural referents unless specifically stated otherwise. In other words, the use of articles in the above description and in the claims associated with this disclosure allows for "at least one" of the subject item. Furthermore, it should be noted that such claims may be drafted to exclude any optional element. Accordingly, this statement is intended to serve as a predicate for the use of such exclusive terminology, 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 language, the term "comprising" in the claims associated with this disclosure shall 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 shall be given the broadest possible commonly understood meaning while maintaining the validity of the claims.

[0237] The scope of the present invention is not limited to the examples provided and / or this 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 a variety of 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 disclosure. For example, while blocks are presented in a given arrangement, alternative embodiments may perform similar functionality with different components and / or circuit topologies, and some blocks may be deleted, moved, added, subdivided, 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 can 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 subcombinations 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 spacing; the one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuthal directions; The unit cells are repeated at a period of about 10 nm to 1 μm or less. Optical system. (Item 2) Item 10. The optical system of item 1, wherein the one or more first nanobeams and the second nanobeam are directed at an angle relative to each other, causing a phase difference between visible light diffracted by the one or more first nanobeams and visible light diffracted by the second nanobeam. (Item 3) Item 2. The optical system of item 1, wherein the phase difference is twice the angle. (Item 4) Item 10. The optical system of item 1, wherein the wavelengths within the visible spectrum correspond to blue light, green light, or red light. (Item 5) Item 10. The optical system of item 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 1, wherein each of the first nanobeams has the same width. (Item 7) Item 10. The optical system of item 1, wherein each of the second nanobeams has the same width. (Item 8) Item 1, wherein each of the first nanobeams within each of the second nanobeams has the same spacing between each of the first and second nanobeams. (Item 9) Item 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) Item 1, wherein the one or more first nanobeams and the second nanobeam have heights that are smaller than the wavelength. (Item 11) Item 10. 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 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 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) Item 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 incident 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 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. (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 the intensity of 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 diffracted light on the opposite side to the light incident side of the one or more first nanobeams and the second nanobeams. (Item 20) Item 10. The optical system of item 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) Item 1, wherein the one or more first nanobeams and the second nanobeam have a substantially rectangular cross-sectional shape. (Item 24) 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) Item 2. The optical system of item 1, wherein the one or more first nanobeams consist of one first nanobeam. (Item 27) Item 10. The optical system of item 1, further comprising a third set of nanobeams formed by a plurality of third nanobeams elongated in a different orientation relative to the 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) Item 27. The optical system of item 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, and the third azimuthal direction, 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 the 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, wherein the fourth nanobeam is 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 the 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 azimuthal direction and the third azimuthal direction are rotated approximately 90 degrees relative to each other. (Item 36) Item 1, the optical system of item 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) Item 1, wherein the one or more first nanobeams and the second nanobeam are embedded in a transparent spacer layer. (Item 40) Item 40. The optical system of item 39, wherein the transparent spacer layer has a refractive index that is less than the refractive index of a bulk material of one or more of the first nanobeams and the second nanobeam. (Item 41) Item 10. The optical system of item 1, wherein a metal reflective layer is formed over the one or more first nanobeams and the second nanobeam. (Item 42) Item 10. The optical system of item 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) Item 43. The waveguide of item 42, wherein the substrate is formed from a material whose refractive index is less than the bulk refractive index of the 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 a user's eye and display augmented reality image content, the head-mounted display device comprising: a frame configured to be supported on the user's head; a display disposed on the frame; Equipped with At least a portion of the display one or more waveguides, the one or more waveguides being transparent and positioned at locations in front of the eyes of the user when the user wears 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 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 Equipped with Item 10. The optical system of item 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, and the diffraction grating comprises 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, the metasurface 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 azimuthal directions; The method wherein 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 nanobeams of each unit cell have 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; 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 spacing; the one or more first nanobeams and the plurality of second nanobeams are elongated in different azimuthal directions; the unit cell repeats at 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 of the wavelength onto the 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. 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 sub-wavelength spacing; and Equipped with The optical system, wherein the first set of nanobeams and the second set of nanobeams have different orientations.

2. 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 each 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 that are 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. The optical system of 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. 8. The optical system of claim 6 or claim 7, wherein the substrate is configured such 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 repeat 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 oriented at a 90 degree angle relative to each other.

12. 2. 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 normal to the surface.

13. a light source configured to emit light at said wavelength onto said metasurface; a spatial light modulator configured to modulate light from the light source and output the modulated light onto 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 diffraction light.

16. 1. A head-mounted display device configured to project light into a user's eye and display augmented reality image content, the head-mounted display device comprising: a frame configured to be supported on the user's head; a display disposed on the frame; Equipped with At least a portion of the display 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, whereby the one or more waveguides 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 sub-wavelength spacing; and Equipped with A head-mounted display device, wherein the first set of nanobeams and the second set of nanobeams have different orientations.

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

18. 18. A display device according to 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. 1. 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 being disposed adjacent to the first set of nanobeams and separated from one another by sub-wavelength spacing; wherein the first set of nanobeams and the second set of nanobeams have different orientations.

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

Images